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D Mixing and CP Violation

D Mixing and CP Violation. 1. Introduction 2. Phenomenology 3. Measurements Decays to CP eigenstates WS 2-body decays Multibody decays t-integrated CP asymmetries 4. Averages 5. Constraints on NP models. B oštjan Golob

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D Mixing and CP Violation

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  1. D Mixing and CP Violation • 1. Introduction • 2. Phenomenology • 3. Measurements • Decays to CP eigenstates • WS 2-body decays • Multibody decays • t-integrated CP asymmetries • 4. Averages • 5. Constraints on NP models BoštjanGolob University of Ljubljana/Jožef Stefan Institute & Belle/Belle IICollaboration University of Ljubljana “Jožef Stefan” Institute Nara Women‘s University,Aug 6th, 2013

  2. Introduction q2 q1 Mixing of neutral mesons Phenomena in course of life neutral meson P0 cantransform into anti-meson P0 P0 = K0, Bd0, Bs0 and D0 n.b.: p0 are self-conjugated, p0 = p0 q2 q1 P0 P0 History observation of K0: 1950 (Caletch) mixing in K0: 1956 (Columbia) observation of Bd0: 1983 (CESR) mixing in Bd0: 1987 (Desy) observation of Bs0: 1992 (LEP) mixing in Bs0: 2006 (Fermilab) observation of D0: 1976 (SLAC) mixing in D0: 2007 (KEK, SLAC) (evidence of) 6 years 4 years 14 years 31 years

  3. Mixing phenomenology Time evolution Schrödinger equation eigenvalues mass states P1,2 evolve in time according to m1,2 and G1,2: Flavor states state initially produced as pure P0 or P0 for some more details see p. 39-40

  4. Mixing phenomenology Time evolution Flavor states state initially produced as pure P0 or P0 can at a later time t be P0 or P0, depending on values of mixing parameters x, y: n.b.: if P0 P0 produced in quantum coherent state (e.g. Y(4S) B0 B0) time evolution is different, see p. 41

  5. Mixing phenomenology Vuj* Vci Vcj Vui* u c W+ D0 D0 d, s, b d, s, b W- c u K+ D0 D0 K- Mixing rate Phenomenology for approximate derivation and some more details see p. 43-47 DCS SU(3) breaking 2nd order perturb. theory Dm=2(q/p)M12 DG=2(q/p)G12 x,y = g(Dm, DG)=f(M12,G12) short distance |x| O(10-5) long distance, difficult to calculate; A.F. Falk et al., PRD65, 054034 (2002) G. Burdman, I. Shipsey, Ann.Rev.Nucl.Sci. 53, 431 (2003)

  6. Mixing phenomenology Mixing of neutral mesons Observables (B-factories, hadron machines) |x|, |y| << 1  Decay time distribution of experimentally accessible states D0, D0 sensitive to mixing parameters x and y, depending on final state n.b.: at charm factories observables are different, see p. 63-66 for some more details dN(D0f)/dt is different function of x, y (and q/p) for different Af, Af

  7. Mixing phenomenology Mixing of neutral mesons Observables 1 .4 0 Bs P(P0P0) P(P0P0) x=26, y=0.15 1 4 Gt 1 .4 0 1 .1 0 Bd x=0.8, y=0 D0 log scale! x=0.01, y=0.01 1 4 Gt 1 4 Gt

  8. CPV phenomenology Vud p+ CPV in charm sector Tiny CPV: complex CKM matrix phase; D0(and other processes involving charm hadrons): first two quark generations; CKM elements ≈ real; VCKM V*cd D0 p- expected level of CPV asymmetries O(10-3)

  9. CPV phenomenology CP violation in charm Parametrization ...is sometimes messy RD ≠1: Cabbibo suppression 3 types of CPV: AD ≠0: CPV in decay appears only if two amplitudes with different weak and strong phases contributing; in D meson decays this is only the case for SCS decays, e.g. D0 K+K- for some more details see p. 49 AM ≠0: CPV in mixing f ≠0 : CPV in interference n.b.: (RD), AfD, AM, f << 1

