Non-perturbative corrections to the Drell-Yan transverse momentum distribution

We study non-perturbative corrections to the transverse momentum distribution of vector bosons in the Drell-Yan process. Factorizing out the Sudakov effects due to soft gluons we express their contribution to the distribution in the form of the vacuum averaged Wilson loop operator. We calculate the non-perturbative contribution to the Sudakov form factor using the expansion of the Wilson loop over vacuum fields supplemented with the expression for non-local gauge invariant field strength correlator. Although the Wilson loop is defined in an essentially Minkowski kinematics, the part of the non-perturbative contribution depending on the invariant mass of the produced vector bosons is governed by asymptotics of the correlator at large space-like (euclidean) separations and therefore can be calculated using conventional non-perturbative methods. Applying the results of lattice calculations we found that the obtained expression for the non-perturbative power corrections is in qualitative agreement with known phenomenological expressions at large transverse momenta and deviate from them at small transverse momenta.