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M hnh Chun ca Vt l Ht c bn trch t K Yu Ht Higgs v M Hnh Chun, nxb Tri Thc 2014 Phm Xun Ym

Khi thuyt Tng i rng ca Einstein thay th thuyt Vn vt Hp dn ca Newton, n khng nhm chnh sa i cht nh lut nghch o bnh phng m l loi b khi nim c bn cho rng hp dn l lc ht mt vt th bi cc vt th khc. Trong thuyt Tng i rng, ta khng cp n lc m quan tm n cong ca khng gian v thi gian. Tuy h qu - ca vic thay th lut hp dn Newton bng thuyt Tng i rng - l c sa i cht xu (nh hn mt phn triu) nhng tin on v s vn hnh ca H Mt Tri, nhng thuyt ca Einstein lm mt cuc cch mng trong nhn thc v t nhin. Ngy nay, chng ta cn mt cuc cch mng khc na. Steven Weinberg

Tm tt - Vt l ht c bn c mc tiu tm hiu, tin on, phn loi, sp xp, khm ph nhng c tnh cng nh nhng nh lut chi phi s vn hnh ca cc thnh phn s cp cu to nn vt cht trong ton v. M hnh Chun (the Standard Model, SM) ca vt l vi ht l l thuyt din t ton vn v nht qun h thng ca nhng vin gch s cp ca vt cht di tc ng ca ba trong bn lc c bn ca T nhin: lc in-t, lc ht nhn mnh v lc ht nhn yu t vn vt hnh thnh v bin ha. Lc hp dn, din t bi thuyt Tng i rng, l lc c bn th t m s ho nhp vi ba lc ca SM hy cn ng cha hin thc c, chnh l cuc cch mng m Weinberg nu ra trn, do trng lc khng l i tng ca bi vit.

Bi gm bn phn: PHN I: Nhp , phc ha v dn gii tng quan c gi lm quen vi nhng thut ng v khi nim ch yu ca SM, qua c ci nhn bao qut v nhng ti ca th gii vi m. PHN II: M t nhng hin tng in hnh lin quan n cc ht quark, thnh phn c bn ca ht nhn nguyn t. Quark b chi phi ch yu bi lc mnh gn kt chng cu to nn hadron gm hai loi l baryon (ht c spin bng m in hnh l proton v neutron) v meson (spin 0, 1 m in hnh l meson hay pion). Trong tin trnh khm ph ra lc mnh, l thuyt Yukawa ng vai tr m ng, theo tng tc ca cc baryon l do s trao i cc meson gia chng. Th nng Coulomb 1/R ca lc in-t v th nng Yukawa emR/R ca lc mnh theo th t l do trao i photon v meson (vi khi lng 0 v m). Th nng Coulomb l mt trng hp c bit ca th nng ph qut Yukawa: khi m 0, emR/R

Night thoughts of a quantum physicist. Bulletin of the American Academy of Arts and Sciences, Vol. 49, No. 3 (Dec., 1995),pp. 51-64.

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1/R, m cng ln th tm truyn R ca lc cng nh, photon khng c khi lng nn lc in-t truyn i v hn (nguyn l bt nh Rm ).

Nguyn l i xng c khai thc vi dng c ton hc l nhm SU(3) khm ph nhng tnh cht c th, phong ph ca cc ht c bn, th nht l hng v sc ca quark, th hai l cng thc ph qut GNN (Gell-Mann, Nakano, Nishijima) chi phi cc hadron, cc ht c bn v cc lc. Cng thc GNN cng l kim ch nam nh hng cho s ho nhp gia lc in-t v lc yu, ch ca PHN IV.

Ta nh bng tun hon Mendeleev trong ha hc, cc nhm bi baryon v meson c th sp xp theo hnh tm cnh u n m Gell-Mann mn danh t Bt chnh o ca nh Pht ch nh chng.

PHN III: Trnh by phng php c bn khm ph ra Sc ng hc lng t (QCD), nh lut chi phi s vn hnh ca quark. Trc ht cn thu trit mt nguyn l cc k phong ph gi l i xng Chun nh x (Local Gauge Symmetry), nn tng ca in ng hc lng t (QED), tc l thuyt v lc in-t c hon tt thi tin SM. Nguyn l ny c m rng v khai thc khm ph ra hai nh lut c bn khc ca SM l QCD ( PHN III) v in-Yu ( PHN IV). QED i xng chun nh x QCD v in-Yu i xng chun xc nh l phi tn ti nhng boson chun mang spin 1 truyn ti lc cho quark v lepton tng tc, nhng boson chun ny tun theo phng trnh Maxwell (cho photon ca lc in-t) v Yang-Mills (cho gluon ca lc mnh v W, Z ca lc yu). Hai tnh cht c th ca QCD l T do tim cn v N l hng ngoi gii thch quark v gluon b gn cht khng thot ni ra ngoi hadron nhit (nng lng) thp. Tri li vi nng lng cng cao th quark v gluon cng t do, chng khng b gn kt cht ch trong hadron. chnh l trng thi ca vt cht thu Big Bang v cc my gia tc c nng lng cc k ln. PHN IV: Dnh cho lc ht nhn yu v s ho nhp ca n vi lc in-t tr thnh thuyt in-Yu, nh cao ca SM. B cc ca PHN IV gm ba ch : M u vi neutrino v hai tnh cht c th ca lc yu l s vi phm i xng phi-tri (P), v i xng vt cht-phn vt cht (CP). Th hai, khi nghin cu hai hin tng c trng ca lc yu: k tnh bin chuyn thnh phn k tnh vi Glashow, Iliopoulos, Maiani (GIM) v s vi phm i xng CP vi Kobayashi, Maskawa (KM), cc tc gi trn tin on (v thc nghim sau xc nhn) s hin hu ca ba loi vt cht mi l din t bi cc quark duyn (charm, c), y (bottom, b) v nh (top, t); minh ha mi tng quan su sc gia hai lc mnh v yu. Cui cng nh lut chi phi lc yu c khm ph qua hai giai on: i xng chun v thuyt Yang-Mills vi nhm SU(2) lin kt hai dng trung ho in tch ca lc yu v lc in-t ho nhp chng. C ch BEH (Brout, Englert, Higgs) - tn ca ba trong su tc gi xut ra n - th hin s ph v t pht ca php i xng chun bi trng Higgs mang khi lng cho hai boson W, Z ca lc yu. S pht hin boson Higgs CERN ngy 04 thng 7 nm 2012 cng vi gii Nobel vt l 2013 vinh tng Franois Englert v Peter Higgs chng kin mt chng c va khp li v mt trang s mi ang l dng trong vt l ht. Khp chng c v hon tt mt on ng di l tt c 17 loi ht c bn c thc nghim khm ph y . iu ny khng nh s vng chc ca SM, mt h hnh m t y mi pht trin sau ny u phi da vo vn xa hn na. M chng mi, v c ch BEH thc s ln ngi. C ch ny c th nh hng n nhiu ngnh khc, n ra i nh mt lin i su sc gia hai ngnh khc bit: vt

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l cht ngng t (siu dn in-t) v vt l ht (lc yu ca neutrino). y l ln u tin con ngi khm ph ra mt lc mi l, din t bi trng Higgs, mang khi lng cho vt cht, c th coi nh lc c bn th nm ca T nhin bn cnh bn lc quen thuc trc .

Bn Phn u tng i c lp. Nhng chi tit mang tnh k thut u c trnh by trong phn Ch thch.

Phn I-Nhp

Neutrino l mnh nh nht ca thc ti vt cht m con ngi tng hnh dung ra, ci ln nht l v tr.

Clyde Cowan v Frederick Reines

Trong cu m u ca bn bo co v s kin ln u tin pht hin ra vi ht neutrino l phn ng ht nhn Savannah River (South Carolina, M), hai nh vt l Cowan v Reines (gii Nobel 1995) dng ng t hnh dung ra, iu gy cht ngc nhin cho ngi vit bi ny khi c cu ln u, nhng ngm li mi thy su sc. Thc th, khi con ngi xy dng c mt h thng nhng tng v suy lun cht ch, nht qun cng nhng ngn t tng xng din t v gii thch th gii bn ngoi cng nh khm ph nhng hin tng mi l v nhng nh lut chi phi s vn hnh ca chng, th theo ngha h hnh dung ra thc ti ca T nhin m Ht c bn v V tr l v d in hnh v ci m chng ta hiu bit v hai th gii thi cc v cng nh cng nh v cng ln . Ht c bn c vai tr no trong cuc tm kim ci ngun ca con ngui trong v tr ni qu kh vi tng lai, chng ta t u n, l g, v u, nhng cu hi mun thu. S hiu bit v ht c bn (vin gch vi m khng th chia ct cu to nn vt cht) hay v tr (tng th v m bao trm vn vt c khng gian v thi gian) khng duy nht m thay i, cch tip cn v bn cht ca chng thng trm theo cc thi i v cc nn vn hin. Ht ri thi xa xa khi kim, mc, thy, ha, th l 5 thnh phn s cp ct li ca vt cht. Mi cch y trm nm phn t vn c coi l ht s ng. Ngy nay chng ta bit phn t ch l tp hp ca nhiu nguyn t khc nhau lin kt bi electron ngoi vi, m mi nguyn t li c cu to bi ht nhn ca n vi nhng electron dao ng xung quanh, ri ht nhn nguyn t cng do proton cng neutron kt hp vi nhau m thnh, sau ht proton v neutron l hai quark u, d gn kt bi gluon cu to nn. C th nh nhng con bp b Nga lin hi cha ng nhau, chui di ca nhng vi ht i t phn t n quark l c mt qu trnh khm ph bn b khi ln lc xung, l thuyt cng thc nghim cht ch an xen. Cng vy, nhn thc v v tr bin i t thuyt a tm trc thi Copernic, Galileo cho ti thuyt N Bng (Big Bang) hin i, theo thu hng hoang cch y gn 14 t nm, v tr l mt t im k d cc nng cc c nhanh chng gin n, tuy gia tc gin n gim dn trong khong 7 t nm u nhng sau li vt tng ln. Mt phm tr k diu nhng khc vi ht c bn nn s khng cp tip y. Khoa hc ni chung l hnh trnh khm ph lin hi, mi mi i tm, khng c im tn cng. Vt l ht c bn c mc tiu l tm kim, phn loi sp xp cc thnh phn s cp ca vt cht v phm kh nhng tnh cht cng nh nhng nh lut c bn chi phi s vn hnh ca chng. SM l l thuyt din t ton vn v gii thch nht qun nhng c trng ca nhng vin gch s ng cu to nn vt cht, di tc ng ca 3 trong 4 lc c bn ca T nhin: lc in-t, lc ht nhn mnh v lc ht nhn yu t vn vt c hnh thnh v bin ha. Ht c bn tiu biu hn c l electron c khm ph ln u tin bi Joseph John

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Thomson nm 1897. Electron chnh l gc ngun ca hin tng in-t m ngay t thi xa xa con ngi cm nhn thy khi nhn sm st cng nh khi ch xt h phch. T nh n ln quang thi xa xa n iPad tn k thi nay, du n ca electron v hnh trung ngy cng m nt trong i sng con ngi. Hin tnh ca cc ht c bn1 c tm lc trong s (Hnh 1), chng gm ba phn: th nht l mi hai ht c spin 1/2 nh quark v lepton c gi ngn gn l trng vt cht; th hai l bn boson chun c spin 1 gm photon ca lc in-t, gluon g ca lc mnh, hai boson W, Z ca lc yu, gi chung l trng lc; th ba l boson Higgs c spin 0 ng vai tr ch yu to nn khi lng cho vn vt (boson W, Z, quark, lepton).

Hnh 1: S cc ht c bn trong SM.

trung tm hnh, duy nht boson Higgs c mu xm nht nh nhc nh l ht ny, tuy l im mu cht ca SM mang khi lng cho hai boson chun W, Z ca lc yu cng nh cho quark v lepton, nhng ti thi im ca hnh v li cha c thc nghim khng nh, trong khi quark, lepton, boson chun Z, W, , g c thc nghim xc nhn l hin hu. Rt c th,mu xm ca ht Higgs s rc r nh vng v hai nhm thc nghim ATLAS v CMS CERN va tm ra du vt ca n trong my siu gia tc Large Hadron Collider (LHC) ngy mng 4 thng 7 nm 2012, ho thm vi gii Nobel Vt l 2013.

Vt cht (quark cng nh lepton) tng tc vi nhau qua s trao i cc boson chun. Boson chun c vai tr lm trung gian ni kt v truyn ti lc cc vin gch vt cht c bn (quark hay/v lepton) tng tc vi nhau. C 6 loi quark mang k hiu u (up), d (down), s (strange), c (charm), t (top), b (bottom) v 6 loi lepton bao gm 3 ht e (electron), (muon), (tauon) mang in tch m e, v 3 ht neutrino e, , trung ha in tch, theo th t 3 ht neutrino ny bao gi cng snh i vi 3 ht electron, muon, tauon trong tng tc ca chng. S cn bng s lng 6 loi quark v 6 loi lepton khng phi ngu nhin m c lin quan su sc n tnh i xng chun v tnh ti chun ha trong l thuyt trng lng t, nn tng trn SM c xy dng. Lc mnh gn kt ht c bn quark u, d trong ht nhn nguyn t v lm cho vt cht vng bn. Lc in-t din t s tng tc ca electron vi hai quark u, d trong ht nhn nguyn t to nn nguyn t ca cc nguyn t ha cht trong bng tun hon Mendeleev cng nh ca cc t bo sinh vt trn tri t. Lc yu ca quark v lepton chi phi s phn r ca cc ht nhn nguyn t, cc phn ng nhit hch trong lng cc ngi sao, mang nh sng cho bu tri ban m cng nh pht tn hng t ht neutrino tng giy ang xuyn qua da tht chng ta.

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Lc mnh ca cc quark trao i gluon g gia chng vi nhau c gi l Sc ng hc lng t (Quantum Chromodynamics vit tt l QCD) thut ng ny m phng ch in ng hc lng t (Quantum Electrodynamics hay QED), l thuyt c hon tt thi tin SM din t lc in-t ca cc ht mang in tch trao i photon . Do SM bao gm lc mnh (QCD), lc in t (QED) v lc yu; hn na lc in-t v lc yu li c hp nht thnh lc in-yu (Electroweak). Nu in tch l tnh cht c trng gn b vi lc in-t cng nh khi lng gn b vi lc hp dn, th sc tch (color charge) l ch thm mt tnh cht lng t c trng ca cc ht quark. Cng nh danh t quark, danh t sc dng y l thut ng ring ca ngnh vt l ht c bn, n chng c mi lin h no vi mu sc xanh, trong ngn ng thng thng. Thc th, trong vt l lng t, c mt nh l lin kt spin vi php thng k Fermi-Dirac, theo cc fermion (ht c spin 1/2) khng th cng chung sng trong mt trng thi vt l xc nh bi nng lng, spin, vn tc, v tr, hay bt k mt c tnh no khc. V d hai fermion khi chung mt im khng gian th chng phi c hoc vn tc hoc chiu quay ca spin khc nhau; nu cng vn tc th spin ca chng phi quay ngc chiu hoc khng cng mt v tr. l nhng ht c c tnh mnh m, s phn b trng thi cc ht fermion phi tun theo php thng k Fermi-Dirac. Thng k ny c th phn no gii thch ti sao xp x cng mt mt electron nhng c vt cch in, c vt li dn in, thm ch siu dn in-t. Tnh cht ny ca cc fermion hon ton tri ngc vi tnh ho ng, chung sng ca cc boson (mang spin s nguyn nh 0, 1) minh ho bi chm nh sng laser vi nhiu photon trong cng mt trng thi.

