1305.6464 (H. M. Asatrian et al.)

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

H. M. Asatrian, C. Greub

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.

View original: http://arxiv.org/abs/1305.6464