Timelike showers with jet recoils

Abstract

We propose a new way to impose four-momentum conservation on timelike parton-shower branchings, allowing for recoil to be imparted not only to individual partons but also to groups of partons, "jets". In this work we present an explicit realisation of this idea for a dipole parton-shower, using angular ordering to decide which partons are grouped into jets in a way that does not require explicit jet clustering at each stage of the evolution. We verify that the algorithm satisfies next-to-leading logarithmic (NLL) accuracy criteria, from numerical fixed-order tests as well as resummation tests across a range of observables. Our conclusion is that jet recoils provide a viable path for adapting existing dipole/antenna-type showers to achieve NLL accuracy.

Figures (10)

• Figure 1: A three-parton system $\bar{q} q g_1$ emitting a gluon, $g_2$. Four distinct angular phase-space regions are highlighted, with the emission being shown in region 1.
• Figure 2: Illustration, as in Refs. Dasgupta:2018nvjvanBeekveld:2022zhl, of incorrect recoil assignment for PanLocal ($\beta_\text{ps} = 0$), which leads to the wrong NLL terms (the PanLocal shower is NLL-accurate for $\beta_\text{ps} > 0$). The top panel shows the Lund plane coordinates of a first emission $g_1$ and the contour along which a second emission $g_2$ is produced, in green. The lower two panels show the change in the first emission's transverse momentum ($\ln k_t / \tilde{k}_t$) and rapidity ($\eta-\tilde{\eta}$) due to the emission of $g_2$. The large recoil given in region $\eta_1 < \eta < 0$ is problematic at NLL, whereas the shaded region around $\eta \simeq \eta_1$ contributes only at NNLL.
• Figure 3: Same as Fig. \ref{['fig:wrong-NLL-fo']} for the jet-recoil attribution described in section \ref{['sec:example-as2']}.
• Figure 4: Lund plane and cartoon of event showing which partons are identified as $\mathcal{J}$. The new emission is shown in green and the partons comprising the jet in blue. The blue arrow on the Lund plane indicates the region of phase space in which particles will be included in $\mathcal{J}$.
• Figure 5: Illustration of the connection between intervals and regions of the Lund plane for the $\bar{q} g_1$ dipole in the above three-parton event. The coloured lines on the cartoon of the event correspond with the colour of the Lund leaf on which an emission appears, and thus which parton(s) in the diagram are considered as the emitter.