  10. Intermezzo D mixing and CPV (in Nara) back in ~2005 D0D0 .... 10-5 – 10-2 ACP........... 10-3 ?????

  11. Exp. methods Experimental methods Common exp. features tagging (B-factories, hadron machines) D*+ →D0ps+ charge of psflavor of D0; DM=M(D0ps)-M(D0) (or q=DM-mp)  background reduction decay time (B-factories) D0 decay products vertex; D0 momentum & int. region; p*(D*) > 2.5 GeV/c eliminates D0from b → c (for easier notation:Gt → t) 100 mm 200 mm for some more details see p. 50

  12. Exp. methods n.b.: dN(D0f)/dt is different function of x, y (and q/p) for different Af, Af Experimental methods Decay modes methods/precision/measured parameters depend on the decay mode final states: semileptonic CP states WS hadronic 2-body states multi-body self conjugated states and some decays which are a combination of those examples Experimental methods Decay modes methods/precision/measured parameters depend on the decay mode final states: semileptonic CP states WS hadronic 2-body states multi-body self conjugated states and some decays which are a combination of those examples n.b.: x, y ~ 10-2 f, AM~ 10-3 example K+ln K+K- K+p – KSp -p+ K+p -p0 sensitivity to x2+y2 yCP=y cosf-(Am/2)x sinf see p.51 - 52 linear in y linear in y ‘ linear in x, y linear in x‘, y‘ x, y, q/p see p.61 - 62

  13. CP eigenstates Decays to CP eigenstates Principle D0→ K+K- / p+p- CP even final state; if no CPV: CP|D1> = |D1> |D1> is CP even state; only this component of D0/D0 decays to K+K- / p+p-; measuring lifetime in these decays t =1/G1; D0→ K-p+ K-p+: mixture of CP states  t=f(1/G1,1/G2) |D1> t1 t1 K+K- p+p- K-p+ D0 |D2> t2 t2 for derivation see p. 53

  14. CP eigenstates Belle, PRL 98, 211803 (2007), 540fb-1 Decays to CP eigenstates Results D0→ K+K- / p+p-, as wellK-p+ simultaneous binned likelihood fit to decay-t, common free yCP c2/ndf= 1.084 (ndf=289) + first evidence (one of ...) for D0 mixing dominant syst.: t acceptance linearity; small residual bias in t; K+K-/p+p- and K-p+ratio Belle preliminary, arXiv:1212.3478, 976fb-1 for some more details see p. 54-56

  15. CP eigenstates Belle, PRL 98, 211803 (2007), 540fb-1 Decays to CP eigenstates Results D0→ K+K- / p+p-, as wellK-p+ measuring lifetime in K+K-/p+p –decays separately for D0 and D0 CPV in mixing mixing induced CPV Belle preliminary, arXiv:1212.3478, 976fb-1

  16. WS 2-body Vus* Vud* p+ K+ p- WS 2-body decays Principle D*+→ D0pslow+ RS:D0 → K-p+ WS:D0 → D0 → K+p- or WS:D0 → K+p- (DCS) interference between mixing and DCS for WS decays Vcs Vcd p- D0 D0 K- CF D0 K+ DCS d: unknown strong phase DCS/CF; not directly measurable at B-factories; directly accesible at charm-factories  for derivation see p. 57

  17. WS 2-body WS 2-body decays Results D0 → K+p- NWS 4000; (note: P worse than for K+K-) RD = (3.03 ± 0.16±0.10 ) ·10-3 x’2= (-0.22 ±0.30±0.21) · 10-3 y’= (9.7 ±4.4±3.1) · 10-3 likelihood contours 3.9s BaBar, PRL 98, 211802 (2007), 384fb-1 1s 2s 3s 4s 5s first evidence (2nd of ....) for D0 mixing for some more details see p. 58

