-2betas Measurement from a fit to untagged Bs-> J/psi phi data

Transcription

1 -2betas Measurement from a fit to untagged Bs-> J/psi phi data Géraldine Conti Géraldine Conti 1.

2 Outline Part 1 : Introduction What is -2β s? How to measure -2β s? What s new about -2β s? Why is LHCb the horse to bet on? Part 2 : Sensitivity Studies for the Untagged Fit Standard Model case New Physics case Géraldine Conti 2.

3 What is -2betas? Géraldine Conti 3.

4 The CKM matrix in the SM The CKM matrix connects the EW eigenstates (d,s,b ) of the down-type quarks with their mass eigenstates (d,s,b) : For one (i,j) pair (i j) : - Constraint on 3 complex numbers (k=u,c,t) - In the complex plane, the 3 numbers represent the sides of a triangle. Unitary triangles Géraldine Conti 4.

5 The Bs Unitary Triangle For i=s and j=b (B s unitary triangle) : * β s is the smallest angle of the b-s unitary triangle Very small * λ 0.22 is one of the 4 Wolfenstein parameters ( sin(θ Cabbibo )) λ-dependence of the CKM matrix elements : Géraldine Conti 5.

6 Bs J/Psi Phi decay and Bs-Bs oscillation B s J/ψφ decay : The tree diagram dominates, with a single weak phase : B s - B s oscillation : Before decaying into J/ψφ, B s mesons can also first oscillate into B s, with a B s mixing phase : The interference between the two possible paths to J/ψφ gives rise to the CP violating phase : Géraldine Conti 6.

7 How to measure -2betas? Géraldine Conti 7.

8 Measuring -2betas : Angular Analysis B s J/ψ(µ + µ - )φ(k + K - ) is a Pseudo-scalar to Vector-Vector decay : Spin : In the B s rest frame, the possible orbital angular momenta L for the final state are : L={0, 1, 2} (spin conservation). The CP eigenvalues of the final state are : CP(J/ψ) CP(φ) (-1) L = +1, -1, +1 The final state is an admixture of CP-even (L=0,2) and CP-odd (L=1) states. An angular analysis is required to disentangle statistically between the final states with the two different CP eigenvalues. Two bases can be considered : 1 ) Transversity Basis 2 ) Helicity Basis Géraldine Conti 8.

9 Right-handed Coordinate system : x axis : defined by the direction of the φ in the J/ψ rest frame y axis : defined by the plane of the K + K - system, with p y (K + )>0 z axis : defined by the normal to the plane of the K + K - system Transversity Basis Dighe et al., PLB 369, 144 (1996) [arxiv:hep-ph/ ] Transversity Angles : θ Tr = polar angle of the positive lepton (µ + ) in the J/ψ rest frame ϕ Tr = azimuthal angle of the positive lepton (µ + ) in the J/ψ rest frame ψ Tr = angle between the x axis and the K + in the φ rest frame Géraldine Conti 9.

10 Right-handed Coordinate system : Helicity Basis z axes : two are defined, one in each of the J/ψ and φ rest frames, with respect to the direction of these particles in the B s rest frame x axis : defined as to be the same in the two daughter rest frames. y axis : is opposite between the two frames (right-handed coord. systems) x χ b y x χ a z z y K. Abe et al., [arxiv:hep-ex/ v1], 2 March 2001 Helicity Angles : θ a = polar angle of the positive lepton (µ + ) in the J/ψ rest frame θ b = polar angle of the K + in the φ rest frame χ = χ a + χ b = azimuthal angle between the two planes Géraldine Conti 10.

11 Transversity vs Helicity Bases They are equivalent, but lead to different physical observables. Amplitudes in the transversity basis : A 0 and A correspond to final states with CP-even eigenvalues (L=0,2). A corresponds to final states with CP-odd eigenvalue (L=1). Direct access to CP-related quantities. Amplitudes in the helicity basis : H 0 corresponds to an helicity λ= 0 (equivalent to the transverse A 0 ) H +1 corresponds to an helicity λ=+1 H -1 corresponds to an helicity λ= -1 Easier to describe the angular acceptances (see later in Part 2). Géraldine Conti 11.

