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The mirror did not seem to be operating properly: A guide to CP violation

C hris P arkes 12/01/2006. The mirror did not seem to be operating properly: A guide to CP violation. :. Section 1: Symmetries. :. Emmy Noether. Symmetries. Role of symmetries in physics e.g. translational -> momentum conservation rotational -> angular momentum conservation

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The mirror did not seem to be operating properly: A guide to CP violation

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  1. Chris Parkes 12/01/2006 The mirror did not seem to be operating properly: A guide to CP violation :

  2. Section 1: Symmetries :

  3. Emmy Noether Symmetries • Role of symmetries in physics • e.g. translational -> momentum conservation • rotational -> angular momentum conservation • Time -> energy conservation • Fundamental Symmetries we will study • Parity (P) – spatial inversion • Charge Conjugation (C) – particle/ anti-particle • CP • CPT

  4. Parity - Spatial Inversion P operator acts on a state |y(r, t)> as Hence for eigenstates P=±1 e.g. hydrogen atom wavefn |y(r,, )>=(r)Ylm(,) Ylm(,)= Ylm(-,+) =(-1)l Ylm(,) So atomic s,d +ve, p,f –ve P |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 Hence, Electric dipole transition l=1P=- 1

  5. Parity cont. • Conserved in strong & emag. Interactions • Parity multiplicative |> = a b, P=PaPb • Proton • Convention Pp=+1 • QFT • Parity fermion -> opposite parity anti-fermion • Parity boson -> same parity anti-particle • Angular momentum • Use intrisnic parity with GROUND STATES • Also multiply spatial config. Term (-1) l scalar, pseudo-scalar, Vector, axial(pseudo)-vector, Jp = 0+ , 0-, 1-, 1+ -,o,K-,Ko all 0- , photon 1-

  6. Parity Violation Discovery“-” problem Actually K+ Postulated Yang& Lee, 1956 • Same mass, same lifetime, BUT • +, (21%) P  =+1 • ++-, (6%) P  =-1 C.S. Wu et. al., Phys. Rev. 105, 1413 (1957)  e- (E,p) B field  Co60Nuclei spin aligned Beta decay to Ni*60 Spin axial vector -> maximal violation V-A theory, neutrino handedness Parity e- (E,-p)

  7. o   +  A = J, hence C=-1 Thus, C|o> =(-1)2|o> = +1 |o> Charge Conjugation Particle to anti-particle C operator acts on a state |y(x, t)> as Only a particle that is its own anti-particle can be eigenstate of C, e.g. C|o> = ±1 |o> G , isospin rotation I3 ->-I3, e.g. + -> -

  8.   left-handed  left-handed Charge & Parity -> Parity ->  right-handed  right-handed  Neutrino helicity • Massless approximation • Goldhaber et al. Phys Rev 109 1015 (1958)

  9. Time

  10. flavour eigenstates CP conjugated KS mass eigenstates KL Let us have a quick look at nature.... Neutral kaon system Three pion decay, very little phase space

  11. Initial state at t = 0 S = 0 S = 0 CPLEAR T invariance test Rate differenceKoKo  KoKois T violation

  12. Experiment at LEAR ring at CERN 1990-1996

  13. Discovery of T violation • direct observation of T violation • Detailed balance expts difficult due to strong/em. effects

  14. Electric Dipole Moments • Energy shift due to say, neutron, being in weak electric field • e.d.m. (measured in e cm) • TdT-1= d, but only available direction is J so • d=const.J • TJT-1= -J, hence d=0 • Also for electron, and (less obviously) atomic nuclei • (linear term in E not present) Spin precession fequency of ultracold neutrons in a weak magnetic field. d(n) 6.3x10-26 ecm, also d(e) 1.6x10-27 ecm (sussex)

  15. CPT Invariance • Particle->anti-particle, reverse time, invert space. • CPT |(r,t)> = |(-r,-t)> • Lagrangian invariant under CPT • Lorentz invariant • Unique ground state • Spin-statistics (Fermi/Bose)…. • No appealing theory of CPT violation exists

  16. CPT Consequences(1) • Particle/anti-particle mass equality

  17. CPT Consequences (2) • Particle/anti-particle width equality

  18. Section 2: Introducing CP in SM :

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

  20. 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 Assuming not initial conditions, but dynamic. Cannot allow all inverse reactions to have happened

  21. CP Violation key dates • 1964 CP Violation discovery in Kaons • 1973 KM predict 3 or more families • ….. • …..erm…not…much… • …. • 1999 Direct CP Violation NA48/KTeV • 2001 BaBar/Belle CP Violation in B’s • 200? LHCb physics beyond the SM?

  22. VudVus Vub VcdVcs Vcb VtdVts Vtb u c t d s b U = D = CP Violation in SM: CKM matrix • SM weak charged current • V-A form LH states LVijUigm(1-g5) DjWm • Vij isthequark mixing matrix, the CKM matrix • for 3 famillies this is a 3x3 matrix • U,D are up/down type quark vectors e.g. W- Coupling Vcd c d

  23. CKM continued • Cabibbo (1963) and Kobayashi & Maskawa (1973) • Realised mass and flavour eigenstates • need not be the same • Weak interaction generations • Related to physical quark states by CKM matrix ud’ c s’ t b’ Values of elements a purely experimental matter d’ s’ b’ d s b = VCKM

  24. 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 • 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

  25. K&M Predict 3 famillies(Prog. Theor. Phys. 49, 652(1973) ) • Only 3 quarks discovered • Charm predicted by GIM mechanism • CP violation discovered • Phase ei(wt+) Tei(-wt+) • i.e. Violates T/CP • Hence predict three (or more) famillies! • Now parameterize 3x3 CKM in 4 parameters

  26. PDG, 3 angles + phase 3 angles 12, 23, 13 phase  Cij= cos ij Sij=sin ij C12 S12 0 -S12 C12 0 0 0 1 • 0 0 • 0 C23 S23 • 0 -S23 C23 R12 = R23 = C13 0 S13 e-i 0 1 0 -S13e-i 0 C13 R13 = VCKM = R23 x R13 x R12

  27. Wolfenstein’s parameters  = S12, A=S23/S212, =S13cos/ S13S23, =S13sin/ S12S23 VCKM VCKM(3) terms in up to 3 CKMterms in4,5 A ~ 1, ~ 0.22, ≠ 0 but  ≠ 0 ???

  28. 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:

  29. More triangles • Area of all the triangles is the same (6A2) • Two triangles (db) and (ut) have sides of similar size • Easier to measure, (db) is often called the unitarity triangle ’=, =-’, =-’ Bottom side A3 normalised to 1  = -arg(Vts)  = arg(Vts) (,)

  30. CP in SM summary • Study of CP violation is the analysis of the CKM matrix to verify if it is consistent with the standard model. • If not New Physics! • Will CP lead to SM ?

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