Coherent Parton Showers with Local Recoils

TL;DR

The paper develops a dipole-type parton shower formalism based on Catani–Seymour subtraction kernels with local energy-momentum conservation at every branching. By carefully choosing recoil strategies, phase-space boundaries, and an evolution variable tied to the dipole kinematics (notably the invariant mass $s_{ik}$ and transverse momentum $p_\perp^2$), the authors achieve correct soft-gluon coherence and Sudakov factors while enabling straightforward NLO matching. They provide detailed kinematic parametrizations for final- and initial-state radiation, including explicit phase-space factorization and splitting probabilities for all spectator configurations, and demonstrate that soft and collinear limits reproduce the expected QCD behaviour with controlled recoil effects beyond NLL. The framework paves the way for implementations that combine exact momentum conservation, soft coherence, and robust NLO matching, improving the theoretical reliability of parton showers for LHC phenomenology.

Abstract

We outline a new formalism for dipole-type parton showers which maintain exact energy-momentum conservation at each step of the evolution. Particular emphasis is put on the coherence properties, the level at which recoil effects do enter and the role of transverse momentum generation from initial state radiation. The formulated algorithm is shown to correctly incorporate coherence for soft gluon radiation. Furthermore, it is well suited for easing matching to next-to-leading order calculations.

Figures (3)

• Figure 1: Allowed phase space regions for emissions from a final-final dipole expressed in the Dalitz variables $x_k=2Q\cdot p_k/Q^2$ for a dipole of mass $s_{ij}=100\ {\rm GeV}$ and infrared cutoff $\mu=5 {\rm GeV}$. The shaded region is accessible for emissions off the parton $i$, whereas the area enclosed by the solid line is accessible for emissions off parton $j$. The area enclosed by the dotted line is an example of the phase space excluded when starting at a scale lower than $s_{ij}$. Note that the infrared cutoff is exaggerated for illustrative purposes only. In practice, almost the whole physical phase space will be available.
• Figure 2: Available phase space for a final-initial dipole with invariant momentum transfer $\sqrt{s_{aj}}=\sqrt{-t}=100\ {\rm GeV}$ and an infrared cutoff of $5\ {\rm GeV}$. The shaded region is accessible starting at the hard scale, the region enclosed by the solid line is an example of the phase space excluded when starting at a lower scale. The phase space regions for an initial-final dipole are identical. For a final-initial dipole, the variables are $x_p=x$, $z_p=z$, for the initial-final one $x_p=x$, $z_p=1-u$. Note that in the latter case $u\to 1$ and $u\to 0$ correspond to a collinear limit.
• Figure 3: Available phase space for emissions off an initial-initial dipole of mass $100\ {\rm GeV}$ with $\tau=0.02$ and infrared cutoff $5\ {\rm GeV}$. The shaded region is the available phase space when starting from the hard scale, the region enclosed by the solid line is an example of the phase space excluded when starting at a lower scale.