Charge Conjugation Invariance Charge conjugation reverses the sign

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 g Q B L m +2. 79 -e -1 0 +e +1 0 ½ћ eћ 2 mc -e 0 +1 eћ -2. 79 2 mc -eћ 2 mc ½ћ ½ћ +e 0 -1 0 0 0 +eћ 2 mc 0 ½ћ ћ

Charge Conjugate Operator C 2| p > = | p > Obviously on a proton state but applied singly C| p > = | p > or even Although C| + > = | - > | + > C | > = | > Particles that are their own antiparticle are eigenstates of C i. e. plus the mesons at the centers of all our multiplet plots: , ,

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 p tells us c (p 0 ) = (-1) = +1 + like parity, a multiplicative quantum number This seems to explain why or why p 0 w p 0

While strong and electromagnetic interactions (productions or decays) are invariant under CHARGE CONJUGATION weak interactions: C : ( + m + + n m ) - m - + n m 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 : ( + m. L+ + n. L m) - m. R- + n. R m restores the invariance!

considering the observed neutrino states Neutrino, n spin, momentum, s n spin, momentum, Neutrino, n p p spin, s momentum, CP C anti. Neutrino, P pseudovector s anti. Neutrino, n spin, momentum, p s p

K 0 = ds K 0 = sd C C | K 0 > = | K 0 > CP | K 0 > = - | K 0 > antiparticles of one another 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 > Here K 1 and K 2 are NOT anti-particles of one another but each (up to a phase) is its own anti-particle! Different CP states must decay differently, if the weak interaction satisfies CP invariance! K 1 CP = +1 final states : p+p- or p 0 p 0 K 2 CP = -1 final states : p+p-p 0 or p 0 p 0 p 0 and, in fact kaon beams are observed to decay differently along different points of their path! K 1 “long”-lifetime 10 -8 sec (travel ~3 km before decaying! K 2 “short”-lifetime 10 -11 sec (travel ~5½ m before decaying!

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 Ko Ko a particle becoming its own antiparticle! Ko Ko s d s u u W- s d W- d Ko u u d W+ s Ko