Abstract
We study the power corrections to Transverse Momentum Distributions (TMDs) by analyzing renormalon divergences of the perturbative series. The renormalon divergences arise independently in two constituents of TMDs: the rapidity evolution kernel and the small-b matching coefficient. The renormalon contributions (and consequently power corrections and non-perturbative corrections to the related cross sections) have a non-trivial dependence on the Bjorken variable and the transverse distance. We discuss the consistency requirements for power corrections for TMDs and suggest inputs for the TMD phenomenology in accordance with this study. Both unpolarized quark TMD parton distribution function and fragmentation function are considered.
Highlights
By [26] and [27] implement an ansatz within the standard CSS approach with b∗-prescription in the impact parameter space
We study the power corrections to Transverse Momentum Distributions (TMDs) by analyzing renormalon divergences of the perturbative series
In order to describe this effect in the modern TMD framework, we recall that the definition of TMDs requires the combination of the Soft Function matrix element with the transverse momentum dependent collinear function
Summary
Throughout the paper we follow the notation for TMDs and corresponding functions introduced in [14]. The main subject of the paper is the dependence of TMDs on the parameter b which is generically unrestricted since it is a variable of Fourier transformation It is int√eresting and numerically important to consider the range of small b (here and later b = b2). The matching coefficient for TMDFF Cf→f satisfies the same set of evolution equation with only substitution of PDF splitting function P (x) by the FF ones, P(z)/z2 [14]. Using these equations one can find the expression for the logarithmic part of the matching coefficients at any given order, in terms of the anomalous dimensions and the finite part of the coefficient functions. The expressions for the anomalous dimensions, the recursive solution of the RGEs and the explicit expressions for the coefficients C and C can be found, e.g. in [14]
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