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Precise Determination of |V cb |, |V ub |, and the b-quark mass from inclusive B decays

Precise Determination of |V cb |, |V ub |, and the b-quark mass from inclusive B decays. Oliver Buchmüller CERN. |V cb | at the ~1% level - The new BABAR result as an example Towards a ~5% measurement of |V ub | - what can we lean from b cl and bs

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Precise Determination of |V cb |, |V ub |, and the b-quark mass from inclusive B decays

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  1. Precise Determination of |Vcb|, |Vub|, and the b-quark mass frominclusive B decays Oliver Buchmüller CERN • |Vcb| at the ~1% level • - The new BABAR result as an example • Towards a ~5% measurement of |Vub| • - what can we lean from bcl and bs • bs and its senitivity to „new physics“ • - how tight are the constraints really? DESY TUESDAY SEMINAR 21/09/2004

  2. CP Violation in the Standard Model(SM) The expected size of CP violation in the SM is much too small to explain N(q)/N(anti-q)~10-9 CKM Matrix The elements of the CKM matrix are the only source of CP violation in the SM Unitarität N(q)/N(anti-q) ~ 10-20 much to small! The area of the triangle is proportional to the CP violation in the SM Measurements of the angles and sides of the triangle represent a fundamental test of the SM!

  3. |Vub/Vcb| describes a circle in the (,) plane The sides of the triangle A measurement of a length of a triangle is as good as a measurement of an angle!

  4. The Trinagle Today sin2 has become a precision measurement and is now the best know quantity of the triangle! If we want to sufficiently over constrain the triangle we need to improve the other measurements as well!  |Vcb| and |Vub|

  5. |Vcb| und |Vub| from semilleptonic B decays Why semileptonic B decyas? For |Vxb| we need to have a bx transition (trivial) Need a precise theoretical framework to translate the measurements on “meson level” into “quark level” (not trivial) b BXl mit l=e, bcl W c No „colour activity“ between W  l and c quark  semileptonic decays are theoretical necessity!

  6. The Inclusive Approach The advantage of being inclusive! QCD«mb : inclusive decays admit systematic expansion in QCD/mbNon-pert corrections are generally small and can be controlled Hadronization probability =1, approximately insensitive to details of meson structure as QCD«mb (at least far from perturbative singularities) can be expressed as double series in s and QCD/mb (OPE) with parton model as leading termNo 1/mb correction!

  7. The Heavy Quark Expansion (HQE) • Short-distance physics encoded in coefficients of operator products • (to some order in as). Calculable! • Long-distance physics encoded in exp. values of products of quark operators • (to some order in 1/mb). NOT calculable! Must be determined empirically. Need to get access to the not very well know HQE parameters!

  8. Access to the HQE Parameter The HQE not only predicts the inclusive decay rates but also inclusive differential decay distributions for semileptonic decays (e.g. moments of the lepton energy spectrum). Measure (a lot) moments of inclusive kinematic distributions Extract HQE parameters (e.g. mb) from a fit to all moments Compare predicted inclusive decay rate with its measurement sl = sl (B, BRsl) |Vcb|

  9. M1(Mx) M2(Mx) M3(Mx) M1(El) M2(El) M3(El) Pioneering Work DELPHI CLEO mb,kin(1GeV)= 4.58 +0.06fit+0.05sys GeV mc,kin(1GeV)= 1.15 +0.09fit+0.08sys GeV mp2 (1GeV) = 0.41 +0.04fit+0.04sys GeV2 rD3 (1GeV) = 0.05 +0.02fit+0.01sys GeV3 Input constraints: mb= 4.57  0.10 GeV mc= 1.05  0.30 GeV Multi parameter fits to moments but sensitivity was limited …

  10. The B Factory BABAR and PEPII LINAC SLD BABAR

  11. BABAR AND PEPII e+e-  4s(10.58 GeV)  BB (96%, 4% non-BB) 3.1 GeV 4s(10.58 GeV) 9 GeV BB production threshold

  12. A Tough Race Competition is important: Both B factories perform very well (15/06/2004) BABAR 227 fb-1  BELLE 275 fb-1 RUNIV  500 fb-1 (ca. 550 Mio BB events) Better than expected and gives hope for the future. RUNIII BABAR results of this talk are based on 82 fb-1 ca. 90 Mio BB events RUNII RUNI

  13. p Breco D* e- Vcb e+ Brecoil l ν Xc Semileptonic B Events: Access to Vcb and Vub A theoretical necessity … No color interaction between W and c-quark (Vub) W b c “CKM Matrix” “Tree Level” “Detector Level” … but an experimental challenge! • Need to fully reconstruct the semileptonic B Event in order to get access to the kinematic information of the signal B decay “Neutrino Reconstruction” 

