Cracking the Unitarity Triangle

Transcription

1 Cracking the Unitarity Triangle Latest Results from BABAR Masahiro Morii Harvard University NEPPSR 2004, Craigville, MA

2 Unitarity Triangle Already seen it a few times this week VV + VV + VV = 0 ud ub cd cb td tb VV ud VV cd ub cb γ α VV td VV cd β tb cb How is this triangle measured experimentally? Using CP violation, of course, right? August 2004 M. Morii, Harvard 2

3 How to Violate CP Complex coupling constant (= weak phase) CKM matrix in the SM has 1 such phase Interference between 2 diagrams with different phases e.g., tree and penguin diagrams for B 0 K + π (Carlo s talk) With 2 diagrams, the size of the CPV is A CP = 2 A A sin φ sin δ 1 2 A CKM information in the weak phase φ A 1 / A 2 ratio, δ usually not calculable + A weak phase difference strong phase difference Observing CPV doesn t necessarily teach us us much about its its origin August 2004 M. Morii, Harvard 3

4 B 0 Mixing to the Rescue B 0 and B 0 mix, i.e., they turn into each other Weak phase = 2 *2 ( VV tb td ) arg = 2β Mass eigenstates are linear combinations B = p B + q B L H 0 0 B = p B q B 0 0 p + q = B H and B L differ in mass ( m), but not in lifetime ( Γ = 0) A little exercise in QM gives us Pure B 0 state after time t Pure B 0 state after time t b t d W + W mt q mt B B () t = e e cos B i sin B 2 p 2 d t b 0 im t Γt 0 0 p mt mt B B () t = e e i sin B + cos B q im t Γt 0 0 August 2004 M. Morii, Harvard 4

5 Mixing and Interference Pure B 0 state, after time t, decays into a CP eigenstate f CP Both B 0 or B 0 can decay into f CP Interference between mixed and unmixed paths Calculate the CP asymmetry Neat problem for undergrad. QM 0 B 0 B mixing 0 fcp H B = Af f CP 0 fcp H B = Af A () t = = C cos( mt) + S sin( mt) 0 0 N( B ( t) fcp ) N( B ( t) fcp ) CP 0 0 f f N( B ( t) fcp) + N( B ( t) fcp) 2 1 λ 2Imλ q A C S λ η p A f f f f = 2 f = 2 f = f 1+ λf 1+ λf f CP eigenvalue decay term mixing term August 2004 M. Morii, Harvard 5

6 Golden Modes Suppose the decay B 0 f CP goes through a single diagram A CP and A CP differ only by the sign of the weak phase Mixing term q/p is known to be almost pure phase Weak phase is 2β Things get nice and simple C 0, S η sin(2 β 2 φ) f f f q A λ = η = η e CP f f f pacp e 2iβ 2iφ A A CP CP = e = = + A () t = η sin(2β + 2 φ)sin( mt) CP For golden decays, the the amplitude S ff of of the the time-dependent CP CP asymmetry measures the the weak phase f 2iφ August 2004 M. Morii, Harvard 6

7 Measuring CP Violation A 0 0 N( B ( t) fcp ) N( B ( t) fcp ) CP 0 0 f f N( B ( t) fcp ) + N( B ( t) fcp ) () t = = C cos( mt) + S sin( mt) Experiment must do 3 things: Produce and detect B f CP events Typical branching fraction: Need a lot of lot of lot of lot of B s Separate B 0 from B 0 = Flavor tagging Use Υ 4S B 0 B 0 and tag one B Measure the decay time Measure the flight length βγct But B s are almost at rest in Υ 4S decays Solution: Asymmetric B Factory August 2004 M. Morii, Harvard 7

