Resummation of transverse momentum distributions in distribution space

Transverse momentum distributions are an important observable at hadron colliders for both SM measurements and BSM searches. Final states of invariant mass Q are dominantly produced at small transverse momentum qT, where the spectrum is dominated by large Sudakov double logarithms ln(qT/Q) which need to be resummed to all orders to obtain a reliable theory prediction. The resummation is conveniently achieved by solving (renormalization group) evolution equations in impact parameter space, which is Fourier conjugate to transverse momentum space. However, it has been a long-standing issue whether the resummation is also possible directly in transverse momentum space. I will illustrate the difficulties arising in momentum space and derive the momentum space solution based on a new method to solve evolution equations with distributional boundary conditions.