Precision determinations of V cb and V ub

Transcription

1 Precision determinations of V cb and V ub Probing weak interactions and CP violation in the quark sector with semileptonic B decays Bob Kowalewski University of Victoria April, 2004 R.V. Kowalewski 1

2 Outline Importance of testing CKM picture of CP B factories the luminosity frontier HQET and OPE for heavy quarks NEW NEW V cb from inclusive decays (b clν) V cb from exclusive decays (B D * lν) Soon V ub from inclusive decays (b ulν) Soon V ub from exclusive decays (B πlν) April, 2004 R.V. Kowalewski 2

3 Weak interactions of quarks Historically fruitful area of research τ / θ puzzle (1950s) Parity violation (1956) Flavour oscillations (1956 (K 0 ), 1987 (B 0 )) CP violation (1964 (K 0 ), 2001 (B 0 )) The only verified mechanism for CP violation is the non-trivial phase in CKM matrix B factories allow precision studies of CKM Rare B decays offer window on new physics April, 2004 R.V. Kowalewski 3

4 CKM matrix The Wolfenstein++ parameterization is used here Buras, Lautenbacher, Ostermaier, PRD 50 (1994) d s b λ 8λ λ Aλ ( ρ iη) VCKM = λ+ 2 A λ 1 2( ρ+ iη) 1 2λ 8λ ( 1+ 4A ) Aλ Aλ 1 ( ρ + iη)( 1 2λ ) Aλ + A( 2 ρ iη) λ 1 2 A λ u c t shown here to O(λ 5 ) where λ = sinθ 12 = 0.22 V us, V cb and V ub have simple forms by definition Free parameters A, ρ and η are order unity April, 2004 R.V. Kowalewski 4

5 A Unitarity Triangle λ, A, ρ and η At the 1% level: λ = V = sinθ λ = ± At the 2% level: A= 2 / λ A = 0.84 ± 0.02 V and V ub V us cb td ρη - plane c V V us cb Unitarity: 1+ R +R = 0 R R u t η R u ( ρ, η) γ R t β ( 0,0) ( 1,0) = = V V V V γ ud cd td cd = V V V V α ub cb tb cb * argv ub, t ρ 2 u + (1 ρ) η 2 2 ρ e + η α = π γ β ( 2 1 λ / 2 ) ρ = ρ η = ( 2 1 λ / 2 )η i γ 2 e iβ April, 2004 R.V. Kowalewski 5

6 Constraints on CKM Good precision (and improving) on sin2β V ub / V cb is powerful; improvements will have impact η These two measurements alone could show a violation of unitarity ρ April, 2004 R.V. Kowalewski 6

7 B factories PEP-II/BaBar and KEK-B/Belle Asymmetric e + e - colliders, s = GeV Approved in 1994, first data in 1999 CP violation observed in 2001 Luminosity records continue to be set Two big success stories Focus of this talk is on BaBar Belle results will be mentioned where relevant April, 2004 R.V. Kowalewski 7

8 PEP-II and KEK-B Asymmetric e + e - colliders April, 2004 R.V. Kowalewski 8

9 Luminosity (as of April 7, 2004) Both B factories are running extremely well: Belle BaBar L max (10 33 /cm 2 /s) best day (pb -1 ) total (fb -1 ) Belle April, 2004 R.V. Kowalewski 9

10 BaBar detector General purpose collider detector F-B asymmetric due to boost of CM increasing radius Crossings every n*4.2 ns Standalone 5-layer Si tracker for low-p T (<0.1 GeV) Low-mass drift chamber with He-isobutane gas Unique ultra-thin imaging Cherenkov detector DIRC BaBar CsI (Tl) e + (3.1 GeV) CsI(Tl) crystal calorimeter e - (9 GeV) Instrumented flux return SVT DCH IFR April, 2004 R.V. Kowalewski 10

