Particle Physics II Chris Parkes CP Violation 4th Handout CP Violation Parity & Charge conjugation Helicity of the neutrino Particle anti-particle oscillations CP violation measurement in Kaons CP violation theory in CKM matrix Predicting b-quark Distinguishing Matter & Anti-matter Sakharov conditions Chris Parkes

Matter and anti-matter asymmetry: CP-violation CP-violation is violation of charge conjugation and parity distinguishes between matter and antimatter Not just a naming convention Responsible for matter-antimatter asymmetry in Universe Equal amounts of matter & anti-matter in the big bang Elements Parity violation Charge conjugation and parity violation in muon decay, CP conservation Mixing in the K0 system CP violation in the K0 system

Parity and charge conjugation Revision Parity is spatial inversion and reverses vectors r-r; p-p P operator acts on a state |y(r, t)> Hence for eigenstates P=±1 |y(r, t)>= cos x has P=+1, even |y(r, t)>= sin x has P=-1, odd |y(r, t)>= cos x + sin x, no eigenvalue Charge conjugation (C) particles anti-particles reverses: charge, magnetic moments, baryon number, strangeness Only particles that are their own anti-particles are eigenstates of C (e.g. photon, π0, J/ψ…)

Parity Violation in weak interactions Revision Parity Violation in weak interactions The “ -” puzzle (1950s) Two particles +, (21%) P =+1 ++-, (6%) P=-1 found to have same lifetime and mass  same particle? BUT opposite parity Actually K+  weak decay Led Lee and Yang to propose that parity may not be conserved in weak interactions

Observation of parity violation Revision Search for parity violation in b-decay Need to observe parameter that is sensitive to parity scalars aa Vectors p-p Pseudo-scalar pa.pbpa.pb Axial-vector L.p-L.p  combination of momentum and spin Measure <J>.pe = angular distribution of electrons with respect to nuclear spin Spin parity: e- (E,-p) 60Co60Ni*+e-+ne Use g from Ni*Ni to monitor spin alignment J J B field Parity Co60Nuclei spin aligned Beta decay to Ni*60 e- (E,p) Rate ≠ Rate

Helicity and the neutrino In angular momentum we choose the axis of quantisation to be the z axis. Lets choose this axis along the particle momentum direction. Helicity is the component of the spin along the momentum direction. A spin ½ particle can thus have helicity +1 (ms=+ ½) or –1 (ms=- ½ ) p p +1 -1 Right-handed s Left-handed s Not so interesting for a massive particle, as not Lorentz invariant, but consider the neutrino. Only left-handed neutrinos exist and right-handed anti- Helicity is a pseudo-scalar Operating with P on this reverses p, not spin, produces a right-handed neutrino. Do not observe: Operating with C on this produces a left-handed anti-neutrino. Do not observe: Operating with C and P on this produces a right-handed anti-neutrino. Do observe! Weak force violates Parity, but CP OK?

Measuring Helicity of the Neutrino Goldhaber et. al. 1958 Bettini p252 Consider the following decay: Electron capture K shell, l=0 photon emission Momenta, p Eu at rest Neutrino, Sm In opposite dirns Select photons in Sm* dirn spin e-   S=+ ½ S=+ 1 right-handed OR right-handed S=- ½ S=- 1 Left-handed Left-handed Helicities of forward photon and neutrino same Measure photon helicity, find neutrino helicity

Neutrino Helicity Experiment Tricky bit: identify forward γ Use resonant scattering! Measure γ polarisation with different B-field orientations Vary magnetic field to vary photon absorbtion. Photons absorbed by e- in iron only if spins of photon and electron opposite. 152Eu magnetic field Fe γ γ Pb Forward photons, (opposite p to neutrino), Have slightly higher p than backward and cause resonant scattering NaI 152Sm 152Sm PMT Only left-handed neutrinos exist Similar experiment with Hg carried out for anti-neutrinos

Charge Inversion Particle-antiparticle mirror P C Parity Inversion Spatial mirror CP

Particle anti-particle oscillations Neutral Mesons can oscillate into Anti-particles: K0↔ K0, (also B0, B0s, D0)

K0-mixing Strangeness is violated in weak decays K0 and K0 can mix via diagrams

CP-violation Observed states are: Ks0  p+p-, p0p0 Essentially K10 CP=+1 short lifetime 89ps KL0  p+p-p0, p0p0p0 Essentially K20 CP=-1 long lifetime 51ns (due to available energy) BUT KL0 (CP=-1)  p+p- (CP=+1) is observed CP is violated in weak decays Observed states are now mixtures of CP=+1 and CP=-1 states Experimentally |e|=2.3x10-3, so CP violation small effect

Charge Inversion Particle-antiparticle mirror P C Parity Inversion Spatial mirror CP

CPT theorem T is time reversal transformation A general theorem states that in any relativistic quantum theory in which signals cannot travel faster than the speed of light, CPT must be an invariant CP is violated  T must also be violated

