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_. u. d. u. e. e . W links members of the same weak isodoublet. W -. within a single generation. u. d. The decay conserves charge, but does NOT conserve iso-spin ( up ness/ down ness). d. _. u. d. u. e. e . W -. However, we even observe some - PowerPoint PPT Presentation
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u
d
e
e
_uu
dd
eepn
W
W links members of the same weak isodoublet
within a single generation
The decay conserves charge,but does NOT conserve iso-spin
(upness/downness)
u
d
e
e
_uu
dd
eepn
W
However, we even observe some strangeness-changing weak decays!
d uu
du
s
p
du
Ku ds
ss
s
su_
_
→ + ν 63.43% of all kaon decays
→ 0 + 21.13%
_
→ e + νe
_0.0000155%
u sK
νe
W
u sK
u u
W
u
d
_
u
d
e
e
_uu
dd
eepn
W
d uu
du
s
p
du
Ku ds
ss
s
su_
W
_
W
Cabibbo (1963)
Glashow, Illiopoulous, Maiani [GIM] (1970)
Kobayashi & Maskawa [KM] (1973)
Suggested the eigenstates of the weak interaction operators(which couple to Ws)
are not exactly the same as the “mass” eigenstatesparticipating in the STRONG interactions
(free space states)
The weak eigenstates are QUANTUM MECHANICAL admixtures
of the mass eigenstates
dweak = c1d + c2s where, of course c12 + c2
2 = 1
= sinθcd + cosθcs
To explain strangeness-changing decays, Cabibbo (1963) introduced the redefined weak iso-doublet
udc
=u Intended to couple to the
Jweak current in the Lagrangian
u
d
W
cosc
u
s
W
sinc
“suppressed”
sinc 0.225cosc 0.974
dcosc + ssinc
θc 13.1o
The relevant term, JweakW , then comes from:
iWigBigi iL
22 21
Y0)( Ldu† †
Ld
u
Bigi R
21Y0Ru †
Ru
i0Rd †
Rd ig1 BYR
2
Lcg
du )(22 † †
Ld
u
W3 W1iW2
W1iW2 W3
Lcg
du )(22 † †
Ld
u
W3 0
0 W3
0 W1iW2
W1iW2 0+
From which follows a NEUTRAL COUPLING to
c
c d
udu
g
10
01
22 = uu - dcdc
_ _
))(cos(sinsincos 22 dssdssdduucccc
d sK
0
Z 0
a coupling to astrangeness changing
neutral current!
u sK+
u d+
Z 0
BUT we do NOT observe processes like:
u sK+
u d Though we do see the very similar processes:+
Z 0
u sK+
u u0
W
d sK
0
u
W
W
d sK
0
Z 0
These are suppressed,but allowed (observed).
Compare to 0e+e
0
Also e+e
Glashow, Illiopoulous, Maiani [GIM] (1970)
even before charmed particles were discovered (1974) and the new quark identified,
proposed there could be a 2nd weak doublet that followed and complemented the Cabibbo pattern:
ccc
csscc
s
csc
g
10
01)(
22
So that the meaured Cabibbo “angle” actually represented a mixing/rotation!
s
d
s
d
cc
cc
cossin
sincos
so that:
ccsd
u
d
u
sincos
ccsd
c
s
c
cossin
orthogonal!
then together these doublets produce interactions of:
uu – dcdc + cc scsc
_ _ __
= uu + cc – (dcdc + scsc)
= uu + cc – (ddcos2θc + sinθccosθc (ds + sd) + sssin2θc
_ _ __
ccsdd sincos
ccsds cossin
ddsin2θc sinθccosθc (ds + sd) + sscos2θc)
= uu + cc – dd – ss_ _ __
_ _ _ _
_ _ _ _
absolutely NO flavor-changing neutral current terms!
1965 Gellmann & PaisNoticed the Cabibbo mechanism, where was the weak eigenstate,
allowed a 2nd order (~rare) weak interaction that could potentially induce the strangeness-violating transition of
cc sds cossin
K o K
o
a particle becoming its own antiparticle!
u u
s
d s
d
Ko
Ko
W
u
u
s
d s
d
Ko
Ko
W W