CP Violation in B 0 s mesons Results from a flavor tagged analysis of B 0 s  J/ y f

1. CP Violation in B0s mesons Results from a flavor tagged analysis of B0s J/y f Joe Boudreau University of Pittsburgh Experimental results from CDF (and other experiment)

2. Vub*Vud Vtb*Vtd b Vcb*Vcd A very brief abstract of this talk first. The following topics will be developed: Vcb*Vcs CDF and D0 use B0s J/y f to measure CKM phases. We determine from this decay the quantity bs. This is in exact analogy to B factory measurement of the b, an angle of the unitarity triangle. The standard model makes very precise predictions for both angles. But other new particles & processes, lurking potentially in quantum mechanical loops such as box diagrams and penguin diagrams can change the prediction. Vub*Vus bs Vtb*Vts

3. t c u c u t u t c W+ W+ W+ W+ W+ W+ W+ W+ W+ s d b s d b s d b The interaction of quarks with the charged weak current is governed by one Universal coupling constant modulated by a matrix, the CKM matrix:

4. Vub*Vud Vtb*Vtd b Vcb*Vcd Unitarity triangles, a graphical representation of the unitarity of the CKM matrix Vub*Vud + Vtb*Vtd + Vcb*Vcd=0

5. There are six unitarity triangles. The one we shall talk about today is the (bs) unitarity triangle, and, especially, its angle bs , which is predicted precisely, now measured, too: Vub*Vus+ Vtb*Vts+ Vcb*Vcs=0 Vcb*Vcs Vub*Vus bs Vtb*Vts

6. CP Violation ≠

7. CP Symmetry • The operator that transforms matter into antimatter in quantum • mechanics is the CP operator. • CP = composition between two transformations: • P (parity): spatial inversion. Left-handed particle->Right handed • particle. • C (charge conjugation): Inverts every internal quantum number, • like electric charge, isospin… => turns a particle into • its antiparticle. • CP turns a left-handed particle into a right-handed antiparticle. • CP symmetry says [H,CP]=0: • * eigenstates of the Hamiltonian are eigenstates of CP • * transitions from CP even states to CP odd states do • not occur. • * amplitudes for particular processes are equal to those • of the CP-conjugate process.

8. CP Violation: discovered in 1964… (Cronin, Fitch) attributed in 1973 to the Higgs, Yukawa sector… (Kobayashi, Maskawa) experimentally validated in this decade by Belle, Babar CDF http://ckmfitter.in2p3.fr/ The verification of the model was carried out by validating its chief prediction, the Unitarity of the CKM matrix elements.

9. There are 12 observed instances of CP violation. 1. Indirect CP violation in the kaon system (eK) 2. Direct CP violation in the kaon system e’/e 3. CP Violation in the interference of mixing and decay in B0→ J/yK0. 4. CP Violation in the interference of mixing and decay in B0->h’K0 5. CP Violation in the interference of mixing and decay in B0->K+K-Ks 6. CP Violation in the interference of mixing and decay in B0->p+p- 7. CP Violation in the interference of mixing and decay in B0->D*+D- 8. CP Violation in the interference of mixing and decay in B0->f0K0s 9. CP Violation in the interference of mixing and decay in B0->yp0 10. Direct CP Violation in the decay B0K-p+ 11. Direct CP Violation in the decay B rp 12. Direct CP Violation in the decay B p+p- Also: Direct CP Violation in the decay B-K-p0

10. B Mixing

11. There are two states in the B0s system, the so-called “Flavor eigenstates” They evolve according to the Schrödinger eqn and M, G Hermitian Matrices u, c u, c G: Absorptive diagrams M: Dispersive diagrams

12. The mixing of eigenstates gives rise to oscillations of frequency Dm, determined by the magnitude of the box diagram The phase of the diagram gives the complex number q/p, with magnitude of very nearly 1 (in the standard model).

13. Mixing phenomenology: Mixing probability Mixing occurs when a B0s decays as a B0s. Decay to a flavor specific final state eg (Ds+p-) tags the flavor at decay. One of three tagging algorithms tags the flavor at production. Good triggering, full reconstruction of hadronic decays, excellent vertex resolution, and high dilution tagging are all essential for this measurement, which made news in 2006.

14. There is a similarity here to Faraday rotation, in optics: rotation of the • polarization of light: • Start with polarized light. • Decompose it into two states of circular polarization. • In a sugar solution these states propagate with different speeds. • So one helicity arrives early, or, there is a phase difference. • When the two beams recohere, the polarization has rotated.