CPLEAR- some parameters Kaon Oscillation d s W- u, c, t u, c, t _ _ W+ s d - K0 K0 u, c, t d W- _ _ _ W+ s _ _ u, c, t s d Rate difference Ko Ko  Ko Ko is T violation CPLEAR- some parameters Beam – 106 anti-protons /s into Hydrogen target Fast online trigger selection of events ~ 103/s Ability to separate charged pions / kaons using Cherenkov, dE/dx, Time of flight discriminate in momentum range 350-700 MeV/c Can detect and reconstruct Ks vertex to ~ 60 lifetimes c~2.6 cm Observe events over ~ 4 Magnetic field (0.4T) and tracking leads to particle momentum determination (~5% accuracy)

CPLEAR T invariance test measure 1) Identify Ko / Ko at production: produced in association with K+/K- 2) Identify Ko / Ko at decay from charge of lepton: (S = 0) (S = 0) Get positron: Or electron: ν ν e+ e- W+ W- s u s u Ko π - Ko π+ d d d d

Experiment at LEAR ring at CERN 1990-1996 Pions from kaon decay

Discovery of T violation CPLEAR,1998 Currently the only direct observation of T violation Measure asymmetry in rates Number of lifetimes T, or equivalently CP, violated by this tiny amount

CP violation in SM - - How do we include CP violation CKM matrix ? K0 One diagram only for simplicity - d s W- K0 K0 c t _ _ W+ s d _ _ d s - W+ K0 K0 c t W- s d Hence difference in rates: CP violation introduced by making CKM matrix terms complex

Number of Parameters in CKM n x n complex matrix, 2n2 parameters Unitarity n2 constraints n2 parameters Phases of quark fields can be rotated freely (n-1)2 parameters (remove one per row) Real parameters, rotation (Euler) angles n(n-1)/2 real Phases (n-1)(n-2)/2 phases n=2, 1 real, 0 phase n=3, 3 real, 1 phase

K&M Predict 3 famillies (Prog. Theor. Phys. 49, 652(1973) ) Only 3 quarks discovered Charm predicted by GIM mechanism CP violation discovered Hence predict three (or more) famillies! Discovery of b quark p+(Cu,Pt)Υ (upsilon) +X Similar to J/ψ discovery. At Fermilab 1977 Precision measurements in e+e- Again narrow resonances Υ (1s), Υ (2s), Υ (3s), b bbar 3S1 states of bottom ‘atom’ Cornell

CKM – Unitarity Triangle Three complex numbers, which sum to zero Divide by so that the middle element is 1 (and real) Plot as vectors on an Argand diagram If all numbers real – triangle has no area – No CP violation Hence, get a triangle ‘Unitarity’ or ‘CKM triangle’ Triangle if SM is correct. Otherwise triangle will not close, Angles won’t add to 180o Imaginary Real

Unitarity conditions j=1,3 No phase info. j,k =1,3 jk hence 6 triangles in complex plane db: sb: ds: ut: ct: uc:

CKM Triangle - Experiment Find particle decays that are sensitive to measuring the angles (phase difference) and sides (probabilities) of the triangles Measurements constrain the apex of the triangle Measurements are consistent CKM model works, 2008 Nobel prize

Rate depends on top quark mass B-mixing Mixing also possible in the neutral B/D-systems B0d B0s (discovered 2006) D0 (discovered 2007) B-system is best laboratory for CP violation studies heavy system allows calculations ‘long lifetime’ CP violation observed in B-system Babar/Belle (2000) LHCb: New physics in loops Rate depends on top quark mass C. Parkes, P.Soler - s b u,c,t

CP Violation: Why is it interesting ? Fundamental: The Martian test C violation does not distinguish between matter/anti-matter. LH/RH are conventions CP distinguishes matter from anti-matter CP says preferred decay KLe+ve- Least Understood: CP Violation is ‘add-on’ in SM Parity violation naturally imbedded in coupling structure CP requires a complex phase in 3 generation CKM matrix, allowed but not natural

CP: Why ? cont. Problem Powerful: delicately broken symmetry Very sensitive to New Physics models Historical: Predicted 3rd generation ! Baryogenesis: there is more matter ! N(antibaryon) << N(baryon) << N(photons) Fortunately! 1 : 109 Sakharov (1968) Conditions Baryon number violation CP violation Not in thermal equilibrium Problem Not enough CP violation in CKM ! Assuming not initial conditions, but dynamic. Cannot allow all inverse reactions to have happened

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Muon decay e± m± m± Consider muon decay P e± Experimental results q P-q e± By C-invariance cannot distinguish between particle and anti-particle  identical lifetimes  identical decay distributions P-invariance  the rate should be the same for q and –q Results show both C and P invariance are violated BUT Lifetimes are the same  C respected for this Experimental results

Muon decay Results show both C and P invariance are violated BUT m+ Lifetimes are the same  C respected for this Solution: CP is conserved (almost!) in weak interactions Under C m+  m- Under P q  p-q m+ m-