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Inclusive determination of V ub in the kinetic scheme

Inclusive determination of V ub in the kinetic scheme. Paolo Gambino Università di Torino and INFN Torino. A new theoretical analysis. kinetic scheme . Wilsonian infrared cutoff µ ~1 GeV: contribution of soft gluons absorbed into definition of HQE parameters AND distribution function(s)

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Inclusive determination of V ub in the kinetic scheme

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  1. Inclusive determination of Vubin the kinetic scheme Paolo Gambino Università diTorino and INFN Torino Paolo Gambino 15/12/07 Vxb Heidelberg

  2. A new theoretical analysis • kinetic scheme. Wilsonian infrared cutoff µ~1 GeV: contribution of soft gluons absorbed into definition of HQE parameters AND distribution function(s) • Fermi motion: finite mb SF, includes all subleading corrections • local OPE breaks down at high q2: need to model the tail, consistent with positivity, WA naturally emerge. • Triple differential distribution including all known pert and nonpert effects, c++ code published in PG, P.Giordano, G.Ossola, N.Uraltsev, JHEP10(2007)058 Paolo Gambino 15/12/07 Vxb Heidelberg

  3. Perturbative corrections In the kin scheme soft gluon emission is inhibited the spectrum has only collinear singularities • no resummation of collinear logs • complete implementation of O(αs2β0) corrections -5% in Vub PG,Gardi,Ridolfi Paolo Gambino 15/12/07 Vxb Heidelberg

  4. Fermi motion (I) Leading SF resums leading twist effects, mb ∞ universal, q2 indep Finite mb distribution functions include all 1/mb effects, non-universal no need for subleading SFs This factorization formula perturbatively defines the distribution functions Paolo Gambino 15/12/07 Vxb Heidelberg

  5. local OPE prediction The variance gets negative Fermi motion (II) Importance of subleading effects Paolo Gambino 15/12/07 Vxb Heidelberg

  6. The high q2 tail Higher dimensional operators are not suppressed at high q2 leading to pathological features. Origin in the non-analytic square root In the integrated rate the singularity is removed by the WA operator: needs modelling for q2 spectrum Model I OPE WA matrix element BWA parameterizes global properties of the tail Paolo Gambino 15/12/07 Vxb Heidelberg

  7. b Σq u q High q2 (II) Two models of the high q2 tail q2>q*2 plus a δ(q2-mb2) for the rest of WA 8.5 < q*2 <13.5 GeV2 NB: O(1) mixing between WA and Darwin ops. The isosinglet part of WA can be substantial. Tail analysis is complementary to B+/Bd Paolo Gambino 15/12/07 Vxb Heidelberg

  8. Functional forms About 100 forms considered, large variety. Small uncertainty (1-2%) on Vub Paolo Gambino 15/12/07 Vxb Heidelberg

  9. Theoretical errors • Parametric errors generally dominant, in particular mb, 3-4% • Perturbative corrections 2-3% • Functional form 1-2% • Modelling of the q2 tail and WA depending on cut from 0 to 7%. WA tends to decrease Vub Overall theory errors are 5-9%, depending on the cuts. Paolo Gambino 15/12/07 Vxb Heidelberg

  10. Vubdeterminations Paolo Gambino 15/12/07 Vxb Heidelberg

  11. Constraining Weak Annihilations An example Paolo Gambino 15/12/07 Vxb Heidelberg

  12. Vub determinations with BWA(1GeV)=0.0188 Paolo Gambino 15/12/07 Vxb Heidelberg

  13. Summary • New method available, theory errors investigated in detail • high q2 determination has larger errors, WA tend to decrease Vub • possibility to constrain WA using q2 spectrum • Vub is slightly lower, is it? Paolo Gambino 15/12/07 Vxb Heidelberg

  14. Basic functional forms Paolo Gambino 15/12/07 Vxb Heidelberg

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