16. In B mesons ….: B0 B0 t b s W W Bs0 Bs0 s b t I needed two polarizing filters for the demonstration. CDF needs initial state flavor tagging, and looks at decays to flavor-specific final states.

17. Δms= 18.56 ± 0.87(stat) ps-1 (D0 CONF Note 5474) (PRL 97, 242003 2006)

18. Many of the “new” CP observables are “CP violation in the interference of mixing and decay”: Vub*Vud Vtb*Vtd b Vcb*Vcd |B0> | J/y K0s > |B0> BABAR, BELLE have used this decay to measure precisely the value of sin(2b) an angle of the bdunitarity triangle

19. CP violation in the interference of mixing and decay: Imagine we filter for circularly polarized light, here at the end: B0 B0 Interference of mixing and decay: Uses decay to CP eigenstates to analyze the mixing. Measures q/p relative to A/A (ratio of decay amplitudes) Physical observable Sin(2b) = 0.728 ± 0.056(stat) ±0.023(syst) K. Abe et al., Phys. Rev. D71, 072003 (2005).

20. There was a fourfold ambiguity in the Belle, Babar measurement of b. Two are irreducible: all observables upon either sin(2b) or cos(2b) The B factory experiments resolved this with a complicated decays B J/y K0* A decay to two vector mesons, a final state which is neither CP even nor odd, but CP-mixed.

21. B0s→J/yf. B->V V decay to actually three distinct final states (S-wave, P-wave, and D-wave). S,D Wave: CP even, short-lived, light. P Wave: CP odd, long-lived, heavy. These “final” states are actually intermediate states (final state is m+m-K+K-) so there is interference. * Pure S, P,or D wave states would have distinct angular distributions. * With a mix of orbital angular momentum final states one can separate the decays on a statistical basis (angular analysis)

22. Spin correlation of the vector mesons resembles that of the two photons • two photons in positroniumdecay. • Polarization of vector mesons can be perpendicular (CP odd), or parallel (CP even) • And also longitudinal (CP even) • Distributions in the angles q, f, and y sensitive to polarization. A. S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Phys. Lett. B 369, 144 (1996), 184 hep-ph/9511363.

23. Time dependence of the angular distributions: { A, A||, A0 }: transition amplitude <Bs0|P>to each final states { P, P||, P0 } { Ā, Ā||, Ā0 }: transition amplitude <Bs0|P> “ “ “ “ “ “ “ “ “ “ In the physical B0s,phys meson the flavor content changes (B0s-B0s oscillations) with fast frequency of 17.77 ± 0.12 ps-1 The amplitude <Bs,phys0(t)|P> = A(t) (amplitude for a particle born as a B0s to decay into the state |P> after a time t) decays and oscillates.

24. This innocent expression hides a lot of richness: * CP Asymmetries through flavor tagging. * sensitivity to CP without flavor tagging. * sensitivity to both sin(2bs) and cos(2bs) simultaneously. * Width difference * Mixing Asymmetries … formula suggests an analysis of an oscillating polarization.

25. CP Violation in the interference of mixing and decay for the B0s system Take: q/p from the mixing of B0s- B0s Take: Ā/A from the decay into { P, P||, P0 } Form: the (phase) convention-independent and observable quantity: This number is real and unimodular if [H,CP]=0

26. Babar, Belle an ambiguity in bby analyzing the decay B0J/y K0* which is BV V and measures sin(2b) and cos(2b) This involves angular analysis as described previously J/y K0* | P|| > |B0> | P0 > |m+m-K0sp0> |B0> |B0> | P >

27. Today I will tell you about an analysis of an almost exact analogy, |Bs0>  J/y f (but I think that in the B0s system the phenomenology is even richer! Because of the width difference! ) J/y f | P|| > |Bs0> | P0 > |m+m-K+K-> |Bs0> |Bs0> | P >

28. This is a complicated business but there is a nice analogy one can do to understand what happens to B0s and in the decay to J/y f: CP violation ~ a preferred direction in the space B0s/B0s in mixing or in the decay. Birefringent zone/ weak interaction, box diagrams, DG/G10%. Interference on the far screen angularanalysis Polarizing Filter initial state flavor tagging. Filtered slits CP even and odd final states

29. The decay B0sJ/yf obtains from the decay B0J/y K0* by the replacement of a d antiquark by an s antiquark b d s W W B0→J/y K0* c W d c b s s W W B0→J/yf c W s c We are measuring then not the bd unitarity triangle but the bs unitarity triangle: Vub*Vud Vtb*Vtd Vcb*Vcs b Vub*Vus bs Vtb*Vts Vcb*Vcd

