B Physics Beyond CP Violation

Transcription

1 B Physics Beyond CP Violation Semileptonic B Decays Masahiro Morii Harvard University MIT LNS Colloquium, 2004

2 Outline Introduction: Why semileptonic B decays? CP violation Unitarity Triangle V ub vs. sin2β V ub from inclusive b ulv decays Measurements: lepton energy, hadron mass, lepton-neutrino mass Theoretical challenge: Shape function V ub from exclusive b ulv decays Measurements: B πlv Theoretical challenge: Form factors Summary LNS Colloquium 2004 M. Morii, Harvard 2

3 History of CP Violation (1) 1964: Cronin & Fitch discover CPV K L (thought to be CP = 1) decayed into π + π (CP = +1) 1973: Kobayashi-Maskawa mechanism proposed g Vud Vus Vub dl u c t µ L L L Vcd Vcs V s W + L = γ cb L 2 hc µ + Vtd Vts V tb b L Unitary matrix V CKM translates mass and weak basis 3 real parameters + 1 complex phase ( ).. The only source of CPV in the Minimal SM 1974: charm quark, 1975: τ lepton, 1977: bottom quark LNS Colloquium 2004 M. Morii, Harvard 3

4 History of CP Violation (2) 1970s 90s: CPV in K 0 -K 0 mixing (ε) studied in great details ~1999: Direct CPV in K 0 decays (ε') confirmed KM mechanism most likely explanation 1999: BABAR and Belle start taking data 2001: CPV in B 0 decays (sin2β) measured Agrees with expectation from the KM mechanism Kobayashi-Maskawa mechanism is likely the dominant source of the CP violation observed in the lab Is it the sole source? LNS Colloquium 2004 M. Morii, Harvard 4

5 Quantitative Test CKM matrix has 4 free parameters V 1 λ Aλ ( ρ iη) CKM = λ 1 2 λ Aλ + O( λ ) 3 2 Aλ ( 1 ρ iη) Aλ All but the two smallest elements V ub and V td are well measured In order to test the KM-only hypothesis: λ Interpret measurements assuming the minimal SM is correct Either CPV or non-cpv as long as they are sensitive to V ub and V td Turn them into constraints on (ρ, η) and compare It would be nice to express this graphically 1 Wolfenstein parameterization LNS Colloquium 2004 M. Morii, Harvard 5

6 Unitarity Triangle V CKM is unitary VV + VV + VV = 0 ud ub cd cb td tb This is neatly represented by the familiar Unitarity Triangle VV ud VV cd ub cb η γ ρ V V = 1 CKM CKM α β VV td VV cd tb cb 1 VV td α = arg VudV VcdV β = arg VV td VudV γ = arg VcdV * tb * ub * cb * tb * ub * cb Each measurement constrains the apex position (ρ, η) The only complex phases of O(1) in the minimal SM LNS Colloquium 2004 M. Morii, Harvard 6

7 Consistency Test Compare the measurements (contours) on the (ρ, η) plane If the SM is the whole story, they must all overlap The tells us this is true as of today Still large enough for New Physics to hide Precision of sin2β outstripped the other measurements Must improve the others to make more stringent test LNS Colloquium 2004 M. Morii, Harvard 7

8 Next Step: V ub Zoom in to see the overlap of the other contours It s obvious: we must make the green ring thinner Left side of the Triangle is VV VV ud ub cd cb Uncertainty dominated by ~15% on V ub Measurement of V ub is complementary to sin2β Goal: Accurate determination of both V ub and sin2β LNS Colloquium 2004 M. Morii, Harvard 8

9 Measuring V ub Best probe: semileptonic b u decay b V ub The problem: b clv decay u ν Tree level decoupled from hadronic effects 2 GF Γ( b u ν ) = V 2 ub m 192π 2 5 b Γ( b u ν ) V 1 Γ ub 2 ( b c ν ) V 50 cb 2 How can we suppress 50 larger background? LNS Colloquium 2004 M. Morii, Harvard 9

