Related papers: Scattering amplitudes over finite fields and multi…
I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational…
We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an…
We review some of the recent advances in the computation of one-loop scattering amplitudes which led to the construction of efficient and automated computational tools for NLO predictions. Particular attention is devoted to unitarity-based…
The simplification and reorganization of complex expressions lies at the core of scientific progress, particularly in theoretical high-energy physics. This work explores the application of machine learning to a particular facet of this…
The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
We calculate the general planar dual-conformally invariant double-pentagon and pentabox integrals in four dimensions. Concretely, we derive one-fold integral representations for these elliptic integrals over polylogarithms of weight three.…
We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute…
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\Lambda$…
Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis…
We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on…
A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…
We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for $n$ scattering particles into a $\sigma$-moduli multivariate polynomial of what we call the $\textit{standard form}$. We show that a…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point…
Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…
We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…