  14. Kinematic of Semileptonic B Events • Use fulll reconstructed B sample: • „Tag“ B is full reconstructed and the signal B is identified via the lepton. Incomming momentum of the two beams are well measured X-System 4 gemessene Größen (e.g. Mx) Pe- Pe+ Reco. B: 4 measured quantities (EPEPII ,PPEPII) bekannt! Lepton 3 measured quantities (e.g. El) • Energy and Momentum Conservation • Ebreco + EX +El+E- EPEPII= 0 • Pbreco + PX +Pl+P- PPEPII= 0 • 4 Constraints + Mass Constraint M(Breco)=M(X,l,)  + 1 Constraint Neutrino 3 unmeasured quantities 5 Constarints–3 unmeasured quantities = 2 times overconstraint System „2C kinematic fit“ • full reconstruction of the entire semileptonic event (especially Mx und El)

  15. Fully reconstructed hadronic B-decay Semileptonic decay of other B Identify Lepton (e or ) reaming tracks and neutral objects define the X-System Mx determined by 2C kinematic fit Sideband subtraction of the combinatoral B background Y(4S) Hadron Moments <Mxn> high mass final states  2250 2000 1750 1500 1250 1000 750 500 250 0 signal background Mx2[GeV2/c4] Events / 1.8 MeV/c2 BABAR 7114 signal events, 2102 combinatoral bg. Out of 90 Mio BB events! 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 mES[GeV/c2]

  16. etag BABAR Btag e- e+ Bsig esig ν Lepton Moments <ELn> “double lepton tag” “e+e-” unlike sign Select events with two identified electrons: e+e- and e±e Unfolded primary electron spectrum for BXl “e±e” like sign Subtract irreducible bg. and unfold the number of primary electrons from the two samples (“ARGUS method”).

  17. High mass states Mx Mx <Mx> (ELCUT) and <EL>(ELCUT) Measure moments over a large rage in phase space  as function of a cut in the lepton energy A cut in the lepton energy will restrict the phase space for high mass states production (D**, D*). Thus <Mx> (ELCUT) and <EL>(ELCUT) will probe the underlying “decay dynamic” of BXcl events.

  18. Phys.Rev.D69:111103,2004 Reduction of high mass final states BABAR BABAR BABAR BABAR Increase of the mean Ecut Ecut Ecut Decrease of truncated BR Ecut <Mx> (ELCUT) and <EL>(ELCUT) Phys.Rev.D69:111104,2004

  19. HQE Fit • Use dedicated HQE for every measured observable: • clv (BR, lifetime) • Hadron Mass Moments <Mxn>(Ecut) • Lepton Energy Moments <Eln>(Ecut) (Fit parameters are in red) • |Vcb| „master“ formula : • : • i-th central El moment for El>E0: • i-th Mx moment and El>E0 : • i-th E moment and E>E0 : From BXs Extract the HQE parameter mb,mc,2,G2, D3, LS3and |Vcb| as well as BRclv from a simultaneous fit to all moment measurements (27+1*). Experimental and theoretical errors and their correlations are all accounted for in the fit. * Only external input to the fit is: B lifetime B+B0 =1.6080012 ps

  20. Combined Fit to Ee and Mx Moments • |Vcb| „master“ formula : • : • i-th central El moment for El>E0: • i-th Mx moment and El>E0 : Calculations taken from Gambino and Uraltsev, hep/ph 0401063 high correlation between measurements : this fit uses solid points only

  21. Phys. Rev. Lett. 93:011803,2004 hep-ex/0404017 Strong correlation between mb and mc: kinetic mass scheme mb(1 GeV) – mc(1 GeV) = (3.44±0.03exp±0.02HQE±0.01αs) GeV BABAR BABAR 2D projections of the fit result: BABAR 2=1 ellipses Fit Results

  22. |Vcb| and BR(BXl) A better comparison is the total semileptonic BR. The from the HQE Fit extracted BR is roughly 30% more accurate than the HFAG average. sets roughly the scale of improvement But comparison is not on “equal footing” because the input (e.g. B lifetime and BR ) as well as the theoretical error assumption are not the same  job of HFAG

  23. mb(mb) = 4.22 ± 0.06 GeV mc(mc) = 1.33 ± 0.10 GeV BABAR b-quark and c-quark mass Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262 See also report from CKM WS hep-ph/0304132

