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|V xb | from semileptonic B decays

|V xb | from semileptonic B decays. Paolo Gambino INFN Torino. A set of interdependent measurements. Not only BR are relevant: various asymmetries, spectra etc. X. B. What do they have in common?. Simplicity : ew or em currents probe the B dynamics.

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|V xb | from semileptonic B decays

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  1. |Vxb| from semileptonicB decays Paolo Gambino INFNTorino Paolo Gambino Beach 2006 Lancaster

  2. A set of interdependent measurements Not only BR are relevant: various asymmetries, spectra etc Paolo Gambino Beach 2006 Lancaster

  3. X B What do they have in common? Simplicity: ew or em currents probe the B dynamics Simplicity is almost always destroyed in practical situations... Paolo Gambino Beach 2006 Lancaster

  4. VCKM Determination of A A can be determined using |Vcb|or |Vts| Two roads to |Vcb| EXCLUSIVE INCLUSIVE Paolo Gambino Beach 2006 Lancaster

  5. l v b c D* B d FB→D*(1) = ηA [1 - O(1/mb,1/mc)2] |Vcb| from BD*l At zero recoil, where rate vanishes. Despite extrapolation, exp error ~ 2% Main problem is form factor F(1) The non-pert quantities relevant for excl decays cannot be experimentally determined Must be calculated but HQET helps. THE NON-PERT UNKNOWNS MUST BE CALCULATED, CANNOT BE MEASURED Lattice QCD: F(1) = 0.91+0.03-0.04 Sum rules give consistent results Needs unquenching (under way) Even slope may be calculable... δVcb/Vcb~ 5% and agrees with inclusive det, despite contradictory exps BDl gives consistent but less precise results; lattice control is better Paolo Gambino Beach 2006 Lancaster

  6. F(1)BD =1.074(18)(16) first unquenched resultFermilab/MILC Paolo Gambino Beach 2006 Lancaster

  7. Paolo Gambino Beach 2006 Lancaster

  8. far reaching consequences • New Babar BD*lv |Vcb|excl = 3.76 (3)stat(13)syst(18)th x10-2 2 away from previous result! and far from inclusive next WA will likely be lower than it was but higher than this • Reduction of systematics for lept endpoint |Vub| extraction (better understanding of background) Paolo Gambino Beach 2006 Lancaster

  9. Paolo Gambino Beach 2006 Lancaster

  10. can be expressed as double series in αs and ΛQCD/mb (OPE) with parton model as leading termNo 1/mb correction! The advantage of being inclusive ΛQCD«mb : inclusive decays admit systematic expansion in ΛQCD/mbNon-pert corrections are generally small and can be controlled Hadronization probability =1 because we sum over all states Approximately insensitive to details of meson structure as ΛQCD«mb (as long as one is far from perturbative singularities) Paolo Gambino Beach 2006 Lancaster

  11. OPE (HQE): A double expansion can be expressed in terms of structure functions related to Im of • The leading term is parton model, ci are series in αs • New operators have non-vanishing expection values in B and are suppressed by powers of the energy released, Er~ mb-mc • No 1/mb correction! HQE = Heavy Quark Expansion OPE predictions can be compared to exp only after SMEARING and away from endpoints: they have no LOCAL meaning Paolo Gambino Beach 2006 Lancaster

  12. Leptonic and hadronic spectra Total rate gives CKM elmnts; global shape parameters tells us about B structure Paolo Gambino Beach 2006 Lancaster

  13. 1,2 O(1/mb2): mean kin.energy of b in B State of the art Known corrections up to 1/mb3: OPE/HQE predictions are only functions of possible cuts and of heavy quark masses must be carefully defined: short distance, low scale Paolo Gambino Beach 2006 Lancaster

  14. 1,2 1,2 Gremm,Kapustin... O(1/mb2): mean kin.energy of b in B State of the art Known corrections up to 1/mb3: OPE/HQE predictions are only functions of possible cuts and of Paolo Gambino Beach 2006 Lancaster

  15. Known corrections up to 1/mb3: OPE/HQE predictions are only functions of possible cuts and of 1,2 1,2 Gremm,Kapustin... Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG Perturbative Corrections: full O(αs) and O(β0αs2) available For hadronic moments thanks to NEW calculations Trott Aquila,PG,Ridolfi,Uraltsev State of the art Paolo Gambino Beach 2006 Lancaster