8 Three Ingredients 0 0 N( B ( t) fcp ) N( B ( t) fcp ) CP 0 0 f f N( B ( t) fcp ) + N( B ( t) fcp ) A () t = = C cos( mt) + S sin( mt) e Ingredient #1: Signal reconstruction Υ(4S) B reco B 0 e + B 0 µ + e µ - B tag π - Ingredient #2: Flavor tagging π + z ~ βγc t Ingredient #3: t determination August 2004 M. Morii, Harvard 8

9 Asymmetric B Factory Collides e + e at E CM = m(υ 4S ) but with E(e + ) E(e ) PEP-II: 9 GeV e vs. 3.1 GeV e + βγ = 0.56 The boost allows measurement of t Collides lots of them: 2.4A(e + ) 1.6A(e ) PEP-II luminosity /cm 2 /s = 9.2 Hz/nb That s >3x the design σ ( ee + bb) 1nb August 2004 M. Morii, Harvard 9

10 PEP-II Luminosity Run 4 Run 4 BABAR has accumulated 244 fb 1 of data Run 4 (Sep 03-Jul 04) was a phenomenal success August 2004 M. Morii, Harvard 10

11 Detector: BABAR Charged particle momentum with a drift chamber in a 1.5 T field Photon energy with a CsI(Tl) crystal calorimeter Muons detected after penetrating iron yoke Particle ID with a Cerenkov detector (DIRC in BABAR, aerogel in Belle) Precise vertex with a silicon strip detector August 2004 M. Morii, Harvard 11

12 Physics Results Will walk through the 3 angles and 2 sides VV ud VV cd ub cb γ α VV td VV cd β tb cb Almost everything is PRELIMINARY All ICHEP 2004 results from BABAR/Belle are found at BABAR results use data samples between 80 to 227M BB events August 2004 M. Morii, Harvard 12

13 Angle β from b ccs Golden mode of CP violation Tree diagram dominates No weak phase in decay A CP ( t) = η sin(2 β )sin( mt) f B 0 b d c J/ψ c s d K Clean measurement of angle β 0 cc pair can be J/ψ, ψ 2S, χ c1, or η c They are all CP = 1 sd pair can be K S (CP = +1), K L ( 1), or K *0 (mixed) Total 7730 candidates (78% purity) found in 227 M BB events August 2004 M. Morii, Harvard 13

14 Time-Dependent A CP Fit (cc) K S (CP odd) modes J/ψ K L (CP even) mode sin2β = ± (stat) ± (sys) 205 fb -1 August 2004 M. Morii, Harvard 14

15 Unitarity Triangle CKM fit without sin(2β) measurement CKM fit with sin(2β) measurement Precise measurement of sin2β agree with the SM expectation August 2004 M. Morii, Harvard 15

16 Angle β from b sss b sss decay dominated by the penguin diagram b sss b ccs In the SM, A = A = sin 2 New Physics may enter the loop A CP may not agree! φ K S is pure-penguin Small BF: η K S has tree diagrams too Suppressed by small V ub A CP affected by 0.01 to 0.1 Larger BF: CP CP β b d s φ, η s s d u u W η s d K K 0 0 August 2004 M. Morii, Harvard 16

17 B 0 φ K S B 0 φ K S candidates Time-dependent CP asymmetry B 0 tag 114 ± 12 events B 0 tag A CP S φ = 0.29 ± 0.31(stat) K S Combining φ K S and φ K L together, we get S φk fb -1 = 0.50 ± 0.25(stat) (syst), C = 0.00 ± 0.23(stat) ± 0.05(syst) August 2004 M. Morii, Harvard 17 φk

18 B 0 η'k S B 0 φ K S candidates Time-dependent CP asymmetry B 0 tag B 0 tag 205 fb -1 S C η ' K 0 η ' K 0 = 0.27 ± 0.14(stat) ± 0.03(syst) = 0.21± 0.10(stat) ± 0.03(syst) S is 3.0σ from sin2β from ccs A CP August 2004 M. Morii, Harvard 18