  18. WS 2-body • WS 2-body decays • Results • D0 → K+p– • equivalent measurement • separately for D0, D0 • (x’2,y’,RD) → (x’±2, y’±,RD±); y’ .04 0 -.04 D0 D0+D0 (no CPV) CPV in mixing CPV in decay D0 values from BaBar, PRL 98, 211802 (2007), 384fb-1 -4 0 4·10-3x’2

  19. Multibody Multi-body self conjugated states Principle example D0→ KS p+ p- different types of interm. states; CF: D0→ K*-p+ DCS: D0→ K*+p- CP: D0→r0 KS if f = f  populate same Dalitz plot; relative phases determined (unlike D0→K+p-); specific regions of Dalitz plane → specific admixture of interm. states → specific t dependence f(x, y); t D0→KSp+p- by studying the decay time evolution of Dalitz plane → access directly x, y “t-dependent Dalitz analyses” for some more details see p. 59-60

  20. Multibody Multi-body self conjugated states Results D0→ KS p+ p- Nsig= 530∙103 P95% usually fit to t-integrated Dalitz first to establish the appropriate model; 3-dim fit (m+2, m-2, t); complicated, ~40 free param.; possibility of multiple solutions; projection of fit in Dalitz plane Belle, PRL 99, 131803 (2007), 540fb-1 K*X(1400)+ K*(892)+ r/w K*(892)-

  21. Multibody Multi-body self conjugated states Results D0→ KS p+ p- projection of fit in t distrib. Belle, PRL 99, 131803 (2007), 540fb-1 CPV in mixing mixing induced CPV t [fs] dominant syst.: model dependency (param. of resonances); Dalitz model for bkg.; Belle preliminary, T. Peng, EPS2013, 920fb-1

  22. ACP t-integrated CPV mesurements asymmetry of t-integrated rates; CPV in decay, but also (for D0) CPV in mixing and mixing induced CPV; However.... measuring absolute rates instead of decay-t distrib. involves sensitivity to acceptance Aep: p+ / p- detection eff. asymmetry, D*+/-→D0p+/-; e.g. due to different p+/-interactions on detect. material AFB: forward-backward asymmetry g*/Z0→ c c; AFB is an odd function of qD (in CMS); vanishes if integrated over qD; since working in bins of qp(correlated with qD) need to correct for it ACPf: physical CPV asymmetry Aeh: possible further eff. asymmetries between h+/h-in f / f

  23. ACP t-integrated CPV mesurements detector induced asymmetries: must be determined from control data samples; example: D+→ KSh+, h=K, p charged mesons: CPV in decay only; control data sample: Ds+→ f h+, (CF decay, no ACP expected) Arec(D → KSp+ ) - Arec(Ds → fp+ )  ACP(D → KSp+) (technically much more involved due to pp , qp , qDCMSdependence) CPV in K0 system  even in absence of CPV in D system some asymmetry expected assuming AFBD = AFBDs: subtraction yields ACPD for some more details see p. 74

  24. Averages yCP measurements Averages Method c2 fit including correlations among measured quantities HFAG, http://www.slac.stanford.edu/xorg/hfag/ y [%] 4 0 -4 d=30o yCP (CP states) d=0 WS decays (Kp) RM (semileptonic) x, y (t-dependent Dalitz) -4 0 4 x [%]

  25. Averages Averages Inputs HFAG, http://www.slac.stanford.edu/xorg/hfag/ K+K-/p+p- KSh+h- semileptonic K+p-p0 Cleo-c

  26. Averages Averages Inputs HFAG, http://www.slac.stanford.edu/xorg/hfag/ K+p- ACP

  27. Averages Averages Inputs HFAG, http://www.slac.stanford.edu/xorg/hfag/ ACP

  28. Averages Averages Results HFAG, http://www.slac.stanford.edu/xorg/hfag/ no CPV point no mixing point c2/n.d.f. = 75.4/(41-10) ? for some more details see p. 67

