Lecture 2: CPV in B system

Transcription

1 1/39 Lecture 2: CPV in B system CTEQ Summer School Rhodes, Greece - July 2006 Franco Bedeschi, Istituto Nazionale di Fisica Nucleare Pisa, Italy

2 2/39 Outline Reminder CKM matrix Basic theory CP violation in B system β, α, γ, β s (χ) Current status of B-factory measurements Estimate of Hadron Collider experimental reach Global picture and implications on new physics

3 3/39 b-decays: CKM matrix V ub / V cb is related to fraction of b-hadron decays with no charm in final state Hard to measure at hadron colliders. Done at CLEO, LEP, B-factories V td / V ts is related to mixing (see later) Hadron colliders are very competitive and are the only place where V ts can be measured directly The angles of the triangle are related to CP violation Hadron colliders and B-factories complement each other in these difficult measurements λ V cb (ρ+iη) Charmless V ub * α η V td Mixing λ V ts (1-ρ-iη) γ ρ 1 Angles: CP violation β

4 4/39 CP violation classification CP transformation flips sign of weak phases and leaves strong phases unchanged in amplitudes CP violation in decay A(Bf) A(B f) CP violation in mixing (already discussed) N(BB) N(BB) CP violation in the interference between a decay with mixing and one without mixing

5 5/39 CP violation in B decays CPV through interference of decay amplitudes Γ(B f) Γ(B f) +ϕ ϕ δ ϕ δ ϕ δ Γ = + ϕ δ Γ = + Γ Γ ϕ δ

6 6/39 CP Violation in the B System CPV through interference between mixing and decay amplitudes Directly related to CKM angles for single decay amplitude ϕ = β ϕ

7 7/39 Mixing mediated CPV (1) CPV from interference of unmixed and mixed decays to a common final state A(Bf) A(Bf) Definitions: Use again equations of time evolution of B states: B(0) f B(0) f

8 8/39 Mixing mediated CPV (2) A CP = asymmetry between two processes -S C -A Simpler when A contains a single weak phase φ D Phase of V td (V ts )

9 9/39 Bd: CKM angle β Select CP eigenstates with no weak phases in decay A CP = sin(2β) sin( mt), λ = 1 Pure tree: B d ψ K 0 S b B d W - c c s d ψ K 0 S BR ~ 10-3 Pure penguin: B d φ K 0 S b u, c, t B d W - s s s d φ K 0 S BR ~ 10-5

10 10/39 CKM angle β Current results dominated by B- factories Tevatron experiments: comparable statistics but smaller tagging power Experimental considerations: Very similar to mixing analysis Very important dilution calibration We measure D sin(2β) Expected accuracy from time dependent fit (x d = m d τ d ): ~ 1 ~ 1.7 ~ 1

11 sin 2β = ± ± CKM angle β x10 6 BB 227x10 6 BB sin 2β = ± ± /39 Events / 4 MeV/c 2000 a) B J/ψK S 0 B ψ(2s)k S B χ c1 K S 0 B η c K S Events / 2 MeV b) 0 B J/ψK L (GeV/c ) m ES E (MeV) 10 2 sin 2β = ± ± 0.023

12 12/39 CKM angle β Pure penguins sensitive to new physics in loops Interesting to compare pure tree with pure penguins BaBar/Belle find Penguin systematically lower then Tree 2.8 σ effect more statistics will tell Belle Naïve avg

13 13/39 Sin 2β at Tevatron CDF Run 1 result is based on: ~ 400 B 0 J/ψ K 0 S All available taggers: Opposite side: lepton, Jet-charge Same side: pion charge correlation Result: sin(2β) = ~ 400 Run II 1 fb -1 B ψ K 0 S Expect σ(sin(2β)) = 0.13 for 1 fb for 5 fb -1 Asymmetry Vs. lifetime

14 14/39 Model independent limits on new physics M 12 = M 12 SM +M 12 BSM = M 12 SM (1+he iσ ) m = 2 M 12, arg(m 12 ) = β Combined measurement of mixing frequency and mixing phase provides strong model independent limit on new physics contributions 95% CL 68% CL 10% CL Not excluded

15 15/39 Limits on new physics (2) Status much less constrained in the case of the Bs Need to measure the phase β s. even with a large error! Feasible only at hadron colliders Before CDF result With CDF Bs mixing data