11 Y(4S) experiments e + e - Y(4S) B + B - and B 0 B 0 ~ 50% each B nearly at rest (βγ ~ 0.06) in 4S frame overlapping decays Asymmetric beam energies boost into lab: (βγ) 4S ~0.5 off peak (q=u,d,s,c) on peak σ BB = 1.1 nb BB qq 2m B April, 2004 R.V. Kowalewski 11

12 Understanding B decay b quark weak decay is complicated by QCD Both perturbative (m b ) and non-perturbative (Λ QCD ) effects Tools: Heavy quark symmetry Heavy Quark Effective Theory Operator Product Expansion (HQE effective field theory) Lattice QCD April, 2004 R.V. Kowalewski 12

13 Heavy Quark Symmetry Heavy quark is invisible to gluon probes with de Broglie wavelength λ g >> 1/m Q HQ spin and mass (flavour) are good symmetries as m Q /Λ QCD Departures from HQ symmetry can be expressed as (Λ QCD /m Q ) n corrections In several important cases, the (Λ QCD /m Q ) 1 term vanishes (Luke s theorem) April, 2004 R.V. Kowalewski 13

14 V cb from exclusive b clν decays: B 0 D *+ lν April, 2004 R.V. Kowalewski 14

15 Heavy Quark Effective Theory Based on HQ symmetry for Q Q Applies to b c transitions, e.g. B D * lν Departures from HQ limit ~ (Λ QCD / m c ) k All B D (*) lν transitions are governed by one form factor (the Isgur-Wise function ξ(w), w = v B v D* 1) in the HQ limit In HQ limit, F(1)=ξ(1)=1 (D * at rest in B rest frame) Extract F(1) V cb from rate dγ/dw (w 1) Calculate F(1) using non-perturbative methods April, 2004 R.V. Kowalewski 15

16 B D * lν Separate fit in each w bin peaking bkg April, 2004 R.V. Kowalewski 16

17 B D * lν Measure differential decay rate (w = D * boost in B frame [1-1.5]) ( ν ) * dγ B D 2 GF = G( w) V ( ) 3 cb dw 48π ( F w ) 2 2 In HQ limit F(w) ξ(w). In HQET parameterize as expansion in (1-w) F( w) = F(1) 1 + (1 w) + c(1 w) +... or F 2 2 ( ρf ) A ( w) 1 2wr+ r 2 ( w) 2 1 R ( w) 1 ( 1 R ( w) ) with w 1 2 w 1 = (1 r) (1 r ) 2 4w 1 2wr+ r 2 w+ 1 1 r + w 2 V( w) A( w) m w w r = w w m 2 R 1( ) and R 2( ) and A( 1 ) A( 1 ) w A1( w) = A1( 1) 1 8 ρ z (53ρ 15) z (231ρ 91) z A + with z = 1 A1 A1 w expansion in z April, 2004 R.V. Kowalewski 17 D B * 0 extrapolate to w=1

18 B D * lν (preliminary results) High statistics sample w resolution ~ 0.04 dn dw db = ε ( w) 0 * (B D ν) dw Main uncertainties from FF ratios R 1 and R 2, extrapolation to w=1, D ** composition, slow π + efficiency Using F(1)=0.92±0.03 (from LQCD 1 ) 1 S. Hashimoto et al., PRD 66 (2002) April, 2004 R.V. Kowalewski 18

19 V cb from inclusive b clν decays B X c lν April, 2004 R.V. Kowalewski 19

20 OPE for b clν transitions b clν described by OPE in (1/m b ) n and α s k non-perturbative parameters arise at each order: Λ (=m B -m b ) µ π2 (aka λ 1 ), µ G2 (aka λ 2 ) at (1/m b2 ) ρ 1-2, T 1-4 at (1/m b3 ) parton-hadron duality assumed predicts many observables testable April, 2004 R.V. Kowalewski 20

