Dirac Equation under parity exchange where r    r +  Looks like this satisfies a new equation No longer looks like Dirac’s eq That assumed P  (r,t)→  (  r,t) and simply neglects the 4-momentum-dependent spinor components!

Whereassatisfies the Dirac equation (in the original coordinate system) It iswhich satisfies Dirac in the inverted system.  0 0  0 0 applying r   r so P  (r,t)=  0  (  r,t)

 0 0 =   1 The parity of a fermion is the opposite of its antifermion.

You just showed in homework: VECTORAXIAL VECTOR This V-A coupling clearly identifies a parity- VIOLATING interaction The relative sign between these two terms changes under PARITY! The full HAMILTONIAN cannot conserve parity!

As we have seen ELECTROMAGNETIC and STRONG INTERACTION terms in addition to free particle terms in the lagrangian CONSERVE PARITY Up until 1956 all the laws of physics were assumed to be “ambidextrous” (invariant under parity). The biological handedness on earth was assumed to be an evolutionary accident. heart on left side intestines winding in same sense many chemicals synthesized by plants and animals definite handedness DNA (no underlying physical constraint)

1956 Chen Ning YangTsung Dao Lee T.D. Lee and C.N. Yang challenged the assumption that the laws of physics are ambidextrous… …pressing for more experimental evidence for the conservation or violation of parity Recall: not ALL conservation principles survive decay!

Between Christmas of 1956 and New Year's Day, physicists at the National Bureau of Standards operated the low temperature equipment being assembled in this photograph. The vertical tube (upper right) contained 60 Co, a beta-ray counter, and basic thermometry. A vacuum flask (lower left) is being placed around the tube to provide insulation to maintain low temperatures.

Chien-Shiung Wu Columbia University clock-wise: Ernest Ambler, Raymond W. Hayward, Dale D. Hoppes, Ralph P. Hudson National Bureau of Standards

A crystal specimen of cerium magnesium nitrate containing a thin surface layer of of radioactive 60 Co was supported in a cerium magnesium nitrate housing within an evacuated glass vessel. 2 cm above an anthracene crystal scintillator transmitted its light flashes through a lucite rod out to a photomultiplier. The magnets on either side were used to cool by adiabatic demagnetization. Inductance coils are part of the thermometry.

Page 90, Ernest Ambler's Notebook for December 27, The first of two successful runs began at 12:04 (middle of page). Hudson's notation “Field on” refers to the magnetic field produced by the solenoid. The crystal was cooled and the 60 Co nuclei were polarized in one direction. Hudson later added “PARITY NOT CONSERVED!” (see top of the page). After again cooling the crystal and polarizing the 60 Co nuclei in the opposite direction, the physicists observed the opposite behavior of the  -particle counts with time. An initially high counting rate of  -particles was observed to decrease as the crystal warmed and the 60 Co nuclei became randomly polarized. “  counts decrease”

For 60 Co, at 1 K radiation pattern is uniform in all directions. At lower temperatures the radiation pattern becomes distorted most easily detected by a  -detector aligned with the sample axis though frequently an azimuthal detector is also used.

 →  →  →  → The distribution of emitted  directions PEAK in the direction of nuclear spin

 →  →  →  → J nucleus · p emitted electron →→ identifying an observable quantity that is NOT invariant to parity! Here’s a physical processes whose mirror image does NOT occur in nature!

Of course we have already described experiments that determined π   →    ν  always left-handed always left-handed Which strengthens the PARITY-VIOLATING observations: (π   →    ν  ) P L L R R doesn’t exist! Weak interactions do NOT conserve parity!

Charge Conjugation Invariance Charge conjugation reverses the sign of electric charge Maxwell’s equations remain invariant! (charge/current density and the things derived from them: E and H just change sign) In Relativistic Quantum Mechanics this is generalized to particle  antiparticle exchange Proton p Antiproton p Electron e- Positron e+ Photon  Q +e  e  e +e 0 B +1  L  0    ½ћ ½ћ ½ћ ½ћ ћ eћ 2mc eћ 2mc  eћ 2mc +eћ 2mc

Charge Conjugate Operator Obviously C 2 | p > = | p > on a proton state i.e.  plus the mesons at the centers of all our multiplet plots:   , ,  , ,  Particles that are their own antiparticle are eigenstates of C Although C |   > = |   > or even C |   > = |   >  |   > but applied singly C | p > = | p >  | p >

E and B fields change sign under charge conjugation C |  > =  |  > it makes perfect sense to assign the photon c =  1 Then the dominant decay mode of  tells us c (  0 ) = (-1)(-1) = +1 like parity, a multiplicative quantum number             This seems to explain why or why

While strong and electromagnetic interactions (productions or decays) are invariant under CHARGE CONJUGATION weak interactions: C : (     + +   )        +   both left-handed ??? Recalling that Dirac particle/antiparticle states have opposite parity maybe the appropriate invariance is to a simultaneous change of particle antiparticle with parity flipped! CP : (     L + + L   )      R  + R   restores the invariance!

considering the observed neutrino states momentum, p spin,  Neutrino, momentum, p spin,  antiNeutrino, P C CP momentum, p spin,  Neutrino, momentum, p spin,  antiNeutrino, pseudovector

K 0 = ds K 0 = sd C | K 0 > = | K 0 > antiparticles of one another CP | K 0 > =  | K 0 > K 0 s are pseudo-scalars same pseudo-scaler nonet as  s and  s So the normalized eigenstates of C P (the states that serve as solutions to the equations of motion) must be and CP | K 1 > =  | K 1 > CP | K 2 > =  | K 2 >

CP | K 1 > =  | K 1 > CP | K 2 > =  | K 2 > K 1  CP = +1 final states : K 2  CP =  1 final states :  +   or  0  0  +    0 or  0  0  0 Here K 1 and K 2 are NOT anti-particles of one another but each (up to a phase) is its own anti-particle! K 1 “long”-lifetime sec (travel ~3 km before decaying! K 2 “short”-lifetime sec (travel ~5½ m before decaying! Different CP states must decay differently, if the weak interaction satisfies CP invariance! and, in fact kaon beams are observed to decay differently along different points of their path!

1955 Gellmann & Pais Noticed the Cabibbo mechanism, where was the weak eigenstate, allowed a 2 nd order (~rare) weak interaction that could potentially induce the strangeness-violating transition of K o a particle becoming its own antiparticle! uu s d s d KoKo KoKo WW u u s d s d KoKo KoKo WW WW