Tree-level contribution to \bar{B} -> X_d gamma using fragmentation functions

TL;DR

This paper calculates the tree-level contributions to the inclusive radiative decay X_dgamma using fragmentation functions, providing a detailed photon energy spectrum analysis for the budgamma transition.

Contribution

It introduces a method to evaluate collinear photon emission contributions using fragmentation functions and solves the evolution equations numerically for the first time in this context.

Findings

Photon energy spectrum calculated for budgamma transition.

Fragmentation functions from ALEPH data effectively absorbed collinear singularities.

Comparison made between massless and massive light quark cases.

Abstract

We evaluate the most important tree-level contributions connected with the b-> u \bar{u} d gamma transition to the inclusive radiative decay \bar{B}-> X_d gamma using fragmentation functions. In this framework the singularities arising from collinear photon emission from the light quarks (u, \bar{u} and d) can be absorbed into the (bare) quark-to-photon fragmentation function. We use as input the fragmentation function extracted by the ALEPH group from the two-jet cross section measured at LEP, where one of the jets is required to contain a photon. To get the quark-to-photon fragmentation function at the fragmentation scale \mu_F \sim m_b, we use the evolution equation, which we solve numerically. We then calculate the (integrated) photon energy spectrum for b-> u \bar{u} d gamma related to the operators P^u_{1,2}. For comparison, we also give the corresponding results when using nonzero (constituent) masses for the light quarks.