Paolo Gambino Beach 2006 Lancaster 1 |V xb | from semileptonic B decays Paolo Gambino INFN Torino

Paolo Gambino Beach 2006 Lancaster 2 A set of interdependent measurements b → c l νtreeBR~10%|V cb | b → u l νtree~10 -3 |V ub | b → s  loop~ new physics, |V ts | b → d  loop~ new physics, |V td | Not only BR are relevant: various asymmetries, spectra etc

Paolo Gambino Beach 2006 Lancaster 3 What do they have in common? INCLUSIVEEXCLUSIVE OPE: non-pert physics described by B matrix elemnts of local operators can be extracted by exp suppressed by 1/m b 2 Form factors: in general computed by non pert methods (lattice, sum rules,...) symmetry can provide normalization Simplicity: ew or em currents probe the B dynamics B X Simplicity is almost always destroyed in practical situations...

Paolo Gambino Beach 2006 Lancaster 4 EXCLUSIVE Determination of A V CKM A can be determined using |V cb | or |V ts | Two roads to |V cb | INCLUSIVE

Paolo Gambino Beach 2006 Lancaster 5 |V cb | 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. Lattice QCD: F(1) = Sum rules give consistent results Needs unquenching (under way) Even slope may be calculable... F B →D * (1) = η A [1 - O(1/m b,1/m c ) 2 ] B  Dl gives consistent but less precise results; lattice control is better δV cb /V cb ~ 5% and agrees with inclusive det, despite contradictory exps THE NON-PERT UNKNOWNS MUST BE CALCULATED, CANNOT BE MEASURED B D*D* bc d l v

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

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8 far reaching consequences New Babar B  D * lv |V cb | excl = 3.76 (3) stat (13) syst (18) th x  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 |V ub | extraction (better understanding of background)

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10 The advantage of being inclusive Λ QCD «m b : inclusive decays admit systematic expansion in Λ QCD /m b Non-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 Λ QCD «m b (as long as one is far from perturbative singularities) α s and can be expressed as double series in α s and Λ QCD /m b (OPE) with parton model as leading term No 1/m b correction!

Paolo Gambino Beach 2006 Lancaster 11 HQE = Heavy Quark Expansion A double expansion can be expressed in terms of structure functions related to Im of OPE (HQE):  The leading term is parton model, c i are series in α s  New operators have non-vanishing expection values in B and are suppressed by powers of the energy released, E r ~ m b -m c  No 1/m b correction! 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 heavy quark masses must be carefully defined: short distance, low scale State of the art Known corrections up to 1/m b 3 : OPE/HQE predictions are only functions of possible cuts and of 1, 2 O(1/m b 2 ): mean kin.energy of b in B

Paolo Gambino Beach 2006 Lancaster 14 State of the art Known corrections up to 1/m b 3 : OPE/HQE predictions are only functions of possible cuts and of 1, 2 Gremm,Kapustin... 1,21,2 O(1/m b 2 ): mean kin.energy of b in B

Paolo Gambino Beach 2006 Lancaster 15 Perturbative Corrections: full O( α s ) and O(β 0 α s 2 ) available For hadronic moments thanks to NEW calculations Trott Aquila,PG,Ridolfi,Uraltsev Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG State of the art Known corrections up to 1/m b 3 : OPE/HQE predictions are only functions of possible cuts and of 1, 2 Gremm,Kapustin... 1,21,2

Paolo Gambino Beach 2006 Lancaster 16 Using moments to extract HQE parameters Central moments can be VERY sensitive to HQE parameters Experiments at Υ(4s) require a CUT on the lepton energy E l > GeV. Provided cut is not too severe (~1.3GeV) the cut moments give additional info We do know something on HQE par. need to check consistency. M B* -M B fixes  G 2 = 0.35±0.03 Sum rules:  G 2    2, ρ D 3  -ρ 3 LS... BUT: OPE accuracy deteriorates for higher moments (getting sensitive to local effects) Variance of mass distribution

Paolo Gambino Beach 2006 Lancaster 17 Global fit to | V cb |, BR sl, 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 There are several differences perturbative quark mass scheme expansion in inverse powers of m c use of HQET relations handling of higher orders estimate of th errors... m c (m c )= ± exp ±0.054 th GeV

Paolo Gambino Beach 2006 Lancaster 19  +unquenching

Paolo Gambino Beach 2006 Lancaster 20 Theoretical uncertainties 1.Missing higher power corrections 2.Missing perturbative effects in the Wilson coefficients: O(  s 2 ), O(α s /m b 2 ) etc 3.Intrinsic charm Bigi, Uraltsev, Zwicky 4.Duality violations How can we estimate all this? Different recipes for 1+3, results for |V cb | unchanged

Paolo Gambino Beach 2006 Lancaster 21 Testing parton-hadron duality What is it? What is it? For all practical purposes: the OPE. No OPE, no duality Do we expect violations? 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? 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? Caveats? HQE depends on many parameters and we know only a few terms of the double expansion in α s and Λ/m b.

Paolo Gambino Beach 2006 Lancaster 22 It is not just V cb... 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) m b -m c is already measured to better than 30 MeV: a benchmark for lattice QCD etc? It tests the foundations for inclusive measurements most V ub 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 |V cb | can be measured to 1%

Paolo Gambino Beach 2006 Lancaster 23 Precision studies need Moments with higher cuts, eg E l cut >1.5 GeV High hadronic moments, eg Modified Hadron moments with N X 2 = M X 2 -2 Λ E X +Λ 2 need q 2 moments, to constrain IC QED effects (also for background in b  u) Moments in b → u, especially q 2 moments with a cut on E l not above 1.5 GeV from theory: Wilson coefficients at O(  s 2 ),O(  s /m b 2 )

Paolo Gambino Beach 2006 Lancaster 24 |V ub | is now the priority ρ = ± η = ±

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 → ulv exclusive 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 q 2 lattice at high q 2 : complement each other q 2 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 |V ub | from B  l FF calculation V ub [10 -3 ] Ball-Zwicky q 2 < § HPQCD q 2 > § FNAL q 2 > § APE q 2 > § full range Unquenched results probably not yet mature: handle with care

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

Paolo Gambino Beach 2006 Lancaster 31 |V ub | (not so much) inclusive |V ub | from total BR(b  ul ) almost exactly like incl |V cb | but we need kinematic cuts to avoid the ~100x larger b  cl background: m X (M B 2 -M D 2 )/2M B q 2 > (M B -M D ) 2... or combined (m X,q 2 ) 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/m b SHAPE 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 Weak annihilation ΣqΣq q b u coefficient of Darwin operator adding 1loop corrections  -dep of WA sets natural scale of non-factorizable flavor-singlet contributions to B WA 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 + /B 0

Paolo Gambino Beach 2006 Lancaster 36 V ub inclusive results 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) A lot can be learned from exp (on shape function from b  s , WA, indirect constraints on s.f., subleading effects from cut dependence,...)

Paolo Gambino Beach 2006 Lancaster 37 BLNP

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

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 (m b ) 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 M X spectrum Babar measured M X 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: q 2 moments and hadronic moments even at low cuts PG,Ossola,Uraltsev

Paolo Gambino Beach 2006 Lancaster 44 Summary of main theory limitations processquantityTh errorneedsgoal B→D * lv |V cb | ~4% New lattice results 1% B→X c lv |V cb | ~1.5% New pert calculations <1% B→ π lv |V ub | ~12% Lattice developments 5-6% B→X u lv |V ub | ~6% More data, checks, synergy th/exp <5%