Paolo Gambino 15/12/07 Vxb Heidelberg1

Inclusive determination of Vub

in the kinetic scheme Paolo Gambino

Università di Torino and INFN Torino

Paolo Gambino 15/12/07 Vxb Heidelberg2

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 Heidelberg3

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(αs2 β0) corrections -5% in Vub

PG,Gardi,Ridolfi

Paolo Gambino 15/12/07 Vxb Heidelberg4

Fermi motion (I)

Leading SF resums leading twist effects, mb ∞ universal, q2 indep

Finite mb distribution functionsinclude all 1/mb effects, non-universalno need for subleading SFs

This factorization formula perturbatively defines the distribution functions

Paolo Gambino 15/12/07 Vxb Heidelberg5

Fermi motion (II)local OPE prediction

The variance gets negative

Importance of subleading effects

Paolo Gambino 15/12/07 Vxb Heidelberg6

The high q2 tail

Higher dimensional operators are not suppressed at high q2 leading topathological features. Origin in the non-analytic square root

In the integrated rate the singularityis removed by the WA operator: needsmodelling for q2 spectrum

Model I

OPE

WA matrix element BWA parameterizes global properties of the tail

Paolo Gambino 15/12/07 Vxb Heidelberg7

High q2 (II)

Two models of the high q2

tail q2>q*2 plus a δ(q2-mb

2)

for the rest of WA

8.5 < q*2 <13.5 GeV2

Σq

q

b

u

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 Heidelberg8

Functional forms

About 100 forms considered, large variety. Small uncertainty (1-2%) on Vub

Paolo Gambino 15/12/07 Vxb Heidelberg9

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 Heidelberg10

Vub determinations

Paolo Gambino 15/12/07 Vxb Heidelberg11

Constraining Weak Annihilations

An example

Paolo Gambino 15/12/07 Vxb Heidelberg12

Vub determinations with BWA(1GeV)=0.0188

Paolo Gambino 15/12/07 Vxb Heidelberg13

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 Heidelberg14

Basic functional forms