Transverse Momentum Dependent Soft Function in SCET to NNLO
We review the factorization theorem for the production of a heavy color-neutral final state with a transverse momentum much smaller than its invariant mass in the framework of soft collinear effective field theory (SCET). This phase space region is plagued by large logarithms of widely separated scales, including large logarithms of rapidity ratios, that need to be resummed for sensible results. In this thesis we use a recently developed formalism that introduces a rapidity regulator in addition to dimensional regularization. This results in an additional renormalization scale, which enables one to also resum rapidity logarithms. The factorized cross sections can be written as a product (convolution) of hard, beam and soft functions in position (momentum) space. We compute the soft function to next-to-next-to-leading-order (NNLO) and determine all relevant anomalous dimensions. Based on the known renormalization group structure, we perform an important cross check of the results by deriving an all order formula for the logarithmic structure of the soft and beam functions. This also allows us to obtain the beam functions to NNLO by comparing to known results in another scheme. With our results, one can now compute the transverse momentum distribution of Higgs production to next-to-next-to-leading-log-prime (NNLL ) accuracy. A new feature in this formalism is that one can directly perform the complete set of relevant scale variations in order to estimate the uncertainty in the resummed cross section.
LU TP 15-32