arXiv subjects

Philip Velie

Publications and source records attributed to Philip Velie.

3 recordsLinked to original sources

arXiv2026

Tree Amplitudes with Charged Matter in Pure Gauge Theory

We describe the implementation and usage of `fermionic_amplitudes.m', a Mathematica package for the computation of tree amplitudes involving arbitrary numbers of gauge bosons and arbitrarily-charged massless fermions of (possibly) distinct flavours in pure (non-supersymmetric) gauge theory. These are given in terms of a basis of partial amplitudes involving distinct-flavoured fermions dressed by specific colour tensors. Distinct-flavour partial amplitudes are expressed as linear combinations of those involving only a single flavour, which may be evaluated as component amplitudes of (maximally) supersymmetric Yang-Mills theory. All relevant colour tensors can be realized as explicit, numeric arrays given any choice of charge generators (for any gauge theory -- including $u_1$); from these, all colour contractions relevant to cross sections may be readily computed. The complete package and a notebook demonstrating its primary usage and functionality are included in this work's submission's ancillary files on the arXiv.

hep-th↗

arXiv2024

A bijection for tuples of commuting permutations and a log-concavity conjecture

Let $A(\ell,n,k)$ denote the number of $\ell$-tuples of commuting permutations of $n$ elements whose permutation action results in exactly $k$ orbits or connected components. We provide a new proof of an explicit formula for $A(\ell,n,k)$ which is essentially due to Bryan and Fulman, in their work on orbifold higher equivariant Euler characteristics. Our proof is self-contained, elementary, and relies on the construction of an explicit bijection, in order to perform the $\ell+1\rightarrow \ell$ reduction. We also investigate a conjecture by the first author, regarding the log-concavity of $A(\ell,n,k)$ with respect to $k$. The conjecture generalizes a previous one by Heim and Neuhauser related to the Nekrasov-Okounkov formula.

math.CO↗

arXiv2021

Parametrization of Quark and Gluon Generalized Parton Distributions in a Dynamical Framework

We present a parametrization of the chiral even generalized parton distributions, $H$, $E$, $\widetilde{H}$, $\widetilde{E}$, for the quark, antiquark and gluon, in the perturbative QCD-parton framework. Parametric analytic forms are given as a function of two equivalent sets of variables $x,ξ,t$ (symmetric frame) and $X,ζ,t$ (asymmetric frame), at an initial scale, $Q_o^2$. In the $X>ζ$ region a convenient and flexible form is obtained as the product of a Regge term $\propto X^{-α+ α' t}$, describing the low $X$ behavior, times a spectator model-based functional form depending on various mass parameters; the behavior at $X<ζ$, is determined using the generalized parton distributions symmetry and polynomiality properties. The parameters are constrained using data on the flavor separated nucleon electromagnetic elastic form factors, the axial and pseudoscalar nucleon form factors, and the parton distribution functions from both the deep inelastic unpolarized and polarized nucleon structure functions. For the gluon distributions we use, in particular, constraints provided by recent lattice QCD moments calculations. The parametrization's kinematical range of validity is: $0.0001 \leq X \leq 0.85$, $0.01 \leq ζ\leq 0.85$, $0 \leq -t \leq 1$ GeV$^2$, $2 \leq Q^2 \leq 100$ GeV$^2$. With the simultaneous description of the quark, anti-quark and gluon sectors, this parametrization represents a first tool enabling a global QCD analysis of deeply virtual exclusive experiments.

hep-ph↗