  29. NP constraints b’ b u c Constraints on NP D mixing represents FCNC of up-type quarks: c  uuc (with B mesons one studies FCNC of down-typequarks, e.g. b  s l+l-) for many NP models charm mixing and CPV provides for parameter constraints complementary to B physics Vub* Vcb u c W+ D0 D0 b W- Vcb Vub* direct comparison of measured x, y values to SM prediction difficult because of lack of accurate prediction In limit of no CPV in decay: x, y, |q/p|, f: calculable from M12, G12, G relation: measurements: Y. Grossman et al., PRL103, 071602 (2009)

  30. NP constraints b b’ b‘ c u Constraints on NP (examples from ) 4th generation of fermions b’ exchanged in loop; |Vub’Vcb’|<1.2 ∙10-3 for mb’ > 400 GeV n.b.: calculations done assuming NP contribution alone (no SM contrib.) Vub’* Vcb’ u c W+ D0 D0 b b’ E. Golowich et al., PRD76, 095009 (2007) W- Vcb’ Vub’* mb’ [GeV] lines of constant |x| approximate allowed area |Vub’Vcb’|

  31. NP constraints Constraints on NP (examples from ) R-parity violating SUSY squark-lepton (or vice versa) exchange in loop; |l‘i2kl‘i1k|>0.01 for > 1 TeV E. Golowich et al., PRD76, 095009 (2007) D0 D0 R couplings aproximately allowed area [GeV] lines of constant |x|

  32. NP constraints Constraints on NP t-integrated CP asymmetry; at B factories <t>=t ; at hadron machines <t>pp <t>KK t t-dependent asymmetry in D0h+h- HFAG, http://www.slac.stanford.edu/xorg/hfag/ LHCb DACP Belle AG, DACP

  33. NP constraints Constraints on NP FCNC mediated by scalar boson h constraints from mh = 125 GeV Br(t ch)  10-2 exp. value G.F. Giudice et al., JHEP 1204, 060 (2012) exp. limit on Br(t ch)

  34. Summary Summary • interest in charm physics boosted when B factories • realized their full potential as charm factories • measurements of mixing and CPV in charm sector went • from first evidence to precise measurements in last ~5 years • x,y ~ O(10-2), established ; ACP ~ O(10-3), no evidence yet • results provide complementary (to B physics) constraints on • NP models • most measurements challenging due to systematic uncertainties • that need to be controlled, challenge also for Belle II

  35. Additional material Experiments Phenomenology CPV in decays Exp. methods Semileptonic decays Decays to CP eigenstates 2-body WS decays Multibody decays Charm factories Averages Belle II sensitivity ACP

  36. Experiments Experiments B-Factories BaBar @ PEPII SLAC Belle @ KEKB KEK on resonance production e+e-→ U(4S) → B0B0, B+B- s(BB)  1.1 nb (~109 BB pairs) c g* continuum production c s(c c) 1.3 nb (~1.3x109XcYc pairs) Nrec(D*+→ D0p+→ K-p+p+) 2.5x106 B-factory= charm factory back

  37. Experiments Experiments Charm-Factories Cleo-c @ CESR Cornell BESIII @ BEPC-II IHEP e+e-→ y(3770) → D0D0, D+D- DD in coherent (C = -1) state back

  38. Experiments Experiments pp Colliders D0, CDF @ Tevatron Fermilab LHCb @ LHC CERN ( - ) We all live with the objective of being happy; our lives are all different and yet the same. diverse exp. conditions to study charm physics huge statistics in more requiring exp. environment Anne Frank (1929 -1945) back

  39. Mixing phenomenology Time evolution Schrödinger equation mixing affects the time evolution → oscillations state initially produced as will evolve in time as if interested in a(t), b(t): effective Hamiltonian H=M-(i/2)G(non-Hermitian) and t-dependent Schrödinger eq.: eigenstates: (well defined m1,2 and G1,2) D. Kirkby, Y. Nir, CPV in Meson Decays, in RPP back