30. = Vub*Vud = O(l3) Vtb*Vtd= O(l3) With l = 0.2272± 0.0010 A = 0.818 (+0.007 -0.017) r = 0.221 (+0.064-0.028) h = 0.340 (+0.017-0.045) One easily obtains a prediction for bs : 2bs = 0.037±0.002 b Vcb*Vcd = O(l3) Vcb*Vcs= O(l2) b’ Vub*Vus= O(l4) Vtb*Vts= O(l2)

31. bs, the phase of Vts is expected to be close to zero in the standard model. and should not lead to detectable CP violation. Small phase, small CP violation However there may be other contributions to CP violation from other sources; This is what makes this an important measurement. ~ ~ ~ ~ Flavor structure of BSM physics unknown

32. “Hidden richness”

33. where i = 0, para, perp and reference material An analysis of the decay can be done with either a mix of B and B mesons (untagged) or with a partially separated sample (flavor tagged). Latter is more difficult and more powerful. B B These expressions are: * used directly to generate simulated events. * expanded, smeared, and used in a Likelihood function. * summed over B and ̅B (untagged analysis only)

34. reference material For reference: expanded, smeared , normalized rates: obtain the overall time and angular dependence:

35. reference material Explicit time dependence is here: … then, replace exp, sin*exp, cos*exp with smeared functions.

36. The analysis of B0s→J/y f can extract these physics parameters: The exact symmetry.. … is an experimental headache.

37. Curiosity #1: cos(2bs) is easier to measure than sin(2bs). It can be done in the untagged analysis for which the PDF contains time dependent terms: Physically this is accessible because one particular lifetime state (long or short) decays to the “wrong” angular distributions. Needs DG≠0; no equivalent in B0J/y K0*. Some fine print: in the interference term, in an untagged analysis, there is a term including sin(2bs); however this term does not determine the sign of sin(2bs) so it does not solve any ambiguity.

38. Curiosity #2: Sensitivity to Dms (tagged analysis only; even in the absence of CP) How much sensitivity? Well, we did not exploit it yet but it could be important news at the LHC!

39. Where does the sensitivity to Dmscome from ? J/y f | P|| > |Bs0> | P0 > |m+m-K+K-> |Bs0> |Bs0> | P >

40. Where does the sensitivity to Dmscome from ? J/y f | P|| > |Bs,L> | P0 > |m+m-K+K-> |Bs,H> |Bs0> | P >

41. Big simplification…: Time dependence of interference term is contained in the factor:  Interference terms tag the flavor at decay.

42. CDF Detector showing as seen by the B physics group. Muon chambers for triggering on the J/y→m+m- and m Identification. Strip chambers, calorimeter for electron ID Central outer tracker dE/dX and TOF system for particle ID r < 132 cm B = 1.4 T for momentum resolution.

43. SVX II ISL Excellent vertex resolution from three silicon subsystems: L00: 1.6 cm from the beam. 50 mm strip pitch Low mass, low M-S.

44. CDF, 2506 ± 51 events .. And in D0, 1967 ± 65 total.. … but 2019 ± 73 tagged events, all tagged. Next, we’ll run through the CDF analysis, show what you get from flavor tagging, then show the D0 results.

45. The Analysis needs the proper decay time, decay angles and flavor-at-production of a B0s or B0s decaying to J/yf. S Modeling of detector sculpting Selection Proper decay time estimation S Flavor Tagging Likelihood fit Extraction of confidence region

46. Artificial Neural Network selection trained on data + MC Uses: • transverse momentum PT and vertex probability prob(c2) of B, • J/y mass and vertex probability of f • pT and Particle ID (TOF, dE/dx) of K+, K- Candidate events should have NN > 0.6

47. We reconstruct B0sJ/yf 2.5K 1.7 fb-1 for untagged tagged analysis B0sJ/yf 2.0K 1.35 fb-1 for flavor-tagged analysis B0 J/y K0* 7.8K 1.35 fb-1 B V V decay for crosscheck of angular analysis B±  J/y K± 19K 1.35 fb-1 Measure dilution of opposite side tagging.

48. Results from 1.7 fb-1 of untagged decays. bs fixed to its Standard Model value

49. Results untagged analysis arXiv:0710.1789 [hep-ex] Standard Model Fit (no CP violation) HQET: ct(B0s)= (1.00±0.01) ct(B0) PDG: ct(B0) = 459 ±0.027 mm

50. More results, untagged analysis Applying the HQET lifetime constraint: