Tree-level contribution to B[over ¯]→X_{d}γ using fragmentation functions

Asatrian, H. M.; Greub, C. (2013). Tree-level contribution to B[over ¯]→X_{d}γ using fragmentation functions. Physical review. D - particles, fields, gravitation, and cosmology, 88(7), 074014-1. Melville, N.Y.: American Physical Society 10.1103/PhysRevD.88.074014

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We evaluate the most important tree-level contributions connected with the b→uu ¯ ¯ dγ transition to the inclusive radiative decay B ¯ ¯ ¯ →X d γ using fragmentation functions. In this framework the singularities arising from collinear photon emission from the light quarks (u , 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 the large electron positron (LEP) collider, where one of the jets is required to contain a photon. To get the quark-to-photon fragmentation function at the fragmentation scale μ F ∼m b , we use the evolution equation, which we solve numerically. We then calculate the (integrated) photon energy spectrum for b→uu ¯ ¯ dγ 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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