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A.Schöning 1 Particle Physics WS 16/17
Weak Decays and Interactions
● parity violation in weak decays● charged currents● muon decay● lepton scattering experiments
A.Schöning 2 Particle Physics WS 16/17
Polarisation in Beta Decays
BILD
only left-handed particles!
polarisation: P =
N 12 − N −
12
N 12 N −
12
A.Schöning 3 Particle Physics WS 16/17
Michel-Spectrum
e e
A.Schöning 4 Particle Physics WS 16/17
Spinors fermions / anti-fermions
u1(R) = √E+m (10pzE+mp x+ip yE+m
)fermions:
anti-fermions:
u2(L) = √E+m (01
px−ip yE+m−p zE+m
)v2,(L) = √E+m (
p zE+mpx+ip yE+m
10
)v1(R) = √E+m (p x−ip yE+m−pzE+m
01
)
(spin polarisation along z-axis)
A.Schöning 5 Particle Physics WS 16/17
Chirality Operator
uR ~ vL ~ 1010
uL ~ vR ~ 0101
5uR = uR
limit m → 0
operator:5 = i 0 1 2 3 =
0 0 1 00 0 0 11 0 0 00 1 0 0
= 0 11 0
5uL =−uL5v L = vL 5vR =−vR
eigenvalues ± 1
note: a right-handed chiral anti-particle has a left-handed helicity
left-handed (chiral) particles: -1right-handed (chiral) particles: +1
right chirality left chirality
A.Schöning 6 Particle Physics WS 16/17
Projection Operator±
=15
2definition:
note: massive fermions must have left-handed and right handed components
(right-handed (chiral) state)
reformulate Dirac Equation:
uR = uR
−uL = uL
uL = 0
−uR = 0
= R
projection:
− = L (left-handed (chiral) state)
i ∂ R =m L i ∂ L =m R
−vR = vR
v L = vL
−v L = 0
vR = 0
fermions anti-fermions
A.Schöning 7 Particle Physics WS 16/17
Vector and Axial Currents
Vector Current:jV =
Axial-vector Current:j A = 5 5 =−5
note:
Left (right)-handed Current:
j L = − jR
=
relations:
j L = 1/2 jV
− j A
jR = 1/2 jV
j A
weak interaction (V-A theory):
in QED: ∂ jV = 0 (conservation of currents)R R , L L
A.Schöning 8 Particle Physics WS 16/17
W-Propagator Effect
cross section
A.Schöning 9 Particle Physics WS 16/17
F2 and F
3 in Neutrino-Scattering
sum
valence
sea
A.Schöning 10 Particle Physics WS 16/17
Measurement of F2
x 18/5
x 18/5
A.Schöning 11 Particle Physics WS 16/17
Fits of Parton Densities
constraintsfrom
e p → ν X
(CC)
A.Schöning 12 Particle Physics WS 16/17
Charged Current Event at H1 (HERA)
ν
νe p → ν X
e- : E=27.5 GeV p : E=920 GeV
A.Schöning 13 Particle Physics WS 16/17
