Electroweak double-logs at small x

TL;DR

This paper analyzes electroweak corrections at small x in high-energy processes, proposing a factorization formula and comparing small-x behaviors of EW parton distributions using DGLAP and BFKL approaches.

Contribution

It introduces a general factorization formula for electroweak corrections and investigates the small-x behavior of EW parton distributions with novel T-channel isospin components.

Findings

Large small-x corrections occur only for T=2, affecting transverse WW interactions.

T=1 components are unaffected by small-x corrections, only feeling the form factor.

Comparison of DGLAP and BFKL approaches reveals different behaviors for T=2 and T=1.

Abstract

We investigate enhanced EW corrections to inclusive hard processes in the TeV energy region with emphasis on the small-x situation, in which the hard scale Q is significantly smaller than the available energy \sqrt{s}= Q/x. We first propose and justify a general factorization formula in which the (double-log) EW form factor at scale Q^2 is factorized from EW parton distribution functions, which satisfy evolution equations of DGLAP type. We then investigate the small-x behavior of the EW parton distributions including the novel ones for non-vanishing t-channel weak isospin T and we compare it with a BFKL-type approach. In either approach we find that large small-x corrections of order \alpha_w \log x \log Q^2/M^2 (M being the EW symmetry breaking scale) are present only for T=2 and not for T=1. This implies that only transverse WW interactions (coupled to T=2) are affected, while the T=1 components feel just the form factor at scale Q^2.