Measuring the apex Vub Vcb and their relative
Measuring the apex: |Vub|, |Vcb| and their relative phase γ (φ3) γ ICHEP '06 Р. Ковалевски R. Kowalewski U. of Victoria Canada |Vcb| Kowalewski |Vub| 1
Motivation n Vub is a key element of the CKM matrix 1 graduate student lifetime (~20 years) ago, we didn’t know that Vub ≠ 0: Was the KM mechanism for CP viable? η UTFit FPCP 2006 Now the precise determination of Vub / Vcb provides a benchmark for testing new physics in other processes β ρ ICHEP '06 Kowalewski 2
Big trees dominate! The decay channels used to study |Vub|, |Vcb| and their relative phase are all dominated by tree diagrams Bb B q Vqb Vcb ℓ KD 0 ν “f” c, u q Vub D 0 B- Lifetime +semileptonic decay determine. V|qb| KInterference allows phase measurement ICHEP '06 Kowalewski 3
The magnitudes |Vcb| and |Vub| ICHEP '06 Kowalewski 4
|Vcb| and |Vub| from semileptonic B decays Semileptonic B decay theory n Large BF, only one hadronic current n Inclusive decays b qℓν: n n Vqb Weak quark decay + QCD corrections OPE in as and 1/mb Exclusive decays B Xℓν: n Form factors: need Lattice QCD These inclusive and exclusive determinations of Vqb are complementary ICHEP '06 Kowalewski 5
|Vcb| and |Vub| from semileptonic B decays Semileptonic B decay experiment n Inclusive decays b qℓν: n n Measure lepton Measure pmiss or associated hadrons Exclusive decays B Xqℓν: n n Vqb Measure lepton and specified hadrons Measurements come from Y(4 S) BB BB Determine non-B contribution using data below BB threshold qq ICHEP '06 Kowalewski 6
See talk of Urquijo, S 10 Inclusive |Vcb| ICHEP '06 Kowalewski 7
|Vcb| from inclusive decays Inclusive decay width n Total decay width for b cℓν: free quark ~1. 014 ~0. 908 decay Perturbative corrections n n r = m c / mb Non-perturbativepower corrections Similar expressions for b uℓν, b sγ Comparison with data relies on quark-hadron duality integrate over “broad” regions of phase space Low-order moments can be calculated reliably ICHEP '06 Kowalewski 8
|Vcb| from inclusive decays Global fit for |Vcb|, mb… Fit predicted moments of inclusive processes b cℓν and b sγ for various cuts on kinematic variables: n e or γ energy cut b-quark mass c-quark mass Matrix elements appearing at order 1/mb 2 and 1/mb 3 Calculations available in “kinetic” and “ 1 S” renormalization schemes n Benson, Bigi, Gambino, Mannel, Uraltsev (several papers) n ICHEP '06 Bauer, Ligeti, Luke, Manohar, Trott PRD 70: 094017 (2004) 47 measured moments used from DELPHI, CLEO, BABAR, BELLE, CDF (and, of course, the B lifetime) Kowalewski 9
|Vcb| (10 -3) 41. 96 ± 0. 23 exp± 0. 35 HQE± 0. 59ΓSL mb [kin](Ge. V) 4. 59 ± 0. 025 exp± 0. 030 HQE μπ2[kin](Ge. V 2) 0. 401 ± 0. 019 exp± 0. 035 HQE |Vcb| determined to <2% Only sinθc known better! kinetic scheme b sγ b cℓν μπ2 (Ge. V 2) |Vcb| from inclusive decays Global fit: results combined 1 S scheme χ2 / Ndof = 19. 3/44 New! χ2 / N ICHEP '06 dof = 5. 7/17 |Vcb| (10 -3) 42. 0± 0. 7 fit± 0. 5αs ± 0. 6 th |Vcb| (10 -3) 41. 5 ± 0. 5 fit ± 0. 2τB mb[1 S](Ge. V) 4. 73 ± 0. 05 fit λ 1[1 S](Ge. V 2) -0. 30 ± 0. 04 fit Kowalewski mb (Ge. V) Buchmüllerand Flächer, PRD 73: 073008 (2006) mb to 1%; crucial for |Vub| [kin]/[1 S] values agree after scheme translation 10
See talks of Dubitzky, Schwanda, S 10 Inclusive |Vub| ICHEP '06 Kowalewski 11
