Comment on double-logarithmic corrections to decays of electroweak bosons

TL;DR

This paper discusses the resummation of double-logarithmic corrections in W and Z boson decays, revealing different Sudakov form factors depending on the boson's on-shell or off-shell status.

Contribution

It clarifies the behavior of DL corrections and Sudakov form factors in electroweak boson decays, including the applicability of dispersion relations with infrared divergences.

Findings

Resummation leads to standard Sudakov form factor for Z decay.

W boson decay exhibits different Sudakov exponents on-shell and off-shell.

Infrared divergences impact the applicability of dispersion relations.

Abstract

We present a short comment on resummation of double-logarithmic (DL) contributions to decays of W and Z -bosons into charged fermion pairs. We show that resummation of DL corrections to the Z -boson decay leads to standard Sudakov form factor with the negative exponent independently of the boson is on-shell or off-shell. In contrast, the Sudakov exponent for the W - decay is negative (positive) when the W-boson is on-shell (off-shell). In this connection we consider applicability of the Dispersion Relations to the case when the imaginary parts contain infrared-divergent contributions.