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  (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 Neutron  -decay Antineutrino absorption Hadronic  decay

M. Cobal, PIF Force carriers of weak interactions are three intermediate vector bosons: W + and W - (mass 80.4 GeV), and Z 0 (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 Z 0 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 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 (> 5 O ) -Large missing transverse momentum carried out by neutrino If pt(W)=0  missing p T = p T (l) - From 43 events observed by UA1, the mass of W was defined as: M W =  0.15 GeV/c 2 And the decay width as:  W = 2.07  0.06 GeV Which corresponds to a lifetime of 3.2x 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:

M. Cobal, PIF 2003 Signature of a Z boson -Pair of leptons (e+e-) with very large momenta -Mass of the Z 0 is then invariant mass of leptons. Knowing M w, M z was predicted to be ~90 GeV/c 2 - UA1

M. Cobal, PIF 2003 Dilepton mass spectra near the Z 0 peak (CDF Collaboration) More precise methods give world average values of M Z =  GeV/c 2  Z =  GeV/c 2 corresponding to a lifetime of 2.6x s Branching ratios of leptonic decay modes of Z 0 are around 3.4% for each lepton generation

M. Cobal, PIF 2003 Carlo Rubbia (1934) Simon van der Meer (1925) Nobel Prize 1984 f or 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 W-W- e-e- e W+W+ u

M. Cobal, PIF 2003 Z0Z0 e e W  exchange results in change of charge of the lepton and hadron taking part. It is called charged-current Z o -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 W-W- e-e- e W+W+ u Z0Z0 u u

M. Cobal, PIF 2003 If we simplify (using same coupling g to quarks and leptons for W and Z) To be compared with for the em scattering If, the amplitude is independent of q 2 in this case we say that the interaction is pointlike Fermi postulated such an interaction (1935), of strenght G, between 4-fermions to describe  -decay As q 2  0: (from measured decay rates)

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 Weak interactions always conserve lepton quantum numbers It is not possible: -Leptonic vertices are characterized by the corresponding strength parameter  W independently on the lepton type involved. -Knowing the decay rate of W  e  one can estimate  W to the first order:  (W  e ) ~0.2 GeV Since the process involves only one vertex and lepton masses ~0   (W  e )~  W M W ~80  W GeV which gives:  W = 1/400 = O(  ) 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: 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  W and G F in zero-range approximation is: where g W is the coupling constant in W-vertices  W =g 2 W /4  by definition. This gives the estimate of  W = 4.2x10 -3 =0.58  -Weak interactions of hadrons: quarks emit/absorb W bosons -Lepton-quark symmetry: corresponding generations of quarks/ leptons have identical weak interactions:

M. Cobal, PIF 2003 The corresponding coupling constants do not change upon exchange of quarks/leptons: g ud = g sc = g W For example, allowed reaction is

M. Cobal, PIF 2003 Weak interactions violate isospin conservation. However there appears to be a selection rule in non-leptonic decays:  I =1/2 Generally obeyed in the decay of the strange particles. Example: Since I  = 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

M. Cobal, PIF 2003 For leptonic decays of strange particles, the isospin cannot be Specified. Empirically saw that the rule is valid:  Q =  S From the relation: Q = I 3 +1/2(B+S) it follows that:  I 3 =1/2 if  Q =  S=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.

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 :  S=0 decays, weak coupling = Gcos   S=1 decays, weak coupling = Gsin  Consequences: The  S=1 baryonic decays are suppressed relative to the  S=0 ones. The coupling constant for Fermi transitions in  -decay becomes Gcos  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  c is the Cabibbo angle, and hence the quark-lepton symmetry applies to doublets like

M. Cobal, PIF : 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:

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  0  is about sec (em interaction) For  0   , time is about sec (em interaction) For  ++  p  time is about sec (strong interaction) The neutron decay via: n  pe  takes 15 minutes! (weak interaction) A new “weak” coupling constant has to be introduced:

M. Cobal, PIF 2003 W+W+ W-W- ,Z,g u d’ ,Z,g e e - W+W+ W-W- ,Z Z