Higher-Order Corrections to Timelike Jets

TL;DR

The paper develops a unitarity-based, all-orders framework for timelike jet evolution using a dipole-antenna shower, enabling systematic matching to tree-level matrix elements for arbitrary parton multiplicities. It casts perturbative corrections as a Markov-chain evolution with Sudakov exponentiation, and introduces a flexible evolution-variable scheme that includes a family of Q_E definitions and trial functions to enable efficient veto-based sampling. Substantial advances include partial two-to-three one-loop and two-to-four tree-level improvements, subleading-color corrections absorbed into leading-color antennae, and a robust method for estimating perturbative uncertainties directly on a single generated sample. The approach is implemented in the Vincia plugin for PYTHIA 8 and validated against LEP data, showing competitive agreement and controlled uncertainties, while offering a pathway toward improved accuracy for LHC backgrounds through multi-jet matching and systematic color and scale variations.

Abstract

We present a simple formalism for the evolution of timelike jets in which tree-level matrix element corrections can be systematically incorporated, up to arbitrary parton multiplicities and over all of phase space, in a way that exponentiates the matching corrections. The scheme is cast as a shower Markov chain which generates one single unweighted event sample, that can be passed to standard hadronization models. Remaining perturbative uncertainties are estimated by providing several alternative weight sets for the same events, at a relatively modest additional overhead. As an explicit example, we consider Z -> q qbar evolution with unpolarized, massless quarks and include several formally subleading improvements as well as matching to tree-level matrix elements through alpha_s^4. The resulting algorithm is implemented in the publicly available VINCIA plugin to the PYTHIA 8 event generator.

Figures (33)

• Figure 1: Contours of constant value of the antenna function, $\bar{a}^0_{ijk}$ for $q\bar{q}\to qg\bar{q}$ derived from $Z$ decay as function of the two phase-space invariants, with an arbitrary normalization and a logarithmic color scale. Larger values are shown in lighter shades. The (single) collinear divergences sit on the axes, while the (double) soft divergence sits at the origin.
• Figure 2: Schematic overview of how the full collinear singularity of parton $I$ and the soft singularity of the $IK$ pair, respectively, originate in different shower types. ($\Theta_I$ and $\Theta_K$ represent angular vetos with respect to partons $I$ and $K$, respectively, and $\Theta_{IK}$ represents a sector phase-space veto, see text.)
• Figure 3: The three phase-space sectors in a color-singlet $g_ig_jg_k$ configuration, using $p_{\perp }$ as the disciriminator for which sector a given emission/clustering/history belongs to.
• Figure 4: Illustration of the branching phase space, eq. (\ref{['eq:phasespace']}), for $q\bar{q}\to qg\bar{q}$, with the original dipole-antenna oriented horizontally, an antenna-like kinematics map (the "Ariadne angle") in which the two parents share the transverse component of recoil, and $\phi$ chosen such that the gluon is radiated upwards.
• Figure 5: Illustration of the $\zeta$ definition, eq. (\ref{['eq:z']}). The physical phase space, shown in grey, is the same on both panes, and the $\zeta$ definition is also the same, but on the left the phase space is shown on a linear scale in the branching invariants and on the right on a logarithmic one.