XIII Probing the weak interaction
1) Phenomenology of weak decays
2) Parity violation and neutrino helicity (Wu experiment and Goldhaber experiment)
3) V- A theory
4) Structure of neutral currents
Parity
→ eigenvalues of parity are +1 (even parity), -1 (odd parity)
Parity is conserved in strong and electromagnetic interactions
Parity and momentum operator do not commute!
Therefore intrinsic partiy is (strictly speaken) defined only for particles AT REST
If a system of two particles has a relative angular momentum L, total parity is given by:
(*) where are the intrinsic parity of particles
Parity is a multiplicative quantum number
Parity of spin + ½ fermions (quarks, leptons) per definition P = +1 Parity of spin - ½ anti-fermions (anti-quarks, anti-leptons) P = -1
Parity of W, Z, photon, gluons (and their antiparticles) P =-1 (result of gauge theory) (strictly speaken parity of photon and gluons are not defined, use definition of field)
For all other composed and excited particles e.g. kaon, proton, pion, use rule (*) and/or parity conserving IA to determine intrinsic parity Reminder:
Parity operator:
Intrinsic parity of spin ½ fermions AT REST: +1; of antiparticles: -1
Wu-Experiment
Idea: Measurement of the angular distribution of the emitted electron in the decay of polarized 60Co nulcei Angular momentum is an axial vector
P
J=5 J=4
If P is conserved, the angular distribution must be symmetric (to the dashed line) Identical rates for and .
Experiment: Invert 60Co polarization and compare the rates under the same angle .
photons are preferably emitted in direction of spin of Ni → test polarization of 60Co (elm. IA conserves parity) Wu-Experiment
MAIN CHALLENGE: get sufficiently polarized source of 60Co
J=5 → M = -5,-4, ..., 4,5
Energy distribution , for only lowest energy level is populated → for given B field (2.3 T) very low temperatures needed
Example: g = 7.5 (60Co), B=2.3 T, T=0.003K
→ 92 % polarized 60Co
Solution Part-I: embedding 60Co in a paramagnetic material
→ still temperatures of T= 0.01K needed
Solution Part-II: adiabatic cooling
Adiabatic Cooling
1926 von Debye proposed method to create low temperature
Fundamental relation of thermodynamics: dU = T dS – p dV
1. Step: isotherm magnetisation - paramagnetic material in helium gas is put into magnetic field - energy levels are split up, only lower once are populated - entropy gets smaller: dS <0 → dU <0, helium gas absorbes heat
2. Step: helium gas removed → thermal isolation of nitrit
3. Step: adiabatic cooling - magnetic field is slowly switched off - split off of energy levels get smaller - system likes to polpulate higher states, however dU = const due to isolation - dS gets larger thus T gets smaller
Two effects needed in the nitrit-crystal to get high degree of polarization
1) need high B field to get polarization
2) switch off B field to lower temperature via adiabatic cooling (B field on → warm up, B field off → cool down)
How does this work?
→ Some paramagnetic materials have large anisotropic distribution of g-Factors (artefact of crystal structure, different binding mechanisms)
- B field for adiabatic cooling in direction with high g-Factor, thus larger split up of energy levels, thus large cooling effect
- B field for polarization in direction of low g-factor, thus only little warm up
Wu-Experiment Requirements:
- 2 B fields in orthogonal directions
- detection of emitted electron (cover a small opening angle )
- detection of emitted gamma (to test polarization of 60Co)
- crystal needs to be located in helium bath first than in vacuum
Wu-Experiment - Results
warming up Goldhaber experiment: What is the helicity of neutrinos?
Indirect measurement of the neutrino helicity in an electron capture experiment
152Eu, J = 0; + e- 152Sm*, J = 1 +
Goldhaber experiment: What is the helicity of neutrinos?
152Sm*, J = 1
152Sm get's small recoil from photon!
152Sm, J = 0
or
direction of spin of photon is opposite of neutrino
emitted in direction of Sm* emitted in opposite direction of Sm*
Two open question: 1) What is the direction of emission of the photon?
2) What is the polarization of the photon? 1) Resonant scattering
Foto of experiment 2) Measurement of polarization of photon
Result Goldhaber Experiment
- Due to geometry of experiment, only resonant scattered photons are detected Helicity of detected photons identical to helicity of neutrino.
- Detect photons which pass trough magnetized iron. B field points in flight direction of photons → measure fraction of LH photons B field points in opposit direction → measure fraction of RH photons
→ Determine polarization of photon:
→ photons are left handed. The measured polarization is compatible with
From a calculation with 100% photon polarization one expects a measureable Value of
Neutrinos are left handed and anti-neutrinos are right handed particles!