12 Transversity basis : Differential Decay Rates Dighe et al., PLB 369, 144 (1996) [arxiv:hep-ph/ ] θ, ψ, ϕ angles Helicity basis : θ a, θ b, χ angles K. Abe et al., [arxiv:hep-ex/ v1], 2 March 2001 Géraldine Conti 12.

13 Time Dependency Parameters : Weak Phase : 2β s = rad (Φ in the formulas above) 2 amplitudes : A 0 2 = 0.556, A 2 = strong phases : δ = rad, δ = 2.91 rad Average Width : Γ s = 0.5(Γ L +Γ H )=0.68 ps -1 Width Difference : ΔΓ s = Γ L -Γ H =0.049 ps -1 Mass Difference : Δm s = m H -m L =17.77 ps -1 * ( A 2 = 1 - A A 2 ) * * * * * Untagged Fit : Δm s terms disappear! * Babar, hep-ex/ (B d J/ψK*) * SM prediction * PDG 2008 Géraldine Conti 13.

14 Back to Reality Real Signal Pdf S 1 (θ,ψ,ϕ,t) Proper time resolution Double Gaussian Angular acceptance (& Proper Time acc.) Histogram or polynomial Mass model Triple Gaussian Signal Pdf = S 1 (θ,ψ,ϕ,t) S 2 (m) *Missing : angular resolution Géraldine Conti 14.

15 It s not the end of the Story P total = f S Signal Pdf + f Pr Prompt Background Pdf (B prompt /S=1.8) Proper time model Resolution Dirac Gaussian Mass model Exponential Angular model Flat Function Proper time model Resolution + (1-f S -f Pr ) Long-lived Background Pdf (B long /S=0.5) Mass model Angular model Exponential Double Exponential Gaussian Flat Function More studies required Géraldine Conti 15.

16 Fitting Unbinned log likelihood fit performed (N events), with : Cos(ψ) Cos(θ) ϕ t * Plots given only for signal Géraldine Conti 16.

17 World News: What s new about -2betas? Friday, August 21, 2009 Tevatron Combined Measurements of 2βs New measurements of 2βs have been made available by LPHE Seminar, 21st August 2009 Géraldine Conti 17.

18 Current constraints on 2betas (Tevatron) From the CDF experiment : From the D experiment : New Physics 2β s ~0.04 in the SM Possible contributions of New Physics. Where can New Physics hide? New particles could contribute to the B s -B s box diagram and potentially modify Φ J/ψϕ from the SM expectation. NP NP Géraldine Conti 18.

19 Place your bets : Why is LHCb the horse to bet on? LHCb CDF D Géraldine Conti 19.

20 LHCb Prospects for 2beta s Large Uncertainties from the Tevatron experiments : High statistics expected at LHCb : For one nominal year at LHCb (2fb -1 ), triggered and offline selected B s J/ψφ signal events are expected. Tagged Analysis With 2fb -1 of data (14TeV) : σ(-2β s ) ~ 0.03 < SM expectation value Géraldine Conti 20.

21 Family Picture : Bs J/Psi Phi Géraldine Conti 21.

22 Path to reach -2betas 3-angle tagged analysis I m working on these steps 1-angle tagged analysis Tagging Calibration and Propertime resolution 3-angle untagged analysis 1-angle untagged analysis Géraldine Conti 22.

23 Sensitivity Studies for the Untagged Fit Transversity Basis used, 3-angle analysis 1 ) Fixing the Strong and Weak Phases 2 ) SM scenario : -2betas ~ 0 3) NP scenario : -2betas ~ -0.6 Géraldine Conti 23.

24 1 ) Fixing the Strong and Weak Phases As a first step, a good check of the fit implementation (update of LHCb ) Strong phases Weak phase δ = rad ; δ = 2.91 rad ; -2β s = Errors on the free parameters (300 toys, same seeds used) : Low Statistics A 0 2 A 2 Γ s 2.0 fb fb fb ΔΓ s Fit Success 300 / / / 300 Géraldine Conti 24.

