Time Dependent Angular Analysis of B s J/Ψφ and B d J/ΨK* decays, and a Lifetime Difference in the B s System (A Short Summary)

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1 Time Depenent Angular Analyi of J/Ψφ an J/ΨK ecay, an a Lifetime Difference in the Sytem (A Short Summary) Colin Gay, Yale Univerity For the CDF II Collaboration Ke Li, C. Gay, M. Schmit (Yale) Kontantin Anikeev, C. Pau (MIT) Colin Gay, Yale Univerity

2 Overview We look for evience of two lifetime in ecay Examine two imilar ecay moe J / ψϕ J / ψ K 0 0, b, W c c, ψ ϕ ( K ) In the ytem, we fin (among other thing ) τ = 1.13 ± 0.0p τ L H =.38 ± 0.03p Γ = 0.46 ± 0.18 ± 0.01 p Γ = ± 0.01 Γ -1 Colin Gay, Yale Univerity

3 Unitarity Triangle Wolfentein parameterization of CKM Matrix 3 Vu Vu Vub 1 λ λ Aλ ( ρ iη) c c Vcb λ 1 λ Aλ 3 Vt Vt V tb Aλ (1 ρ iη ) Aλ 1 U = V V πlν, ρlν,... ππ, ρπ,... VV ub cb u VV c (0,0) γ (ρ,η) α VV V V VV λ λ tb t t t = = cb c Vc b Vt β (1,0) Dlν Dl Dπ,... Γ, ν,... Colin Gay, Yale Univerity

4 Ocillation b Secon orer weak iagram give non-zero matrix element In bai have a non-iagonal Hamiltonian V tb 0 0 uct,, uct,, V t V V W t b tb V t W + V tb b 0 W V t uct,, uct,, V tb W 0 H b M M1 i Γ Γ1 H = M1 M Γ1 Γ M = M ± Re( ( M Γ )) q p i HL, 1 1 Γ =Γ± Im( ( M Γ )) q p i HL, 1 1 Diagonalize an get two tate with eigenvalue i q i λ = M Γ± ( M1 Γ1 ) p i iβ q M, 1 Γ e 1 =± i = p M1 Γ1 1, SM Colin Gay, Yale Univerity

5 Eigentate Chooe phae convention CP = E.g. in the cae, where we expect no phae from CKM H = p + q = 1 1 ( + ) L = p q = ( ) CP-O CP-Even An initial particle or antiparticle i then 1 H L >= ( > + > ) 1 H L >= ( > > ) Kaon Expert Apology: =Strange, not Short L=Light, not Long H=Heavy Colin Gay, Yale Univerity

6 Calculating Matrix Element Γ m Γ Γ continuum b Off-hell tranition contribute to m 0 W V tb V t uct,, uct,, V t V tb W 0 Common moe b O λ 4 ( ) b 0 V t = V cb On-hell tranition contribute to V cb V c W V c c c W V cb Γ 0 Lifetime ifference meaure ame CKM element a ma ifference (ocillation frequency) b Colin Gay, Yale Univerity

7 Contraining Unitarity Triangle F m = m f η m F( m / M ) V V = 0.50 ± p G 1 6π t t W t tb Determine an annulu centere at (1,0), but large error f = 8 ± 3MeV ecay contant an ag (ρ,η) V λv t cb Vt = λv t parameter are almot common to => Goo to meaure ratio m m m = m f f f = ± f Vt V t Γ alo uffer from neeing f an an epen upon V,o cb m Γ goo too (1,0) Colin Gay, Yale Univerity

8 m Γ m Γ λ = m 1 b M1 mt SM Expectation 0.05 from CKM element uppree ince lifetime = on-hell tranition Γ / Γ 1% expecte mall in ytem ( ) m m, Γ Γ Jut a can till be izeable Γ / Γ = 0.1 ± 0.06 Dunietz, Fleicher, Nierte hep-ph/00119 (Intermeiate D tate, e.g., are Cabibbo-allowe) b 0 V c c D D + c V c 0 b Colin Gay, Yale Univerity

9 SM Expectation To firt approx Γ 3 m = π = m m b t (but ee eneke et al for full form NLO analyi, hep-ph/ ) In the following, we efine 1 1 Γ = ( Γ L +ΓH) τ Γ=Γ Γ L H o that 1 τ L 1 τ H Γ =Γ L =Γ+, Γ =Γ H =Γ Colin Gay, Yale Univerity

10 Analyi Sketch J / ψϕ J / ψ K 0 + J / ψ µ µ + ϕ K K 0 + K K π Angular momenta: P VV Total J of final tate = 0 Two pin-1 => J = 0, 1, Orbital L = 0, 1, (S,P,D wave) => Nee 3 amplitue (partial wave, helicity, or tranverity) S,D wave = Parity Even, (CP Even for ) P wave = Parity O, (CP O for ) 1 J / ψϕ J / ψϕ H ( ) = + = CP o L 1 ( ) = = CP even Dientangle ifferent L-component of ecay amplitue => iolate two tate Iolate P-o nicely Colin Gay, Yale Univerity

11 Tranverity Angle z Θ µ + Work in J/Ψ ret Frame KK plane efine (x,y) plane K + (K) efine +y irection y Θ, Φ polar & azimuthal angle of µ+ Ψ helicity angle of φ (Κ ) µ K ϕ Φ K + x Colin Gay, Yale Univerity

12 Decay Angular Ditribution A0 = longituinal pol. amplitue A, A = tranvere pol. amplitue Colin Gay, Yale Univerity

13 Fit Function Γ = CP even Γ L H = CP o UNTAGGED analyi Don t try to tell if initial tate i or Colin Gay, Yale Univerity

