Angular distribution of leptons from the decay of massive vector bosons

TL;DR

This paper analyzes how the angular distribution of leptons from massive vector boson decays depends on transverse momentum, demonstrating the resummation of large logarithmic terms and the preservation of the Lam-Tung relation across all orders.

Contribution

It shows that the large logarithmic terms in helicity structure functions can be resummed similarly to the angular-integrated cross section, maintaining the Lam-Tung relation at all orders.

Findings

Large logarithmic terms originate from the same source as in the angular-integrated cross section.

Resummation of these terms is possible to all orders in the strong coupling constant.

The Lam-Tung relation remains valid as a function of transverse momentum after resummation.

Abstract

We examine the transverse momentum $Q_\perp$ dependence of the helicity structure functions for massive vector bosons of mass $Q$ in hadron reactions. We demonstrate that large logarithmic terms of the form $\ln(Q/Q_\perp)$ in the helicity structure functions have the same origin as the logarithmic terms in the angular-integrated cross section and that they can be resummed to all orders in the strong coupling $\alpha_s$, in the same way as the angular-integrated cross section. As a consequence of current conservation, the resummed part of the helicity structure functions preserves the Lam-Tung relation as a function of $Q_\perp$ to all orders in $\alpha_s$.