Lecture 7 Parity Charge conjugation G-parity CP FK7003

Already done a lot to understand the basic particles of nature Strong, weak,em ? Lepton universality Isospin singlets 175000 Isospin multiplets small small small Neutrino oscillations/mass Quark composition Decay modes Symmetry and QM demands much of what is observed! FK7003

Transforming under parity 1 FK7003

Ways of thinking about parity Possible. Not possible. v ms=-1/2 ms=1/2 + real ”virtual” FK7003

Intrinsic Parity FK7003

Intrinsic Parity FK7003

Calculating parity Particle Parity (P) -1 Pseudoscalar mesons (s=0) p,K,h,D,B -1 Vector mesons (s=1) K*,w,f FK7003

Parity of the photon Dl=+-1 g Atomic energy levels FK7003

Parity of the electron positronium FK7003

Intrinsic parity Particle Parity (P) +1 -1 Electron, muon, tau Positron,antimuon,antitau -1 Quark Antiquark Photon Pseudoscalar mesons (s=0,l=0) p,K,h,D,B.. Vector mesons (s=1,l=0) K*,w,f Ground state baryons (l=0) p,n,S.. FK7003

Question Before Wu’s experiment the t and q particles were observed with the same spin, mass, charge. They were thought to be different particles because they decayed into states with different parities Calculate the parity of the pion system from the second decay. Assume no orbital angular momentum in the final pion system. State which particle t and q is. Which of the decays violates parity ? FK7003

Charge conjugation: C FK7003

Question Show, with the example of a neutrino, that charge conjugation is not a symmetry of the weak force. FK7003

C-parity (C) Same game as for parity! We’ve found a symmetry of the em and strong forces, but not of the weak. Find a quantity conserved in strong and em processes. Most particles are not eigenstates of Particles which are eigenstates are their own particles, eg p0,g,r0 Can also construct eigenstates using particle-antiparticle pairs, eg Particles or multiparticle states have eigen value known as an intrinsic C-parity quantum number, eg g has C=-1 C is a multiplicative quantum number like parity. FK7003

Calculating C C for the lowest mass hadron states (l=0 ) Unless otherwise stated, we will be dealing in this lecture with systems of particles for which l=0. FK7003

Question FK7003

Pseudoscalar mesons (s=0) p,K,h,D,B C and P Particle P C Pseudoscalar mesons (s=0) p,K,h,D,B -1 +1 Vector mesons (s=1) K*,w,f Photon Ground state baryons N/A Charged Leptons 1 Charged anti- leptons C value only applicable for particles which are their own anti-particles FK7003

Formalism A particle is characterised by the form JPC, eg 1-- J=total angular momentum, P=parity(+ = +1,- = -1), C=charge conjugation number (+ = +1, - = -1) In certain situations C is not a useful quantum number – most particles are not eigenstates of C: JP is used. P=1 ”even” parity, P=-1 ”odd” parity C=1 ”even” C-parity, C=-1 ”odd” C-parity FK7003

G-parity FK7003

Particles for which G-parity is relevant (7.34) FK7003

Some decays explained with G-parity ,ppp FK7003

Conserved quantities/symmetries Quantity Strong Weak Electromagnetic Energy  Linear momentum Angular momentum Baryon number Lepton number Isospin - Flavour (S,C,B) Charges (em, strong and weak forces) Parity (P) C-parity (C) G-parity (G) CP T CPT Coming up FK7003

CP  X  C and P are not separately respected in weak decays What about CP ? Original and CP-transformed decays occur with same rate. CP symmetry is respected in many weak processes.  X  FK7003

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Neutral kaons We define a neutral K0 by its quark content (sd), mass (498 MeV), spin (0), isospin (I=1/2,I3=-1/2) - a normal particle ! FK7003

Strategy Test the hypothesis that CP is a good symmetry of the weak force. Try to form CP eigenstates from K0 and K0 and check they decay in CP-conserving ways (recall p gg and C conservation.) FK7003

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Neutral Kaons and Strangeness Oscillations Consider in the kaon rest frame and allow a decay Consider a particle produced at t=0 as a K0 . Amplitude that it is still a K0 at a later time t: FK7003

Probability that it is still a K0 at a later time t: Strangeness oscillation!! FK7003

Kaon oscillations (Niebergall et al., 1974) Intensity 2 4 6 8 2 4 6 8 Time in K0 rest frame (x10-10 s) FK7003

Question To measure the oscillations of a beam of neutral kaons of energy 10 GeV how large should an experiment be ? (Niebergall et al., 1974) Intensity 2 4 6 8 Time in K0 rest frame (x10-10 s) FK7003

Some interpretation and comparisons |DS|=2 Strangeness violated FK7003

Summary Discrete symmetries Next lecture – CP violation Parity (P) Charge conjugation (C-parity) G-parity Fundamental symmetries of nature constrain the behaviour of particles CP Neutral kaons Strangeness oscillations Next lecture – CP violation FK7003