V quark l fermion nn khi cn 3 quark kt hp vi nhau trng thi cn bn (nng lng lin kt cc tiu) to thnh baryon th s kt hp , theo thng k Fermi-Diac, phi phn i xng (i du) trong bt k s giao hon no gia cc cp fermion. V c 3 cp (u-u, d-d, u-d trong tp th 3 quark u, d to nn nucleon nh mt v d, coi Hnh 2) nn tnh phn i xng ny ch c thc hin nu mi quark, ngoi in tch v khi lng, phi mang thm 3 tnh cht mi l na chng t khc bit vi nhau. Thay v gn ba c tnh lng t ny ca quark bng ba con s 1, 2, 3 hoc ba ch ci a, b, c th cc nh vt l ht dng ba mu , xanh, lam mang tn sc tch (color charge). Gi thit v 3 sc tch ca quark sau c chng minh chnh xc bi nhiu thc nghim khc nhau v s c cp trong nhng Phn II, III, IV.

Hnh 2: Ba sc tch ca quark Mi quark, ngoi in tch cn mang 3 sc tch, tng trng bi 3 mu. Proton (phi) cu to bi hai quark u v mt quark d cn neutron (tri) bi hai quark d v mt quark u. Ba sc tch khc nhau ca quark c cn bng u n cui cng proton v neutron trung ho sc tch, cng nh in tch m v dng ca electron v proton cn bng nguyn t trung ho in tch.

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Quark khc lepton ch l ngoi sc tch (lepton khng c sc tch), chng cng mang in tch, nhng in tch ca chng khng phi l s nguyn e nh electron m +(2/3)e cho ba quark u, c, t v (1/3)e cho ba quark d, s, b.

Chnh v quark c c in tch v sc tch nn chng b chi phi bi c 3 lc: in-t, ht nhn yu, ht nhn mnh. Cn electron, muon, tauon v mang in tch v khng c sc tch nn ch b tc ng bi 2 lc: in-t v yu. Neutrino khng c c sc tch ln in tch nn b tc ng duy nht bi lc yu. Hai lc in-t v yu, tuy khc bit v cng tng tc hiu dng, nhng li c nhiu c tnh chung nn kt hp c trong mt tng tc duy nht gi l in-yu, mt trong hai l thuyt tr ct ca SM; tr ct th hai l QCD din t lc ht nhn mnh. S thng nht hai lc in-t v yu trong cng mt quy lut l bc tin ln ca vt l cui th k 20, c th v nh s tng hp ba hin tng in, t v quang cui th k 19. Hai nguyn l nn tng, lm ngn hi ng ch ng cho s hp nht ny, l i xng chun nh x v s ph v t pht ca n. S ph v i xng mt cch t pht ny c gi l c ch BEH, c nhim v mang khi lng cho vn vt. Lc c bn th t, lc hp dn (din t bi thuyt Tng i rng) to nn cu trc ca v tr bao la v chi phi s vn hnh ca cc thin th, cn ba lc phi hp dn ni trn ch yu ch tc ng trong th gii vi m ca vt l ht; ba lc ny u xy dng trn nn tng ca thuyt lng t. Tuy nhin lng t khng ch gii hn trong vt l ht m cn tc ng trong hu ht cc ngnh vt l khc. Du hin din trong c hai th gii vi m v v m, nhng vng h nguyn t v lc hp dn c cng tc ng qu nh (khong 1039) so vi ba lc kia nn c th b qua.

Tri li, ti nhng thi khc ban u ca v n ln (Big Bang) hay khi mt s thin th tn li tr thnh l en (Black hole), trong mt khng gian nn p v cng nh vi nng lng v nhit v cng ln (gi chung l bc tng Planck), th cng trng lc li rt mnh, tng t vi cng ca ba lc phi hp dn. V tt c bn lc cng ng vai tr ch cht trong l en v trong ci khng-thi im Big Bang ban u , chng phi mc nhin ha nhp vi nhau trong cng mt h thng cht ch v nht qun l gii mi hin tng. Tuy nhin, s thng nht cn thit ny gia hai ct tr ca vt l l Tng i rng v Lng t cho n nay cha thc hin ni, mc d c nhiu c gng trong nhiu nm qua. Nguyn do chnh yu l khng nh ba lc phi hp dn thnh cng trong vic c lng t ha v ti chun ha th thuyt Tng i rng cha th nht qun ho hp vi Lng t. l vn hc ba s mt ca vt l hin i, n i hi mt cch mng trong nhn thc v T nhin m Weinberg gi ln trang u bi vit ny.

Tm gc li cu hi trn, ta tr v vi SM ca ht c bn vi khong 30 gii Nobel Vt l trong ba mi nm gn y, Thuyt in-yu v sc ng hc lng t tuy mi ra i nhng nm 1970, khong thi gian tng i ngn so vi nhiu ngnh khoa hc khc trong tin trnh khm ph (l thuyt v thc nghim lun lin kt h tng nhau), SM mang li c mt kho tng tri thc khoa hc s, tin on nhiu hin tng v ht mi l cng nh nhng tnh cht c o ca chng m sau u c thc nghim kim chng vi chnh xc ng kinh ngc. Hy tm k s khm ph dng trung ha in tch ca lc ht nhn yu; ba loi quark c, t, b; hai boson chun W, Z; ch hin hu c ba loi neutrino vi khi lng cc k

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nh; ht mang khi lng 125 GeV/c2 va pht hin thng 7 nm 2012 CERN. S kin lch s ny c cc nh vt l hi hp n ch t nm 1994 khi CERN quyt nh xy dng my gia tc LHC c nng lng cao nht th gii sn tm ht Higgs.

Cng nh trng in-t cho nh sng hay trng hp dn li ht vn vt, trng Higgs trn y v tr. N gi ra cch tip cn mi v khi lng ca vt cht, khc vi quan im c hu coi khi lng l ci g cho trc bi T nhin m khng ai thu hiu ngun gc su xa. Theo SM, khi lng ca vt cht c to ra bi s tng tc ca chng vi trng Higgs tn ti trong chn khng ca v tr ngay t v n ln. Khi u tt c u khng c khi lng, do tng tc vi trng Higgs m vt cht mang khi lng, nng hay nh ty theo cng tng tc ca chng, cng tc ng mnh vi trng Higgs th vt cht cng c khi lng ln. Khng c trng Higgs th khng c khi lng cho vt cht cng nh lc gn kt chng to nn tinh t, v tr, do cng khng th c sinh vt v con ngi. Tuy trng Higgs mang khi lng cho vn vt, nhng ci g mang khi lng 125GeV/c2 cho chnh ht boson Higgs va c thc nghim pht hin. Ngoi ra khong 96% nng-khi lng ca v tr (c gi l nng lng ti v vt cht ti) hy cn nm ngoi s hiu bit hin nay ca con ngi, y l cha k lc hp dn hy cn xa l i vi cc ht c bn thu Big Bang. Vi nhng cu hi cn b ng nh vy, r rng SM cha th l gii p cui cng ca mi vn c bn.

Mt chn tri k th ang n ch, nhng trc ht hy cng nhau hc hi nhng iu m bao ngi siu vit i trc khai ph. Trc khi i vo chi tit ca SM trong nhng phn sau, chng ta hy im qua vi nt tng quan c th ca ngnh vt l ht c bn: 1- Cch tip cn quy gin qua s tm kim nh lut cn bn thuc v bin gii ca tri thc. Trong khi , nhiu ngnh vt l khc c cch tip cn hiu dng v t khi thin v tm hiu, khm ph nhng hin tng xy ra trong cc trng thi vt cht, tc l nhng nghim s (tng ng vi nhng iu kin c th no ) ca nhng nh lut c bn m SM khm ph ra. V d, ht electron tun th phng trnh c bn Dirac, cn vt l cht rn khai thc nhng tnh cht phong ph ca cht bn dn, siu dn do tc ng ca electron trong nhng iu kin a dng ca vt cht. Di cch nhn quy gin ca nh vt l ht c bn th tnh cht ca cc h thng vt cht, d phc tp v phong ph n my, u ng nhin l phi nh vy bi v chng u c cu to bi nhng vin gch s cp tun th nhng nguyn l ca SM v u c iu hnh bi ba lc c bn: in-t, mnh v yu. Mt bn tm kim phng trnh c bn chi phi s vn hnh tng th ca vt cht, bn kia tm ti khai thc cc nghim s phong ph a dng ca phng trnh c bn trong nhng iu kin khc nhau ca mi trng v m m vt cht c t vo. Hai cch tip cn quy gin v t khi b sung cho nhau, cng nh nghin cu c bn v ng dng an xen ln nhau, khng c ci ny th khng c ci kia. 2- Nhng cng ngh tn tin mi nhn v vt liu, in t, siu dn, my tnh c tn dng v khai thc xy dng nhng my siu gia tc v nhng cng c thc nghim cc k phc tp v tinh vi nhm phn tch, khm ph nhng ht c bn v hin tng mi l, kim chng hoc bc b nhng c tnh ca cc ht m l thuyt tin on hay xut. Ngnh Vt l ny i khi c gi mt cch tro phng l i khoa hc (Big Science) v nhng my gia tc v my d tm ht u khng l, c v nh nhng gio ng hay kim t thp k v thi xa xa.

3- S cng tc trao i thng xuyn v cn thit gia nhng nh vt l ht trn th gii v s tp trung nghin cu trong mt vi c quan quy m quc t vi hng ngn nh vt l thng

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trc nh CERN, DESY chu u, Fermi-lab, SLAC, Brookhaven chu M, KEK Nht Bn. S kin thnh lp CERN l mt bi hc vt xa i tng khoa hc thun tu. Trn cnh ng hoang lc c my ch b n c Ferney-Voltaire bin gii Php - Thy S, ngay sau Th chin th hai, nhiu nh vt l u chu tng di tn khp ni v nn pht xt tr v cng ng nghip xy dng nn CERN. V ha bnh v pht trin qua nghin cu c bn, vi s h tr tch cc ca mt s chnh khch Php, c, Anh c tm nhn xa, h chung sc m ng cho s hi sinh v ho gii ca cc nc u chu. Mi nc ring l khng th nhn s v phng tin hon thnh s mng, nguyn tc t chc ca CERN - tp hp ng gp ti nng, ngn qu t nhiu nc - tin phong lm m hnh cho nhiu ngnh hot ng khoa hc khc phng theo t thin vn, sinh hc, thm ch c chnh tr v CERN ra i nhiu nm trc Lin minh u chu. Mng li ton cu (world wide web) ca internet ra i khong nm 1990 c quan ny l mt trong nhng thnh cng k diu ca ng dng nghin cu c bn; my chp hnh scanner trong y hc, cng ngh siu dn in-t to nn nhng khi nam chm khng l l vi v d khc. Hn na, CERN cn dang tay n mi s cng tc ca nhng ti nng n t khp mi min trn tri t, k c nhng nc ang pht trin. y l c hi ngn vng i vi cc ti nng tr Vit Nam tip cn vi nghin cu quc t trong nhng lnh vc thuc ranh gii ca tri thc nhn loi.

Phn II. Chuyn k v quark

Vy l trong nhng khi nim vt l v ha hc, chc chn t nay chng ta phi a vo mt yu t gin on, nhy tng bc; iu m trc y vi nm khng ai thc.

Marcel Brillouin

Yu t gin on m Brillouin ni n gi l Lng t, vy chng ta trc ht hy lm quen vi vi thut ng v khi nim thng c dng trong ngnh vt l ht t nm bt my iu cn bn: lng t, spin, phn vt cht, sc tch v hng v ca quark.

IIa Mt thong Lng t, n v nng lng c bn. Nhng vin gch c bn ca vt cht vy vng trong th gii vi m ca Lng t, vy khi nim ny l g, n t u? Vo cui th k th 19, mt mu thun cn bn c pht hin gia l thuyt in-t v nhit ng hc - hai tr ct ca vt l thi y - vi thc nghim v cng bc x ca vt en2. Thc th, hai l thuyt a n mt h qu phi l l tng nng lng phng x bi vt en phi v hn, nm na nh ngi trc mt bp si hng, bt k nhit cao thp ra sao ta s b t chy ht. H qu phi l ny ch c th c gii p nu c mt yu t hon ton mi l no b sung hon thin h hnh c in trn. Nhn t gi l Lng t tc l n v gin on hay gi nng lng c bn, mt gi thit m Max Planck a ra khi ng tm hiu ph bc x ca vt en. Bng mt hnh ng hu nh tuyt vng tm cho bng c mt cng thc ton hc din t chnh xc cc o lng thc nghim, Planck (v sau Einstein b sung) phi a ra mt tin theo cc vt th vi m, khi dao ng vi tn s , th s phn b nng lng E ca chng phi l nhng n v

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ri rc, gi l lng t, nh 1h, 2h, 3h ... ch khng th lin tc. K l thay nng lng pht ra hay hp th u theo tng n v h l t. Ta nh gia 0 v 1 c mun vn s lin tc khng sao m xu, nhng ch c mi con s thp phn l 0.1, 0.2,...1. Chnh s khc bit gia lin tc v ri rc trong s phn b nng lng ny gii quyt h qu phi l ni trn. Cho bt k mt tn s sng dao ng ca mt vt th vi m v mt nng lng trung bnh kBT quy nh bi nhit , ta ch cn N gi h l t ti kBT ri, Nh kBT, cng ln th N cng nh v nhng gi t (N+1)h tr ln v vt qu kBT nn b kh mnh bi hm m exp (h kBT) khin cho tng nng lng phng x bi vt en tr thnh hu hn. im then cht m Planck gi nh l mt vt ch c th tip nhn hay mt i nhng gi nng lng h. Dng ph bc x ca vt en o c bi cc nh thc nghim, nm 1900 Planck tm ra h 6.551034 J.s. o c ngy nay cho kt qu h 6.6261034 J.s = 4.1341015 eV. s, hng s h t y mc nhin l biu trng ca vt l lng t. Albert Einstein l ngi u tin dng gi thuyt lng t nh sng h din gii hin tng quang in. c tnh ni ti khng lin tc ca lng t c Niels Bohr p dng sng to ra thuyt nguyn t v ng thy ph nng lng ca electron trong nguyn t cng ri rc. Tip theo l Louis de Broglie vn m lng tnh sng-ht ca mi vt th vi m, chng u dao ng nh sng nh sng, v c hc lng t hnh thnh vi nguyn l bt nh ca Werner Heisenberg v phng trnh sng ca Erwin Schrdinger. Lng t ca Planck do khng cn l gi thuyt na m tr thnh mt trong vi nguyn l nn tng ca vt l v khoa hc ni chung m du n ngy cng in m trong sinh hot ca con ngui; khi u t khoa hc, cng ngh ri lan rng sang nhiu kha cnh khc nhau ca trit hc, ngh thut, vn chng. Hng s Planck h trong E = h c gc ngun ch hilfe (ting c l ph tr), chi tit ni ln s khim tn ca nh bc hc ln. Do tnh ton qua hng s rt nh h, danh t vi m trong khoa hc t nhin c hiu nh nhng vt cht kch thc bng hay nh hn mt phn t mt, hay nano-mt. Nh vy mt nhm nguyn t rng di khong nano-mt (kch thc mt nguyn t c 1/10 nano-mt) c th c coi nh ngng ca bt u i su xung th gii vi m trong bao gm nhng ht nh hn na nh electron cng proton v neutron, hai thnh phn ch cht ca ht nhn nguyn t do quark cu to nn.

