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Unitarity Triangle Analysis: Past, Present, Future

Unitarity Triangle Analysis: Past, Present, Future. INTRODUCTION : quark masses, weak couplings and CP in the Standard Model Unitary Triangle Analysis: PAST PRESENT FUTURE. Dipartimento di Fisica di Roma I Guido Martinelli HANOI August 5th-9th 2004.

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Unitarity Triangle Analysis: Past, Present, Future

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  1. Unitarity Triangle Analysis: Past, Present, Future • INTRODUCTION: quark masses, weak couplings and CP in the Standard Model • Unitary Triangle Analysis: PAST • PRESENT • FUTURE Dipartimento di Fisica di Roma IGuido Martinelli HANOI August 5th-9th 2004

  2. C, CP and CPT and their violation are related to the foundations of modern physics (Relativistic quantum mechanics, Locality, Matter-Antimatter properties, Cosmology etc.) Although in the Standard Model (SM) all ingredients are present, new sources of CP beyond the SM are necessary to explain quantitatively the BAU Almost all New Physics Theories generate new sources of CP

  3. Quark Masses, Weak Couplings and CP Violation in the Standard Model

  4. In the Standard Model the quark mass matrix, from which the CKM Matrix and CP originate, is determined by the Yukawa Lagrangian which couples fermions and Higgs Lquarks = Lkinetic + Lweak int +Lyukawa CP invariant CP and symmetry breaking are closely related !

  5. QUARK MASSES ARE GENERATED BY DYNAMICAL SYMMETRY BREAKING Charge +2/3 Lyukawa  ∑i,k=1,N[ Yi,k (qiL HC ) UkR +Xi,k (qiL H) DkR + h.c. ] Charge -1/3 ∑i,k=1,N[ mui,k (uiL ukR) +mdi,k (diL dkR)+ h.c. ]

  6. Diagonalization of the Mass Matrix Up to singular cases, the mass matrix can always be diagonalized by 2 unitary transformations uiL  UikL ukL uiR  UikR ukR M´= U†L M UR (M´)† = U†R (M)† UL Lmass  mup (uL uR +uR uL ) +mch(cL cR +cR cL )+mtop(tL tR +tR tL )

  7. N(N-1)/2 angles and (N-1)(N-2)/2 phases N=3 3 angles + 1 phase KM the phase generates complex couplings i.e. CP violation; 6 masses +3 angles +1 phase = 10 parameters

  8. NO Flavour Changing Neutral Currents (FCNC) at Tree Level (FCNC processes are good candidates for observing NEW PHYSICS) CP Violation is natural with three quark generations (Kobayashi-Maskawa) With three generations all CP phenomena are related to the same unique parameter (  )

  9. Quark masses & Generation Mixing | Vud | = 0.9735(8) | Vus | = 0.2196(23) | Vcd | = 0.224(16) | Vcs | = 0.970(9)(70) | Vcb | = 0.0406(8) | Vub | = 0.00363(32) | Vtb | = 0.99(29) (0.999) e- -decays W e down up Neutron Proton | Vud |

  10. The Wolfenstein Parametrization + O(4)  ~ 0.2 A ~ 0.8  ~ 0.2  ~ 0.3 Sin12 =  Sin23 = A 2 Sin13 = A 3(-i )

  11. The Bjorken-Jarlskog Unitarity Triangle | Vij | is invariant under phase rotations a1 b1 a1 = V11 V12* = Vud Vus* a2 = V21 V22* a3= V31 V32* d1 a2 b2 e1 a1 + a2 + a3 = 0 (b1 + b2 + b3 = 0 etc.) a3 b3 c3  a3 a2 Only the orientation depends on the phase convention a1  

  12. From A. Stocchi ICHEP 2002

  13. sin 2 is measured directly from B J/ Ks decays at Babar & Belle (Bd0 J/ Ks , t) - (Bd0 J/ Ks , t) AJ/ Ks = (Bd0 J/ Ks , t) + (Bd0 J/ Ks , t) AJ/ Ks = sin 2 sin (md t)

  14. DIFFERENT LEVELS OF THEORETICAL UNCERTAINTIES (STRONG INTERACTIONS) First class quantities, with reduced or negligible uncertainties 2) Second class quantities, with theoretical errors of O(10%) or less that can be reliably estimated 3) Third class quantities, for which theoretical predictions are model dependent (BBNS, charming, etc.) In case of discrepacies we cannot tell whether is new physics or we must blame the model

  15. Quantities used in the Standard UT Analysis

  16. THE COLLABORATION M.Bona, M.Ciuchini, E.Franco, V.Lubicz, G.Martinelli, F.Parodi, M.Pierini, P.Roudeau, C.Schiavi, L.Silvestrini, A.Stocchi Roma, Genova, Torino, Orsay THE CKM NEW 2004 ANALYSIS IN PREPARATION • New quantities e.g. B -> DK will be included • Upgraded experimental numbers after Bejing www.utfit.org

  17. PAST and PRESENT (the Standard Model)

  18. Results for  and  & related quantities With the constraint fromms contours @ 68% and 95% C.L. = 0.174  0.048  = 0.344  0.027 [ 0.085 - 0.265] [ 0.288 - 0.397] at 95% C.L. sin 2  = - 0.14  0.25 sin 2  = 0.697  0.036 [ -0.62 - +0.33] [ 0.636 - 0.779]

  19. Comparison of sin 2  from direct measurements (Aleph, Opal, Babar, Belle and CDF) and UTA analysis sin 2 measured = 0.739  0.048 sin 2 UTA = 0.685 ± 0.047 sin 2 UTA = 0.698 ± 0.066 prediction from Ciuchini et al. (2000) Very good agreement no much room for physics beyond the SM !!

