arXiv subjects

Roger J. Hernandez-Pinto

Publications and source records attributed to Roger J. Hernandez-Pinto.

7 recordsLinked to original sources

arXiv2023

Precision studies for the partonic kinematics calculation through Machine Learning

High Energy collider experiments are moving to the highest precision frontier quickly. The predictions of observables are based on the factorization formula which helps to connect small to large distances. These predictions can be contrasted with experimental measurements and the success of this phenomenological approach is based on the correct description of nature. The application of the method to proton-proton colliders brings new challenges due to the proton structure and the detectors efficiency on reconstructing hadrons. Furthermore, since the non-perturbative distribution functions takes an important role to describe the experimental distributions, the presence of them makes the information of the partons diluted. At Leading Order (LO) in perturbative calculations, the momentum fractions involved in hard scattering processes are known exactly in terms of kinematical variables of initial and final states hadrons. However, at Next-to-Leading Order (NLO) and beyond, a closed analytical formula is not available. Furthermore, from the pure theoretical calculation, the exact definition of the momentum fraction is very challenging. In this work, we report a methodology based on Machine Learning techniques for the extraction of momentum fractions for $p+p\toπ^++γ$ using a Monte Carlo simulation including quantum corrections up to Next-to-Leading Order in Quantum Chromodynamics and Leading Order in Quantum Electrodymics. Our findings point towards a methodology to find the fundamental properties of the internal structure of hadrons because the reconstructed momentum fractions deeply relate our perturbative models with experimental measurements.

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arXiv2021

Causal representation of multi-loop Feynman integrands within the loop-tree duality

The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.

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arXiv2021

Universal opening of four-loop scattering amplitudes to trees

The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees. We study the multiloop topologies that first appear at four loops and assemble them in a clever and general expression, the N$^4$MLT {\it universal topology}. This general expression enables to open any scattering amplitude of up to four loops, and also describes a subset of higher order configurations to all orders. These results confirm the conjecture of a factorized opening in terms of simpler known subtopologies, which also determines how the causal structure of the entire loop amplitude is characterized by the causal structure of its subtopologies. In addition, we confirm that the loop-tree duality representation of the N$^4$MLT universal topology is manifestly free of noncausal thresholds, thus pointing towards a remarkably more stable numerical implementation of multiloop scattering amplitudes.

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arXiv2020

Mathematical properties of nested residues and their application to multi-loop scattering amplitudes

The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the novel integrand-level representation of Feynman integrals, which is based on the Loop-Tree Duality (LTD). We explore the behaviour of the multi-loop iterated residues and explicitly show, by developing a general formal proof for the first time, that contributions associated to displaced poles are cancelled out. The remaining residues, called nested residues as originally introduced in Ref. \cite{Verdugo:2020kzh}, encode the relevant physical information and are naturally mapped onto physical configurations associated to nondisjoint on-shell states. By going further on the mathematical structure of the nested residues, we prove that unphysical singularities vanish, and show how the final expressions can be written by using only causal denominators. In this way, we provide a mathematical proof for the all-loop formulae presented in Ref. \cite{Aguilera-Verdugo:2020kzc}.

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arXiv2020

Open loop amplitudes and causality to all orders and powers from the loop-tree duality

Multiloop scattering amplitudes describing the quantum fluctuations at high-energy scattering processes are the main bottleneck in perturbative quantum field theory. The loop-tree duality is a novel method aimed at overcoming this bottleneck by opening the loop amplitudes into trees and combining them at integrand level with the real-emission matrix elements. In this Letter, we generalize the loop-tree duality to all orders in the perturbative expansion by using the complex Lorentz-covariant prescription of the original one-loop formulation. We introduce a series of mutiloop topologies with arbitrary internal configurations and derive very compact and factorizable expressions of their open-to-trees representation in the loop-tree duality formalism. Furthermore, these expressions are entirely independent at integrand level of the initial assignments of momentum flows in the Feynman representation and remarkably free of noncausal singularities. These properties, that we conjecture to hold to other topologies at all orders, provide integrand representations of scattering amplitudes that exhibit manifest causal singular structures and better numerical stability than in other representations.

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arXiv2018

Recent developments from the loop-tree duality

In this talk, we review the most recent developments of the four-dimensional unsubstraction (FDU) and loop-tree duality (LTD) methods. In particular, we make emphasis on the advantages of the LTD formalism regarding asymptotic expansions of loop integrands.

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arXiv2016

Towards gauge theories in four dimensions

The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.

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