  24. New Moment Measurements ICHEP04 has surprised us with a lot more moment measurements from various collaborations: • BABAR: • hep-ex/0403031(Phys.Rev.D69,2004)  Hadron Moments from semileptonic B decays • hep-ex/0403030 (Phys.Rev.D69,2004)  Lepton Moments from semileptonic B decays • BELLE: • hep-ex/0408139(preliminary)  Hadron Moments from semileptonic B decays • hep-ex/0409015(preliminary)  Lepton Moments from semileptonic B decays • hep-ex/0403004 (Phys.Rev.Lett.93,2004)  Photon Energy Moments from BXs decays • CDF: • http://www-cdf.fnal.gov/physics/new/bottom/040428.blessed-bhadr-moments/ •  Hadron Moments from semileptonic B decays • CLEO: • hep-ex/0403052 (Phys.Rev.D70:,2004)  Hadron Moments from semileptonic B decays • hep-ex/0403053 (Phys.Rev.D70:,2004)  Lepton Moments from semileptonic B decays • hep-ex/0108032 (Phys.Rev.Lett.87,2001)  Photon Energy Moments from BXs decays • DELPHI: • hep-ex/0210046  Hadron Moments from semileptonic B decays • hep-ex/0210046  Lepton Moments from semileptonic B decays More than 100 single moment measurements!  perfect playground for consistency tests …

  25. Include Additional Moments in the HQE Fit Include all moment measurements in the fit that are given with a full covariance matrix. BABAR moments only All Moments 2/NDF 0.75 0.55 |Vcb|x10-3 41.390.59(0.62)41.380.45(0.62) mb [GeV] 4.6110.067 4.6100.053 mc [GeV] 1.180.09 1.170.08 BRclv [%] 10.610.17 10.640.14 Very consistent results and the inclusion of the additional moments leads to significant improvements of the extracted fit parameters (e.g. mb ~25%) • Use the extracted HQE parameters as base for the theoretical predictions!

  26. Total Error Best fit Exp. Error Comparison: Hadron Moments Very good agreement! Also the moments not included in the fit agree well with the HQE prediction based on the fit results! Y-axis: HQE prediction - Measurement

  27. But the results from CLEO fit not too well … Total Error Best fit Exp. Error Comparison: Lepton Moments Keep in mined that the moments are highly correlate. Typical  between the two extreme values is ~50% Very good agreement for lepton moments from BABAR, BELLE and DELPHI. Y-axis: HQE prediction - Measurement • Under investigation. Need to properly take into account common systematics, all correlations, etc … but looks like a ~3 difference

  28. (D3, LS3) 1,2 (2, G2) 1,2    mb, mc  Gremm,Kapustin & & Leading order defined in different schemes O(1/mb3) O(1/mb2) — — Comparison with other (independent) determinations In hep-ph/0408002 Bauer et al. have carried out an independent |Vcb| determination based on calculations in the 1s scheme (and other schemes). • A simultaneous fit to all data yields: (hep-ph/0408002 - 1s scheme) |Vcb|=41.90.6(fit)0.1(B) x10-3 mb1s =4.680.4(fit) GeV 1 =-0.230.06(fit) GeV2 (our results - kinetic scheme) |Vcb|=41.40.5(fit) [0.6(theo)] x10-3 mbkin =4.610.5(fit) GeV 2=0.400.04(fit) GeV2 |Vcb|: 41.9 vs.. 41.4 [x10-3]  0.4 vs. 0.4 [GeV2]  4.19 vs. 4.22 [GeV] Comparison: 2= -1 + O(s)  -1 + 0.17 GeV2 translate mb into MS: mb(mb)  Leading HQE parameters are consistent but |Vcb| differs by 1.2% - too much?

  29. But the general picture looks very encouraging …. >2% measurement of |Vcb| + extraction of all HQE parameters to O(1/mb3) Inclusive |Vcb| • The determination of |Vcb| from inclusively defined moments of semileptonic kinematic distributions has entered the phase of a precision measurement. • Moment measurements from various experiments as well as improved • theoretical calculations in the HQE framework allow the extraction of • the O(1/mb3) parameters without any external constraints. • Example BABAR analysis: Phys. Rev. Lett,2004 hep-ex/0404017 Or hep-ph/0408002 1S scheme Bauer et al. • Still a few outstanding issues: • Consistency of CLEO lepton moments • Compatibility of extracted |Vcb| values (inconsistently applied QED corrections?!) • Uncertainty of calculations for the non-integer moment <Mx> and <Mx3>