Hng s Planck h, vn tc nh sng c v hng s G ca lc hp dn Newton l ba hng s c bn chi phi s vn hnh ca vn vt trong v tr, t m mi n v vt l u c th suy din, tnh ton ra.

IIb Yukawa v lc ht nhn mnh. My siu gia tc Large Hadron Collider (LHC) ca CERN l my phng hai chm hadron c gia tc cc k cao va chm nhau sn sinh ra cc ht khc nh hadron, lepton, boson chun vn vn vi mc tiu u tin l sn lng ht Higgs trong s cc ht . Vy trc ht hadron l g? Ly t ting Hy Lp hadros c ngha l mnh, hadron l ht b chi phi bi lc ht nhn mnh, hng s tng tc ca n ln hn rt nhiu hng s tng tc ca lc in-t em= e2/c 1/137 vi = h/2. V d in hnh ca hadron l ht proton (p) mang in tch dng +e v ht neutron (n) khng c in tch, chng l hai thnh phn ch cht gn kt nhau to nn ht nhn ca cc nguyn t trong T nhin.

n gin nht l nguyn t Hydrogen bao gm mt electron dao ng xung quanh mt proton, ht nhn ca nguyn t . Nguyn t Helium c hai electron chuyn ng xung quanh ht nhn ca n bao gm hai neutron v hai proton. iu cn thit mi nguyn t c trung ha in tch, nh ta thy trong thin nhin, l s lng electron phi bng s lng proton m hai nguyn t Hydrogen v Helium minh ha.

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Tt c cc hadron u l nhng hp t cu to bi nhng thnh phn s cp hn gi l quark. Vy hadron v quark l c trng ca lc ht nhn mnh, mt trong bn lc c bn ca T nhin, ba lc c bn khc l in-t, ht nhn yu v hp dn.

Hai chm hadron trong my gia tc khng l LHC chnh xc ra l hai chm proton va chm nhau cc mnh. 1- Hadron (baryon, meson) v Lepton: Ngoi proton v neutron ra cn c bit bao cc hadron khc c pht hin, mt s trong l cc ht c spin nh N, 0, , gi chung l baryon, ting Hy Lp c ngha l nng. Quark l thnh phn s cp cu to nn baryon ni ring v hadron ni chung. Lepton ting Hy lp c ngha l nh i chi vi nng nh mt cch phn bit gia hai loi ht c bn ca vt cht l lepton v quark. Lepton th nht l ht electron e kh quen thuc, ht (muon) c khm ph nm 1936 l v d th hai ca lepton, ht th ba gi l (tauon) pht hin nm 1975. Ba ht e, , u c in tch m e, song hnh cng ba ht neutrino e, , trung ha in tch, 6 lepton ny cng vi 6 quark u, d, c, s, t, b c thy l 12 vin gch c bn ca vt cht phc ha Hnh 1 trong phn Nhp .

gia bn nng (baryon) v bn nh (lepton) l nhng ht trung dung (meson), v d in hnh l meson hay pion. Hadron gm hai loi: baryon c spin 1/2, 3/2... v meson c spin l s nguyn 0, 1... S hin hu ca ht pion v hng (spin 0) c tin on nm 1935 bi Hideki Yukawa (ngi Nht u tin nhn gii Nobel nm 1949) theo lc gn kt proton v neutron trong ht nhn nguyn t l do s trao i meson , ht ny c vai tr lm trung gian truyn ti lc mnh cho proton v neutron tng tc gn kt vi nhau. Sng to ca Yukawa khi ngun t s nhn thc su sc v khi nim trng (field) ca hai lc c bn m con ngi t lu bit r, l lc in-t (din t bi phng trnh Maxwell, ngi tng hp v b sung cng trnh m ng ca Ampre, Faraday) v lc vn vt hp dn (din t bi phng trnh Einstein m rng nh lut Newton). in tch di chuyn to nn trng in-t, pht tn nh sng v tc ng n cc in tch khc khp ni v mi lc. Cng vy khi lng to nn trng hp dn thu ht vn vt khp ni, mi lc. Vy trng l nhn t v cng lm trung gian cho lc tc ng ln mi vt t mt ch no trong khng gian v mt lc no ca thi gian, gi chung l mt khng-thi gian. Trng l mt thc th tn ti khp mi im ca khng-thi gian, khc vi ht ch hin din mt im chnh xc ca khng-thi gian. Trong ngn t ton hc, trng l mt hm s (m bin s l bn to khng-thi gian), hm s ny tun th mt nh lut vt l din t bi mt hay nhiu phng trnh no .

c im ca hai trng c in in-t v hp dn, theo th t chi phi bi hai phng trnh Maxwell v Einstein, l chng biu hin di dng sng lan ta khp khng gian vi vn tc ca nh sng. Nhng khi ha nhp vi th gii ca lng t th sng v ht tuy hai m mt, sng in-t cng xut hin di dng ht ci sng, gi l photon, m Einstein chng minh vi hin tng quang in. Ngc li, Louis de Broglie vi ci nhn thng tu thy ht cng dao ng nh sng thnh trng lng t, iu chng nghim sau bi Clinton Davisson v Lester Germer m ng dng trc tip l s pht minh ra knh hin vi in t.

im quan trng cn nm bt l gia hai electron phi c s trao i sng in-t c lng t ha di dng ht gi l photon, ht ny lm trung gian truyn ti lc in-t cho electron y nhau. Cng vy, gia hai khi lng c s trao i sng hp dn, din t bi ht graviton, chng ht ln nhau. Dng tin ny, Yukawa i xa hn v a ra gi thuyt l gia hai nucleon (tn gi chung cho proton v neutron) phi c s trao i mt ht no

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lm tc nhn cho lc mnh gn kt nucleon trong ht nhn nguyn t khin cho vt cht bn vng ni chung. Ht trung gian n gin nht ca lc mnh m Yukawa xut l meson v hng (spin 0), khc vi photon ca lc in-t c spin 1.

Khng nhng tin on phi hin hu ht pion truyn ti lc ht nhn mnh, ng cn c tnh c khi lng ca n bng cch m phng tnh in hc, theo s trao i ht photon gia hai in tch cho ta th nng e2/R m o hm ca n l lc Coulomb e2/R2 quen thuc, vi R l khong cch gia hai in tch. Thc vy, dng php bin i Fourier cho hm truyn 1/k2 ca photon ni kt hai in tch e, (k l vect xung lng ca photon trung gian, Hnh 3 pha tri trn), ta tnh c th nng e2/R ca lc in-t m de Coulomb nm 1785 o lng v chng nghim. Cng vy, vi g l hng s tng tc pion-nucleon, m l khi lng ca meson , ta c hm truyn 1/(k2+ m2c2) ca pion, ht trung gian ni kt proton v neutron (Hnh 3 pha phi di). Dng php bin i Fourier cho hm truyn pion, Yukawa tnh ra c th nng g2eR /R ca lc mnh, vi = mc/ . Trong h s ta thy tc ng ca lng t qua hng s h ca Planck. Khi khi lng ca meson trung gian bng 0 (trng hp photon), lc Yukawa tr thnh lc Coulomb (m 0, eR /R 1/R) chng t s nht qun ca php tnh ton dng hm truyn ca ht trung gian (nh photon, W, gluon, meson ) ti lc. Vy th nng Coulomb l mt trng hp c bit ca th nng Yukawa ph qut.

Hnh 3: Gin Feynman

Pha tri trn: Photon truyn ti lc in t electron tng tc (QED) .

Pha phi trn: Phn r n p + e + e, boson chun W truyn ti lc yu gia nucleon (n, p) v lepton (electron, neutrino).

Pha tri di: gluon truyn ti lc mnh quark tng tc (QCD).

Pha phi di: meson (gch chm) ni kt hai nucleon din t tng tc proton v neutron.

Richard Feynman l ngn hi ng ca ngnh vt l ht vi cc gin (diagrams), hm truyn (propagators), quy lut (rules) mang tn ng.

Khi lng m ca ht trung gian (photon, meson , hay bt k ht boson trung gian no) cho ta h s hm m eR xc nh di truyn ti R ca lc: R 1/ = /mc, m cng ln bao nhiu th tm truyn R ca lc cng nh by nhiu, iu ph hp vi nguyn l bt nh Heisenberg Rmc h. Mi lin h gia m v R c minh ha bi lc in-t, photon khng c khi lng nn n c th truyn i v hn (m = 0 R = ). Bit di tc ng ca lc mnh R 1015 m do Ernest Rutherford trc kia o lng kch thc ca ht nhn nguyn t, Yukawa suy ra l khi lng ca meson vo khong 140 MeV/c2, nng hn electron gn ba trm ln3. Kt qu quan trng lin i gia khi lng v

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hm m eR c mt im tng ng vi hiu ng Meissner, theo t trng b ngn chn trong cc vt liu siu dn in-t4 , mt ti lin quan mt thit n boson Higgs ca lc yu trong SM m ta s cp sau phn IVe.

2- Nm 1947, meson c pht hin bi cc tia v tr, l cc chm hadron c nng lng cc k cao t cc thin h xa xm bay n v va chm nhng ht nhn nguyn t nm trong kh quyn bao quanh tri t. Do tc ng ca lc mnh, tia v tr sn sinh ra meson theo qu trnh: p + p p + n + + , n + p p + p + , p + p p + p + 0... Sau khi sinh ra bi lc mnh, meson lin phn r bi lc yu, th d + v lepton va sinh ra cng li phn r thnh cc lepton nh hn e + e + , c th tip ni vng sinh hy, sinh bi lc mnh v hy bi lc yu.

Ngoi ra tia v tr cng pht hin meson K nm 1947 v baryon 0 nm 1950, chng l nhng ht mang k tnh u tin c bit n. K tnh (strangeness), mt hng v ca quark, s c cp sau on IIc. Tuy c nng lng cao rt cn thit cho s khm ph ht, nhng tia v tr li tn mt khp khng gian nn chng ch l phng tin mang tnh ngu nhin v kh c th khai thc mt cch h thng. Do my gia tc ht c xy dng nhiu ni t M sang u, d dng thao tc, truy tm, pht hin ra nhiu ht mi l, kinh nghim cho thy gia tc cng cao th cng khm ph ra nhiu hin tng bt ng. My gia tc v hnh trung l biu tng ca ngnh vt l ht, khng c nhng dng c ngy cng honh trng ny th vt l ht kh pht trin thm v thin vn, v tr hc c th tr li vai tr nguyn thy nh mt phng th nghim ln m Thin nhin tng con ngui nu c th khai thc hu hiu.

Vo thi im trc khi SM ra i, hng vi trm hadron nh vy c pht hin bi tia v tr v my gia tc. Bn cht chng l g, c tun th mt trt t no ging nh s sp xp cc nguyn t ho hc trong Thin nhin vi bng tun hon Mendeleev khng? Nhng cu hi m sau ny ta s lm quen v gii p, theo hadron l phc hp ca quark (hay/v phn quark) gn kt vi nhau bi gluon: baryon c cu to bi 3 quark v meson bi quark gn kt vi phn quark. Thc l mt thnh tu ln v ch vi my vin gch c bn m ta xy dng nn tt c cc hadron v din t nht qun nhng tnh cht ca chng.

Phn vt cht ni chung v phn ht ni ring l khm ph k diu ca Paul Adrien Maurice Dirac (1902-1984), mt thin ti tm c Albert Einstein. iu ngu nhin l c hai v u 26 tui khi khm ph ra hai phng trnh nn tng ca vt l E = mc2 v (i mc)(x) = 0 t mi pht trin by gi v sau ny u phi da vo nh mt h hnh ca khoa hc vn cao ln na. Khi kt hp nhun nhuyn c hc lng t vi thuyt tng i hp, Dirac sng to ra phng trnh chi phi s vn hnh ca nhng vin gch s cp cu to nn vt cht nh lepton, quark v rng ra ca tt c cc fermion phc hp khc nh proton, neutron, baryon. Ti sao kt hp? Lng t l iu d nhin cho vt th vi m, cn thuyt tng i hp th ti cn thit din t s chuyn ng vi vn tc rt cao ca cc ht vi m.

Phng trnh5 Dirac l bn giao hng tuyt vi ca s hp phi ni trn, n m ra hai chn tri mi l: th nht l electron mang spin /2, mt c trng c o ca lng t, th hai l s hin hu tt yu ca phn electron (gi l positron) ni ring v ca phn quark, phn ht, phn vt cht ni chung6. Ht v phn ht c cng khi lng nhng tt c cc c tnh khc (spin, in tch, sc tch, hng v) ca chng u ngc du. Carl Anderson khm ph ra positron e+ vo nm 1932. 3- in ng hc lng t (QED)- Thi tin M Hnh Chun khong trc 1950, khi u bi Dirac v kt thc bi Richard Feynman, Julian Schwinger, Sin-Itero Tomonaga, Freeman Dyson, duy nht ch c in ng hc lng t l c hon tt, l l thuyt

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din t tng tc in-t gia cc ht mang in tch. L thuyt hon chnh QED ny kt hp trng in-t c in vi tnh lng t (qua cc tnh cht phi lin tc, xc sut v bt nh ca vt th vi m) thnh trng lng t photon. Cng vy hm s sng electron, nghim s ca phng trnh Dirac cng c lng t ha ln th hai thnh trng lng t electron din t nhng kha cnh sng-ht, phi lin tc, bt nh trong electron v phn ht ca n l positron sinh hy lin hi. Trng lng t QED din t s bin ho, sn sinh v hy dit ca photon, lepton, phn lepton, tng s nhng ht ny khng c nh m bin i, mt c trng ca cc trng lng t tng tc vi nhau. Nh vy, trng lng t l cng c l thuyt rt ph hp vi vt l ht c bn v tnh cht phong ph a dng va sng va ht ca chng vi s lng ht v phn ht sinh hy v bin i khng ngng.

