The Factorisation of the t-channel Pole in Quark-Gluon Scattering

TL;DR

The work develops a current-based factorisation of $2\to n$ QCD scattering in the MRK regime, showing that the $t$-channel pole can be expressed as a contraction of two local currents for quark-gluon processes. It identifies that eight helicity configurations reduce to pure $t$-channel pole structures except for two suppressed channels, for which the $t$-channel description is still preserved after accounting for additional terms. A gauge-invariant definition of the gluon $t$-channel current is introduced, together with the Colour Acceleration Multiplier (CAM) to capture color-flow effects and approach to the MRK limit. Comparisons with full tree-level results indicate that the approach closely reproduces multi-jet amplitudes, with CAM providing noticeable improvement for 3- and 4-jet final states and enabling more reliable all-orders resummation in collider phenomenology.

Abstract

By exploring the scattering of specific helicity states in quark-gluon scattering at tree level we show explicitly that the t-channel pole can be described exactly as a contraction of two local currents. Furthermore, we demonstrate that out of eight non-zero helicity possibilities, only two suppressed channels have contributions that are not pure, factorised t-channel poles. We thereby extract a gauge-invariant definition for the t-channel current generated by the scattering of a gluon. This offers a slight improvement in the description of gluon scattering in the framework of arXiv:0908.2786 for the prediction of n-jet rates at hadron colliders.

Figures (4)

• Figure 1: This figure illustrates the analytic structure of the approximating amplitudes. The $2\!\to\!n$ scattering amplitude is described by a basic $2\!\to\!2$ process of current contractions under a $t$-channel exchange, with effective vertices describing the effect of additional gluon radiation. This ensures the correct MRK limit.
• Figure 2: The $s$-, $t$- and $u$-channel processes which contribute to $q^-(p_a) + g^+(p_b) \to q^-(p_1) + g^+(p_2)$.
• Figure 3: Results for d$\sigma$/d$\Delta y$ and d$\sigma$/d$\phi$ for $ud\to ugd$ (a)--(b), $ug\to ugg$ (c)--(d) and $gg\to ggg$ (e)--(f). $\Delta y$ is the rapidity difference between the most forward and most backward hard jet. The black solid line represents the full matrix element, the red dashed line is the implementation based on the scattering of quark currents Andersen:2009nu, the blue dashed line is this result with the Colour Adjusted Multiplier (CAM) of Eq. \ref{['eq:finalcol']} and the green dashed line has the CAM and the effect of flipped helicities, Eq. \ref{['eq:colsumandaverhelflipamp']}.
• Figure 4: As in Fig.\ref{['fig:3jres']}, but now for the $4j$ final states: $ud\to uggd$ (a)--(b), $ug\to uggg$ (c)--(d) and $gg\to gggg$ (e)--(f).