n n Background b cℓν rate is 50 times signal Restrict kinematics to suppress background: challenge for theory n OPE convergence is compromised: n n n Need light-cone distribution (shape) function of b quark Relate b uℓν directly to b sγ (e. g. Lange, Neubert, Paz, JHEP 0510: 084, 2005) Measure b u rate in regions dominated by b c n Theory fine; must fight large uncertainties from background In all cases sensitivity to mb. N, N» 5 ICHEP '06 q 2 (Ge. V 2) |Vub| from inclusive decays Strategies for isolating b uℓν decays Points are b uℓν simulation b c allowed Kowalewski Ee (Ge. V) 12
|Vub| from inclusive decays Shape function n b sγ spectrum measured by CLEO, Belle, Ba. Bar n SF moments related to HQE parameters hep-ex/0607071 preliminary n Subleading shape functions differ in b sγ, b uℓν Spectrum in lepton tagged events ICHEP '06 Kowalewski 13
|Vub| from inclusive decays New measurements Ba. Bar result: n PRL 96: 221801 (2006) Fully reconstruct 1 B meson; study semileptonic decay of other B n |Vub|=(4. 43 ± 0. 38 ± 0. 25 ± 0. 29) 10 -3 n Measure up to m. X < 2. 5 Ge. V |Vub|=(3. 84 ± 0. 70 ± 0. 30 ± 0. 10) 10 -3 CLEO limit Weak Annihilation contributions: ΓWA / Γb u < 7. 4% (90% CL) PRL 96: 121801 (2006) ICHEP '06 Kowalewski Theory errors are small Will improve – only 88× 106 BB used so far e+ b u ν Isoscalar hadron 14
|Vub| from inclusive decays Theory calculations n Two sets of calculations in use for b sγ and b uℓν n n Bosch, Lange, Neubert, Paz (BLNP): 3 -scale OPE based on HQET, SCET PRD 72: 073006 (2005) Andersen, Gardi (DGE): parton-level calculation, only mb and ΛQCD input JHEP 0601: 097 (2006) n Both provide good description of data; give similar results n Bauer, Ligeti, Luke (BLL): |Vub| using m. X-q 2 cuts ICHEP '06 Kowalewski PRD 64: 113004 (2001) 15
|Vub| from inclusive decays Determination of |Vub| = (4. 49± 0. 19± 0. 27)× 10 -3 (BLNP) Major progress since last ICHEP n n n ICHEP '06 Good C. L. = 41% Error budget (in %; total 7. 3) : ± 2. 2 stat ± 2. 8 exp ± 1. 9 WA ~ exp ± 1. 9 b 2 c model ± 1. 6 b 2 u model ± 4. 2 HQ param ± 3. 8 sub SF ~ theory DGE: (4. 46± 0. 20)× 10 -3 C. L. = 12% BLL m. X-q 2: (5. 02± 0. 26± 0. 37)× 10 -3 C. L. = 77% Many measurements use small fraction of current data samples. Aggressive target for 2008 is 5% Kowalewski 16
See talk of Lopes Pegna, S 10 Exclusive |Vcb| ICHEP '06 Kowalewski 17
|Vcb| from exclusive decays Exclusive b cℓν decays n Heavy-to-heavy transition; HQ symmetry applies unique, universal FF, unit normalization at zero recoil Light d. o. f. unchanged! before b ν after c e form factors phase space D* boost in the B rest frame ICHEP '06 Kowalewski 18
|Vcb| from exclusive decays B D*ℓν form factor n n 3 non-trivial form factors; 4 observables: w and 3 angles HQET-params: ρ2 = -d. F/dw |w=1 , R 1 ~ V/A 1 and R 2 ~ A 2/A 1 Two measurements from Ba. Bar; averaged values: ρ2 = 1. 179 ± 0. 048 ± 0. 028 R 1 = 1. 417 ± 0. 061 ± 0. 044 R 2 = 0. 836 ± 0. 037 ± 0. 022 pℓ (Ge. V) Ba. Bar hep-ex/0607076 preliminary F(1)|Vcb| = (34. 68 ± 0. 32 ± 1. 15)× 10 -3 BF(B 0 D*+ℓ-ν) = 4. 84 ± 0. 39% ICHEP '06 Ba. Bar hep-ex/0602023 Kowalewski w 19