19 Status of Angle β BABAR Belle Measurements of CPV in s-penguin channels improving rapidly Average S < sin2β by 2.7σ (BABAR), 2.4σ (Belle) August 2004 M. Morii, Harvard 19

20 Angle α Consider b uud decay Example: B 0 π + π Decay involves V ub Weak phase γ CP asymmetry should measure b Tree W V ub d u u sin(2β + 2 γ) = sin 2α Not so fast There are penguins Penguin u We can measure sin2α only if the penguins are much smaller than the tree It s about 1/3 in B 0 π + π b V tb W g * V td u d Not so good Is there a better way? August 2004 M. Morii, Harvard 20

21 B 0 ρ + ρ B 0 ρ + ρ has much smaller penguin Known from small B(B 0 ρ 0 ρ 0 ) < (90%C.L.) B(B 0 ρ + ρ ) = (30 ±4 ±5) 10 6 ρ is vector meson η CP depends on the polarization Determine the polarization from decay-angle distribution θ 2 + π π 0 ρ B ρ + θ1 0 π 0 π Longitudinal fraction f L = 0.99 ± 0.03 Almost pure CP eigenstate Φ Longitudinal cos θ cos Transverse sin θ sin fb -1 θ θ August 2004 M. Morii, Harvard 21

22 B 0 ρ + ρ B 0 ρ + ρ candidates Time-dependent CP asymmetry B 0 tag 111 fb -1 B 0 tag S C Simultaneously fit for f L and S, C of the long. component = 0.42 ± 0.42( stat) ± 0.14( syst) long long = 0.17 ± 0.27( stat) ± 0.14( syst) A CP August 2004 M. Morii, Harvard 22

23 Status of Angle α A CP in B 0 ρ + ρ combined with BFs for B 0 ρ + ρ, B + ρ + ρ 0, and B 0 ρ 0 ρ 0 96 ± 10(stat) ± 4(syst) α = deg ± 11(penguin) A promising method for measuring α Agrees with the SM with a large error August 2004 M. Morii, Harvard 23

24 Angle γ Hard to find a good channel that measure γ A lot of not-so-good techniques are being studied Example: B D 0 K, D 0 K S π + π 2 decay diagrams Weak phases differ by γ If D 0 decays into a CP eigenstate, interference violates CP Back to the old question How do we know the relative amplitudes? How do we know the strong phase? August 2004 M. Morii, Harvard 24

25 B D 0 K, D 0 K S π + π Suppose we know the amplitude for D 0 K S π + π as a function of m + = m(k S π + ) and m = m(k S π ) Total decay amplitude should be M m m f m m r e f m m B K K i( δ γ) + (, + ) = (, + ) + B ( +, ) for Sππ M m m f m m r e f m m B K K i( δ+ γ) (, + ) = ( +, ) + B (, + ) for Sππ Experiments must Determine f(m,m + ) from fit to the D 0 K S π + π Dalitz plot Fit the decay rates for B + and B and extract r B, δ and γ August 2004 M. Morii, Harvard 25

26 Status of Angle γ Sensitivity is proportional to r B ~ V ub / V cb small No sensitivity for r B < 0.1 with current statistics Bayesian probability with flat prior gives r B < 0.18 (90% C.L.) Combining D 0 K and D 0 K * 194 fb -1 γ = (88 ± 41± 19 ± 10) Not a precision measurement Future: combine multiple methods to constrain r B better August 2004 M. Morii, Harvard 26

27 The Sides In addition to the angles, we measure the lengths of the sides VV ud VV cd ub cb γ α VV td VV cd β tb cb Uncertainties of the left and right sides are dominated by the smallest CKM elements V ub and V td August 2004 M. Morii, Harvard 27

