Transverse Momentum Distribution in B Decays

Abstract

We derive the strange quark transverse momentum distribution for the $% b\to sγ$ decay. A resummed formula is presented showing the singularity structure in the impact parameter $b$. We observe the appearance of a new next-to-leading soft singularity. The first term of the coefficient function is calculated to complete the evaluation of the distribution with next-to-leading accuracy and the constant term. The connection with the shape function for the mass spectrum is briefly discussed. The extension of the shape function interpretation to the transverse momentum distribution seems not to be longer possible. The complete perturbative $O(α)$ transverse momentum distribution formula for the $b \to s γ$ process is given. The coefficient function, the double and single logarithmic terms together with the remainder function are explicitely evaluated and presented in analytic form. A resummed expression is also shown.