  20. Theoretical predictions of Sin 2 in the years predictions exist since '95 experiments

  21. Crucial Test of the Standard ModelTriangle Sides (Non CP) compared to sin 2  and K From the sides only sin 2 =0.715  0.050

  22. PRESENT: sin 2 from B ->  &  • and (2+) from B -> DK & B -> D(D*)  FROM UTA

  23. ms Probability Density Without the constraint fromms ms = (20.6 ± 3.5 ) ps-1 [ 14.2 - 28.1] ps-1 at 95% C.L. With the constraint fromms +1.7 ms = (18.3 ) ps-1 [ 15.6 - 22.2] ps-1 at 95% C.L. -1.5

  24. Hadronic parameters fBs √BBs = 276  38 MeV 14% lattice fBs √BBs = 279  21 MeV 8% UTA 6% 4% fBd √BBd = 223  33  12 MeV lattice fBd √BBd = 217  12 MeV UTA BK = 0.86  0.06  0.14 lattice (+0.13) BK = 0.69 UTA (-0.08)

  25. Limits on Hadronic Parameters fBs √BBs

  26. PRESENT (the Standard Model) NEW MEASUREMENTS

  27. sin 2 from B ->     B B B   

  28. sin 2 from B ->  • could be extracted by measuring

  29. sin 2 from B -> 

  30. PRESENT & NEAR FUTURE I cannot resist to show the next 3 trasparencies

  31. MAIN TOPICS • Factorization (see M. Neubert talk) • What really means to test Factorization • B  and B K decays and the determination of the CP parameter  • Results including non-factorizable contributions • Asymmetries • Conclusions & Outlook From g.m. qcd@work martinafranca 2001

  32. CHARMING PENGUINS GENERATE LARGE ASYMMETRIES A = BR(B) - BR(B) BR(B) + BR(B) BR(K+ 0)  typical A ≈0.2 (factorized 0.03) BR(K+ -) Large uncertainties BR(+-) From g.m. qcd@work martinafranca 2001

  33. Tree level diagrams, not influenced by new physics

  34. FUTURE: FCNC & CP Violation beyond the Standard Model

  35. CP beyond the SM (Supersymmetry) Spin 0 SQuarks QL , UR , DR SLeptons LL , ER Spin 1/2 Quarks qL , uR , dR Leptons lL , eR Spin 1/2 Gauginos w , z , , g Spin 1 Gauge bosons W , Z , , g Spin 0 Higgs bosons H1 , H2 Spin 1/2 Higgsinos H1 , H2

  36. In general the mixing mass matrix of the SQuarks (SMM) is not diagonal in flavour space analogously to the quark case We may eitherDiagonalize the SMM z , , g FCNC QjL qjL Rotate by the same matrices the SUSY partners of the u- and d- like quarks (QjL )´ = UijLQjL or g UjL UiL dkL

  37. In the latter case the Squark Mass Matrix is not diagonal (m2Q )ij = m2average 1ij + mij2 ij = mij2 /m2average

  38. Deviations from the SM ? Model independent analysis: Example B0-B0 mixing (M.Ciuchini et al. hep-ph/0307195)

  39. Second solution also suggested by BNNS analysis of B ->K,   decays SM solution

  40. TYPICAL BOUNDS FROM MK AND K x = m2g/ m2q x = 1 mq = 500 GeV | Re (122)LL | < 3.9  10-2 | Re (122)LR | < 2.5  10-3 | Re (12)LL (12)RR | < 8.7  10-4 from MK

  41. from K x = 1 mq = 500 GeV | Im (122)LL | < 5.8  10-3 | Im (122)LR | < 3.7  10-4 | Im (12)LL (12)RR | < 1.3  10-4

  42. MB and A(B J/ Ks ) MBd = 2 Abs | Bd|H |Bd| B=2 eff A(B J/ Ks ) = sin 2  sin MBd t 2  = Arg | Bd|H |Bd| eff B=2 eff eff sin 2  = 0.734  0.054 from exps BaBar & Belle & others

  43. TYPICAL BOUNDS ON THE -COUPLINGS A, B =LL, LR, RL, RR 1,3 = generation index ASM = ASM (SM)  B0 | HeffB=2| B0 = Re ASM + Im ASM + ASUSY Re(13d )AB2+ i ASUSY Im(13d )AB2

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