Thuyt QED c mt cu trc tnh ton cht ch v nht qun gi l phng php nhiu lon (perturbative method) bng cch trin khai thnh chui cc ly tha ca hng s tng tc in t em 1/137. V em

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trin vt l ht, t khi nim hng v ca vt cht ra i, mang hng cho quark. c sn sinh ra bi s va chm gia cc hadron trong tia v tr hay trong my gia tc, nhng ht V ny c mt tnh cht lng t l lng l bao gi cng ghp i, biu l thnh hai vt ging nh ch V khi c sn sinh bi cc tng tc mnh ca ht nhn nguyn t. Cu hi u tin l ti sao hai ht cp i trong V li d dng c sinh ra cng mt im, trong khi mt ht duy nht li khng c to ra, iu tri ngc vi tri nghim bnh thng?

Ngc nhin khng km l sau khi c sinh ra, mi nhnh trong cp i ca V li phn r thnh vi ht quen bit nh hay/v nucleon vi cng rt nh so vi cng phn r mnh hn nhiu ca cc ht khc (nh baryon N hay meson chng hn phn r rt nhanh ra nucleon hay ). L do l N (hay meson ) u n gin ch l nhng ht cng hng do nucleon v kt t nn chng li phn r nhanh chng ra nucleon (hay ) bi lc ht nhn mnh, khc hn vi hai nhnh ca V b phn r rt chm bi lc ht nhn yu. Phn tch k lng nhng hin tng ny a ti kt lun l phi hin hu mt tnh cht lng t mi l no m sau ny c gi l hng v ca quark (v phn quark) chng cu to nn cp hadron v phn hadron nh hai nhnh ca V. Mi nhnh mang mt i lng mi l i lp nhau v lun i km nhau, ta nh photon ca lc in-t sn sinh ra hai nhnh l cp ht v phn ht ca chnh n nh cp e e+, + ch khng phi cp e + hay e+, v nh vy khng c s bo ton s lng electron hay s lng muon. Murray Gell-Mann, gii Nobel 1969, gi i lng c bo ton bi lc mnh l k tnh7 v trc khng ai bit vt cht mi l ny m ch thy vt cht bnh thng bn vng nh nucleon to nn bi quark u, d khng hng v thi. Phn ng + + n K+ + 0 l mt v d v s bo ton k tnh ca lc ht nhn mnh. Khi u t hadron khng hng v l + v n, chng va chm nhau sn xut ra V gm hai nhnh l K+ v 0. Mi nhnh phi mang k tnh s v i ngc nhau chng t trit tiu v bo ton k tnh ca h thng K+ v 0, trong 0 c quark s v trong K+ c phn quark . Ht V c pht hin u tin l cp meson K+, K hay cp K0, phn K0; K+ cu to bi cp

u, K bi s, K0 bi d, phn K0 bi s. Baryon 0 l do cc t hp ca 3 quark u, d, s cu to nn. Sau khi c sn sinh ra, cc hadron k nh K+ v 0 li phn r bi lc yu, lc ny vi phm k tnh, K+ 0 + e+ + e, K+ + + 0, 0 p + e + e, 0 p + l vi v d ca hadron phn r bi lc yu vi phm k tnh (v tri K+ , 0 mang k tnh cn v phi khng c k tnh). Cc phn r K+ 0 + e+ + e v 0 p + e + e cho ta nhn ra mt iu rt quan trng l dng lc yu ch bin chuyn vi in tch thay i nh K+ 0 hay 0 p, m chng trung ho (in tch khng thay i) nh K+ + hay 0 n. Khi lc mnh sn sinh ra quark s, n lin phn r v mt i k tnh bi lc yu, hn na thc nghim cho bit k tnh mt i phi di dng thay i in tch s u m khng phi di dng trung ho (in tch khng thay i) l s d. Khng c dng lc yu thay i hng v m chng thay i in tch, s trit tiu dng lc yu s d ny chnh l im khi u cho c ch GIM (Glashow, Iliopoulos, Maiani) tin on s hin hu ca quark duyn m ta s cp sau Phn IVc . Tm li lc ht nhn mnh bo ton hng v ca quark, trong khi lc ht nhn yu vi phm hng v ca n. Khng nhng vi phm hng v, lc yu cn vi phm php i xng tri-phi (i xng P), v php i xng vt cht-phn vt cht (i xng CP) m chng ta s cp Phn IV v thuyt in-Yu. Cho n cui nhng nm 1950, vi trm hadron c pht hin bi thc nghim, ngoi cc hadron bnh thng khng mang hng v nh meson , , ... v baryon N, N...( l

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nhng cng hng do nucleon v pion hp t), cn c nhiu hadron khc mang k tnh nh meson K v baryon 0, , ...

Quan st nhng c trng ca chng (khi lng, spin, cc kiu sn xut v phn r) tm ra nhng quy lut chi phi chng mt cch nh tnh v sp xp chng mt cch c h thng theo tng nhm bi (coi hnh 5), nm 1953 Murray Gell-Mann, ng thi vi Kazuhiko Nishijima v ng nghip Tadao Nakano tm ra mt ng thc mang tn GNN (Gell-MannNakanoNishijima) ni kt ba i lng Q, Iz, Y ca hadron, vi Q l in tch (tnh theo n v in tch +e), Iz l thnh phn chiu xung trc z ca vect spin ng v8 I v Y l siu tch9. l:

Q = Iz + Y/2 (cng thc GNN) tng ct li trong GNN l phi c mt s lng t mi l no (gi l siu tch Y) c bo ton trong s sn sinh hadron (c baryon ln meson) bi lc ht nhn mnh, nhng khi hadron phn r bi lc ht nhn yu th Y khng cn c bo ton na m b vi phm. Ngoi Y ra, phi b sung thm mt thnh phn no khc na ca hadron din t ng lot hai hin tng (bo ton v vi phm) tri ngc ny. Thnh phn b khuyt gi l spin ng v (k hiu Iz) c bo ton bi lc mnh nhng cng b vi phm bi lc yu, hai i lng Y v Iz ny gn b mt thit vi nhau nh mt quy lut chi phi c ba lc in-t, mnh v yu. Khi Y thay i mt n v th Iz thay i na n v lm sao cho tng s ca chng li chnh l in tch Q, mt i lng bt bin ca in-t. B ngoi c v gin n nhng do tnh ph qut ca cng thc GNN i vi cc ht (hadron, quark, lepton), cc lc tng tc (mnh, yu, in-t) v cc php i xng, n l kim ch nam nh hng sau ny cho cu trc ca hai lc yu v in-t trong s thng nht chng thnh thuyt in-Yu, hai lc u c I 0 (bi Iz ) v I = 0 (bi Y).

ng thc GNN cn c dng tm ra in tch ca quark. Thc th, v phi cn 3 quark gn kt vi nhau to thnh baryon, nn s baryon b ca quark l (ph ch 9), do :

u (Iz = 1/2, Y = 1/3), d (Iz = 1/2, Y = 1/3), s (Iz = 0, Y = 2/3) c (Iz = 0, Y = 4/3), b (Iz = 0, Y = 2/3), t (Iz = 0, Y = 4/3)

t y ta tnh c in tch +()e cho ba quark u, c, t v ()e cho d, s, b. Vic pht hin ra hng v k ca vt cht bi lc mnh m ng cho lc yu pht trin v a n h qu tuyt vi l s hin hu tt yu ca ba hng v mi l ca vt cht, l: duyn, y v nh m sau c thc nghim kim chng thnh cng. Meson K0 ng vai tr quan trng trong mi lin h hu c gia hai lc mnh v yu a n s tin on ny. Quark duyn bi Sheldon Glashow, John Iliopoulos v Luciano Maiani (c ch GIM), hai quark y v nh bi Makoto Kobayashi v Toshihide Maskawa (c ch KM) din t s bt i xng gia vt cht v phn vt cht. Khng nhng tin on ba hng v mi l ca vt cht m ngay c khi lng ca cc quark duyn v nh cng c c lng chnh xc bi nhng tnh ton phc tp cc vng kn lng t, soi ng cho thc nghim d tm v o lng tnh cht ca chng. Php tnh ton nhng vng kn ny (m Hnh 4 minh ha) c xy dng bi Gerardus t Hooft v ngi thy hng dn lun n tin s Martinus Veltman. Mc tiu ca hai v l chng minh thuyt in-Yu ca Sheldon Glashow, Abdus Salam v Steven Weinberg cng c hon chnh nh QED ngha l cng nh lc in-t, lc yu c th ti chun ha 10 (renormalization) v t thuyt in-Yu thng hoa v c mt khun kh tnh ton hon ho, cht ch v nht qun nh QED. Him thy ngnh khoa hc no c ba gii Nobel ch vi lun n tin s: t Hooft chng minh s ti chun ha ca in-Yu, Politzer v Wilczek vi t do tim cn (asymptotic freedom) ca quark v gluon trong QCD. in-Yu v QCD l hai tr ct xy dng nn SM ca vt l ht.

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IId- Gell-Mann, con s 3 v bt chnh o.

Tm kim mt trt t no gia c mt rng hn lon ca vi trm cc loi hadron c bit thi 1960, xp t chng mt cch tun t v h thng l mc tiu phi gii quyt trc tin i xa hn na. Khi u cuc hnh trnh l tng ca Enrico Fermi vi cc ht khng hng v (quark u, d theo ngn t thi nay), theo meson l hp t ca nucleon v phn nucleon, ri n Shoichi Sakata m rng sang cc ht c k tnh theo 3 baryon p, n v 0 ng vai tr ch ng cu to nn cc hadron c (v khng c) k tnh. V d + cu to bi p, K bi 0, nhng Sakata ch gii hn phm vi meson cn i vi nhng baryon khc nh , 0, , 0 th m hnh Sakata nh b tay, khng th cu to chng vi p, n, 0 mt cch trc tip m phi kt hp vi meson v K to thnh, v d + = 0 +, = 0

K... B sung khuyt im v m rng kch bn ca Sakata, Gell-Mann nhn thy l gia cc hadron (c meson ln baryon) c mt php i xng ng tr chng, l nhm i xng unita SU(3) ca 3 vt th (quark) b ngoi tng t nh 3 baryon p, n, nhng hon ton khc v bn cht. Ch cn 3 vin gch c bn ca vt cht m Gell-Mann gi l 3 quark11 u, d, s cng vi 3 phn quark , , cu to nn tt c cc meson v baryon m ngi ta bit thi im trc nm 1974, sp xp chng theo mt trnh t nht qun, a ra nhiu tin on m in hnh l baryon vi khi lng c tnh sn, trc khi thc nghim khm ph ra.

V meson cu to bi quark v phn quark, chng l t hp ca mt trong 3 quark u, d, s gn ghp vi mt trong 3 phn quark , , , nh vy c thy tng cng c 9 cp quark-phn quark, chia lm hai biu din 8 v 1 ca nhm SU(3): 3 x 3 = 8 + 1. Biu din 8 gm c d,

u, d, ( u d), ( u + d 2 s), u, s, s theo th t l 8 meson K0, K+, , 0, 0, +, phn K0 , K ca Hnh 5. Cn baryon l hp t ca ba quark qi qj qk vi i, j, k l bt k mt trong ba hng v u, d, s, vy c thy c 33 = 27 b ba: 3 x 3 x 3 = 8 + 8 + 10 + 1. Trong biu din 8 ta nhn ra tm baryon ca Hnh 5: n, p, 0, , 0, , 0, th d + = uus, = sds (so snh vi m hnh Sakata + = 0+, = 0K ta thy r s khc bit), trong biu din 10 c baryon = sss mang spin 3/2, tin on bi Gell-Mann.

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Hnh 5: Nhm bi hadron (meson v baryon) c sp xp cn i trn hnh tm cnh u n theo to Iz

(trc ngang) v Y (trc thng ng) gp nhau trung tm (0 v 0). Ba i lng Q, Iz v Y ca nhng hadron tun th ng thc GNN. Gell-Mann gi cch xp t nhm bi hadron theo hnh tm cnh u n l Bt

chnh o, mn ch nh Pht.

Ngoi ra li cn thm mt con s 3 na, nhng ln ny khng phi l 3 hng v u, d, s ca quark m l 3 sc tch , xanh, lam s c tn dng khm ph ra nh lut c bn chi phi s vn hnh ca quark, l Sc ng hc lng t (QCD) m Gell-Mann cng gp phn sng to. Nhm SU(3)C dng trong QCD l nhm i xng gia 3 sc tch, cn phn bit vi nhm i xng SU(3)F gia 3 hng v u, d, s ca quark m biu din 8 ca n l hai hnh bt gic trong Hnh 5. Lc mnh QCD c mt c trng duy nht v c o m cc lc khc khng c, l tnh cht t do tim cn, theo nhit cao (nng lng E ln) quark v gluon khng gn b vi nhau na v c t do, hng s tng tc QCD ca chng nh dn nh 1/Log(E) khi E tng. T do tim cn ca QCD cho php ta dng phng php nhiu lon nh QED trin khai thnh chui cc ly tha ca QCD 0.

Ngc li nhit bnh thng (E nh), quark v gluon b gi cht trong cc hadron. Tnh cht l lng v c o ny, mnh danh n l hng ngoi (infrared slavery), coi nh l h qu ca s ko di lin tc t E ln xung E nh ca 1/Log(E), hm ny tng khi E gim v nh vy lm cho QCD >> 1.

V E v di R lin i nghch vi nhau theo nguyn l bt nh E R h (coi phn IIb) nn h qu ca n l hng ngoi l cng ca lc mnh gn kt quark li tng ln vi khong cch R ca quark, cng y chng ra xa tch ri chng th lc gn kt chng li cng mnh hn ln ko gi chng li vi nhau. Quark mi mi b cm t trong hadron, nhit bnh thng trong i sng hng ngy, quark khng sao thot ra ngoi hadron l mt, khng nh electron nhan nhn khp ni. iu cn nhn mnh l hadron khng mang sc tch v 3 sc tch ca quark u ha quyn vi nhau lm mt trung bnh hadron c trung tnh v sc tch, cng nh electron v proton trit tiu in tch ca nhau cc nguyn t trung ha in tch. IIe- Quark c tht vi vi thc nghim tiu biu. Tuy khng trc tip ra mt nh lepton hay boson chun nhng s hin din gin tip ca quark v gluon rt rch ri trong nhiu thc nghim c lp vi nhau v tnh cht ca chng c nghim chng chnh xc. Vic truy tm quark, thnh phn s ng cu to nn hadron, cng ta nh Rutherford nm 1911 khm ph ra proton trong ht nhn nguyn t. Khi bn chm nguyn t Helium (tia alpha) vo mt phin vng mng, mt phn chm alpha quay ngc tr li (tn x vi gc ln hn 90), Rutherford suy ra l ht nhn nguyn t phi cha mt ci g rt nh v cng mang in tch dng nm trung im ca nguyn t, chnh l ht proton. Quark cng c pht hin nh vy bi chm electron p mnh vo nucleon v thy xut hin n bt ng nhiu tn x vi gc rt ln, Hnh 6.

