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arxiv 1305.6464 v1 pith:VA32BDLI submitted 2013-05-28 hep-ph

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

classification hep-ph
keywords fragmentationgammafunctionphotonfunctionslightquark-to-photonquarks
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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