Inclusive determination of V ub in the kinetic scheme
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Transcript of Inclusive determination of V ub in the kinetic scheme
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