Lecture 5 Weak Interac/ons

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1 Lecture 5 Weak Interac/ons M - µ ν µ 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 1

2 Weak Charged Currents Exchange of heavy W + or W bosons (M W = 80 GeV) Lepton couplings are e ν e µ ν µ τ ν τ (or their an/par/cle equivalents) No lepton flavour changes allowed All lepton couplings are the same (g) Quark couplings are d i u i (u i =u,c,t, d i =d,s,b) All possible quark flavour changes allowed Coupling strength depends on flavours (g V CKM ) Weak coupling is related to Fermi constant: G F = g G F = 1.16 x 10-5 GeV - 8M W 6/1/10 Par/cle Physics Lecture 5 Steve Playfer

3 Descrip/ons of β Decays Quark level u d e + ν e or d u e ν e with coupling V ud = not directly observable because there are no free quarks Hadron level n p e ν e is allowed (free neutron life/me τ n = 886s) p n e + ν e is forbidden m p < m n (free proton is stable) For hadronic transi=ons there are form factors Nuclear level β + decay e.g. Na Ne* e + ν e β decay e.g. 60 Co 60 Ni* e ν e which type occurs depends on the energy available (Q) For nuclear transi=ons there are also nuclear matrix elements 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 3

4 Neutrino mass from Tri/um β Decay Kurie plot m(ν e ) < ev Shape near endpoint (maximum electron energy) is sensi/ve to ν e mass Actual energy spectrum dγ/de e = E e (Q- E e ) has been converted to a straight line Q=18 kev 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 4

5 Neutrinoless Double β Decay Can only occur if ν e is the same as ν e Majorana neutrino hypothesis otherwise there have to be two an/neutrinos in the final state. Recent experiments use 76 Ge, 100 Mo or 113 Cd 76 Ge: normally decays via ββ with ν e (half life 10 1 years) 76 Ge: Q = Σ E e = 039 kev is a signal for ββ with no ν? Evidence claimed by one group in 001 (controversial) 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 5

6 Feynman rules for β decay W boson propagator 1/(q M W ) Lepton vertex has dimensionless coupling constant g Quark vertex has coupling V ud g Lepton current is u(ν e ) γ µ (1 γ 5 ) u(e) Quark current is u(d) γ µ (1 γ 5 ) u(u) V A theory Vector current γ µ Axial- vector γ µ γ 5 Note that weak currents have a factor (1 γ 5 ) compared to electromagne/c γ µ 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 6

7 Calcula/ng β Decay Rates For q << M W the matrix element squared can be wrihen in terms of the Fermi constant and the lepton and quark currents: M = G F u(ν e ) γ µ (1 γ 5 ) u(e) u(d) γ µ (1 γ 5 ) u(u) J e J q Summing over final state spins and neglec/ng the electron mass the lepton current gives: J e = 8 E e E ν ( 1 + cos θ eν ) In superallowed β decay can neglect hadronic or nuclear effects because lepton wavelengths are much larger than 1 fm (Halzen & Mar/n P.59) Par/al decay rate is: dγ/de e = G F E e (Q- E e ) / π 3 Total decay rate is: Γ = 1/τ = G F Q 5 / 30 π 3 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 7

8 ν e Muon Decay M = G F u(ν e ) γ µ (1 γ 5 ) u(e) u(ν µ ) γ µ (1 γ 5 ) u(µ) J e J µ Michel spectrum is: dγ = G F m µ E e ( 3 4E e ) (with E e < m µ /) de e 1π 3 m µ Decay rate and life/me: Γ µ = G F m µ 5 19π 3 τ µ = 1/Γ =.197µs Similar results can be obtained for τ e ν e ν τ and τ µ ν µ ν τ Branching frac/ons Β (τ e) ~ Β (τ µ)~ 0 % Β (τ hadrons)~ 60 % τ τ = 91 fs 6/1/10 Par/cle Physics Lecture 5 Steve Playfer τ µ = 1/Γ =.197µs

9 Searches for Lepton Flavour changing µ e 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 9

10 Lepton Flavour changing τ decays 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 10

11 Weak Neutral Currents Exchange of heavy Z 0 bosons (M Z = 91 GeV) All charged leptons and (an/)neutrinos have couplings No lepton or neutrino flavour changes are allowed All quark and an/quarks have couplings No quark flavour changes are allowed Neutral currents are wrihen: u γ µ (c V c A γ 5 ) u Vector and axial- vector couplings depend on fermion type 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 11

12 Electron Neutrino Scahering Neutrino- electron scahering NC + CC An/neutrino- electron scahering NC + CC 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 1

13 Muon Neutrino Scahering Muon neutrino and an/neutrino- electron scahering NC NC Muon produc/on (inverse muon decay) CC No ν µ µ + on electrons (would need an e + or proton target) 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 13

14 ν µ Scahering Cross- sec/ons Inverse muon decay (ν µ e µ ν e ) M = 16 G F s dσ = G F s σ = G F s dω 4π π Muon neutrino scahering (ν µ e ν µ e ) dσ = G F s [(c V + c A ) + (c V c A ) (1 - y) ] dy 4π where (1 y) = 1+cosθ σ = G F s (c V c V c A + c A ) 3π c V = 0.03, c A = 0.50 For an/neutrino scahering change c A c A All cross- sec/ons increase with CM energy squared s 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 14

15 ν e Scahering Cross- sec/ons Electron neutrino scahering (ν e e ν e e ) dσ = G F s [( + c V + c A ) + (c V c A ) (1 - y) ] dy 4π dσ = G F s [ (1 + g L ) + g R (1 - y) ] dy π where g L = (c V + c A )/ and g R = (c V c A )/ σ = G F s [ (1 + g L ) + g R ] π 3 In LAB frame σ ~ E ν cm (E ν in GeV) For an/neutrino scahering change c A c A or g L,R g R,L All cross- sec/ons increase with CM energy squared s 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 15

16 L E P νe scahering experiment 6/1/10 Par/cle Physics Lecture 5 Steve Playfer 16