10 Detecting b ulv Inclusive: Use m u << m c difference in kinematics Maximum lepton energy 2.64 vs GeV First observations (CLEO, ARGUS, 1990) used this technique Only 6% of signal accessible How accurately do we know this fraction? Exclusive: Reconstruct final-state hadrons B πlv, B ρlv, B ωlv, B ηlv, Example: the rate for B πlv is dγ( B π ν) dq G 24π 2 F = ub π + V p f ( q ) How accurately do we know the FFs? 2 b c b u Form Factor (3 FFs for vector mesons) E LNS Colloquium 2004 M. Morii, Harvard 10

11 Inclusive b ulv There are 3 independent variables in B Xlv Take E l, q 2 (lepton-neutrino mass 2 ), and m X (hadronic mass) 2 E q ν 6% 20% m X 70% Technique Efficiency Theoretical Error E l Straightforward Low Large q 2 Complicated Moderate Moderate m X Complicated High Large Where does it come from? LNS Colloquium 2004 M. Morii, Harvard 11

12 Theoretical Issues Tree level rate must be corrected for QCD Operator Product Expansion gives us the inclusive rate Expansion in α s (m b ) (perturbative) and 1/m b (non-perturbative) G Γ( B X ν ) = u 2 F V 2 5 ub mb s 1 O 3 192π b B α 9λ2 λ π 2mb V ub u X u ν known to O(α s2 ) Suppressed by 1/m b 2 Main uncertainty (±10%) from m b5 ±5% on V ub But we need the accessible fraction (e.g., E l > 2.3 GeV) of the rate LNS Colloquium 2004 M. Morii, Harvard 12

13 Shape Function OPE doesn t work everywhere in the phase space OK once integrated Doesn t converge, e.g., near the E l end point Resumming turns non-perturb. terms into a Shape Function b quark Fermi motion parallel to the u quark velocity Smears the quark-level distribution observed spectra Rough features (mean, r.m.s.) are known ( ) f k + Details, especially the tail, are unknown 0 Λ= M m B b k + LNS Colloquium 2004 M. Morii, Harvard 13

14 Shape Function What to Do? Measure: Same SF affects (to the first order) b sγ decays Measure E γ spectrum in b sγ Caveat: whole E γ spectrum is needed Only E γ > 1.8 GeV has been measured Background overwhelms lower energies Compromise: assume functional forms of f(k + ) Example: Extract f(k + ) Predict E l spectrum in b ulv a (1 + a) x k+ ( ) (1 ) ; Fit b sγ spectrum to determine the parameters Try different functions to assess the systematics parameters f k+ = N x e x= Λ (Λ and a) to fit E γ LNS Colloquium 2004 M. Morii, Harvard 14

15 CLEO hep-ex/ SF from b sγ Belle hep-ex/ CLEO and Belle has measured the b sγ spectrum Belle f ( k + ) E γ Fit 3 models tried BABAR result on the way Statistical errors dominate the uncertainty around the peak Model dependence important in the tail LNS Colloquium 2004 M. Morii, Harvard 15

16 Predicting b ulv Spectra OPE + SF can predict triple-differential rate De Fazio, Neubert (JHEP 9906:017) 3 d Γ B Xu 2 de dmxdq ( ν ) Every experiment uses DFN for simulating b ulv signal 2 E q ν 6% 20% m X 70% Unreliable in the SF region where OPE converges poorly Small m X and small q 2 X is jet-like The right tool: Soft Collinear Effective Theory LNS Colloquium 2004 M. Morii, Harvard 16

17 Soft Collinear Effective Theory Developed since 2001 by Bauer, Fleming, Luke, Pirjol, Stewart PRD63:014006, PRD63:114020, PRD65: Applied to b ulv in the SF region by several groups Bauer, Manohar (PRD70:034024) Bosch, Lange, Neubert, Paz (NPB699:335) Lee, Stewart (hep-ph/ ) Caveat: Works only in the SF region We tried implementing an event generator with limited success Wanted: Theoretically-sound b ulv Monte Carlo generator THAT WORKS LNS Colloquium 2004 M. Morii, Harvard 17

