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

Understand

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.