21 April, 2004 R.V. Kowalewski 21

22 Spectral moments: M X k, E e k Measure hadronic mass and lepton energy moments (in presence of minimum lepton energy cut) Compare with OPE calculation ( 3 ) ( k Calculations available to O m ) B and O α S, k = 1 or 2 Applying OPE calculations to real hadrons (duality) requires summing over a large enough phase space Spectral moments should be insensitive to duality A complete set of calculations is available in one renormalization scheme (soon to come in a second scheme) April, 2004 R.V. Kowalewski 22

23 Electron spectrum measurement Exploit angular correlations in di-electron events Extract partial BF and moments, compare with theory ARGUS method April, 2004 R.V. Kowalewski 23

24 Electron energy moments Correct for BB mixing, b ueν, backgrounds, Bremsstrahlung, QED radiation, elec id and misid... Extract 0 th 3 rd moments vs E e,cut partial BF: April, 2004 R.V. Kowalewski 24

25 Measuring M X in b clν decays Analysis strategy: fully reconstruct one B and study semileptonic decays of the recoiling B Require E miss p miss kinematic constraints fit for better m X resolution (σ~0.35 GeV) B-factory statistics make it possible Recoil M X 2 M x calibration curve, applied event-by-event Fully reconstructed April, 2004 R.V. Kowalewski 25

26 Hadronic mass moments Method validated on data using partiallyreconstructed D * lν decays (π s -l correlations) Extract M k X, k=1..4 as a function of E e,cut Main systematic uncertainties: non b clν background simulation of track and neutral reconstruction 2 M X modeling of QED radiation B-reco sideband subtraction April, 2004 R.V. Kowalewski 26

27 Fit to moments Fit E e and M X moments vs. E 0 to set of parameters: V cb, B(b clν), m b, m c, µ π2, µ G2, ρ D3, ρ LS 3 8 unkowns, observables (with reasonable correlations) cross-check lepton vs. hadron moments compare V cb with D * lν result compare non-perturbative parameters with other determinations April, 2004 R.V. Kowalewski 27

28 April, 2004 R.V. Kowalewski 28

29 Cross-checks of fit results E e moments calculated up to α s2 β 0 ; M X moments to α s (higher orders small compared with exp error) Separate fits to E e and M x moments agree well Overall power of E e and M X moments is comparable Values for µ G2 and ρ LS3 are consistent with independent measurements based on m B* -m B and HQ sum rules. April, 2004 R.V. Kowalewski 29

30 OPE preliminary fit results April, 2004 R.V. Kowalewski 30

31 Comparison of inclusive and exclusive V cb determinations B D * lν HFAG average from D*lν V cb = (40.1 ± 0.9 exp ±1.8 theo ) 10-3 BaBar (preliminary) D*lν V cb = (37.3 ± 1.5 exp ±1.6 theo ) 10-3 BaBar (preliminary) HQE fit to semileptonic moments V cb = (41.4 ± 0.4 exp ±0.4 HQE ±0.6 theo ) 10-3 F(1)=0.92±0.03 April, 2004 R.V. Kowalewski 31

32 V ub from inclusive q 2 decays u X u OPE gives V ub from Γ(B X u lν) to <5% Challenges: separate b u from b c calculate V ub from partial rate after b c suppression cuts review of published results and methods new method outlook April, 2004 R.V. Kowalewski 32

33 Finding b u decays here here April, 2004 R.V. Kowalewski 33

34 Lepton endpoint Experimentally clean for E e > 2.3 GeV m m 2m 2 2 B D Can t go below E e ~ 2.2 GeV due to b c background OPE breaks down when restricted to endpoint region (need twist expansion in which power corrections are resummed into a light cone distribution function, or shape function, which must be measured ) Determine shape function from b sγ or perhaps from semileptonic decays Best measurements give σ Vub / V ub ~ 0.15 B April, 2004 R.V. Kowalewski 34

35 Mass of recoiling hadrons Larger phase space (~70%) means smaller theoretical uncertainties (but not that simple ) Experimentally more challenging; need either B tagging (cleanest, very low efficiency) or simulated annealing (poor S/B, higher efficiency) Combine with q 2 (invariant mass of e-ν pair) to improve theory error? Early measurements show promise April, 2004 R.V. Kowalewski 35