14 Decay Moe S J/ψφ J/ψ µ + µ - K + Compare the two imilar topologie φ K - J/ψ µ + µ - K + J/ ψ K K 0 π - <L>~1 mm S SV σ L ~30 µm <L>~1 mm SV σ L ~30 µm PV σ x ~ σ y ~0 µm PV σ x ~ σ y ~0 µm Colin Gay, Yale Univerity

15 Sample Selection ~60 pb-1 taken up to Feb 004 (tart of COT problem now fixe!!) Track Selection P T > 0.4 GeV Well-meaure in Central Tracker All 4 track have Silicon Detector hit J/Ψ Selection P T > 1.5 GeV Ma within 80 MeV of PDG J/Ψ trigger path (unbiae in lifetime) Momenta (P T ) K >.6 GeV, > 6.0 GeV φ >.0 GeV, > 6.0 GeV Ma winow φ : 6.5 MeV K : 50 MeV Cloet Kπ aignment to K choen (=wap~10 %) meon Vertex: Contrain J/Ψ ma Primary vertex from beamline Colin Gay, Yale Univerity

16 Detector Acceptance coθ ϕ coψ 40 M ecay generate flat in angular variable Shape how effect of cut an etector culpting Colin Gay, Yale Univerity

17 Ma an Lifetime Projection ( ) Γ Γ.01 i mall in SM =>Fit to 1 lifetime cτ = 46 ± 15 ± 4µ m 0 PDG = ± 4.µ m Colin Gay, Yale Univerity

18 + Lifetime N ~ 3300 CDF Run II: PDG: τ = ± p u τ = 1.671± p u -1-1 Colin Gay, Yale Univerity

19 Angular Projection ( ) Sieban ubtracte, acceptance correcte projection Full Likelihoo Fit i imultaneou in angular variable Can t ee correlation in thee projection Colin Gay, Yale Univerity

20 Amplitue v. aar/elle Colin Gay, Yale Univerity

21 Reult Perform two fit 1. Uncontraine: Fit ata a ecribe. Contraine: Invoke SM contraint (Expecte true to ~1%) Γ = ( ) Γ +Γ =Γ 1 H L Since et τ = 1.54 ± p 1 τ Lτ H p Γ = τ + τ = ± L H Colin Gay, Yale Univerity

22 Ma an Lifetime Projection () Uncontraine Fit τ τ L H = 1.05 ± 0.0p =.07 ± 0.03p Γ = 0.47 ± 0.01 p Γ = ± 0.01 Γ CP-o fraction ( τ H ) ~ % Colin Gay, Yale Univerity

23 Lifetime Projection ( ) Contraine Fit SM Preict Γ =Γ to ~1% : contrain in fit Remember, can t ee angular eparation of CP eigentate in projection τ = 1.13 ± 0.0p τ L H =.38 ± 0.03p Γ = 0.46 ± 0.18 ±.01 p Γ = ± 0.01 Γ -1 Colin Gay, Yale Univerity

24 Main Fitting reult Any two at a time Colin Gay, Yale Univerity

25 Sytematic Alignment From high-tatitic Lifetime Fit moel Proceure ia Cro-fee Detector Acceptance + an J/ ψ tuie Monte Carlo - ata matching K-π wap Non-reonant ecay ackgroun angular moel Unequal amount of Colin Gay, Yale Univerity

26 Sytematic Colin Gay, Yale Univerity

27 Cro Check: Fit ample i ~4 time a large a Fit ample with fit function Split ample into 4 ubample of ize ~ ample ize Note: Thi i not a meaurement of Γ / Γ Colin Gay, Yale Univerity

28 Cro Check: an CP o fraction CP-o fraction Cut (µm) >0 >150 >300 >450 Fitte (%) 0.1 ± ± ± ± 11.6 Preicte (%) CP-o fraction Cut (µm) Fitte (%) Fit to amplitue ONLY, uing ifferent minimum lifetime cut. Clear CP o fraction increae ugget relative large lifetime ifference on the two component Angular itribution i aying the ame thing a the lifetime information >0 >150 >300 > ± ± ± ± 4.9 Expect contant Colin Gay, Yale Univerity

29 Prob(0), Prob(SM) Performe 10,000 Toy MC fit to etimate the probability of a fluctuation Input Γ/Γ = 0 Uncontraine Fit 1/315 give Γ/Γ > 0.65 Contraine Fit 1/718 give Γ/Γ > 0.71 Input Γ/Γ = 0.1 (SM preiction) Uncontraine Fit 1/84 give Γ/Γ > 0.65 Contraine Fit 1/04 give Γ/Γ > 0.71 Note: Thee anwer the quetion: If true value = X, what i the chance to ee our meaurement Not the ame a aking: If true value=our meaurement, what i the chance of meauring X Colin Gay, Yale Univerity

30 Unitarity Triangle (bae on contraine fit, toy MC etimate + Gauian theory error) Colin Gay, Yale Univerity

31 Concluion We nee more ata! Combination of amplitue an lifetime analyi very powerful tool amplitue meaure with preciion J / ψ K comparable to aar/elle an agree well lifetime agree with PDG J / ψϕ ~00 how evience of two lifetime component Γ = 0 rule out at 1 in 700 o (with Γ =Γ contraint) Firt meaurement of lifetime ifference 1/00 o that SM central value (0.1) give our meaurement Γ Γ = 0.46 ± 0.18 ±.01 p = 0.71 ± ± 16 µ m Γ Colin Gay, Yale Univerity