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Particle Physics II

Particle Physics II. 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.

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Particle Physics II

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  1. Particle Physics II 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

  2. 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

  3. 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…)

  4. Parity Violation in weak interactions Revision 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

  5. 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

  6. 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 s Right-handed 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?

  7. 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 right-handed OR S=- ½ S=- 1 Left-handed Left-handed • Helicities of forward photon and neutrino same • Measure photon helicity, find neutrino helicity

  8. 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

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

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

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

  12. 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

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

  14. CPT theorem • T is time reversal transformation t-t • 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

  15. CPLEAR- some parameters Kaon Oscillation d s W- u, c, t u, c, t _ _ W+ - d s K0 K0 u, c, t _ d s W+ W- _ _ _ _ u, c, t d s Rate differenceKoKo  KoKois T violation • 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)

  16. 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

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

  18. 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

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

  20. 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

  21. 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

  22. 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

  23. 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:

  24. 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

  25. B-mixing Rate depends on top quark mass • 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 C. Parkes, P.Soler - s b u,c,t

  26. 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

  27. CP: Why ? cont. • 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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  29. Muon decay e± m± m± Consider muon decay q P 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

  30. Muon decay Results show both C and P invariance are violated BUT 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-

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