16 Sin 2β s expectations 16/39 Use CP asymmetry in B s ψφ 80% CP-even Reduced asymmetry S ψφ = 60% sin 2β s Could reach σ(a) ~ 0.15 ~ early LHC-B sigma S(Psi ph SVT 0.1 triggers 672 events in 1 fb -1 0 J/psi+Psi' J/ψ triggers PSI + TTT 986 events in 1 fb Int. Lumi (fb-1) J/psi phi ed2=0.07

17 17/39 Sin 2α α=π-β-γ (sin(α) = sin(β+γ)) Need decay with weak phase γ B d π + π -, ρ + ρ - but: serious penguin contamination at same order in λ S, C 0 Unfolding penguins requires complex isospin analysis involving also other decay modes: BR and A CP of B d π 0 π 0, B π π 0 Done at B-factories At the Tevatron can measure both B d π + π - and B s K + K - then assume SU(3) symmetry B d B d d b d W + ud u TreeTree b W + d u,c,t u u Penguin π - π + π - π +

18 18/39 Sin 2α at B-factories B d π + π - asymmetries at 0.15 errors Some discrepancy between BaBar and Belle B d ρ + ρ - is lucky: Small penguin contribution and > 95% longitudinal polarization Added Dalitz analysis of B d ρ + π - B d π + π -

19 19/39 Bh + h - at Tevatron Large B d π + π - signals Can measure A ππ, S ππ with accuracy comparable to B factories isospin analysis impossible, but measurement can be combined to B-factories to add accuracy to asymmetries Can measure direct CP violation in B d Κ + π - decays Checks B-factories Can measure also B s Κ + Κ - and the associate asymmetries Allows determination of γ under the assumption of SU(3) symmetry

20 20/39 Bh + h - at Tevatron Produce both B d and B s ππ, Kπ, KK Mass peaks overlap Statistical separation achieved with combination of kinematics and PID 6200 events 50% more B s π+π than BaBar

21 21/39 Direct CP in B d Κ + π Interference between penguin and tree diagrams First observed at B-factories: A CP BaBar = A CP Belle = Current Tevatron result with 360 pb -1 A CP CDF = Small systematics from calibration with huge sample of DKπ Expect resolution at B-factories level with 1 fb -1 already on tape 1% CDF (360 pb -1 ) CDF blind (1 fb -1 ) Babar 200fb -1 Belle 350fb -1 L int

22 22/39 (S ππ, A ππ ), (S ΚΚ, A ΚΚ ) expectations Expected CP asymmetry resolutions in Bdππ and Bs KK Can reach resolution at 0.2 level comparable to B-factories for ππ Will measure also Bs asymmetry with comparable resolution B-factories can t do it! Can use to measure γ 85 fs seen Scaling from current yields

23 23/39 Measuring γ with Bhh Interpretation of asymmetries (Fleischer, PLB459, 1999) Parameterize in terms of CKM phase γ, β β from ψk 0 S d e iθ = hadronic Penguin/Tree Assume SU(3) symmetry d e iθ same for B d ππ, B s KK (~ 20%) A dir (ππ) = -2d sinθ sinγ + O(d 2 ) A dir (KK) = 2λ 2 sinθ sinγ + O((λ 2 /d) 2 ) d(1-λ 2 ) A mix (KK)= 2λ 2 cosθ sinγ + O((λ 2 /d) 2 ) d(1-λ 2 ) - A mix (ππ)= sin2(β+γ)+2d cosθ x (cosγ sin2(β+γ)-sin(2β+γ)+ O(d 2 ) B d B d b d b W + d u,c,t u u d W + ud u Tree Tree d ~ 0.3 θ???? Penguin π - π + π + π -

24 24/39 Can solve for d, θ and γ Measuring γ with Bhh Worse case when sin θ ~ 0 assumed Fit result when γ = 60, β = 22.2, θ = 0 σ γ ~ 10 ± 3 degrees Chisquare chisquare curve for gamma with theta= Fit depends not just on sin gamma 20% SU(3) breaking effects Gamma in degrees

25 25/39 Measurements of γ Methods for γ determination at B-factories GLW, ADS, Dalitz Recent development at Tevatron and perspectives

26 Determining γ in B ± D (*)0 K (*)± 26/39 Favored (T) Color suppressed (C) A 1 λ 3 A 2 λ 3 (ρ 2 +η 2 ) e -i γ e iδ Interference if same D 0 and D 0 final states: A tot =A 1 +A 2 Interference if same D 0 and D 0 final states: A tot =A 1 +A 2 Theoretically clean (no penguins) 3 parameters r B, γ and δ 0.36±0.04 F CS [0.2,0.6] (0.3 for B 0 D 0 π 0 ) r B