|Vcb| from exclusive decays |Vcb| from B D(*)ℓν n n New HFAG average including updated form-factors F(1)|Vcb| = (36. 2 ± 0. 8)× 10 -3 Using (Quenched LQCD, PRD 66: 014503 (2002)) (inclusive: |Vcb|=(42. 0± 0. 7)× 10 -3 n n ICHEP '06 Work needed on both experiment and theory to reach the precision of the inclusive determination Similar measurements on B Dℓ-ν are harder; in progress Kowalewski 20
See talks of Dubitzky, Schwanda, S 10 Exclusive |Vub| ICHEP '06 Kowalewski 21
|Vub| from exclusive decays B π ℓν n New Ba. Bar B 0 π -ℓ+ν n n CLEO hep-ex/0607060 High statistics ν-reco method Significantly improved precision ISGW 2 model: C. L. = 0. 07% Data consistent with Lattice QCD and Becirevic-Kaidalov preliminary q 2 n New CLEO B 0 π -/ρ- ℓ+ν n preliminary Good quality ν-reco All q 2 combined mπℓν ICHEP '06 Kowalewski 22
|Vub| from exclusive decays B πℓν with low background n n Reconstruct (tag) one B in hadronic or semileptonic decay Compare what’s left with signal ICHEP '06 π0ℓν Belle hep-ex/0604024 Ba. Bar hep-ex/0607089 1. 38 ± 0. 19 ± 0. 14 1. 12 ± 0. 25 ± 0. 10 π0ℓν (s. l. tag) x 2τ0/τ+ 1. 43 ± 0. 26 ± 0. 16 1. 35 ± 0. 33 ± 0. 19 π+ℓν (had tag) 1. 49 ± 0. 26 ± 0. 06 1. 07 ± 0. 27 ± 0. 19 π0ℓν (had tag) x 2τ0/τ+ 1. 60 ± 0. 32 ± 0. 11 1. 52 ± 0. 41 ± 0. 20 ρ0ℓν / ηℓν 1. 33 ± 0. 23 ± 0. 18 0. 84± 0. 27± 0. 21 ρ+ℓν / η’ℓν 2. 17 ± 0. 54 ± 0. 32 <1. 3 π+ℓν Belle 253 fb-1 BF (10 -4) ρ+ℓν Preliminary Ba. Bar 211 fb-1 Semileptonic tag π0ℓν ρ0ℓν Hadronic tag (s. l. tag) Kowalewski 23
|Vub| from exclusive decays New |Vub| from B πℓν New Averages of tagged and untagged methods are comparable n New New For |Vub|: n n New Lattice QCD: q 2>16 Ge. V 2 Light-cone sum rules: q 2<16 Ge. V 2 New FF normalization errors dominate; task for theory, CLEO-c n New (inclusive: |Vub|=(4. 49± 0. 34)× 10 -3 FF calc Vub [10 -3] 6% uncertainty FF norm (ps-1) Ref Ball-Zwicky 5. 44 ± 1. 43 PRD 71: 014015 (2005) HPQCD 1. 46 ± 0. 35 PRD 73: 074502 (2006) FNAL 1. 83 ± 0. 50 hep-lat/0409116 APE '06 ICHEP 1. 80 ± 0. 86 Nucl. Phys. B 619: 565 (2000) Kowalewski Experimental error on |Vub| ~ 6% 24
See talks of Marchiori, Krokovny, S 8 The phase: γ (φ3) ICHEP '06 Kowalewski 25
The relative phase γ (φ3) Interference between tree-level decays; theoretically clean Favored: Vcb Vus* B- s b u u c u K(*)D(*)0 Common final state f K(*)D(*)0 u Vcs* Vub: suppressed s c u b B- u Parameters: γ, (r. B, δB) per mode Three methods for exploiting interference (choice of D 0 decay modes): • Gronau, London, Wyler (GLW): Use CP eigenstates of D(*)0 decay, e. g. D 0 Ksπ0, D 0 π+ π • Atwood, Dunietz, Soni (ADS): Use doubly Cabibbo-suppressed decays, e. g. D 0 K+π • Giri, Grossman, Soffer, Zupan (GGSZ) / Belle: Use Dalitz plot analysis of 3 -body D 0 decays, e. g. Ks π+ πICHEP '06 Kowalewski 26
The angle γ (φ3) GLW-based analyses Measure asymmetry between B+/B- for CP even/odd D decays n 8 -fold ambiguity on γ and the fractional decay rates to CP eigenstates: Hard to disentangle r. B from γ and δB Recent results: Belle (PRD 73: 051106, 2006), Ba. Bar (PRD 73: 051105, 2006) Belle 275 106 BB B+ DCP+K+ Signals seen in CP-even and CP-odd D decays CP-even D 0 modes B+ DCP-K+ B+ DCP+π+ CP-odd D 0 modes ICHEP '06 Ba. Bar 232 106 BB B+ DCP-π+ Similar measurements exist in B+ D*0 K+ Kowalewski 27
DCP K* D*CP K DCP K The angle γ (φ3) GLW averages Implications for r. B and γ discussed later ICHEP '06 Kowalewski 28