  30. Unitarity Triangle and |Vcb| What have we learned … 5% vs. 2%

  31. |Vub| today … and its (current) limitations |Vub| has crossed the ~10% error barrier! Already quite an accomplishment but we want more (target ~5% error) Error Budget |Vub| |Vub|  [0.09(exp) 0.1(SF) 0.05(HQE)] Need to work hard on the extraction of the shape function parameter and a better determination of mb • 10% - experimental error: • With increasing statistic BABAR and BELLE will be able to significantly improve this error! • 10% - “shape function” error: • Limited knowledge of the shape function leads to the largest theoretical uncertainty. Currently the shape function parameter are obtained from the BELLE photon energy spectrum from bs • 5% - “HQE” error: • OPE based translation of the measured Brulv into |vub|. The limiting factor is the uncertainty of the b quark mass!

  32. g b s <E> mb Photon Energy Spectrum • Besides “new physics” the radiative penguin decay bs probes also very important SM quantities such as the b-quark mass and the “Fermi motion”. bs Heavy Quark Limit mb 8 <E> =mb/2and <(E-<E>)2 >= 2/12 Complementary information to semileptonic decays <(E-<E>)2 > Fermi Motion (2) • Probes directly mb while bcl is most sensitive to mb-mc Gives access to the shape function(b quark distribution function) for the heavy to light quark transition

  33. The experimental challenge Before all cuts After almost all selection cuts udsc BB Schnitt bs BR ~ 10-4 The very difficult background situation requires a lower cut on the photon energy to measure relevant quantities like BRbsor the moments of the spectrum. How far can we go down …?

  34. The Measured Spectrum CLEO 2001 BELLE 2004 E>1.8 GeV E>2.0 GeV Ecut=1.8 GeV: BELLE <E> =2.292 0.043 GeV <E2> - <E>2 =0.0305 0.0100 GeV2 Ecut=2.0 GeV: CLEO <E> =2.346 0.034 GeV <E2> - <E>2 =0.0226 0.0070 GeV2

  35. Shape Function Parameter The shape function from bs and bul are related and it is possible to use the photon energy spectrum to extract the shape function parameter valid for bul decays (Caveat: 1/mb corrections) HFAG:Use the BELLE photon energy spectrum to determine the shape function (hep-ex/0407052) Fit true underlying photon spectrum via a Monte Carlo simulation to the measured spectrum (similar to an unfolding)

  36. HQE Prediction for <E> and <(E-<E>)2 > New HQE calculation from Benson, Bigi and Uraltsev in the kinetic scheme [O(1/mb3); O()] (soon to be published) Comparable to those for clv moments. • i-th E moment and E>E0 : Caveat: For tight cutoffs the expansion scale QMB-2Ecut(“hardness”) becomes to small for a reliable 1/Q expansion  Bias in the leading HQE parameters mb am 2 Benson et al provide also predictions for the bias effect as a function of the cutoff Expected bias at 2Ecut=2.0 GeV: mb 40 MeV ; 2 0.1 GeV2 In the following consider both scenarios: HQE prediction only HQE prediction & bias correction

  37. Consistency between bs and b cl Use extracted HQE parameters from the clv moment fit to predict the moments of the photon energy spectrum. “bias corrected HQE” “HQE only” Moment measurements agree well with HQE prediction obtained from the clv moment fit. Evidence that bias correction is needed for moments above E>1.8 GeV But we can do more … Use the shape function parameter which ft the BELLE spectrum to obtain the moments as a function of the cut. (Test: agrees nicely at E=1.8 GeV with the direct measurement from BELLE) Remarkable agreement with HQE prediction Strong evidence, especially from the second moment, that bias corrections are needed above above E>1.8 GeV.

  38. What can we learn from this? • The HQE parameter extracted from b cl events are the same as the one obtained from b s events (e.g. mbfrom clv=mbfrom s) • We can use the enormous potential of our clv moment measurements to predict the moments of the photon energy spectrum and to extract the shape function parameter from it! … very important for |Vub| • There is compelling evidence that for E>1.8 GeV the HQE prediction have to be bias corrected (as claimed in hep-ph/0308165) We need more moment measurements as a function of E to to established this bias effect …but the current evidence is already strong.

