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Giulia Ricciardi Università di Napoli “Federico II”, Italy

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Giulia Ricciardi

Università di Napoli “Federico II”, Italy

XLIst Rencontres de Moriond- March 19th, 2006

- Semileptonic B decays spectra
LD effects due to soft interactions between the heavy quark and the light degrees of freedom.

Large perturbative (PT) contributions at threshold

- At threshold different scales: the hard scale Q is determined by the final total energy EX

- LD effects manifest themselves in PT in the form of series of large infrared logs
large logs in PT “signal” LD effects

- Large logs in PT theory need to be resummed
- universality of LD effects studied by comparing the logarithmic structure of different spectra in PT
- Universality is looked for into a similar factorization structure

- Universality is limited by different kinematics of different spectra
- comparison with hadron mass spectrum of
- All semileptonic spectra are divided in two classes,
- pure SD relation with the radiative decay (Hadron energy spectrum)
- No such pure SD relation (Hadron mass spectrum, electron spectrum,spectrum )

- Threshold region characterized by different scales
- presence of PT logs terms to be resummed at all orders
Q always indicates the hardest scale Q= 2 EX

- Also in the radiative decay B -> Xs g threshold logs to be resummed

- Resummed (cumulative) differential distribution
- with
- In the two body decay the hadron energy fixes the hard scale Q, by kinematical reasons

- is the (cumulative) resummed QCD form factor
- is a short distance coefficient function, independent on ts
- is a remainder function, vanishing for ts_ 0

In

one can obtain a general resummation formula for the triple

differential distribution

where w=2EX/mb and x=2 El/mb and

The infrared logs can be organized in a series and factorized

into the universal form factor S

where Q = 2 EX and by definition

- All single distributions can be obtained by the most general triple differential distribution

- is the universal QCD form factor, which now is evaluated for a coupling with a general argument
Q= w mb = 2 EX

- In the tree body decay at tree level, the hadron energy is no more fixed at the b quark mass, as in the radiative decay

- All distributions can be obtained by integrating the triple differential distribution:
can be divided into two classes, according to the fact that it is necessary or not to integrate over the hadron energy,

1) no integration over EX-directly related via short distance (SD) coefficients to the photon spectrum in the radiative decay.

the same structure of threshold logs

f.i. single distribution in EX

2) obtained by integrating over EX— CANNOT be directly related via SD coefficients to the photon spectrum in the radiative decay.

not same structure of threshold logs

f.i. single distributions in the invariant hadronic mass mX2, in the charged electron energy, in the lightcone variable p+

Example: spectrum in hadron energyw=2 EX/mb

Two integrations from the triple differential factorized form, but EX

not integrated over

Since the coefficient function does not depend on u, the second

integration only involves the QCD form factor and the remainder

- At EX < mb/2 there are no large logs
w= 2 EX/mb

- At EX > mb/2 large logs appear, which can be resummed (Sudakov shoulder +universality)

- Such distributions do not have the same log structure than the radiative decay—therefore cannot be simply related via short distance coefficients
- F.i. if we compute the NLO distribution in the invariant hadron mass squared
- differ to first order with radiative decay,
- that is , f.i. and so on

- In the resummation formula of the triple differential spectrum we have that the resummed QCD form factor depends explicitly only on
- This is therefore the argument of the factorized infrared logarithms
- expanding the resummed expression up to we find agreement with previous fixed order calculation (De Fazio, Neubert)

- the argument of the running coupling is the hard scale Q, that is the hadronic energy
- The correct argument need to be verified at 2nd order in the coupling constant, since
- Only available 2nd order calculation: corrections to
order to the distribution in the light cone momentum (Hoang, Ligeti and Luke);

with such scale correctly prediction of

terms

- Critical analysis of factorization and universality for semi-inclusive B decays
- LD effects manifest themselves in PT series of large IR lgs—universality implies identical series of large logs-same factorization structure
- Resummation formula for the triple differential distribution
- Semileptonic spectra into two groups
1) Distributions not integrated over EXLD structure comparable directly with radiative decay

2) opposite behaviour respect to

distributions integrated over EXLD structure not directly

comparable