M. Cobal, PIF 2003
Weak Interactions • Take place between all the quarks and leptons (each of them has a weak charge) • Usually swamped by the much stronger em and strong interactions • Observable weak interactions either involve
1) ν (which do not undergo em and strong interaction) 2) quarks with a flavor change • Like in QED and QCD, the force carriers are spin-1 bosons that couple to quarks and leptons
−−
+
−
+→
+→+
++→
π
ν
nc
enpvb
epna
e
e
Σ)
)
) Neutron β-decay Antineutrino absorption Hadronic Σ decay
M. Cobal, PIF 2003
- Force carriers of weak interactions are three intermediate vector bosons: W+ and W- (mass 80.4 GeV), and Z0 (91.2 GeV) - The three bosons are very massive particles → weak interactions are very short ( ~ 2x10-3 fm) - Before the Electroweak theory was developed all observed weak processes were charged current reactions (e.g. B-decay) mediated by W+ and W- bosons - Electroweak theory predicts a neutral current caused by Z0 boson Predicted neutral current reaction: no muon in final state
M. Cobal, PIF 2003
First dedicated experiment to study vectorbosons: SPS proton- antiproton collider at CERN (detectors UA1 and UA2)
Mechanism of W/Z production in pp annihilation
M. Cobal, PIF 2003
From the quark point of view, processes are quark-antiquark annihilations: To obtain sufficient cms energies, proton and antiproton beams at SPS had energy of 270 GeV each
00 ,
,
ZddZuu
WudWdu
→+→+
→+→+ −+
W boson, UA1 detector in 1982
M. Cobal, PIF 2003
Signature of a W boson - A lepton with large momentum (> 10 GeV/c) emitted at a wide angle to the beam (> 5O ) - Large missing transverse momentum carried out by neutrino If pt(W)=0 ⇒ missing pT = pT(l) - From 43 events observed by UA1, the mass of W was defined as: MW = 80.33 ± 0.15 GeV/c2
And the decay width as: ΓW = 2.07 ± 0.06 GeV Which corresponds to a lifetime of 3.2x10-25 s - Branching ratios of leptonic decay modes of W are about 11% for each lepton generation
M. Cobal, PIF 2003
W bosons can be pair-produced in e+e- annihilation, and the up-to-date world average for the W-mass is:
2/06.039.80 cGeVMW ±=
M. Cobal, PIF 2003
Signature of a Z boson - Pair of leptons (e+e-) with very large momenta - Mass of the Z0 is then invariant mass of leptons. Knowing Mw, Mz was predicted to be ~90 GeV/c2 -
µµ −+−+ →→→ ZeeZZXpp or with
UA1
M. Cobal, PIF 2003
Dilepton mass spectra near the Z0 peak (CDF Collaboration)
More precise methods give world average values of
MZ = 91.187±0.007 GeV/c2
ΓZ = 2.490 ±0.007 GeV/c2
corresponding to a lifetime of 2.6x10-25 s
Branching ratios of leptonic decay modes of Z0 are around 3.4% for each lepton generation
M. Cobal, PIF 2003
Carlo Rubbia (1934) Simon van der Meer (1925)
• Nobel Prize 1984 for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction
M. Cobal, PIF 2003
W± exchange results in change of charge of the lepton and hadron taking part. It is called charged-current 1) Purely leptonic processes: 2) Purely hadronic processes: 3) Semileptonic reactions: RECALL: leptonic weak interaction processes can be built from a certain number of reactions corresponding to basic vertices
WαW-
e-
νe
WαW+
u
d
µννµ ++→ −−ee
p+→Λ −π
eepn ν++→ −
M. Cobal, PIF 2003
WαZ0
νe
νe
• W± exchange results in change of charge of the lepton and hadron taking part. It is called charged-current • Zo-exchange does not and is called a neutral current reaction • The small value of the aw constant can be put in relation with the high mass of the bosons
WαW-
e-
νe
WαW+
u
d
pW
p
W
EMW mM
mM
262 10 10 ≅→≅
= −α
α
WαZ0
u
u
M. Cobal, PIF 2003
• If we simplify (using same coupling g to quarks and leptons for W and Z)
( ) ( )2,
2
22
ZWMqgqf+
=
To be compared with for the em scattering 2
2
qe
• If , the amplitude is independent of q2 in this case we say that the interaction is pointlike Fermi postulated such an interaction (1935), of strenght G, between 4-fermions to describe β-decay As q2 → 0: (from measured decay rates)
2,
2ZWMq <<
252
210 −−≅≡ GeV
MgGW
M. Cobal, PIF 2003
Given the two basic vertices, one can derive 8 basic reactions:
These processes are virtual: 2 or more have to be combined to conserve energy
M. Cobal, PIF 2003