  39. Ecut=1.8 GeV: <E> =2.312 0.024 GeV <E2> - <E>2 =0.0329 0.0026 GeV2 Ecut=1.8 GeV: BELLE <E> =2.292 0.043 GeV <E2> - <E>2 =0.0305 0.0100 GeV2 Ecut=2.0 GeV: <E> =2.341 0.025 GeV <E2> - <E>2 =0.0222 0.0024 GeV2 Ecut=2.0 GeV: CLEO <E> =2.346 0.034 GeV <E2> - <E>2 =0.0226 0.0070 GeV2 Moment Predictions Predictions for the HQE fit based on cl moments Experimental Results • The HQE fit results would constrain the moments of the photon energy spectrum by a factor ~2 better than the current experimental measurements. Using this information for the extraction of the shape function parameters will significantly improve the theoretical uncertainties on Vub! Getting much closer to a 5% theoretical error |Vub| |Vub|  [0.09(exp) 0.1(SF) 0.05(HQE)] |Vub| |Vub|  [0.09(exp) 0.05(SF) 0.04(HQE)]

  40. Unitarity Triangle - The Future?! Vcb ~ 1% and Vub ~5%(theo) 5% (exp)

  41. bs: very sensitive to “new physics” “New physics” can contribute in the loop … b s …and would lead to an increase of BR(bs) Tight constraints on “new physics parameter” which are especially important for the search at the LHC/LC.

  42. However, a new paper (hep-ph/0408179) from M. Neubert claims that perturbative uncertainties have been underestimated in the theoretical calculations of BRSM: BRSM0.6 100% increase of the uncertainty for the SM prediction! BR(BXs) Today BRHFAG=3.540.3 BRSM =3.700.3 Slide from the ICHEP04 Plenary Talk of Ahmed Ali (DESY).

  43. MH BR(bs) 0.65 Neubert - hep/ph 0408179 200 Potential Impact on “New Physics” Constraints For illustrative purpose only - the TYPEII Two Higgs Doublet Model BR(bs) tan Since the bs decay is very sensitive to certain contributions from „new physics“ a significant incraese of the theoretical uncertainties would soften a lot of rather tight (indirect) limits on „new physics“ processes (e.g. 2HDM). ICHEP2004 BR(bs)

  44. hep-ph/0408179 How can we validate the prediction? According to hep-ph/0408179, also the prediction of the first moment of the photon energy spectrum <E> must suffer from large perturbative uncertainties:  <E> ~0.06 GeV (mb~ 120 MeV) to be continued ... The prediction from hep-ph/0408179 are compatible with the data (E=[1.6,2.0]) but the HQE prediction in the kinetic scheme from Bigi et al. describe the data over the entire cut range much better than the claimed  <E> ~0.06 GeV (mb~ 120 MeV).  Evidence that perturbative (and non-perturbative) uncertainties are under control? In any case, the multitude of moment measurements represent a tool to scrutinize the prediction power of the theory  important for bs and its sensitivity to new physics.

  45. Today 2007?

  46. BACKUP - UT Fits ---------------------------------------------------------- Vcb_err : 0 ( 0.2% ) | 2% | 5% ---------------------------------------------------------- ===> Lmax (flat Likelihood) ---------------------------------------------------------- rho_bar : 0.21 +- 0.05 eta_bar : 0.35 +- 0.02 ---------------------------------------------------------- ===> L*e^{-1/2} ---------------------------------------------------------- rho_bar : 0.22 +- 0.12 | 0.22 +- 0.12 | 0.21 +- 0.14 eta_bar : 0.34 +- 0.05 | 0.34 +- 0.06 | 0.35 +- 0.07 ---------------------------------------------------------- ===> L*e^{-2} ---------------------------------------------------------- rho_bar : 0.21 +- 0.17 | 0.20 +- 0.18 | 0.19 +- 0.20 eta_bar : 0.35 +- 0.08 | 0.35 +- 0.08 | 0.36 +- 0.11 ---------------------------------------

  47. mb(mb) = 4.22 ± 0.06 GeV mc(mc) = 1.33 ± 0.10 GeV Backup - RESULTS Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262 See also report from CKM WS hep-ph/0304132

  48. Backup Lepton Moment Measurement

  49. Based on events with one high energetic electron p* > 1.4 GeV/c , J/Y-veto „tag electron“ , originates predominantly from semileptonic B-decays Look for oppositely charged electrons : Selecting B X e n Decays „ARGUS-Method“ Backgrounds (MC) Signal (MC) pe[GeV/c] pe[GeV/c] pe[GeV/c] 1.0 0.5 0.0 -0.5 -1.0 B‘s at rest : no angularcorrelation between e+ & e e+ & e „back-to- back“ J/y cut 0 0.5 1.0 1.5 2.0 2.5 0 0.5 1.0 1.5 2.0 2.5

  50. Sizable contribution of „upper Vertex“ processes : dominant source of syst. uncertainties at low energies Raw Spectra & Backgrounds mostly Electrons / 50 MeV/c mostly

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