25 2 ) SM scenario : -2betas~0 Motivations : New param. to avoid the peak at -π a = cos(δ ) D0 collaboration, PRL 102, (2009) -2β s = 0 All terms containing the strong phase δ cancel out. Errors on the free parameters (300 toys, same seeds used) : A 0 2 A 2 Γ s ΔΓ s a Fit success 2 fb / fb / fb / 300 Remark : When the δ input value goes away from the -π value, the peak disappears. Géraldine Conti 25.

26 3) NP scenario : -2betas ~ -0.6 Ideal case : All parameters floating ( A 0 2, A 2, Γ s, ΔΓ s, δ, δ, -2β s ). Not possible with an untagged fit : δ and -2β s parameters not well calculated (see below) Input Value : δ = Input Value : δ = 2.91 δ σ(δ ) δ δ Input Value : -2β s = β s σ(-2β s ) Try to fix the strong phases Géraldine Conti 26.

27 3.1) Fixing the Strong Phases δ = 2.91 ; δ = β s σ(-2β s ) Asymmetric errors Errors on the free parameters (300 toys, same seeds used) : A 0 2 A 2 Γ s ΔΓ s -2β s Fit Success 2 fb / fb ? 300 / fb ? 300 / 300 Géraldine Conti 27.

28 3.2 ) Constraining the Strong Phases Motivations : From M. Gronau and J. L. Rosner, Flavor symmetry for strong phases and determination of β s, ΔΓ in B s J/ψφ, [hep-ph] arxiv: , Term added to the likelihood (Correlated Gaussian constraints) : Constraints on δ (µ δ =2.91, σ δ =0.2) and δ (µ δ =-2.93, σ δ =0.2) This leaves some freedom compared to the previous case. I m working on this at the moment Géraldine Conti 28.

29 Transversity vs Helicity Bases Transversity basis Helicity basis = φ H Motivations : From M. Gronau and J. L. Rosner, Flavor symmetry for strong phases and determination of β s, ΔΓ in B s J/ψφ, [hep-ph] arxiv: , Géraldine Conti 29.

30 Angular Acceptances Acceptance = Transversity basis Triggered & offline selected true events Theoretical distribution Helicity basis more Cos(θ T ) Cos(θ H ) less ϕ T φ H *Cos(ψ) acceptance not shown, because ψ is the same angle in the two bases. Géraldine Conti 30.

31 Helicity basis expressed in terms of transverse angles : θ a, θ b, χ angles expressed with θ, ψ, ϕ angles M. Gronau et al, arxiv: , This trick allows to use the time-dependent transverse amplitudes. Géraldine Conti 31.

32 Conclusions CDF and D measurements of -2β s very encouraging, but suffer from high statistical uncertainties. At 14TeV, LHCb could reach in one nominal year (2fb -1 of data) a statistical uncertainty on σ(-2β s )~0.03 (tagged analysis), which is the order of magnitude of the value predicted by the Standard Model. The untagged analysis does not need tagging calibration, it can be therefore performed on first data. For 2fb -1 of data, the statistical uncertainty on -2β s from the untagged fit in the case of New Physics (input value : -2β s ~-0.6) is σ(-2β s )~0.19. A one-angle (or only time-dependent) analysis has the advantages of requiring less statistics and being more robust for low statistics, with as drawback a worse sensitivity I have started studying them The Sensitivity study of the 3-angle analysis using the helicity angles, and its comparison with the one using the transversity angles, is also planned. Géraldine Conti 32.

33 How the Angles are calculated 1) Boost particles (J/ψ,φ,µ +,µ -,K +,K - ) from the lab to the B candidate rest frame. 2.a) Boost the µ + and µ - particles in the J/ψ rest frame. 2.b) Boost the K + and K - particles in the φ rest frame. Boosting the {µ +,µ - } system from the lab to the J/ψ rest frame Boosting first to the B rest frame and then to the J/ψ rest frame. 3) Calculate the angles. Géraldine Conti 33.

34 2 ) SM scenario : Weak Phase ~ 0-2β s = 0 All terms containing the strong phase δ cancel out. Free parameters : A 0 2, A 2, Γ s, ΔΓ s, δ In the δ distribution, ~35 (over 300) fit output values are ~-π. Input δ = 3.35 (3.35= π) Output δ = 3.36 Output δ = π Géraldine Conti 34.