Kinematic power corrections in TMD factorization theorem

TL;DR

This paper studies the series of kinematic power corrections in TMD factorization, deriving and summing them to improve theoretical predictions and address phenomenological challenges.

Contribution

It derives and sums a series of kinematic power corrections in TMD factorization, restoring key symmetries and providing a more accurate theoretical framework.

Findings

Summed KPCs restore charge conservation and frame invariance.

The resulting expression resembles a free-quark hadronic tensor.

Numerical estimates show an almost constant shift in cross-sections.

Abstract

This work is dedicated to the study of power expansion in the transverse momentum dependent (TMD) factorization theorem. Each genuine term in this expansion gives rise to a series of kinematic power corrections (KPCs). All terms of this series exhibit the same properties as the leading term and share the same nonperturbative content. Among various power corrections, KPCs are especially important since they restore charge conservation and frame invariance, which are violated at a fixed power order. I derive and sum a series of KPCs associated with the leading-power term of the TMD factorization theorem. The resulting expression resembles a hadronic tensor computed with free massless quarks while still satisfying a proven factorization statement. Additionally, I provide an explicit check of this novel form of factorization theorem at the next-to-leading order (NLO) and demonstrate the restoration of the frame-invariant argument of the leading-power coefficient function. Numerical estimations show that incorporating the summed KPCs into the cross-section leads to an almost constant shift, which may help to explain the observed challenges in the TMD phenomenology.