Khi phn tch chi tit cc s liu thc nghim v phn b tn x nng lng cao, iu ngc nhin tri ngc vi trc gic thng thng l cc thnh phn c bn (quark v gluon) cu to nn nucleon hu nh khng cht no b gn kt cht ch m li dao ng t do trong nucleon. Tnh cht t do tim cn ca QCD gii thch iu ny v nng lng cao th hng s tng tc QCD 0, quark thoi mi vy vng khng b b cht trong hadron.

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Hnh 6: Pha trn: nu nguyn t c electron v ht nhn tn mc khp ni th chm tia alpha bn vo s i

thng khng b quay ngc tr li. Pha di: v nguyn t c mt ht nhn rt cng v nng nm trong trung tm, mt phn chm alpha bn vo s b quay ngc tr li vi gc ln hn 90.

in tch phn s ca quark cng c xc nh r rt khi so snh tit din tn x ca electron v ca neutrino12. Cn 3 sc tch ca quark cng c chng minh t nht bi hai loi thc nghim hon ton c lp chng cht g lin i: tit din (e + e + hadrons) v tc phn r ca pion ra hai photon: 0 + .

V hadron l do quark cu to nn, do s sn sinh hadron bi e + e+ hadrons cng tng ng nh e + e+ j j + q j vi tng cng tt c 6 hng v (u,d,s,c,b,t) ca quark qj v phn quark j, chng u c to ra t photon. Thc vy, khi e v phn ht ca n e+ t hi, chng t hy bin thnh nng lng thun khit tng trng bi photon o vi khi lng 0 v bng tng nng lng ca e v e+. Khi lng ca photon o ny li sinh ra cc cp vt cht-phn vt cht, tng trng bi cc cp quark. Khi so snh e + e+ j ( j + qj ) vi e + e+ + +, ta nhn thy v khng c sc tch v in tch ca muon cng khc quark, nn t s r gia (e + e+ hadrons) v (e

+ e+ + +) chnh l r = Nc j Qj2, vi Nc l s lng ca sc tch (Nc = 3) v Qj l in tch ca quark j (theo n v +e). Nu tng nng lng ca cp e + e+ (cng l ca cp quark qj j c sn xut ra) di ngng khi lng ca cp quark duyn, th r = 3{(2/3)2 + 2(1/3)2} = 2. Nu vt qua khi lng ca cp quark duyn th r = 3{2(2/3)2 + 2(1/3)2} = 10/3, qu ngng ca quark y th r = 11/3, tt c cc kt qu trn u c thc nghim kim chng thnh cng. Trn nguyn tc, gi tr tim cn ca r l r 5 khi vt qu khi lng ca cp quark nh. ng gp ca 1 vng kn lng t trong QCD cho kt qu chnh xc r = Nc j Qj2 {1+ s /} vi s 0.15 l hng s tng tc ca QCD, so vi hng s tng tc in-t em 1/137. Tc phn r ca 0 + tnh ton bng vng lng t hnh tam gic theo quy trnh 0 ( u d) + s cho ta kt qu nh hn thc nghim 9 ln nu ta qun khng tnh n bnh phng ca h s sc tch (Nc = 3). u c th l ngu nhin m hai thc nghim hon ton xa l cng a n mt kt lun chung l quark phi c Nc = 3 sc tch. Phn III-Sc ng hc lng t (QCD)

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Chng ti, nhng nh vt l ht, thc s khng my quan tm n ht m ch trng n nhng nguyn l c bn, chng ti dng ht nh nhng cng c tm hiu nhng nguyn tc nn tng tim n trong .

Steven Weinberg Nh mo u phn Nhp , nh lut din t lc mnh gn kt cc ht c bn quark c gi l Sc ng hc lng t (vit tt QCD). Thut ng sc (sc tch) trong QCD chp mn ch in (in tch) trong in ng hc lng t (QED). Nhng nm 1950 thi tin M Hnh Chun, QED l l thuyt hon ho duy nht ca ngnh vt l ht c bn din t tng tc in-t. QED, m Feynman gi l hn ngc ca l thuyt trng lng t, t ti mc chnh xc mt phn mi t khi so snh thc nghim v tnh ton; hai v d l momen-t lng cc d thng ca electron v cc trng thi nng lng cc k tinh vi ca nguyn t hydrogen. Nguyn l i xng ng vai tr ct ty cho s hon tt ca QED ni ring v cho s khm ph nhng nh lut vn hnh v cu trc ca vt l ht c bn ni chung. N ri sng ch ng pht hin ra hai nh lut tng tc c bn mi l l QCD v in-Yu. Tht vy, c 3 lc: mnh, in t v yu u b chi phi, iu hnh bi mt nguyn l cn bn gi l i xng chun nh x (local gauge symmetry), mt cng c nhim mu pht hin ra c 3 nh lut c bn ni trn. i xng ny xc nh trc ht l phi tn ti nhng boson chun mang spin 1 truyn ti lc cho quark v lepton tng tc, nhng boson chun ny tun theo phng trnh Maxwell (cho photon ca lc in-t) v Yang-Mills (cho gluon ca lc mnh v W, Z ca lc yu). Lch s khm ph QED thc ra i con ng ngc li: electron v dng in ca n ly t phng trnh Dirac chnh l ngun to nn trng in-t photon (din t bi phng trnh Maxwell); t tng hp chng hnh thnh nh lut tng tc gia electron v photon (QED). Khi phn tch cu trc ton hc ca QED th nguyn l i xng chun nh x c pht hin. i xng ny t tr thnh ngn hi ng trong ngnh vt l ht, khi khai thc v m rng n th hai nh lut ca tng tc mnh v yu c khm ph; theo th t chng mang tn QCD v in-Yu. Tm li:

QED i xng chun nh lut Yang-Mills: QCD v in-Yu

IIIa- Vi iu v i xng.

Trong tin trnh khm ph cc nh lut khoa hc, nhiu nh nghin cu ly ngun cm hng trong ci p cn i hi ho ca thin nhin quan st, tm ti, suy lun, sng to. Ci p c th ch quan trong ngh thut, vn chng, hi ha, m nhc nhng trong khoa hc t nhin n khch quan, nh lng v mang tn gi i xng vi dng c ton hc l nhm i xng phn tch, xp t th t cc trng thi, pht hin phng trnh din t quy lut tng tc ca h thng v tin on nhng h qu kim chng bi thc nghim. S tm kim nhng i xng v s vi phm tun t ca n, cng nh xc nh c nhng g bt bin trong vt l l phng php ch ng ph bin v hu hiu trong cng cuc khm ph. i xng c nh ngha theo nh ton hc Hermann Weyl (1885-1955) nh sau: mt nh lut khoa hc mang mt tnh i xng nu n biu hin khng h thay i khi ta tc ng ln n bi mt php bin chuyn. Hnh cu l mt minh ho r rt ca mt vt th i xng: php quay trong khng gian ba chiu vi bt k mt gc no chung quanh tm ca hnh cu khng lm n thay i hnh dng. Ni cch khc, ng knh ca hnh cu l mt bt bin ca php quay chung quanh tm ca n. C hai nh l v cng phong ph - khm ph bi nh n ton hc Emmy Noether nm 1918 - theo khi mt tnh i xng chi phi mt h thng vt l no th phi c mt nh lut

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bo ton km theo, v nh vy phi c mt i lng bt bin tng ng. nh l th nht lin i n tnh i xng ton b (global symmetry) hm ngha l php bin chuyn khng ph thuc vo tng im ca khng-thi gian, din t bi t-vect x. nh l th hai lin i n tnh i xng nh x (local symmetry) hm ngha l php bin chuyn ph thuc vo x, n phong ph hn nhiu v nh m pht hin mt trng tng tc mi l gi l boson chun c spin 1 v iu k diu tip theo l khm ph ra phng trnh din t s tng tc ca chng.

Bn thn ca mi nh lut cn bn vt l nhiu khi tun th mt php i xng no m nh nghin cu cn tm kim ra.

V d ca nh l Noether th nht l lut bo ton nng lng, h qu ca tnh i xng ton b bi s chuyn i tnh tin ca thi gian (mt th nghim thc hin hm nay, nm trc hay tun sau, trong cng mt iu kin, cng u ging ht nhau). Tnh i xng bi s chuyn i tnh tin ca khng gian (th nghim thc hin trong cng mt iu kin ti H Ni, Paris, Washington u nh nhau) cho ta nh lut bo ton xung lng. Hai nh lut bo ton ny, theo th t, din t tnh ng nht ca thi gian (lc no cng th) v ca khng gian (u cng vy). Ngoi ra cn c i xng bi php quay chung quanh mt trc, n a n nh lut bo ton xung lng gc. nh lut ny din t tnh ng hng ca khng gian (bt k chiu hng no cng tng ng nh nhau). ng nht v ng hng l hai i xng c bn ca khng gian v thi gian. Mt v d ca nh l Noether th hai l s bo ton in tch, h qu ca php i xng chun nh x trong lc in-t. in tch chng bao gi mt i hay sinh ra c, n bt bin bi php bin chuyn chun (gauge transformation). Danh t chun, cng do Hermann Weyl a ra, hm l khng c mt thang chun mc, mt thc o tuyt i no trong cch tnh ton, ong m, o lng gi tr ni ti ca cc i lng khoa hc. Mt hay mt nm nh sng, n v nhit Fahrenheit hay Celsius u tng ng, ch l c l ca con ngi. Bt bin bi i xng chun hm l gi tr t ti ca mt i lng khng ph thuc vo phng cch, mc thc, n v m ta dng o lng, tnh ton.

i xng chun ng mt vai tr cc k quan trng trong tin trnh khm ph, khi u trong in t v sau lan rng sang nhiu ngnh khoa hc nh vt l ht, vt l cht rn, v tr thin vn v hnh trung km theo nhng ng dng k diu trong cng ngh lin i n nhng ngnh ny13. Vy i xng chun v bin chuyn chun l g? Ai trong chng ta khi lm quen vi c hc lng t u bit rng bnh phng ln ca hm s sng |(x)|2 ca electron cho ta xc sut trng thi ca n. Ta thy ngay php bin chuyn chun (x) eie(x) (x) vi bt k mt hm thc (x) no u khng lm thay i |(x)|2 ca electron. Bin chuyn chun (chuyn pha) c hai c tnh l lin tc (v (x) l hm lin tc ca x) v nh x. Tnh t nh x nhn mnh (x) tu thuc vo bin s x, ch vit tt ca t-vect x (ct, x) din t khng-thi gian bn chiu. Cng vy phng trnh Maxwell ca photon, din t bi t-vect in th A(x), khng thay i bi php bin chuyn A(x) A(x) (1/e) (x)/x, ta thm vo hay bt i o hm (x)/x ca bt k hm (x) no trong A(x) cng khng lm thay i phng trnh Maxwell. nh lut in-t bt bin bi php bin chuyn A(x) A(x) (1/e) (x)/x v (x) eie(x) (x) vi bt k hm thc (x) no14.

C th, ta mng tng i xng ny nh sau: in th ca tri t l mt triu volt v hai cc in trong nh l 1000000 volt v 1000220 volt, nhng my ca chng ta chy vi 220 volt khng h trc trc mc du hng triu volt in th ca qu t. Ci quan trng l hiu s ca in th ch khng phi bn thn ca in th mi im x ca khng-thi gian. V (x)

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l bt k hm g, c mun ngn in th ty tin khc nhau mi ni trong hon v bao la, nhng nh lut chi phi s vn hnh ca chng phi c iu chnh ra sao cho ta mt trng in t duy nht, lc in t trong my ca chng ta cng l lc in t trn cc thin th. H qu ca i xng nh x l s lng in tch bao gi cng c bo ton trong cc qu trnh vt l, chng bt bin vi thi gian v khng gian. l ngha vt l ca cc loi i xng nh x, n tc ng ln c bn lc c bn: hp dn, mnh, in-t, yu.

IIIb-T i xng n nh lut. 1- Theo thuyt tng i rng (lut hp dn), mi ngi quan st bt k h chuyn ng ra sao u bnh ng nh nhau, ngi di chuyn vi gia tc cng c th ni h ng yn v h c th thay th lc m h b tc ng ln bng lc hp dn m h b t vo. S tng ng gia gia tc v trng lc c th minh ha qua hnh nh quen thuc ca phi hnh gia l lng ng yn trong ha tin bay vi gia tc ln. N phn nh tng m Einstein coi nh mn nguyn nht trong i ng: mt ngi rt t trn cao xung khng cm thy sc nng ca mnh. Theo ngha , lc hp dn tun th mt php i xng nh x, n bo m rng tt c cc h quy chiu mi im ca khng-thi gian u tng ng vi nhau. 2- i xng chun nh x khng nh tnh bt bin ca nh lut in-t bi nhng chuyn di ca in tch t im ny n im kia ca khng-thi gian. Cng th, i vi lc mnh ca ht nhn nguyn t th hai ht proton v neutron u hon ton bnh ng, nh lut tng tc mnh ca ht nhn khng thay i bi s hon chuyn proton neutron bt k im no trong khng-thi gian. V y l im ct li: S tng ng ca mi h quy chiu (bt k chng chuyn ng c hay khng c gia tc) i hi phi c lut hp dn v xc nh c lut hp dn di dng phng trnh Einstein ca thuyt tng i rng15. 3- nh lut tng tc in-t gia electron vi photon cng c th c pht hin nh vy. M u ch c mt trng electron (x), vi iu kin l hon chuyn (x) eie(x) (x) khng lm bin i dng ca hm Lagrange16 (x)(i mc)(x) ca electron. i hi ny a ti h qu l phi hin hu mt trng t-vect A(x). Thc vy, o hm /x p t ln eie(x) (x) b buc mt trng A(x) no phi hin hu v phi hon chuyn ra sao trit tiu h s (x) v gp phn lm cho hm Lagrange bt bin bi hon chuyn (x) eie(x) (x). Hn na, trng A(x) v tenx lin i F A (x) A(x) li tun th phng trnh Maxwell, vy A(x) chnh l trng photon. Kt qu cui cng cho hm Lagrange bt bin l c hai trng electron (x) v photon A (x) phi gn kt di dng e (x)(x)A(x), m cng thc ny chnh l nh lut tng tc in-t (QED) gia electron vi photon, k th thay! 4- Cng theo cch lp lun nh trn, ta s i t i xng gia proton v neutron trong cc qu trnh ca ht nhn nguyn t pht hin ra nh lut tng tc ca chng, nh lut ny l phin bn u tin ca l thuyt chun Yang-Mills. Thc th neutron ging ht nh proton trong nhng tc ng ca chng lnh vc ht nhn nguyn t, vy php i xng nh x gia hai thnh phn proton v neutron ca nucleon ( bt k mt im no ca khng-thi gian) i hi tng tc mnh phi c din t di dng ca mt phng trnh c th no . Chen Ning Yang cng ng nghip Robert Mills bn lun v tnh bt bin ca lc mnh di s hon chuyn proton neutron v tm ra nh lut tng tc p ng php i xng ny. Cng trnh cc k phong ph gi l l thuyt chun Yang-Mills17 vi nhm i xng SU(2) gia hai i tng l proton v neutron.

