Lecture: Standard Model of Particle Physics Heidelberg SS 013 Weak Interactions II 1
Important Experiments Wu-Experiment (1957): radioactive decay of Co60 Goldhaber-Experiment (1958): radioactive decay of Eu15 Muon Decay: Michel spectrum Pion Decay: branching ratios Nuclear Beta Decays Neutrino-Nucleon Scattering (neutrino antineutrino)
Neutron Decay Lagrangian d u: G μ L= ( d γ (1 γ 5 )u) (v γμ (1 γ 5 ) e) Decay Width Γ= G F c1 Δ 15 π 5 3 with c1 = cos ΘC Δ = 78 kev Note: the d and u mass eigenstates are not weak eigenstates the neutron decay is not a simple d u decay (quarks are not free) 3
Test of Lorentz Structure? Fermi transition Gamov Teller transition vector Momentum coupling axialvector Momentum coupling? + Spin helicity 0* n -1 p + Spin helicity -1 +1 e- ν- 0* n - p -1 +1 e- ν- What is the relative contribution of V and A couplings in nuclear decays? Use a more general Lagrangian: G μ 5 5 L= (n γ (1 α γ ) p) (v γ (1 γ ) e) μ ca with α = cv The strength of the axial-coupling is related to the neutron lifetime! 4
Measurement of the Neutron Lifetime Techniques: (ultra) cold neutron traps in-beam decays electron detectors n p e νe proton detectors electron-proton coincidence method 5
Neutron Lifetime Trap I J.Byrne et al. Phys.Lett. 9B 3 (1980) 6
Neutron Trap II 7
Results Neutron Lifetime Significant tensions between experiments! Best value (PDG 010): derived from this value: τn = 885.7 s ca α= = 1.694±0.008 cv 8
Prediction for ca/cv Valence quark wave function of the neutron : Detailed calculation of vector/axial-vector contributions gives: ca/cv = 5/3 Mismatch between experiment and prediction due to: p QCD corrections 9 ν- e spin flip π Relativistic corrections Neglected sea quarks in the neutron e- n WQCD corrections modify axial-coupling
Prediction for ca/cv Valence quark wave function of the neutron : Detailed calculation of vector/axial-vector contributions gives: ca/cv = 5/3 Mismatch between experiment and prediction due to: Relativistic corrections Neglected sea quarks in the neutron QCD corrections 10 e- u ν- e spin flip gluon d WQCD corrections modify axial-coupling
Overview Weak Decay Processes Weak decays of quarks and leptons (fermions) μ e νμ ν e leptonic decay n p e νe Λ p e νe Λ p π Q q W± semileptonic decays semileptonic decays ( S=1) hadronic weak decays ( S=1) heavy quark decays ( C=1, B=1, T=1) W-Boson decays: Charged currents can mediate interactions between different lepton and quark generations (mixing) W l ν l W q q 11
K-Meson Decays Γ G F m5s ms 150 MeV Lifetime τ ~ 10-8 s K + π 0 l+ ν K + π 0 π 0 π+ 1
Hadronic Decays of D-mesons Γ G F m5c mc 1.5 GeV D + K 0 π+ Lifetime τ ~ 0.5 ps D + π+ π 13 D + π+ K 0
Weak Decays of B-mesons Γ G F m5b mb 4.5 GeV B 0 D0 π 0 Lifetime τ ~ 1.5 ps B 0 D+ π B 0 D+ l ν l 14 ν
Decay of the Top quark 5 Γ G F m t mt 17 GeV Lifetime τ ~ 10-5 s 15
Summary Weak Interaction left handed fermions: right handed fermions: ( I 3 =+ 1/ I 3 = 1/ I 3 =0 νe νμ μ ) ( )( ) e L ν e, R νμ, R e R μ R L ντ τ ( ) L ντ, R τr ( ) ( ) ( ) u d ur dr L c s L cr sr t b L tr br W-bosons couple only on fermions with weak isospin! 16
Weak Scattering Experiments Question: What is the difference between: A) scattering experiments in classical mechanics B) weak scattering experiments? 17
Weak Scattering Experiments Question: What is the difference between: A) scattering experiments in classical mechanics B) weak scattering experiments? Answer: Despite the fact that αem=1/17 is much smaller than αweak~1/30 electromagnetic interactions (A) is much more dangerous than (B) weak interactions Video of a classical scattering experiment 18
Strength of Weak Interaction Question: Why is the weak interaction so weak if αweak~1/30 is much stronger than αem=1/17? 19