28 Left Side V ub Rate of b ulv decay is proportional to V ub 2 Leptonic part is free from strong final-state interaction Γ( b u ν ) V 1 Γ ub 2 ( b c ν ) V 50 cb Must suppress 50 larger b clv decays Traditional approach: select events with large lepton energy Endpoint above kinematical limit for the b clv decay Only ~6% of b ulv events are accessible 2 b V ub b c b u u ν August 2004 M. Morii, Harvard 28 E l

29 Lepton Endpoint Select electrons in 2.0 < E l < 2.6 GeV Accurate subtraction of background is crucial! Data taken below the Υ 4S resonance for non-bb background Fit the E l spectrum with b ulv, B Dlv, B D * lv, B D ** lv, etc. to extract Data (continuum sub) MC for BB background Data (eff. corrected) MC B( B X eν ) = (1.73± 0.22 ± 0.33 ) 10 u exp theo Turn into 3 V ub exp theo HQET = (3.94 ± 0.25 ± 0.37 ± 0.19 ) fb -1 August 2004 M. Morii, Harvard 29

30 Hadronic Mass and q 2 E l is not the only kinematic variable available There are 3 independent variables Consider m X (hadronic mass) and q 2 (lepton-neutrino mass 2 ) ~70% of b ulv has m X < m D High efficiency + smaller extrapolation Cut on q 2 is less efficient (~20%) but smaller theoretical errors 2 E q ν m X August 2004 M. Morii, Harvard 30

31 Recoil Method Must reconstruct all decay products to measure m X or q 2 E l was much easier B mesons produced in pairs Reconstruct one B in any mode Rest of the event contains exactly one recoil B Find a lepton in the recoil B Remaining part must be X in B Xlv Calculate m X and q 2 For m X < 1.7 GeV and q 2 > 8 (GeV) 2 BB ( Xlν ) = (0.88 ± 0.14 ± 0.13 ± 0.02 ) 10 u stat exp syst (m,a) syst V ub stat exp syst theo syst lepton = (4.92 ± 0.39 ± 0.36 ± 0.46 ) 10 Fully reconstructed B hadrons August 2004 M. Morii, Harvard 31 b v 3 3 X 80 fb -1

32 Status of V ub Different approaches for V ub pursued to tackle theoretical uncertainty Largest error from the shape function Determined by CLEO measurement of photon energy spectrum in b sγ Future improvement from New techniques More data helps Theoretical progress Better measurement of b sγ 80 fb -1 August 2004 M. Morii, Harvard 32

33 Right Side V td B 0 mixing involves virtual top exchange Once B s mixing rate is measured B 0 mixing rate B s mixing rate What can we do besides waiting for Tevatron? Radiative penguin decays b s/d γ Expect Γ( b dγ ) V Γ( b sγ ) V m m d s 2 td 2 ts V B( B ργ) B( B K γ) = V * + td 6 2 V V td ts 2 2 ts 2 b d W + W - Reachable at B Factories d b August 2004 M. Morii, Harvard 33

34 B ρ γ Main background from non-bb events Jet-like geometry Use event shape variables Neural Net B K * γ is 40 larger Particle ID with the Cherenkov detector Combine ρ + γ, ρ 0 γ and ωγ, assuming Γ = Γ = Γ ( B ρ γ) 2 ( B ρ γ) 2 ( B ωγ) B( B ργ) = (0.6± 0.3± 0.1) < (90%C.L.) 191 fb -1 A little smaller than expected by the SM August 2004 M. Morii, Harvard 34

35 Status of V td B(B ργ) limits the length of the right side Bound comparable to that from the mixing Theory errors from ρ vs. K * form factor difference and weak annihilation Observing B ργ with additional statistics will be very interesting Without theory errors 95% C.L. limit including theory errors August 2004 M. Morii, Harvard 35

36 Summary The unitarity triangle is under attack from all directions Huge data sample allow more and more measurements In addition to sin2β, many measurements are reaching interesting precisions CPV in penguin decays, B ρρ, B ulv, B ργ, Will we crack the unitarity triangle? August 2004 M. Morii, Harvard 36