- Weak interactions always conserve lepton quantum numbers It is not possible: - Leptonic vertices are characterized by the corresponding strength parameter αW independently on the lepton type involved. -Knowing the decay rate of W→eν one can estimate αW to the first order: Γ(W→eν) ~0.2 GeV Since the process involves only one vertex and lepton masses ~0 ⇒ Γ(W→eν)~ αWMW~80αWGeV which gives: αW= 1/400 = O(α) similar to the electromagnetic one
M. Cobal, PIF 2003
Analogues of electron-electron scattering by photon exchange
Time ordering implies changing the sign of the current! A conventional muon decay looks like:
ee νµν µ +→+ −−
Including higher order diagrams:
M. Cobal, PIF 2003
Since W bosons are very heavy, interaction can be approximated by a zero-range interaction: Taking into account spin effects, the relation between αW and GF in zero-range approximation is: where gW is the coupling constant in W-vertices αW=g2
W/4π by definition. This gives the estimate of αW = 4.2x10-3=0.58α
- Weak interactions of hadrons: quarks emit/absorb W bosons - Lepton-quark symmetry: corresponding generations of quarks/ leptons have identical weak interactions:
22
2 42 W
W
W
WF
MMgG πα
==
M. Cobal, PIF 2003
The corresponding coupling constants do not change upon exchange of quarks/leptons: gud = gsc = gW
For example, allowed reaction is )( µµ νµνµπ +→+→ −−− ud
M. Cobal, PIF 2003
Weak interactions violate isospin conservation. However there appears to be a selection rule in non-leptonic decays:
ΔI =1/2 Generally obeyed in the decay of the strange particles. Example: Since IΛ = 0 this rules states that the nucleon and the pion must be in a I =1/2 state. Looking at the Clebsh-Gordan coefficients: As confirmed by experiments
0π
π
+→
+→ −
n
p
Λ
Λ
3/10
0=
→+→
→+ππ
π
pRatenRatenRate
ΛΛ
Λ
M. Cobal, PIF 2003
For leptonic decays of strange particles, the isospin cannot be Specified. Empirically saw that the rule is valid:
ΔQ = ΔS From the relation: Q = I3 +1/2(B+S) it follows that: ΔI3=1/2 if ΔQ = ΔS=1 Example: If one considers the hyperon leptonic decay modes: The rates are roughly 20 times smaller than those expected if the couplings were the same as for the S-conserving decay.
observednotSQen
observedSQen
e
e
1
1
=≠++→
==++→++
−−
ΔΔΣ
ΔΔΣ
ν
ν
ννν +→++→++→ −−−−− eenep ee ΛΞΣΛ
M. Cobal, PIF 2003
Gell-Mann and Levy (1960) and Cabibbo (1963) proposed a way out: The baryon state of spin-parity ½+ form an octet as we saw. However, this symmetry is broken in nature, and the baryon get all different masses. In the splitting, there is no a priori way to determine how the weak coupling is divided. Cabibbo postulated that, for :
ΔS=0 decays, weak coupling = Gcosθ ΔS=1 decays, weak coupling = Gsinθ
Consequences: The ΔS=1 baryonic decays are suppressed relative to the ΔS=0 ones. The coupling constant for Fermi transitions in β-decay becomes Gcosθ rather than G.
M. Cobal, PIF 2003
In more detail: the “quark mixing” hypothesis was introduced by Cabibbo: d- and s-quarks participate the weak interaction via the linear combinations:
Parameter θc is the Cabibbo angle, and hence the quark-lepton symmetry applies to doublets like
cc
cc
sdssdd
θθ
θθ
cossin'sincos'
+−=
+=
'' sc
anddu
M. Cobal, PIF 2003
1967-68: Electroweak Theory of Glashow, Salam and Weinberg
Proposes that the coupling g of W and Z to leptons and quarks is the same as that of the photon:
g = e The weak and em interactions are unified From the measured value of G, it was expected that:
GeV
GGeM ZW 904
, ≈≈≈πα
M. Cobal, PIF 2003
M. Cobal, PIF 2003
• Nobel Prize 1979 for their contributions to the theory of the unified weak and electromagnetic interaction between elementary particles, including, the prediction of the weak neutral current
Sheldon Lee Glashow (1932) Abdus Salam (1926 – 1996) Steven Weinberg (1933)
M. Cobal, PIF 2003
• Self-coupling W-Z
• Couplings with photons
M. Cobal, PIF 2003
Summary of interactions
M. Cobal, PIF 2003
Decay time of π0→γγ is about 10-16 sec (em interaction) For Σ0→Λγ, time is about 10-19 sec (em interaction) For Δ++→pπ, time is about 10-23 sec (strong interaction) The neutron decay via: n →peν takes 15 minutes! (weak interaction) A new “weak” coupling constant has to be introduced:
642
1010 −=
≅
EM
S
strong
EM
αα
ττ
( )( )
2
10
23
1010
≈≈
+→
+→−
−
S
W
ss
nn
αα
πτπτ
Σ
Δ
610−≈Wα
M. Cobal, PIF 2003
W+ W-
γ,Z,g
u d’
γ,Z,g
νe e-
W+ W-
γ,Z
Z