27 The GLW Method & observables 27/39 Clean but statistically limited: Bf(B - D 0 K - ) Bf(D 0 cp) 10-6 Asymmetry B-/B+ for CP=+1/-1 Ratio of Bf for CP/non CP A CP A CP- $$ γ=60 o r B =0.1 8 fold ambiguity on γ! " ## R CP R CP+ γ=60 o γ=30 o γ=30 o! A CP+ γ=90 o Weak sensitivity to r B γ=90 o R CP- Strong phase δ (radians) Strong phase δ (radians)

28 R CP and A CP World Averages 28/39 CP- CP- CP+ CP- CP+ CP- CP+ D 0 K* D* 0 K D 0 K CP+ CP- CP+ CP- CP+ GLW measurements alonedo do not not constraintγ/φ γ/φ 3. on γ and r 3. Information on γ and r B B from from combinationwith other methods.

29 Dalitz Analysis of B - D (*)0 [K S π + π ]K - 29/39 A.Giri, Y.Grossman,A.Soffer & J.Zupan, Phys.Rev. D68, (2003) Calibrate with large sample of D0 A 1 = A(B - D 0 K - ) A 2 = r B e -iγ e iδ A(B - D 0 K - ) A D (m 2 Ksπ-,m2 Ksπ+ ) A D (m 2 Ksπ+,m2 Ksπ- ) Get r B, γ, δ from simultaneous fit of the K s π + π - dalitz plot density of B - and B + data dσ(m-,m+) A D (m-,m+) 2 + r B2 A D (m+,m-) 2 B - B + m- m+ and γ+γ Need precise knowledge of A D (m -2,m +2 ) Sensitivity to γ is here! +δ) ] + 2 r B Re [ A D (m-,m+)a D *(m+,m-)e i ( γ+δ Some model uncertainty in the γ/φ 3 measurement γ/φ

30 Belle results γ/φ 3 : Dalitz 30/39 3 =! "#$% 2 m 0 D 2 m 0 D Obtain from tagged D 0 (D *+ D 0 π + ) Continuum sample 2 m + 2 m + m + =m(k s π + ), m =m(k s π ) WA: CKM-Fitter γ=

31 31/39 γ summary from B-factories WA: γ =

32 32/39 GLW γ prospects at Tevatron Same γ searches possible at Tevatron No tagging so statistics pays off in full Work in progress: Show status of GLW analysis

33 33/39 GLW γ at Tevatron (1) First step achieved with 360 pb -1 Measured R = BR(B + D 0 flav K + ) BR(B + D 0 flav + ) = (stat) (sys) Use combination of PID and kinematics as in Bhh case

34 34/39 GLW γ at Tevatron (2) Next step iterate procedure on CP D meson decays For same D K statistics obtain same resolution as Belle Yield comparison: Belle 500fb -1 : expect 36k D 0 π+ CDF 1 fb -1 : 26k D 0 π+ 6 fb -1 : 150k D 0 π+ Tevatron could provide significant improvement of measurement of γ with this method

35 35/39 Global fits Can test consistency of all measurements performing global fits of CKM parameters using all available measurements Two major efforts on the market CKM fitter UT fitter

36 36/39 CKM fitter EPS05+CDF Global fit results UT fit 2006 Excellent consistency with Standard Model!!!

37 Look for hints of discrepancies Partial measurement comparisons: angles vs. sides 37/39 () +",- "ρ+"-. " Sides & ' () *+",-. "-/ ρ+".0, "/ Angles

38 Partial measurement comparisons: loop vs. tree 38/39 Tree Loop

39 39/39 Conclusions CKM is established as the primary source of CP violation On average the SM describes well all present measurements New physics in b d transitions is highly constrained b s transitions have become major new focus Tree/penguin discrepancies in sin(2β) Improved accuracy required to resolve this Also α and γ need better resolution Measurements at hadron colliders can be competitive and complementary (B s ) to B-factories Very interesting to see evolution with full B-factories and Tevatron statistics toward the end of the decade New data from LHC-B with LHC startup could continue and extend the Tevatron program Future new facilities like Super B factories could continue the work started by BaBar and Belle