18 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 light-flavor background Fit the E l spectrum with b ulv, B Dlv, B D * lv, B D ** lv, etc. to measure BABAR E l (GeV) B (10-4 ) 4.85 ± 0.29 stat ±0.53 sys BABAR hep-ex/ Data (continuum sub) MC for BB background CLEO PRL 88: BELLE-CONF-0325 Data (eff. corrected) MC CLEO ± 0.15 stat ±0.35 sys Belle ± 0.11 stat ±0.10 sys LNS Colloquium 2004 M. Morii, Harvard 18

19 Lepton Endpoint BABAR hep-ex/ CLEO PRL 88: BELLE-CONF-0325 Translate B into V ub using the SF parameters from Belle E l (GeV) B (10-4 ) V ub (10-3 ) BABAR ± 0.29 stat ±0.53 sys 4.40 ± 0.15 exp ±0.44 th CLEO ± 0.15 exp ±0.35 sys 4.69 ± 0.23 exp ±0.63 th Belle ± 0.11 exp ±0.10 sys 4.46 ± 0.23 exp ±0.61 th Recalculated by the Heavy Flavor Averaging Group Lower E l cut-off reduces theoretical uncertainty to ~10% But theorists raise possibilities of additional uncertainties Sub-leading SFs, 4-quark operators, weak annihilation LNS Colloquium 2004 M. Morii, Harvard 19

20 Measuring m X and q 2 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 v lepton Fully reconstructed B hadrons X LNS Colloquium 2004 M. Morii, Harvard 20

21 Recoil B Sample Reconstruct B mesons in 0 Y = nπ + n K + n K + n π + ± ± S 4 n 1 n2 6 + < n 3 < 3 n 4 < 3 ~1000 channels used Efficiency ~0.2%/B Yield and purity from m B fit 0 (*) B D Y + Recoil B is a clean and unbiased sample of B mesons Charge and 4-momentum known Ideal for measuring branching fractions + (*)0 + B D Y LNS Colloquium 2004 M. Morii, Harvard 21

22 Recoil B Xlv Find an l = e ± or µ ± (p l > 1GeV) in recoil B and require Total event charge = 0 If it s a B ±, Q l = Q B Missing 4-momentum consistent with a massless neutrino B hadrons 2-C kinematical fit to determine p X 4-momentum conservation m v = 0, m B = m B m X resolution ~ 350 MeV Sample is mostly b clv at this stage v lepton X LNS Colloquium 2004 M. Morii, Harvard 22

23 Charm Suppression Suppress b clv by vetoing against D (*) decays D decays usually produce at least one kaon Reject events with K ± and K S B 0 D *+ ( D 0 π + )l v has peculiar kinematics π + almost at rest w.r.t. D *+ D *+ momentum can be estimated from π + alone 2 2 Calculate m = ( p for all π + B p ν * p ) D Reject events consistent with m v = 0 Vetoed events are depleted in b ulv Used to validate simulation of background distributions We ve got (m X, q 2 ) distribution of a signal-enriched sample LNS Colloquium 2004 M. Morii, Harvard 23

24 Extracting b ulv Signal Fit m X to extract B(B X u lv) Best variable for charm rejection Best statistical error Strong shape-function dependence Fit m X vs. q 2 to extract B(B X u lv) Restrict to, e.g., m X < 1.7 GeV, q 2 > 8 GeV 2 Reduced shape-function dependence Unfold detector effects to get true m X spectrum Limited statistical power Potential for constraining shape function LNS Colloquium 2004 M. Morii, Harvard 24

25 BABAR 80fb -1 hep-ex/ Fitting m X BABAR BABAR Simple fit in m X shows clear b ulv signal Signal modeled by DFN with Belle SF Translate to V ub V ub stat sys theo = (5.22 ± 0.30 ± 0.31 ± 0.43 ) 10 stat syst theo B( B X lν ) = (2.81± 0.32 ± 0.31 ) 10 u Theoretical error ~8%, but strong dependence on the shape function V ub moves by if CLEO SF parameters are used 3 3 LNS Colloquium 2004 M. Morii, Harvard 25