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M phng phng php ny vo trng hp ca quark mang sc tch bng cch thay th nhm i xng SU(2) gia proton v neutron bi nhm i xng SU(3)C gia 3 sc tch ca quark, thuyt Yang-Mills xy dng vi SU(3)C do mang tn Sc ng hc lng t (QCD) v boson chun ca n l gluon. i xng chun nh x gia ba sc tch ca quark din t tnh bt bin ca QCD bi nhng chuyn ri ca sc tch t mt im khng-thi gian ny n mt im khng-thi gian kia. IIIc- T do tim cn v n l hng ngoi. V mt cu trc ton hc th s hon chuyn ca N vt th bi nhm i xng SU(N) c biu din vi (N2 1) ma trn N N, tng ng vi (N2 1) boson chun ni kt N vt th vi nhau. Vi nhm SU(2) ta c 3 ma trn Pauli, vi nhm SU(3) ta c 8 ma trn Gell-Mann v QCD c 8 boson chun (gluon) ni kt quark; c gluon ln quark u mang sc tch. V nhng ma trn ca SU(N) phn giao hon (ab ba) nn i xng chun vi nhm SU(N) mang tn i xng chun khng giao hon. Mt h qu c o do tnh khng giao hon ca nhm SU(N) trong l thuyt Yang-Mills ni chung (v nhm SU(3)C trong QCD ni ring) l cc (N2 1) boson chun phi trc tip tc ng gia chng vi nhau, khc vi in-t khng c tng tc trc tip ny. Thc th nhm i xng U(1) ca QED l eie(x) ch c mt thng s (x), tng ng vi mt boson chun (photon) nn ng nhin i xng chun U(1) giao hon. Theo nh l Noether, h qu ca i xng SU(3)C trong QCD l s bo ton sc tch, cng nh h qu ca i xng U(1) trong QED l s bo ton in tch. Tc ng trc tip vi nhau gia cc gluon l gc ngun ca tnh cht t do tim cn18, theo , cng ca lc mnh gim i khi nng-xung lng E dng thm d quark tng ln, hng s tng tc QCD nh dn nh 1/Log(E) khi E tng. Trong vng nng lng cao, quark v gluon khng lin kt cht ch vi nhau na v c t do; ngc li, vng nng lng thp (nhit bnh thng), quark v gluon b gi cht trong cc hadron. Tnh cht l lng ny, mnh danh n l hng ngoi, c th coi nh h qu ca s ni di lin tc t E ln xung E nh ca hm 1/Log(E), hm ny tng khi E gim lm cho QCD >> 1. V khong cch khng gian R v nng-xung lng E t l nghch theo nguyn l bt nh, tnh n l hng ngoi khin cho cng QCD ca lc mnh gn quark vi nhau li tng ln vi khong cch ca hai quark, cng y chng ra xa tch ri chng th lc gn kt chng li cng mnh hn ln ko gi chng vi nhau, tri ngc vi lc Coulomb ca in-t b gim theo bnh phng ca khong cch gia hai in tch. Quark b cm t trong hadron, nhit bnh thung chng khng sao thot ra ngoi l mt. Tnh cht c o t do tim cn ca QCD mang gii Nobel 2004 cho Gross, Politzer v Wilczek. Khi phn tch chi tit cc s liu thc nghim v phn b tn x, iu ngc nhin l nng lng cao (nhit ln), cc thnh phn c bn quark v gluon hu nh khng cht no b gn kt cht ch trong cc hadron. Tnh t do tim cn ca QCD gii thch iu ny v nng lng cao th lc mnh nh dn, quark thoi mi vy vng t do trong hadron. Cng vy trong my gia tc c nng lng cao hay cc thin th bng pht, c tnh t do tim cn tin on quark cng nh gluon khng cn gn cht vi nhau na m tp hp v m ca chng tr thnh lng v qunh nh mt, mt trng thi mi ca vt cht gi l quark-gluon plasma. Trong nhng giy pht u tin ca V N Ln BigBang vi nng lng, nhit , p sut, mt cao cng cc, quark v gluon hon ton t do khng cn cht no gn kt, tng tc vi nhau, vt l thi nguyn thy thc l n s! Khi v tr ngui dn, entropy tng trng, lc mnh gia quark gluon tng dn, gn kt chng thnh hadron v vt cht ni chung tr nn phc tp. c im cn nhn mnh ca i xng chun nh x l n i hi cc boson chun - lm trung gian s gi cho nhng trng vt cht quark v lepton tng tc vi nhau - phi khng

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c khi lng19. Photon hay gluon l v d ca boson chun khng c khi lng. cng l iu kin tin quyt cho s ti chun ha thnh cng ca QED v QCD. Cui cng cn li lc yu. i xng chun, mt nguyn l mu nhim, c th ng vai tr no cho lc yu khng? Nhn b ngoi th v vng v khi lng MW ca ht trung gian truyn ti lc yu khng nhng khc 0 m li rt ln theo nguyn l bt nh (MW /RW) m di truyn ti ca lc yu RW th cc k nh v n ch tc ng trong ht nhn nguyn t. y vy m cu hi mang v tuyt vng ni trn c c li gii p, nhng phi qua nhiu chng ng kh khn m ngon mc mang tn gi l s ph v t pht ca i xng chun nh x, iu lin i n boson Higgs cp sau Phn IV v thuyt in-Yu.

Phn IV-Hp m trong vng in-Yu

L do hin nhin l hu ht cc thnh vin ch cht ca ban L thuyt CERN khng quan tm ti tng tc yu v khng tuyn dng nhng nh vt l tr c tim nng lm vic .

John Iliopoulos, Lch s ca CERN (1993)

Trong nhng phn trc, chng ta lm quen vi hai trong ba lc c bn ca T nhin: lc in-t (QED) v lc ht nhn mnh (QCD), phn cui ny dnh cho lc ht nhn yu. Quark c in tch v sc tch nn b chi phi bi c ba lc: in-t, ht nhn mnh, ht nhn yu. Electron, muon, tauon mang in tch nhng khng c sc tch nn chu s tc ng ca hai lc: in-t v yu. Neutrino khng c c sc tch ln in tch nn duy nht ch c lc yu iu hnh chng. Thut ng yu thong nghe nh chuyn ph vn, ngay c i vi nhiu nh vt l ht trc nm 1970 nh Iliopoulos nhc nh trn y. Thc ra ngc li mi ng khi bit rng lc yu chi phi s phn r ca ht nhn nguyn t, ch cht iu hnh nhng phn ng nhit hch trong cc thin th, pht tn nng lng cc k cao mang nh sng cho bu tri ban m, phng ra mun t ht neutrino tng giy pht ang xuyn qua da tht chng ta. S tng hp nhit hch trong tm li mt tri lm n nng rc ti chng 20 triu l hin tng pht x neutrino bi lc yu (Hnh 7).

Hnh 7: tng hp nhit hch: 4 H He + 2 e+ + 2 e

Mi cch y c 18 ngn nm trong giai on cui cng ca thi k bng h, tuyt ph dy c bao trm phn ln tri t, ngay c vng xch o. Ngi tin s c th thot khi nn tuyt chng bi ci lnh kinh hong ny, v may thay trong thi k bng lnh th ni la li hot ng cc k mnh, kh nng lan to nhanh chng xung mt t qua hin tng nh knh. Nhit lng phun ra t ni la l do phng x neutrino ca Uranium trung tm tri t.

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Tin trnh tm hiu v khm ph nh lut ca tng tc yu khong u nhng nm 1970 ng vai tr quyt nh v m ng khai phng cho Vt l Ht thng hoa vi nhng pht hin k diu nh: ba hng v mi ca vt cht l duyn (charm), y (bottom), nh (top); boson chun ca lc yu W v Z; ch hin hu c ba loi neutrino vi khi lng cc k nh, nhng khi lng qu nh b c th o lng bng cch xc nh s hon chuyn gia ba loi neutrino e ; boson Higgs mang khi lng cho vn vt v tr hnh thnh trong c con ngi. C hai lc mnh v yu u c din t bi thuyt Yang-Mills vi nhm i xng SU(3)C ca ba sc tch cho lc mnh v nhm i xng SU(2)W ca cp i quark u, d (hay cp i lepton e, e) cho lc yu. Hn na lc in-t (nhm i xng U(1)) li ha nhp vi lc yu nn cu trc ca SM c biu din ngn gn nh tch s ca ba nhm i xng : SU(3)C SU(2)W U(1) theo th t chi phi ba lc mnh, yu v in-t. IVa- Neutrino, ci thu ban u. S pht hin ra lc yu m u nm 1896 khi Henri Becquerel (gii Nobel 1903) quan st thy mt s ht nhn nguyn t t nhin phng x m khng do mt tc ng no t bn ngoi. Mt trong nhng bc x t nhin l s phn r Carbon-14 ra Nitrogen-14 km theo electron v neutrino gi l phn r , din t bi n p + e + e.

Thc ra trc nm 1930 chng ai ng thi c neutrino c m ch bit electron thi v ngh rng n p + e, nhng nu th th lut bo ton nng lng b buc electron ch c mt nng lng duy nht l E = En Ep. Ngc nhin bit my khi o lng nng lng ca electron, th thy ph nng lng ca n l c mt ng cong lin tc vi bt k mt tr s no nm gia 0 v En Ep. Chng l nh lut ph qut nht ca khoa hc, nh lut bo ton nng lng, li b vi phm trong trng hp c bit ca phn r sao? Ngay c Niels Bohr (gii Nobel 1922), v trng lo ca trng phi Copenhagen v cch din gii c hc lng t, ngi t nn tng cho l thuyt nguyn t, cng min cng chp nhn s vi phm ny. Nhng Wolfgang Pauli (gii Nobel 1945) khng th ng vi cch tha hip d di y ca Bohr, bo ton nng lng l nh lut ph qut m tt c mi hin tng phi tuyt i tun th. gii p nghch l ny, nm 1931, Pauli gi nh l c mt ci g pht ra cng vi electron (s n p + electron + ci g ) chia s vi n tng s nng lng En Ep. V neutron trung ho in tch v cp proton-electron trit tiu in tch ca nhau nn ht gi nh bi Pauli phi trung ha khng mang in tch, n cng phi mang spin nh electron v hu nh khng c khi lng. Hn na, so vi phng x rt nhanh ca in t (nh tia X) th phn r li rt chm chp, cng phn r rt nh nn c gi l lc yu v neutrino hon ton b chi phi bi lc ny. Khc vi electron mang in tch, ht gi nh bi Pauli nh nh t v vn hnh duy nht bi mt lc m cng tng tc li rt nh nn xc nh s hin hu ca n bng thc nghim l mt iu cc k kh khn v Pauli nh tuyn b: Ti cht phm mt iu tai qui l gi nh s tn ti ca mt ht nhng li khng c phng cch thc nghim no d tm ra n c. T nay mang k hiu , ht ma rt kh nm bt ny chnh l neutrino (neutron nh), tn t bi Enrico Fermi (gii Nobel 1938), v gio hong ca nn vt l , khi ng ghp trung ho (neutro) vi nh xu (ino), hai ngn t gn b vi qu hng ng. Ln u tin nm 1955 ht e c pht hin bi Clyde Cowan v Frederick Reines (gii Nobel 1995) trong mt thc nghim l in ht nhn Savannah River. Ngy nay chm neutrino c sn sinh d dng t cc my gia tc ht m LHC ca CERN ng vai tr hng u th gii. Nhng neutrino khng ch sn sinh trn tri t, cn c mun t neutrino trong v tr t cc thin th xa xm k c mt tri n vi chng ta, vn l lm sao d c ra, ri xc nh

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cng o lng tnh cht ca chng. Cc nh vt l-thin vn dng nhiu my mc rt khc nhau tm bt, quan st neutrino.

Hnh 8: My d neutrino Super-Kamiokande

Kamiokande (Nht), my d l mt bnh khng l cha 50 ngn m3 nc tinh khit nh pha l trong lung linh hng ngn thit b in t tinh vi t di hm m thic (Hnh 8), nhm IMB t my trong hm m mui Ohio (M), Baksan (Nga) i quan st neutrino t su trong rng ni Caucasus. Ngy 23 thng 2 nm 1987 ba i thin vn-neutrino ny quan st o lng c c thy 24 ht n t mt siu tn tinh (supernova) SN1987A trong thin h ln Magellan (st cnh Di Ngn h) cch y 163 ngn nm n bng, m chi sng rc r tng ng vi mi t mt tri v pht tn hng h sa s, tng cng 1058 ht neutrino.

IVb- Thi xa vng.

1- Do thc nghim pht hin ra, lc yu c c im l n vi phm i xng gng (P) v i xng vt cht-phn vt cht (CP) trong khi cc lc in-t v mnh tun th hai i xng ny. P v CP l nhng i xng gin on, khc vi tnh lin tc ca i xng chun. Bn hnh dung i xng gng nh sau: tay phi (hay tri) ca ta c hnh trong gng ht nh tay tri (hay phi), v ci ta gi l pha phi hay pha tri ch l mt c l gia con ngi. Khng c g cho ta phn bit c mt hin tng ngoi gng v hnh chiu ca hin tng trong gng, s o ngc khng gian x x khng lm thay i nhng hin tng, chng bt bin. Thp ra c knh soi hnh xung nc trong vt pha l ca H Gm ma thu l biu hin ca i xng gng ton vn, thp vi hnh chng sao phn bit.

Khong u nhng nm 1950 thc nghim pht hin mt iu kh hiu l meson K+ lc th phn r ra 2 pion, lc ra 3 pion. Nu lc yu tun th i xng gng th l mt nghch l v tnh chn l ni ti20 ca K+ (meson 0) b buc n ch c phn r ra 3 pion thi. Hai nh vt l Trung Quc M L Chnh o (T.D. Lee) v Dng Chn Ninh (C. N. Yang), gii Nobel 1957 khi tm hiu v phn tch nghch l trn bn gi nh l lc yu vi phm i xng gng P. Cng lm vic i hc Columbia nh L Chnh o, nh n vt l thc nghim Ng Kin Hng (Chien-Shiung Wu) bn lun vi ng v phng cch kim chng gi thuyt ny bi thc nghim v h nhn ra vai tr quyt nh ca spin trong v kim chng s vi phm i xng gng. B Wu khm ph trong qu trnh phn r ca Cobalt phn cc l electron ch pht ra theo pha ngc chiu vi trc phn cc ca Cobalt21; r rng c mt bt i xng trong s phn phi electron chung quanh trc phn cc, chng t lc yu vi phm ti a i xng gng.