The angle γ (φ3) ADS-based analyses Use DCS decays to reach same final state, e. g. n favored suppressed favored Modes D*K and DK* also used Small product BF but comparable amplitudes large potential asymmetry Direct dependence Additional parameters r. D and δD DCSD charm; r. D (Kπ)= 0. 0603 ± 0. 0025 D*0 D 0π and D*0 D 0γ have opposite CP ICHEP '06 Kowalewski 29
The angle γ (φ3) ADS results New Ba. Bar result in [K+π-π0]DKBa. Bar preliminary hep-ex/0607065 226 106 BB No signal yet in suppressed modes m. ES Belle result in [K+π-]DKBelle hep-ex/0508048 386 106 BB [K+π-]D K- [K-π+]D K- ΔE ICHEP '06 Implications for r. B and γ discussed later Kowalewski 30
The angle γ (φ3) Dalitz analyses n Measure B+/B- asymmetry across Dalitz plot decay amplitude Sensitivity to γ in interference term Mirror symmetry between D 0 and D 0 Dalitz plots Determine f in flavor-tagged D*+ D 0π+ decays n Includes GLW (D 0 Ks ρ0, CP eigenstate) and ADS (D 0 K*+π-, DCS 2 -body decay) regions 2 -foldambiguityon γ: ICHEP '06 (γ, δ) → (γ+π, δ+π) Kowalewski 31
n n Select D*+ [Ksπ+π-]π+ from e+e- cc; ~4 105 events Fit to coherent sum of 15 -16 Breit-Wigner amplitudes plus a non-resonant term Ba. Bar 270 fb-1 preliminary Excellent fits obtained m 2 - (Ge. V 2) The angle γ (φ3) Dalitz model for Ksπ+πBelle 357 fb-1 preliminary hep-ex/0604054 Main contributors: • K*-(892) π+ • K s ρ0 • K*0(1430) π - m 2+ (Ge. V 2) • K*-(892) π+ m 2(π+π-) Ge. V 2 • non/broad resonant Model-independent approach (GGSZ) using CP-tagged D 0 studied by Bondar, Poluektov in hep-ph/0510246 ICHEP '06 Kowalewski Improved modeling (e. g. Kmatrix formulation) under study 32
The angle γ (φ3) Dalitz plots n Plots shown are representative; both experiments have analyzed DK, D*K and DK* decays DK+ 347 106 BB ICHEP '06 Ba. Barpreliminary DK- D*K+ 386 106 BB Kowalewski D*K- Belle hep-ex/0604054 33
The angle γ (φ3) Results on γ n n n HFAG averages for x± = r. B cos( δB ± γ ) , y± = r. B sin( δB ± γ ) UTfit find γ = 78± 30° based on B- D(*) K(*)- decays Note: σγ depends significantly on the value of r. B Contours do not include Dalitz model errors 2γ r. B ICHEP '06 Kowalewski 34
The angle γ (φ3) sin(2β+γ) 2 common final states via BB mixing really favored: Vcb Vud* d B 0 b u d c d π- D(*)π+ D(*)+ Time-dependent effect (due to B 0 -B 0 mixing) Vcd* Vub: really suppressed c d u b d B 0 d Parameters: γ, 2β (r, δB) per mode Large BF but small r. B (<2%) small CP asymmetry r. B must be estimated from B 0 Ds+π – using SU(3) ICHEP '06 Kowalewski 35
The angle γ (φ3) B 0 D 0 K 0 feasibility study Ba. Bar hep-ex/0604016, soon in PRD Vub B 0 D 0 Vcb D 0 B 0 K*0 B 0 D 0 K*0 • Interference of B 0 D 0 K 0 with B 0 D 0 K 0 (K 0 and K 0 mix) ΔE • Determine r. DK* in related decay B 0 D 0 K*0 • Ba. Bar find no signal: r. DK* < 0. 4 @90% c. l. • This mode may be harder to use for sin(2β+γ) than predicted; implications for LHC-b ICHEP '06 Kowalewski 36
The angle γ (φ3) Related measurements Nice ideas, nice work, but not much impact yet for γ r. Dπ from B 0 Ds(*)π -, SU(3) B 0 Ds a 0, 2 Ba. Bar hep-ex/0604012, 226 106 BB Ba. Bar PRD D 73 : 071103 (2006) 226 106 BB B D*D* preliminary Ba. Bar PRD 73: 112004 (2006) BF and charge asymmetries measured for all B D(*) modes; provides input for sin(2β+γ) from B 0 D(*)+D(*)time-dependent asymmetries B 0 D 0 K+ π Ba. Bar PRL 96: 011803 (2006) Ba. Bar show that B D 0 K+πnot promising for measuring γ ICHEP '06 Kowalewski 37
