Giulia ricciardi universit di napoli federico ii italy
This presentation is the property of its rightful owner.
Sponsored Links
1 / 17

Giulia Ricciardi Università di Napoli “Federico II”, Italy PowerPoint PPT Presentation


  • 67 Views
  • Uploaded on
  • Presentation posted in: General

Giulia Ricciardi Università di Napoli “Federico II”, Italy. XLIst Rencontres de Moriond- March 19th, 2006. Introduction. Semileptonic B decays spectra LD effects due to soft interactions between the heavy quark and the light degrees of freedom.

Download Presentation

Giulia Ricciardi Università di Napoli “Federico II”, Italy

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Giulia ricciardi universit di napoli federico ii italy

Giulia Ricciardi

Università di Napoli “Federico II”, Italy

XLIst Rencontres de Moriond- March 19th, 2006


Introduction

Introduction

  • 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


Introduction 2

Introduction (2)

  • 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


Introduction 3

Introduction (3)

  • 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 )


Ld effects

LD effects

  • 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


Radiative decay

Radiative decay

  • Resummed (cumulative) differential distribution

  • with

  • In the two body decay the hadron energy fixes the hard scale Q, by kinematical reasons


Giulia ricciardi universit di napoli federico ii italy

  • is the (cumulative) resummed QCD form factor

  • is a short distance coefficient function, independent on ts

  • is a remainder function, vanishing for ts_ 0


Semileptonic decays

Semileptonic decays

In

one can obtain a general resummation formula for the triple

differential distribution

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


Semileptonic decays1

Semileptonic decays

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


Semileptonic decays2

Semileptonic decays

  • 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


Classes of semileptonic spectra

Classes of semileptonic spectra

  • 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+


Class 1

Class 1

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


Single distribution in e x

Single distribution in EX

  • 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)


Class 2

Class 2

  • 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


Check 1 of resummation formula

Check 1 of resummation formula

  • 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)


Check 2 of resummation formula

Check 2 of resummation formula

  • 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


Conclusions

Conclusions

  • 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 EXLD structure comparable directly with radiative decay

    2) opposite behaviour respect to

    distributions integrated over EXLD structure not directly

    comparable


  • Login