Abstract
We present the first public implementation of antenna-based QCD initial- and final-state showers. The shower kernels are 2rightarrow 3 antenna functions, which capture not only the collinear dynamics but also the leading soft (coherent) singularities of QCD matrix elements. We define the evolution measure to be inversely proportional to the leading poles, hence gluon emissions are evolved in a p_perp measure inversely proportional to the eikonal, while processes that only contain a single pole (e.g., grightarrow qbar{q}) are evolved in virtuality. Non-ordered emissions are allowed, suppressed by an additional power of 1/Q^2. Recoils and kinematics are governed by exact on-shell 2rightarrow 3 phase-space factorisations. This first implementation is limited to massless QCD partons and colourless resonances. Tree-level matrix-element corrections are included for QCD up to mathcal {O}(alpha _s^4) (4 jets), and for Drell–Yan and Higgs production up to mathcal {O}(alpha _s^3) (V / H + 3 jets). The resulting algorithm has been made publicly available in Vincia 2.0.
Highlights
The basic differential equations governing renormalisationgroup-improved perturbation theory for initialstate partons were derived in the 1970s [1,2,3]
The DGLAP kernels themselves are derived in the collinear limit of QCD, which is dominated by radiation off a single hard parton, the destructive-interference effects [10] which dominate for wide-angle soft-gluon emission can be approximately accounted for in this formalism; either by choosing the shower evolution variable to be a measure of energy times angle [11] or by imposing a veto on non-angular-ordered emissions [12]
We presented the first publicly available antenna shower for initial and final state in Vincia 2.0, with focus on antenna functions and kinematic maps for initial-state radiation
Summary
The basic differential equations governing renormalisationgroup-improved (resummed) perturbation theory for initialstate partons were derived in the 1970s [1,2,3]. Shower algorithms rely on several further improvements that go beyond the LO DGLAP picture, including: exact momentum conservation (related to the choice of recoil strategy), colour-flow tracing (in the leadingNC limit, related to coherence at both the perturbative and non-perturbative levels), and higher-order-improved scale choices (including the use of μR = p⊥ for gluon emissions and the so-called CMW scheme translation which applies in the soft limit [31,32]). Each of these are associated with ambiguities, with Sect. Additional material, as referred to in the text, is collected in the Appendices
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