The angle γ (φ3) See talks of Vagnoni, T’Jampens, S 8 Current status of UT Tree-level determination: information on phase γ (φ3) not yet constraining All constraints: compatible with SM, but tension exists between sin 2β and |Vub/Vcb| “ 2 -σ” bands ICHEP '06 Kowalewski 38
Summary n n Today: What to look for in 2008: n n n ICHEP '06 “ 2 -σ” bands 2 ab-1 from the B factories (>doubling of data sample) error on |Vub/Vcb| of ~5% error on γ: ~10 -15° ? (r. B …) LHC-b will have initial data The heavy flavor program will restrict the space in which theories for the new physics to be seen at LHC can operate Kowalewski 39
Backup slides ICHEP '06 Kowalewski 40
Tale of two fitters CKMfitter (frequentist ) ICHEP '06 UTFit (Bayesian) Kowalewski 41
|Vub| from inclusive decays Theory calculations n Bosch, Lange, Neubert, Paz (BLNP) n n n Andersen and Gardi: Dressed gluon exponentiation (DGE) n n ICHEP '06 Decompose into Hard, Jet and Shape functions using HQE and SCET: H×J ×S Same formalism used to extract mb and μπ2 from b sγ Predictions over full phase space, reasonable error analysis Critique: 3 scales between ΛQCD and mb Only mb and αS as input parameters Gives good description of b sγ spectrum Agrees fairly well with BLNP on b uℓν rates Critique: some (but not all) consider it a model; Kowalewski 42
|Vcb| from inclusive decays Global fit: Input measurements n Moments used in fit, from B Xcℓν and b sγ Buchmüllerand Flächer, Phys. Rev. D 73 (2006) 073008 Moment Experiment Electron energy Hadronic mass Delphi 3 3 CLEO need full covar 4 CDF Belle Ba. Bar ICHEP '06 Photon energy 1 2 need full covar 4 14 13 3 Kowalewski 43
|Vcb| from exclusive decays B Xcℓν using tagged samples n n Reconstruct D(*)Xℓ-ν across from a fully reconstructed B+ or B 0 meson; Mmiss 2 provides new kinematic handle Belle reported last year Belle BFs for B D(*)πℓν: BF (in %) Phys. Rev. D 72: 051109, 2005 Also report BF(B- D*0ℓ-ν) = 6. 06 ± 0. 25 stat%; and BF(B 0 D*+ℓ-ν) = 4. 70 ± 0. 24 stat%. n n ICHEP '06 New Ba. Bar preliminary result: BF(B- D*0ℓ-ν) = 6. 8 ± 0. 4% BF(B- D 0ℓ-ν) = 2. 3 ± 0. 3% BF(B- D**0ℓ-ν) = 1. 9 ± 0. 3% (includes D(*)πℓν; translated from relative fractions into BFs by this speaker assuming these modes saturate b cℓν) New D 0 result D D* D(*)π (preliminary) BF(Bs Ds 1(2536)ℓν) = 0. 86 ± 0. 16 Kowalewski 44
|Vcb| from exclusive decays The BF(B D*ℓν) puzzle n n n The largest B BF is B D*ℓν (~6%), yet B K*γ (~4× 10 -5) is known as well, and perhaps better… (HFAG winter) average: BF(B 0 D*+ℓ-ν) = 5. 35 ± 0. 20%; CL=3. 8% Consider RD* = BF(B- D*0ℓ-ν) / BF(B 0 D*+ℓ-ν); we expect RD* = τ+ / τ0 = 1. 071 ± 0. 009 Total BF(B Xℓν) consistent with isospin n Naively combining Belle and Ba. Bar results: RD* = 1. 32 ± 0. 07 (20% and 3. 5σ from isospin!) Ba. Bar preliminary Ee BF(B+ Xeν) / BF(B 0 Xeν) = 1. 084 ± 0. 041 ± 0. 025 ICHEP '06 Kowalewski 45
Importance of r. B n n The uncertainty on γ (φ3) depends strongly on the value of r. B, which is currently not well known Predictions for how σγ will evolve with luminosity have significant uncertainty r. B Belle φe ICHEP '06 Kowalewski 46
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