Strength of Weak Interaction Question: Why is the weak interaction so weak if αweak~1/30 is much stronger than αem=1/17? Answer: elm. IA 1. Coupling weak IA e ( 0.3) g ( 0.65) 0 (e, g= 4 π α)
Strength of Weak Interaction Question: Why is the weak interaction so weak if αweak~1/30 is much stronger than αem=1/17? Answer: elm. IA 1. Coupling e ( 0.3). Propagator Q =1 ev weak IA g ( 0.65) i gμ ν + qμ q ν /mw μν i g q q m W Q =1 MeV Q =1 TeV low energy i gμ ν 8 G F = mw 0.64 10 (e, g= 4 π α) 1 1 Ratio(elm./weak) ( )/( ) 0.64 1010 q mw 0.64 10 mw ~ 80 GeV 1
Strength of Weak Interaction At high mass scales E~100 GeV the weak interaction is stronger than the electromagnetic interaction Neutrino-nucleon scattering experiments require neutrino beams of about Eν ~100 GeV to test weak interactions at reasonable rates σ ~ O(1pb) because of the propagator effect e νe νμ μ F σ (νμ e μ ν e ) G s neutrino-electron scattering
Production of (Myon) Neutrino Beams Production reactions: 3
CHARM Detector 4
CHARM Detector Why marble? 40 0 Ca(CO3 ) is an iso-scalar target (same amount of d and u quarks) 5
CHARMII Detector 6
CHARMII Detector 7
Detection of Myon Neutrinos in CC νμ N μ X long track identified as muon (minimum ionising particle) length of track is a measure of the muon energy 8
(Anti-) Neutrino-Nucleon Scattering Neutrino-Nucleon: G dσ ( νμ d μ u) = F s dω 4π u μ t W d νμ neutrino-nucleon scattering Anti-Neutrino-Nucleon: G dσ + ( ν μ u μ d ) = F t dω 4π d μ+ ν-μ W u antineutrino-nucleon scattering 9
(Anti-) Neutrino-Nucleon Scattering Neutrino-Nucleon: G dσ ( νμ d μ u) = F s dω 4π u μ J=0 W d νμ neutrino-nucleon scattering Anti-Neutrino-Nucleon: G dσ + ( ν μ u μ d ) = F t dω 4π d μ+ ν-μ W u antineutrino-nucleon scattering 30
(Anti-) Neutrino-Nucleon Scattering Neutrino-Nucleon: G dσ ( νμ d μ u) = F s dω 4π u μ J=0 W d νμ neutrino-nucleon scattering Anti-Neutrino-Nucleon: G dσ + ( ν μ u μ d ) = F t dω 4π d μ+ J=1 ν-μ W u antineutrino-nucleon scattering 31
(Anti-) Neutrino-Nucleon Scattering Neutrino-Nucleon: G dσ ( νμ d μ u) = F s dω 4π G dσ 1 F ( νμ N μ X ) xs dω 4π u μ J=0 W d νμ neutrino-nucleon scattering isoscalar target Anti-Neutrino-Nucleon: G dσ + ( ν μ u μ d ) = F t dω 4π G dσ 1 t + F ( ν μ N μ X ) x S dω 4π s t / s = (1 cos θ ) = (1 y) d μ+ J=1 ν-μ W u antineutrino-nucleon scattering 3
Lorentz Invariant Kinematics of the Deep Inelastic Scattering Process The virtuality of the exchanged photon is given by: p' neutrino θ Q = q = ( p p ') p positron 1 4 sin / q Relative energy loss (inelasticity): qp ν y = = Eν pp W-boson xp N nucleon relative fraction of parton momentum: q Q x = = q P Sy with cms energy: S = pp 33
Measurement of the Differential νn and anti-νn Cross Section Neutrino-Nucleon: G dσ 1 F ( νμ N μ X ) xs π dy isoscalar target CDHS Anti-Neutrino-Nucleon: G dσ 1 F + ( ν μ N μ X ) x S (1 y) dy π small deviations from above equations due to x-dependence! 34
Measurement of the Total νn and anti-νn Cross Section From simple quark counting: (isoscalar target) σ ( νμ N ) = 3 σ ( ν μ N ) measured value ~ is significantly smaller! Parton dynamics more complex Sea Quarks! 35
Example: Proton Parton Densities multiply by 0! Significant component from sea quarks! 36
(Anti-) Neutrino-Nucleon Scattering νμ d μ u μ νμ u μ d u μ W W νμ d + ν μ d μ u ν μ u μ d d μ+ ν-μ W d _ u νμ + _ μ+ ν-μ u 37 W _ u _ d
Unfolding the Valence Quark Distributions _ dv + dsea + (usea) _ dv + dsea + (usea) _ uv + usea + (dsea) _ uv + usea + (dsea) 38
Structure Functions Relations: Measurement: Extraction of parton densities: 39
F Results xf3 Results 40
Comparison νn versus lepton-n Scattering Due to different couplings: Structure function results obtained in weak interactions agree well with result obtained in electromagnetic interactions! 41
Ratio of dv/uv Result: dv/uv 0 if x 1 4
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