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2- Mt th d khc l i xng vt cht - phn vt cht hay i xng CP, theo cc nh lut vn hnh ca vt cht v ca phn vt cht phi ging ht nhau. Ch C trong CP ch nh in tch v s hon chuyn vt cht phn vt cht l thay i du ca in tch e e+. S hon chuyn vt cht phn vt cht cng lm hon chuyn tri phi (i xng gng P), c hai i xng C v P u i du nn tch CP khng i du, do CP din t s i xng vt cht - phn vt cht. Cn nhn mnh l trong tt c cc ht trung ha in tch, khng phi lc no ht v phn ht cng l mt (nh photon, meson 0, 0 , 0). Phn ln nhng hadron trung ho in tch nh neutron, meson K0, baryon 0, meson B0 u khc phn ht ca chng. Trng hp neutrino rt c th v n l ht c bn duy nht trung ha in tch (quark v ba lepton e, , u khng th), v cu hi neutrino v phn neutrino c khc nhau khng? cha c thc nghim tr li. Nu chng khc nhau th chng c g l, chuyn bnh thng nh neutron khc phn neutron thi v c gi l neutrino Dirac. Nhng nu khng, neutrino cng chnh l phn neutrino, th chng l neutrino Majorana. Bn cht ca neutrino Majorana cc k quan trng v n vi phm lut bo ton s lng lepton m h qu l s hin hu ca phn r kp 0 neutrino: n + n p + p + e + e. V u n + n khng c lepton, v sau c hai electron, vy s lng lepton khng bo ton. Nu neutrino l loi Dirac th phn r kp phi km theo hai e : n + n p + p + e + e + e + e , vi hai e (phn lepton) v hai e (lepton) v sau th s lng lepton c bo ton.

Nu phn r kp vng bng neutrino c thc nghim pht hin th chc chn s l mt bc ngot ca ngnh vt l ht v n vt ra ngoi khun kh ca SM, thuyt ny s phi m rng sang mt h hnh mi. Nm 1964, James Cronin v Van Fitch cng hai cng s vin pht hin s vi phm i xng CP bi meson K0L trung tnh (K0L ch phn r ra 3 pion nu lc yu tun th CP, nhng n cng phn r ra 2 pion, tuy t xy ra hn so vi 3 pion, nh vy vi phm chng mc CP) v hai v nhn gii Nobel 1980. S vi phm i xng CP ca lc yu c xc nhn sau bi nhiu thc nghim khc nhau lin i n cc hadron K (mang k tnh) v B (mang y tnh). Trong ba tng tc c bn phi hp dn, lc in-t v ht nhn mnh u tun th php i xng gin on P v CP, ch lc ht nhn yu mi vi phm chng, ti a vi i xng P, i cht vi i xng CP: lc yu ca ht v ca phn ht khc nhau mc va phi. 3- Cho n u nhng nm 1970, trc khi SM c hon tt, lc yu22 c tip cn di nhn quan mang tnh cht tm thi v hiu dng gi l thuyt Fermi. Thc vy, mc du thuyt ny din t chnh xc nhng qu trnh phn r nng lng thp, nhng nng lng cao E 600 GeV, n t mu thun. Ngun gc ca nghch l ny l thuyt Fermi ch yu din t tc ng ca 4 fermion t chung mt im x (Ch thch 22). V t chung mt im nn bin tng tc ca chng tnh ra l GFE2, nhng nu E 600 GeV th bin ny c xc sut 1, iu ti k. Chin lc t ra gii quyt nghch l ni trn l xem lc yu c tun th mt php i xng chun no khng, v nu c th nh lut c bn ca lc yu trnh c khuyt im ca thuyt Fermi (do hm truyn ca boson trung gian W nn 4 fermion khng t mt im m tch ra 2 im, coi hnh f Ch thch 22), do c nhiu kh nng lc yu cng c hon chnh nh lc in-t. Nhng li ny ra chuyn hc ba l ging nh photon ca in-t, i xng chun b buc boson truyn ti lc yu W phi khng c khi lng23, iu tri ngc vi thc nghim24.

Gii p tha ng vn trn l c mt bc ngot lch s trong tin trnh khm ph SM v cn phi vt qua hai giai on hu nh kh dung ho: (a) xc nhn nh lut ca lc yu l l thuyt chun Yang-Mills v (b) ph v t pht php i xng chun mang khi lng cho boson chun ca lc yu. Nm na nh mt vin nm trng c hai ch: va c i

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xng chun va c khi lng cho boson chun! ngha ca s ph v t pht i xng chun l thc ra i xng ny khng b ph v hon ton m ch b che khut cc b bi h thng vt cht trong trng thi cn bn vi nng lng ti thiu.

IVc- My dm sn kh

Trc khi i xa hn trong qu trnh vt khi thuyt Fermi t nn tng nht qun cho lc yu qua hai giai on ni trn, chng ta hy tm tt nhng nt chnh ca lc ny: 1- Khi quan st v phn tch nhng hin tng xy ra bi tc ng ca lc yu, c my c tnh sau y cn nhn mnh: th nht l dng lc yu thay i in tch khi phn r , th d n p, + 0 ca hadron (tng trng bi quark d u) v , e e ca lepton; th hai l nhng hadron mang hng v (nh k tnh) khi phn r v thay i in tch nh 0 p, K0 + (tng trng bi quark s u) u c cng kh nh khong 5% so vi phn r ca nhng hadron bnh thng khng hng v nh n p, + 0. gii thch nhng hin tng ny, thay v c hai loi quark phn r bit lp d u v s u, Nicola Cabibbo xut l hai quark d v s hn hp bi gc c khi phn r ra quark u theo nh s (d cosc + s sinc ) u; khc vi cc lepton khng hn hp nh , e e. So snh s sinc u vi d cosc u, con s 5% (0.22)2 = tan2c phn nh chnh xc cng phn r ca k tnh 0 p, K0 + so vi n p, + 0 ca hadron khng hng v. V cos2 c 0.95, s phn r ca hadron n p (tng ng vi d cosc u) phi nh hn cht xu phn r ca lepton , iu xc nh bi thc nghim. V K0 v 0 u phn r ra 2 hoc 3 pion, K0 pion 0 nn h qu l phi c s chuyn bin l thng: vt cht c th tr thnh phn vt cht m 0 0 l mt v d. Tuy nhin tnh ton theo thuyt Fermi a n kt qu bt ng l chuyn bin vt cht phn vt cht ln hn o lng thc nghim c vi ngn ln. Ngoi ra cn mt c tnh th ba kh hiu l nhng loi phn r trung tnh i hng v (flavor changing neutral current) u rt him so vi nhng loi phn r in tch i hng v (flavor changing charged current), th d 0 + + khong 104 so vi + + + m tin nghim th khng thy chng c g khc nhau qu ng nh vy. gii quyt nhng nghch l ny, nm 1970 Glashow, Iliopoulos, Maiani (c ch GIM) xut l phi tn ti mt loi quark th t mi l gi l quark duyn c trc giao vi quark u theo nh s (s cosc d sinc ) c km theo (d cosc + s sinc) u phn no trit tiu loi phn r trung tnh i hng v s d. Hn na, s trit tiu c th tnh ton thnh hiu s gia khi lng ca hai quark c v u, do khi lng ca c 1.5 GeV/c2 c tin on trc khi pht hin quark duyn thng 11 nm 1974 ng thi Stanford v Brookhaven vi ht J/(3.1) v mt lot cc ht charmonium khc. S kin pht hin ny c mnh danh sau l cuc cch mng thng 11 ca vt l ht v n m u cho SM thng hoa. 2- Nh trnh by, lc yu vi phm i xng CP, tng tc yu ca vt cht v ca phn vt cht khc nhau. Trong bi cnh 1973 ca vt l ht thi y ang bui s khai, hai nh vt l Nht bn Makoto Kobayashi v Toshihide Maskawa (KM), gii Nobel 2008 tin phong i tm hiu c ch no cho php s vi phm ny. Trc ht KM nhn ra l hn hp ca cc quark khng ch l mt tin ad-hoc a ra bi Cabibbo25 m cn phi m rng thnh ma trn 22 vi nhng h s (cosc, sinc) trc giao vi ( sinc, cosc) qua GIM tin on quark duyn. Sau nhiu cuc vt ln vi ton ng dng, hai v tm ra l ma trn unita 22

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ni trn ch c h s thc nn khng th vi phm i xng CP c. Thc vy, s vi phm CP ch c th xy ra nu ma trn unita hn hp quark c h s phc26. KM chng minh l nu c N cp quark phn r th ma trn NN s c h s phc nu (N1)(N2) 2, vy N 3. Phi hin hu t nht l ba cp hay su quark cho i xng CP b vi phm. T y ra i ma trn phc unita 33 CKM (Cabibbo-Kobayashi-Maskawa), mt thnh phn c bn trong cu trc ca lc yu. Thc l mt tr tng tng phong ph v vo thi bui y quark ch l mt gi thuyt, mt ti t nh, nhiu ngi bi bc k c nhng cy i th nh S.Weinberg, v ngay c nu chp nhn gi thuyt quark th lc y ch bit c ba quark u, d, s cng lm l thm c thnh bn quark thi. Thc nghim lin tip chng t sau ny s ng n, chnh xc ca c ch vi phm CP m Kobayashi v Maskawa (KM) xng. Nm 1974 quark duyn bt u l din ri quark y (nm 1977) v quark nh (nm 1994). Khm ph ca GIM v KM gp phn cc k quan trng cho s hnh thnh ca SM. Chnh su quark trong Hnh 1 sp dc theo ba cp quark (u-d, c-s, t-b) din t tt c nhng c trng ca lc yu vi ma trn 33 CKM hn hp ba cp quark ni trn. Su lepton cng sp dc theo tng cp (e - e, - , - ) nhng vi ma trn hn hp cc lepton khc vi ma trn CKM hn hp cc quark din t s hon chuyn gia 3 loi neutrino e ni on u ca Phn IV. Bi hc rt ta t l gia trm ngn cc hin tng vt l ri rm, iu quan trng l bit nhn xt, phn tch d kin, phn bit ci chnh ci ph v t nhng cu hi ct li c ni dung bao qut, tng quan. Khi u cc tc gi u tp trung nghin cu v nhng c trng ca lc yu: k tnh bin ha v vi phm i xng CP, h qu bt ng li chuyn sang a ht ca lc mnh vi s pht hin ra ba loi quark vt cht mi l l duyn, y v nh. Nh ai c cu t trng vn l gii quyt c na phn ri .

IVd- Lc yu xut pht t i xng chun Yang-Mills 1-Khong nhng nm u 1950, nhiu nh vt l (trong Sidney Bludman, John Clive Ward) tinh nhn ra l gia hai tng tc in-t v yu c nhiu cu trc v tnh cht ng nht, vy hu nh l chuyn ng nhin nu ta s dng phng php rt hiu lc ca i xng chun trong in-t khm ph nhng nh lut vn hnh ca lc yu.

c th ca lc yu l s phn r theo cc cp quark hay cp lepton thay i mt n v in tch. Ly trng hp ca cp lepton e v e (hay cp quark u v d) nh mt v d. Di tc ng ca lc yu, chng thay i in tch e e (hay u d ) vi cu trc vect quay v tri (V A) ca dng lc yu gia hai i tng e v e (Ch thch 22). Vy hu nh ng nhin nhm i xng p ng tnh bt bin ca lc yu bi s hon chuyn ca hai i tng e v e chnh l nhm SU(2) m ta lm quen vi thuyt Yang-Mills phn IIIb, ch cn thay th cp p-n thnh cp e-e.

Ni chung, nhm i xng SU(N) hon chuyn N vt bng (N2 1) ma trn NN, tng ng vi (N2 1) boson chun ni kt N vt ny. Vy nhm i xng chun SU(2) ca lc yu c 3 boson chun W+, W, W3 ni kt e e + W, e e + W+, e e + W3, e e + W3. S hin din ca boson W3 v dng lc yu trung ha in tch e e + W3 gi ngay ra mi lin h no vi dng lc in-t quen thuc ca electron e e + , ci khc nhau duy nht gia chng l cu trc vect (V A) quay v tri ca dng lc yu, trong khi dng lc in-t ch c cu trc vect V.

Cn qu trnh vi neutrino: e e + W3 th hon ton mi l v trc ta ch bit lc yu thay i in tch ca cc ht nh e e hay e e.

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chng minh tnh ng n ca thuyt Yang-Mills dng nhm i xng chun SU(2) nh phc ho trn, vic u tin l kim chng xem c tn x khng thay i in tch chng. Tn x thay i in tch th bnh thng v dng lc yu thay i in tch (m e e l v d), tri li khng thay i in tch th hon ton mi l. Nhm thc nghim Gargamelle CERN nm 1973 cho kt qu e + nucleon e+ hadron (khng thay i in tch), ng nh tin on ca thuyt in-yu; mt s kin lch s ca vt l ht, chng t SM vi thuyt Yang-Mills i ng hng.

V y l im then cht trong tin trnh xy dng cu trc ca SM: khi lc yu b chi phi bi i xng SU(2) th cc cp i lepton hay quark (e v e, u v d nh vi v d) u c spin ng v I = , v nh vy ng thc ph qut ca Gell-MannNakanoNishijima (GNN) m ta lm quen IIc ng nhin ng vai tr hng dn cho s hp nht ca hai lc in-t v ht nhn yu v c hai lc u c chung cu trc Q = Iz + Y/2. V boson W3 l thnh phn th ba tng ng vi Iz 0 nn Glashow (nm 1960) v sau Salam, Weinberg (nm 1967) nhn nh l phi thm mt boson mi l X tng ng vi siu tch Y/2, c hai W3 v X u trung ha in tch. S lin kt gia hai lc in-t v yu c thc hin bng s hn hp27 t nhin (qua mt thng s gc w) gia hai boson W3 ca Iz v X ca Y/2, hoc l gia hai boson chun: Z ca lc yu v photon ca lc in-t. Hn na cng ca hai lc yu v in-t cng lin kt qua gc w.