  40. Mixing phenomenology Time evolution Schrödinger equation eigenvalues q/p: CPV; if CPV neglected q/p=1 P1,2 evolve in time according to m1,2 and G1,2: Flavor states state initially produced as pure P0 or P0 back

  41. Mixing phenomenology Time evolution Flavor states coherent pair production from vector resonance e+e-→V→ P0P0 M. Gronau et al., PLB508, 37 (2001) V=U(4S) B0 V=Y(3770) D0 V=F K0 initial state, C= ±1 back

  42. Mixing phenomenology Mixing of neutral mesons Observables (Charm-factories) coherent production, V(C= -1)→D0D0 t-integrated rate Decay rate of experimentally accessible states D0, D0 sensitive to mixing parameters x and y, depending on final state Since they measure  sensitive to y, x2 back

  43. Mixing phenomenology Vjb* Vid Vjd Vib* b d W+ b d B0 B0 u, c, t u, c, t u, c, t u, c, t B0 W- W+ B0 W- d b b d Mixing rate Phenomenology P0-P0 transition → box diagram at quark level P0: any pseudo-scalar meson; specific example of Bd0 if mi = mj due to CKM unitarity:no mixing back

  44. Mixing phenomenology Vuj* Vci Vcj Vui* u c W+ u c D0 D0 d, s, b d, s, b d, s, b d, s, b D0 W- W+ D0 W- c u u c Mixing rate Phenomenology D0 case the only P0system with uplikeq’s simplified treatment based on dimension serious treatment in CKM unitarity O. Nachmtann, Elem. Part. Phys., Springer-Verlag A.J. Buras et al., Nucl.Phys.B245, 369 (1984) back

  45. Mixing phenomenology Vuj* Vci Vcj Vui* u c W+ D0 D0 d, s, b d, s, b W- u c Mixing rate Phenomenology |VcbVub*|<< |VcsVus*|, |VcdVud*| assuming unitarity in 2 generations  more involved (and correct) calculation: DCS SU(3) breaking A.F. Falk et al., PRD65, 054034 (2002) G. Burdman, I. Shipsey, Ann.Rev.Nucl.Sci. 53, 431 (2003) DCS SU(3) breaking back

  46. Mixing phenomenology u c D0 D0 NP u c Mixing rate Phenomenology 2nd order perturb. theory Dm=2(q/p)M12 DG=2(q/p)G12 x,y = g(Dm, DG)=f(M12,G12) short distance |x| O(10-5) common statement: mixing with large x sign of NP; more appropriate: measurement of x yields complementary constraints on NP models (because of specific uplike q couplings) see formula on p. 4 back

  47. Mixing phenomenology K+ D0 D0 K- Mixing rate Phenomenology 2nd order perturb. theory long distance difficult to calculate; contributes to real and imaginary part  affects x and y; two approaches: OPE exclusive approach I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001) A.F. Falk et al., PRD69, 114021 (2004) (principle can be easy understood, see p. II/26) back

  48. Mixing phenomenology D mixing rate in exclusive approach take as example PP final states: J.F. Donoghue et al., PRD33, 179 (1986) dominant contrib. to mixing; expected Br  minus sign due to relative sign of Vus/Vcd; summing over this states  0 (GIM mechanism); however, in D0 decays SU(3) is broken; in other words, measured Br’s with ri≠1 back

  49. CPV in decay CP violation in charm direct CPV for direct CPV two amplitudes with different strong and weak (CKM) phases are necessary; in D meson decays this is only possible in CS decays with contribution of penguin decays (beside tree contrib.) Vcd V*ud W c d u Vcs V*us W c s u

  50. Exp. methods Experimental methods B-factories decay time D0 decay products vertex; D0 momentum & int. region; p*(D*) > 2.5 GeV/c eliminates D0from b → c hadron machines Tevatron: transverse decay length LHCb: decay length between B (B→ D*X) and D0 vtx Tevatron: impact param. distribution LHCb: using D0 from B (better trigger e and vtx resol.) mm 10 0 int. point B decay vtx D decay vtx back 0 10 mm

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