26 BABAR 80fb -1 hep-ex/ Unfolding m X Measured m X spectrum Background subtraction Detector unfolding Unfold detector efficiency and resolution true m X spectrum NB: error bars are correlated Matches simulation with different shape functions (curves) Not enough statistics to extract shape function parameters BABAR has 3 more data LNS Colloquium 2004 M. Morii, Harvard 26

27 BABAR 80fb -1 hep-ex/ Fitting m X vs. q 2 BABAR Split b ulv signal into {m X < 1.7, q 2 > 8} and elsewhere 2-D fit to measure B in the former region yields B < > = 2 ( mx 1.7, q 8) (0.90 ± stat ± syst 0.02th ) 10 3 LNS Colloquium 2004 M. Morii, Harvard 27

28 Belle 140fb -1 hep-ex/ Fitting m X vs. q 2 Belle Belle has a nearly identical analysis B( m < 1.7, q > 8) = (0.99 ± 0.15 ± 0.18 ± 0.08 ) 10 X 2 3 stat syst th LNS Colloquium 2004 M. Morii, Harvard 28

29 Turning B into V ub BABAR 80fb -1 hep-ex/ Belle 140fb -1 hep-ex/ From Bauer, Ligeti, Luke (hep-ph/ ) V ub π = τ Gm 2 5 B F b B G BABAR Belle Theoretical error ~10% G = ± using Belle SF V ub (10-3 ) 4.98 ± 0.40 stat ±0.39 syst ±0.47 theo 5.54 ± 0.42 stat ±0.50 syst ±0.54 theo BABAR result moves by with CLEO SF params BABAR result moves by with DFN Results are more stable than the m X fit LNS Colloquium 2004 M. Morii, Harvard 29

30 Status of Inclusive V ub E l endpoint m X fit m X vs. q 2 LNS Colloquium 2004 M. Morii, Harvard 30

31 Exclusive b ulv Measure specific final states, e.g., B πlv Good signal-to-background ratio Branching fraction in O(10-4 ) Statistics limited So far B πlv and ρlv have been measured Also seen:b(b ωlv) = (1.3±0.5) 10 4 [Belle hep-ex/ ] B(B ηlv) = (0.84±0.36) 10 4 [CLEO PRD68:072003] Need Form Factors to extract V ub dγ( B π ν) dq G 24π 2 F = ub π + V p f ( q ) 2 LNS Colloquium 2004 M. Morii, Harvard 31

32 Form Factors Form Factors are calculated using: Lattice QCD (q 2 > 16 GeV 2 ) Existing calculations are quenched ~15% uncertainty Light Cone Sum Rules (q 2 < 16 GeV 2 ) Assumes local quark-hadron duality ~10% uncertainty Other approaches All of them have uncontrolled uncertainties LQCD and LCSR valid in different q 2 ranges No crosscheck Unquenched LQCD starts to appear Preliminary B πlv FF from FNAL+MILC (hep-lat/ ), HPQCD (hep-lat/ ) Current technique cannot do B ρlv LNS Colloquium 2004 M. Morii, Harvard 32

33 Measuring B πlv Concentrate on B πlv with q 2 binning CLEO [PRD 68:072003] Reconstruct πlv using missing 4-momentum as the neutrino Belle [hep-ex/ ] Tag B D (*) lv and look at m X distribution LNS Colloquium 2004 M. Morii, Harvard 33

34 CLEO PRD 68: B πlv CLEO Missing 4-momentum = neutrino CLEO has a better solid-angle coverage than BABAR/Belle Reconstruct B πlv and calculate m B and E = E B E beam /2 Clear signal over background Red: ρlv, ωlv, ηlv Yellow: other X u lv Green: Black: continuum (udsc) b clv LNS Colloquium 2004 M. Morii, Harvard 34