Cho n giai on xy dng cu trc lin kt hai lc in-t v yu qua thuyt Yang-Mills SU(2) U(1) ny, tt c bn boson chun (ba ca lc yu W+, W, Z v mt ca lc in-t ) u khng c khi lng v chng tun th i xng chun. 2- Giai on tip l lm sao mang khi lng rt ln cho W+, W, Z ca lc yu ph hp vi thc nghim, trong khi photon ca lc in-t vn gi khi lng bng 0 ? Thch thc ny c gii p bi c ch mang tn Ph v t pht tnh i xng (Spontaneous Breaking of Symmetry, vit tt SBS) m Yoichiro Nambu (gii Nobel 2008) m ng khai sng. Trong vt l, cng nh trong nhiu ngnh khc, c mt s nh nh khoa hc kin thc xuyn ngnh uyn thm, nhn rng ra ngoi ci chuyn mn ca mnh, tm hiu nhng g ph qut mang li cho ngnh mnh mt lung gi mi. Nh vt l Nht bn Nambu i hc Chicago l mt trong s . Chuyn gia v ht c bn nhng ng cng lu tm v c ci nhn bao qut v hin tng Siu dn in-t khc l vi Vt l ht. ng xt thy c ci g lin kt hai ngnh - cu trc ton hc th ging nhau nhng vt l th li khc bit - v nhn ra c tnh cht c th ca SBS m hin tng Siu dn in-t l mt biu hin. M phng hin tng SBS, Peter Higgs v ng nghip sng to ra c ch BEH (Brout, Englert, Higgs)28 bng cch gi nh l phi hin hu mt trng (x) v hng gi l trng Higgs tc ng ln cc boson chun mang khi lng cho chng. Nguyn nhn no thc y Nambu nhn chn ra SBS v su nh vt l xut c ch BEH? l s tm hiu ti sao ht nh sng (photon ) khng khi lng li tr thnh c khi lng khi n di chuyn trong cc vt liu siu dn in-t. Sau Abdus Salam v Steven Weinberg (gii Nobel 1979) dng kch bn BEH xy dng nn thuyt in-yu v tin on boson Z vi dng lc yu trung ha in tch m biu hin c trng nht l s tn x n hi ca neutrino khm ph bi thc nghim Gargamelle29 CERN vo nm 1973. Tuy W , Z c khi lng nhng khi lng ny khng ph v i xng chun SU(2) ca lc yu, i xng ch b thu hp, che khut bi h thng vt cht trong chn khng (trng thi c nng lng cc tiu), tng t nh photon tuy c khi lng trng thi siu dn in-t

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(hiu ng Meissner) nhng i xng chun U(1) ca lc in-t u c b ph v trong ton th. IVe- S ph v t pht tnh i xng (SBS) 1- Vi khi nim s lc: Ta cn phn bit hai iu quan trng khi bn lun v tnh i xng: mt l nh lut vt l din t bi phng trnh, hai l trng thi ca h thng vt l din t bi nghim s ca phng trnh trn. S ph v t pht ca tnh i xng hm ngha l nh lut (hay phng trnh) mang mt php i xng no , trong khi nghim s ca phng trnh y li khng c ci i xng nguyn thy, tnh i xng b thu hp li nhng khng mt i trong h thng vt cht. Tm ra phng trnh (hay nh lut vt l) l mt chuyn, cn gii c c nghim s tha mn iu kin ban u no li l chuyn khc. y iu kin ban u l nng lng cc tiu v nghim s tng ng gi l trng thi cn bn hay chn khng. i xng b ph v mt cch t pht nu phng trnh din t nh lut vt l th i xng nhng trng thi cn bn th khng. i xng khng b ph v hon ton m n ch b thu hp, che khut bi vt cht trong trng thi cn bn. Mt n d c th minh ha khi nim ni trn: ta n u mt thanh g do t thng ng trn bn, lc n c i xng hon ho so vo trc thng Oz ca thanh g trc khi b n, lc ny khng u i bt k mt mt phng thng ng no trong khng gian ba chiu, chng hon ton bnh ng. Nhng h thng vt cht (thanh g b n) s cong i, khi cong nh vy thanh g t n nm trong mt mt phng thng ng no c th, h thng vt cht ch i xng trong mt phng hai chiu, n khng cn mang tnh i xng nguyn thy ca lc trong khng gian ba chiu. Cn trnh s hiu nhm v ngha gia mt bn l SBS theo i xng khng b ph v (ch c trng thi vt cht l bt i xng thi) v bn kia l nhng i xng khc thc s b ph v nh i xng gng (P), i xng vt cht-phn vt cht (CP) hay i xng hng v SUF(3). S hiu lm ny ngay c W. Heisenberg v S. Weinberg cng mc phi lc ban u, hai v coi SBS nh biu trng ca mt i xng xp x, b ph v thc s. 2- V trng thi cn bn c coi l trng thi i xng hon ho nht, n bt bin bi mi chuyn i v do ta c th ngh rng ch c duy nht mt trng thi cn bn hay chn khng, c nh ngha nh trng thi vt cht c nng lng ti thiu. Nhng c nhiu trng hp khng phi nh vy, c th c mun vn trng thi c bn tng ng nhau, chng sao phn bit, ta phi chn c th mt trng thi nht nh no xc nh chn khng. Tnh i xng khng b ph v trong ton th, nhng b ph v mt phn no trong chn khng, l SBS vi Hnh 9 nh mt n d.

Hnh 9 : Hin tng SBS qua mt n d: Th gii hon ton i xng chung quanh trc thng ng, khi em nh

nhn t nh cao cht (nhng bp bnh) ca nn. Sn di vnh nn (trng thi cn bn) vng chc nhng xa trc thng ng, i xng thu hp trong vnh nn i vi em nh nm trn . Nm trong vnh nn, em nh

khng ng l c mt i xng khc nh nn

Hin tng SBS kh ph bin trong vt l m vt liu st-t (kim loi st hay kn) l mt v d. nh lut c bn chi phi cht st-t th hon ton i xng trong s phn phi spin (coi nh nhng la bn nh xu) ca cc nguyn t kn. Spin song song ca chng khng c mt

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chiu hng no gi u th trong ton th khng gian ba chiu. Nhng trong mt thi nam chm ca vt liu st-t, ngha l trong trng thi cn bn ca cc nguyn t kn, th spin song song ca cc nguyn t ny li ch c mt chiu nht nh bc nam, vy trng thi vt liu st t ch cn i xng thu hp trong . Cng vy, siu dn in-t minh ha hin tng SBS. Tnh siu dn ca mt s vt liu nhit thp l mt c trng ca vt l lng t, n khng c in tr, v th n trc xut bt k mt in trng ln nh ngoi p t vo n. Hn na, gn vt liu siu dn th thi nam chm b y ra ngoi, t trng b y ra khi vt liu siu dn, l hiu ng Meissner- Ochsenfeld. Hiu ng ny c th l ci ngun cho xe la trong tng lai c nng ln trn ng ray khi chy (tu m t) khng b lc ma st nn xe la chy nhanh. Nh vy vt liu siu dn ngn chn tm truyn ca trng in-t, n l mt h thng vt cht trong photon ch c th tc ng trong mt khong cch ngn, khc vi bn cht t ti ca sng in-t c th truyn i v hn. Khi chuyn ng trong vt liu siu dn th photon, boson chun ca in-t, b cn tr bi mt bc tng chn v nh vy photon tc ng ging nh mang mt khi lng (Ch thch 4 ca IIb), mc du phng trnh Mawwell ca in-t vn tun theo i xng chun. Bc tng chn trong l thuyt siu dn ca John Bardeen, Leon N. Cooper v Robert Schrieffer (BCS), gii Nobel 1972, l trng thi cn bn ca h thng vt cht vi mun ngn cp Cooper, cp lin kt hai electron c spin i nghch v nh vy cp ny mang spin 0. Mi cp Cooper mang in tch 2e nhng v c spin 0 nn nhng cp ny c th ho ng chung sng ta nh mt ngng t Bose-Einstein. Mi electron th c n v c c tnh mnh m, nhng mt hon cnh c bit no (nhit thp) chng li d kt i, mi cp tuy mnh mai nhng khi t hp ng o li ha ng vn hnh nh mt dng chy thun khit ca mun ngn in tch v vt liu tr nn siu dn. Mc d trong mi trng siu dn, photon c khi lng 0, nhng i xng (x) eie(x) (x) trong nh lut in-t khng b ph v m ch thu hp bi (x) (x) vi h qu l s xut hin trng thi cn bn cc cp chn electron i nghch spin, s lng ca cc cp Cooper khng bo ton m thay i khng ngng, minh ho s ph v i xng. Siu dn l mt biu hin s ph v t pht ca tnh i xng chun; cng vi hin tng st-t, l hai v d ca SBS. 3- Hin tng SBS gip ta hiu ti sao boson chun photon, trn nguyn tc phi khng c khi lng, cui cng li ha ra c khi lng trong hin tng siu dn. N qu l mt diu php khin cho hai boson chun ca lc yu W, Z khi u khng c khi lng da vo c khi lng. Trong c ch BEH, cp Cooper mang khi lng cho photon c thay th bi trng Higgs (x) mang khi lng cho boson chun W, Z ca lc ht nhn yu (Ch thch 28). Nhng hy cn mt vng mc quan trng phi vt qua. Thc vy, mt h qu tt yu ca hin tng SBS (do Nambu nhn ra v Jeffrey Goldstone trin khai thm ri cui cng Goldstone, Salam, Weinberg chng minh thnh mt nh l) l phi tn ti mt ht khng khi lng, khng spin, c gi l boson Nambu-Goldstone (NG). Ta c th cm nhn bng trc gic nh l Goldstone khi quan st em nh trn vnh nn (hnh 9). Em chng cn mt mt cht nng lng no m vn c th di chuyn d dng sut quanh vnh nn v bt k trng thi cn bn no trn vnh nn cng u tng ng nhau. Khng cn cht nng lng no bin chuyn th cng ta nh da vo tc ng ca mt ht nht pho, khng khi lng, khng spin, chnh l boson NG m thc nghim c th d dng pht hin. nh l ny lm au u bao nh vt l khi mun p dng i xng chun v SBS khm ph nh lut ca lc yu v thc nghim chng bao gi thy bng va ca boson NG bao gi

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c (tr trng hp gn ng ca pion c khi lng rt nh so vi cc hadron khc), vy boson NG l mt di sn cng knh ca SBS cn phi loi b. P. Higgs v ng nghip thnh cng trong cch chng minh nht qun c s trit tiu boson NG trong trng hp i xng chun nh x (v ch trong trng hp ny thi) m trc Philip Anderson cng phc ho ra tng c s trit tiu ny trong hin tng siu dn in-t. Mt cch tng qut th bt k ht no c spin 1 v khng khi lng (nh photon chng hn) ch c hai phn cc (spin 1) trc giao vi vect xung lng k ca n. Nu ht spin 1 c thm phn cc th ba (spin 0) nm dc trn k th n s c khi lng. Trong c ch BEH, chnh boson NG spin 0 (coi nh phn cc th ba) mang khi lng cho boson chun W, Z ca lc yu (Ch thch 28).

V i xng chun b ph v mt cch t pht do trng v hng Higgs to nn, trong khi nh lut tng tc ca lc yu thc s vn tun theo i xng chun nn Gerard t Hooft v Martinus Veltman thnh cng trong cch chng minh30 l lc yu cng hon chnh v ti chun ha c nh lc in-t, hai v nhn gii Nobel 1999 v cng trnh ny.

Ta c th tm tt nm na l BEH t hai ch vi mt mi tn qua hnh nh tng trng: boson chun ca lc yu khi u nh tnh nut ba boson NG cui cng tr thnh W+, W, Z0 nng n. Khng nhng mang khi lng cho W, Z, trng Higgs cng mang khi lng cho quark v lepton vi c im l nhng khi lng ny t l thun vi cng tng tc ca chng vi boson Higgs.

Tm kt

Hin tng khm ph boson Higgs m CERN va tm thy du vt rt kh tin ngy 04/07/2012 (v mi y b sung thm nhiu d kin mi ngy cng chnh xc ca hai thc nghim Atlas v CMS) l kt qu lao ng v am m khng ngng ca cc nh vt l khi CERN quyt nh xy dng my gia tc khng l LHC c nng lng cao nht th gii sn tm ht Higgs. N m u mt chng mi trong vt l v y l ln u con ngi khm ph ra mt lc mi l, lc mang khi lng cho vt cht, c th coi nh lc c bn th nm ca T nhin, bn cnh bn lc c bn quen thuc. y cng l ln u xut hin mt ht c bn duy nht c spin 0. Cc ht khc u c spin khc 0: vt cht tng trng bi quark v lepton c spin , cc boson chun W, Z, , g (ni kt v truyn ti thng tin cho cc vin gch c bn ca vt cht tng tc vi nhau) c spin 1. N gi ra cch tip cn mi v khi lng ca vt cht, khc vi quan im c hu coi khi lng l ci g cho trc bi T nhin m khng ai hiu ngun gc su xa. Theo SM, khi lng ca vt cht c to ra bi s tng tc ca chng vi trng Higgs trn y trong chn khng ca v tr t V N Ln. Khi u tt c u khng c khi lng, do tng tc vi trng Higgs m vt cht mang khi lng, nng hay nh ty theo cng tng tc ln hay nh ca chng, cng tc ng mnh vi trng Higgs th vt cht cng c khi lng ln, quark top tng tc mnh m nht, neutrino hay electron qu hng h, cn photon th hon ton v cm vi trng Higgs. Quan im v khi lng c th i khc t nay, s tng tc ca vt cht vi trng Higgs trong chn khng lng t, mt v i no nhit, mi chnh l gc ngun ca khi lng. ng qun l khi lng (tc nng-xung lng l gc ngun ca lc hp dn).

Nh mt li tm kt vi M Hnh Chun, xin trch vi cu m Einstein trnh by trong bi ging v thuyt Tng i rng i hc Glasgow nm 1933: Kt qu cui cng rt gin d, bt k mt sinh vin thng minh no cng c th hiu c mt cch d dng. Nhng ch c th hiu c sau khi tri qua nhng nm thng m thm tm kim mt s tht m ngi ta ch cm thy ch khng th din t chnh xc c. Ngi ta ch c th hiu c iu khi

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lng ham mun ln n mc cung nhit, v khi tri qua nhng giai on tin tng ri nghi ng, nghi ng ri tin tng cho ti mt lc no , bng hiu r c s tht sng sa. Ch Thch Phn I 1Nhng thut ng nh Lng t, Trng lng t, Ti chun ha, Spin, Sc tch, Quark, Lepton, Phn quark, Phn vt cht, i xng chun, Ph v t pht, C ch BEH s dn c cp, gii thch trong nhng phn II,III, IV. Rt kh son mt cun sch gio khoa v ngnh vt l ht trnh c nhn, nhng nu chn th c l y l cun sch hay v d c nht, c th s dng min ph trn https://notendur.hi.is/~ath68/griffiths.pdf

Tc gi David Griffiths ca cun sch cho rng y l thi im a mn vt l ht vo chng trnh c nhn vt l i cng. Ti liu tham kho: - Hi k ca hn 40 tc gi tiu biu (vi 14 gii Nobel) khm ph ra SM: The Rise of the Standard Model, Ed. by Lillian Hoddeson, Laurie Brown, Michael Riordan, and