36 BaBar V ub from tagged analysis Reconstruct B D (*) nπ Select lepton p l >1 GeV; good signal/background Perform kinfit to remaining particles to determine m X Measure BF(B X u lν) m x <1.55 GeV In future consider q 2 to reduce theory error April, 2004 R.V. Kowalewski 36

37 Belle simulated annealing Try to assign particles to s.l. and other B using kinematics (m B, E B, m 2 miss) Validate on D * lν BB S/B poor April, 2004 R.V. Kowalewski 37

38 Lepton-pair invariant mass New method combine E e with q 2 to reduce E e cut (and theory uncertainty); expect few 10 3 events with S/B ~ 0.6. Estimate neutrino momentum based on missing momentum. Resolution is modest but usable Check / limit theory error by using b ulν distributions (e.g. E W + P W m b ). 2 max 2 2 q sh = mb + q 2mB E + 4E s = m max 2 h D B D 0 lνx P miss -E ν Dl b clν b ulν April, 2004 R.V. Kowalewski 38

39 V ub from inclusive semileptonic decays - status and prospects Active area for theory and experiment New analyses with better acceptance and ability to measure decay distributions coming Expect significant progress if HQE parameters measured in b c decays can be used in predictions for dγ(b u) / dy My view 10% measurements of V ub will appear in 2004/05. April, 2004 R.V. Kowalewski 39

40 V ub from B πlν Extracting V ub from exclusive decays requires Form Factors (FF) πlν is the best mode experimentally (low background) and theoretically: Lattice QCD is making good progress on FF measure q 2 = m W2 dependence to constrain theory status and prospects April, 2004 R.V. Kowalewski 40

41 Current status of B πlν CLEO Based on neutrino reconstruction PRD 68, (2003) ( π ν) ( ) B B V ub = 1.33 ± 0.18 ± 0.11± 0.01± ( ) 0.39 = 3.24 ± 0.22 ± 0.13 ± Belle (2001 conference paper, never published) BaBar April, 2004 R.V. Kowalewski 41

42 Tagged analyses Events where companion B is reconstructed are starting to be used: Much better signal/background, kinematic acceptance Much lower yield ( times smaller than untagged) Better for BF, but not yet for determining FF shapes Several tag methods: Better for B + than for B 0 Only for B 0 Fully reconstructed hadronic B decays Fully reconstructed semileptonic B decays to D (*) lν Partially reconstructed semileptonic B decays (π s -l correlation) April, 2004 R.V. Kowalewski 42

43 P r e l i m i n a r y April, 2004 R.V. Kowalewski 43

44 V ub from exclusive semileptonic decays - status and prospects Soon results on B πlν - tagged and untagged analyses Untagged analyses form factor (q 2 ) shape Tagged analyses BF with small experimental systematics, convincing S/B Lattice calculations are becoming more believable Expect σ( V ub )~10% in a year or two. April, 2004 R.V. Kowalewski 44

45 Summary Significant progress on V cb - accuracy 2% (inclusive), 5% (exclusive) Clear progress due to HQE and precise measurements Anticipate improvements in V ub in near future Cleaner and more comprehensive measurements Improvements in theoretical methods B factories are systematically probing the weak and strong interactions of quarks April, 2004 R.V. Kowalewski 45

46 NEW sin2α from B ππ and B ρρ decays BR( ρ + ρ ) = (30 ± 4 ± 5 )10 f NEW = 0.99 ± 0.03 stat syst long (stat) 0.03 ( syst ) 6? Other ingredients in ρρ isospin analysis: ρ BR( ρ ) = (26.4 ± 6.4)10 (BABAR & Belle), ρ + 0 f ( long ρ ) = (BABAR & Belle), BR( ρ ρ ) = (0.62 ± 0.12)10 f ( long ρ ρ ) = Plots from the CKMfitter group: April, 2004 R.V. Kowalewski