Resummed Transverse Momentum Distribution of the Higgs Bosons : Summing Up a Divergent Series.

We present the transverse momentum ($p_T$) distribution for Higgs bosons produced in bottom quark annihilation at the LHC. This process is of importance in the models in which the bottom-Higgs Yukawa coupling is enhanced. At small $p_T$ large logarithms, $log (p_T)$, appear in the distribution at every order of perturbation theory with ever increasing powers. These logarithms originate from soft and collinear emissions in the final state and cause a breakdown of perturbation series. We sum the large logarithms to next-to-next-to leading logarithmic accuracy and match the result to the next-to-next-to leading order distribution at large transverse momenta. Our results provide precise predictions at low and intermediate transverse momenta otherwise inaccessible by fixed order perturbation theory.