  16. Using moments to extract HQE parameters We do know something on HQE par. need to check consistency. • MB*-MB fixes G2= 0.35±0.03 • Sum rules: G2 2, ρD3  -ρ3LS... Central moments can be VERY sensitive to HQE parameters Variance of mass distribution Experiments at Υ(4s) require a CUT on the lepton energy El>0.6-1.5 GeV. Provided cut is not too severe (~1.3GeV) the cut moments give additional info BUT: OPE accuracy deteriorates for higher moments (getting sensitive to local effects) Paolo Gambino Beach 2006 Lancaster

  17. Global fit to |Vcb|, BRsl,HQE Buchmuller & Flacher 06 Based on Gambino & Uraltsev, Benson et al Paolo Gambino Beach 2006 Lancaster

  18. Bauer, Manohar, Ligeti, Luke, Trott 2005 Results in the 1S scheme mc(mc)= 1.224 ± 0.017exp±0.054th GeV • There are several differences • perturbative quark mass scheme • expansion in inverse powers of mc • use of HQET relations • handling of higher orders • estimate of th errors... Paolo Gambino Beach 2006 Lancaster

  19. +unquenching Paolo Gambino Beach 2006 Lancaster

  20. Theoretical uncertainties • Missing higher power corrections • Missing perturbative effects in the Wilson coefficients: O(s2), O(αs/mb2) etc • Intrinsic charm Bigi, Uraltsev, Zwicky • Duality violations How can we estimate all this? Different recipes for 1+3, results for |Vcb| unchanged Paolo Gambino Beach 2006 Lancaster

  21. Testing parton-hadron duality • What is it?For all practical purposes: the OPE. No OPE, no duality • Do we expect violations?Yes, problems prevalently arise because OPE must be continued analytically. there are effects that cannot be described by the OPE, like hadronic thresholds. Expected small in semileptonic decays • Can we constrain them effectively? in a self-consistent way: just check the OPE predictions. E.g. leptonic vs hadronic moments. Models may also give hints of how it works • Caveats?HQE depends on many parameters andwe know only a few terms of the double expansion in αs and Λ/mb. Paolo Gambino Beach 2006 Lancaster

  22. It is not just Vcb ... HQE parameters describe universal properties of the B meson and of the quarks • c and b masses can be determined with competitive accuracy (likely better than 70 and 50 MeV) mb-mc is already measured to better than 30 MeV: a benchmark for lattice QCD etc? • It tests the foundations for inclusive measurements • most Vub incl. determinations are sensitive to a shape function, whose moments are related to μ2 etc, • Bounds on , the slope of IW function (BD* form factor) that are perfectly satisfied by new measurement • ... Need precision measurements to probe limits of HQE & test our th. framework |Vcb| can be measured to 1% Paolo Gambino Beach 2006 Lancaster

  23. Precision studies need • Moments with higher cuts,eg Elcut>1.5 GeV • High hadronic moments, eg <MX6> • Modified Hadron moments <NXn> withNX2= MX2-2 Λ EX +Λ2 need <EXn MX2m> • q2 moments, to constrain IC • QED effects (also for background in b u) • Moments in b→u, especially q2 momentswith a cut on El not above 1.5 GeV • from theory:Wilson coefficients at O(s2),O(s/mb2) Paolo Gambino Beach 2006 Lancaster

  24. ρ= 0.197 ± 0.031 η= 0.351 ± 0.020 |Vub| is now the priority http://www.utfit.org Paolo Gambino Beach 2006 Lancaster

  25. Strictly tree level Paolo Gambino Beach 2006 Lancaster

  26. In detail Bona et al Paolo Gambino Beach 2006 Lancaster

  27. Really an inclusive problem? Paolo Gambino Beach 2006 Lancaster

  28. b→ulvexclusive There is NO normalization of form f.s from HQ symmetry New first unquenched results lattice errors still ~11-15% Sum rules good at low q2 lattice at high q2: complement each other q2 extrapolation from theory bounds plus data: FF normaliza- tion at 1 point is sufficient Ball-Zwicky, Becher-Hill etc Lattice (distant) goal is 5-6% New strategy using combination of rare B,D decays Grinstein& Pirjol Paolo Gambino Beach 2006 Lancaster