35 Belle hep-ex/ B πlv Belle q 2 < 8 8 < q ρlv 2 < < q 2 πlv other X u lv Tag B D (*) lv and look at the recoil B Similar to inclusive V ub measurements on recoil B D (*) lv tag is less pure, but more efficient Hadronic mass distribution shows πlv and ρlv signals LNS Colloquium 2004 M. Morii, Harvard 35

36 CLEO PRD 68: Γ(B πlv) Belle hep-ex/ CLEO Belle Small model-dependence due to efficiency estimation B(B πlv)[10 4 ] B(q 2 > 16 GeV 2 )[10 4 ] CLEO 1.33 ± 0.18 ± ± 0.09 ± 0.05 Belle 1.76 ± 0.28 ± ± 0.17 ± 0.06 LNS Colloquium 2004 M. Morii, Harvard 36

37 CLEO PRD 68: B πlv to V ub Belle hep-ex/ FF from LQCD calculations Average of quenched LQCD results: FNAL 01, JLQCD 01, APE 01, UKQCD 00 Unquenched FNAL+MILC Unquenched HPQCD Uncertainty still large Mainly statistical Expect rapid progress in the next year Unquenched LQCD More data from BABAR, Belle CLEO πlv Belle πlv LNS Colloquium 2004 M. Morii, Harvard 37

38 Summary (1) b sγ E γ Inclusive b clv SSFs E l m X? Shape Function? HQE Fit m b E l Exclusive b ulv Inclusive b ulv m X m X -q 2 duality V ub FF B πlv ωlv, ηlv? WA unquenched LQCD LNS Colloquium 2004 M. Morii, Harvard 38

39 Summary (2) Precise determination of V ub complements sin2β to test the (in)completeness of the Standard Model <10% accuracy around the corner Close collaboration between theory and experiment is crucial V ub We keep pounding on the Triangle until we make a dent on it β LNS Colloquium 2004 M. Morii, Harvard 39

40 Backup Slides

41 Penguins b sss decay dominated by the penguin diagram In the SM, same CP asymmetry as b ccs decays: sin2β New Physics may modify the loop CP asymmetries may not agree Several decay channels are studied B 0 φk S is pure-penguin Small BF: B 0 η K S has larger BF = Tree diagram affects the asymmetry by <0.1 b d s φ, η s s d u u W η s d K K 0 0 LNS Colloquium 2004 M. Morii, Harvard 41

42 Status of Penguins BABAR Belle Penguins disagree with sin2β by 2.7σ (BABAR), 2.4σ (Belle) LNS Colloquium 2004 M. Morii, Harvard 42

43 Sub-leading Shape Functions Shape Function represents non-perturb. effects at O(1/m b2 ) Next order (1/m b3 ) 4 Sub-leading Shape Functions Bauer, Luke, Mannel calculated their effects on E γ (PRD68:094001) and E l (PLB543:261) spectra Neubert (PLB543:269) estimated impact on V ub measurement Errors quoted by HFAG New calculations using SCET appeared recently Lee, Stewart (hep-ph/ ) Bosch, Neubert, Paz (hep-ph/ ) Significant impact on V ub measured with E l endpoint Re-evaluation of the SSF error is due LNS Colloquium 2004 M. Morii, Harvard 43

44 CLEO PRD 68: B πlv to V ub Belle hep-ex/ G 2 2 F Γ 2 2 = ( ) q 16GeV 3 V ub 2 p 24 16GeV π f + q dq V ub Γ LQCD > π calculation Average of quenched LQCD results Γ = 1.92 ± 0.47 ps FNAL 01, JLQCD 01, APE 01, UKQCD 00 Two preliminary unquenched LQCD results Γ FNAL'04 = 1.96 ± 0.51± 0.39 ps qunched 0.12 Γ HPQCD = 1.31± 0.13± 0.30ps 1 3 V ub 10 = Quenched FNAL 04 HPQCD CLEO ± 0.55 ± ± 0.55 ± ± 0.67 ± Belle ± 0.71± ± 0.70 ± ± 0.85 ± LNS Colloquium 2004 M. Morii, Harvard 44