  29. |Vub| from B  l  full range Unquenched results probably not yet mature: handle with care Paolo Gambino Beach 2006 Lancaster

  30. |Vub| inclusive Buchmuller & Flacher fit: but life is not that easy! Paolo Gambino Beach 2006 Lancaster

  31. |Vub| (not so much) inclusive |Vub| from total BR(bul) almost exactly like incl |Vcb| but we need kinematic cuts to avoid the ~100x larger bcl background: mX < MD El > (MB2-MD2)/2MB q2 > (MB-MD)2 ... or combined (mX,q2) cuts The cuts destroy convergence of the OPE, supposed to work only away from pert singularities Rate becomes sensitive to “local” b-quark wave function properties like Fermi motion  at leading in 1/mbSHAPE FUNCTION f(k+) Paolo Gambino Beach 2006 Lancaster

  32. Luke, CKM workshop 2005 Paolo Gambino Beach 2006 Lancaster

  33. Each strategy has pros and cons Luke, CKM workshop 2005 Paolo Gambino Beach 2006 Lancaster

  34. What do we know about the SF? • Its moments can be expressed in terms of m.e. of local operators, those extracted from the b->c moments • It can be extracted from b→s • It can also be studied in b→ulv spectra • It gets renormalized and we have learned how (delicate interplay with pert contributions) • Various subleading SFs appear in bulv Paolo Gambino Beach 2006 Lancaster

  35. b Σq u q Weak annihilation coefficient of Darwin operator adding 1loop corrections • -dep of WA sets natural scale of non-factorizable flavor-singlet contributions to BWA see PG,Ossola,Uraltsev BAD: WA ≤3% in rate but gets enhanced in phase space corners GOOD: WA small but can be experimentally constrained,not only in B+/B0 Paolo Gambino Beach 2006 Lancaster

  36. Vub inclusive results A lot can be learned from exp (on shape function from bs, WA, indirect constraints on s.f., subleading effects from cut dependence,...) Intense theoretical activity: • subleading shape functions • optimization of cuts (P+,P- etc) • weak annihilation contribs. • Resum. pert. effects • relation to bs spectrum (SF free relations, see eg Lange 05) • SCET insight REQUIRES MANY COMPLEMENTARY MEASUREMENTS (affected by different uncert.) There is no Best Method Need triple diff rate. Currently 2 groups have provided HFAG the necessary technology: BLNP(Bosch,Lange,Neubert,Paz) & DGE (Andersen,Gardi) Paolo Gambino Beach 2006 Lancaster

  37. BLNP Paolo Gambino Beach 2006 Lancaster

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  41. 4% th error!! large 2 mostly driven by tension in the exp data Paolo Gambino Beach 2006 Lancaster

  42. Comments on BLNP & DGE • BNLP: the 3 scales are very close, does resummation really improve at NLO, NNLO necessary? SF modelling and uncertainty estimates under control? transition to OPE region? • DGE:difficult to swallow that 1 parameter (mb) works better than an infinity... BUT iff it fits data there may be a lesson to learn. Can systematically include error from subl SFs and other power corrections: there are assumptions but it’s not a model. Check error estimates. • nice agreement so far. Both need full NNLO pQCD & other competitors • Ultimately data decide: use them effectively, to scrutinize DGE & BLNP, any info on b u spectra is essential and get as far from thresholds as possible! Paolo Gambino Beach 2006 Lancaster

  43. Cutting the cuts... New exp analyses based on fully reconstructed events allow high discri mination of charmed final states 2004 Unfolded MX spectrum Babar measured MX moments. Results can be improved by cutting in a milder way than usual It’s time to start using b->u data to constrain SF ! Truncated moments are useful to validate theory and constrain f(k+) & WA: q2 moments and hadronic moments even at low cuts PG,Ossola,Uraltsev Paolo Gambino Beach 2006 Lancaster

  44. Summary of main theory limitations Paolo Gambino Beach 2006 Lancaster

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