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Alexandre Salas-Bernárdez

Publications and source records attributed to Alexandre Salas-Bernárdez.

16 recordsLinked to original sources
arXiv2026

The left-cut for partial waves in terms of physical amplitudes

We derive a novel representation of the partial wave amplitude over the left-hand cut for $2 \to 2$ scattering. We express the left-hand cut of arbitrary isospin and angular momentum partial waves as an integral of right-hand cut imaginary parts. This formulation provides an explicit, exact extraction of the logarithmic branch cut structures, offering a valuable tool to systematically quantify left-hand cut uncertainties in unitarization methods such as the Inverse Amplitude Method or $N/D$ approaches.

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arXiv2026

Unitarity and Unitarization

This article reviews unitarization methods essential for extending Effective Field Theories (EFTs) beyond their perturbative limits, particularly in hadronic and electroweak (EW) sectors. Perturbative EFTs, like Chiral Perturbation Theory (ChPT), often violate unitarity bounds at higher energies, a breakdown observed in phenomena such as $ππ$ scattering resonances. To overcome this, non-perturbative techniques including the Inverse Amplitude Method (IAM), $K$-matrix formalism, and N/D approach are detailed. The IAM and the N/D methods resum perturbative series while preserving fundamental $S$-matrix principles: unitarity, analyticity, and causality, dynamically generating resonant behavior. The article emphasizes the unique role of dispersive frameworks, especially the Roy equations, which rigorously incorporate analyticity and crossing symmetry. It highlights their potential for future application in the electroweak sector, offering a powerful tool to constrain the Standard Model and interpret collider data.

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arXiv2024

Discerning EFTs through multi-Higgs production

In these proceedings we present the main results of [arXiv:2311.04280 [hep-ph]], where we explore the phenomenological implications of multi-Higgs boson production through longitudinal vector boson scattering within the framework of Effective Field Theories (EFTs). We derive compact expressions for effective tree-level amplitudes involving up to four final-state Higgs bosons. Subsequently, we compute total cross sections for scenarios relevant to the LHC, where we observe that the general Higgs Effective Theory (HEFT) prediction avoids the strong suppression found in the Standard Model Effective Field Theory (SMEFT), typically expected to be several orders of magnitude smaller.

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arXiv2024

Production of two, three, and four Higgs bosons: where SMEFT and HEFT depart

In this article we study the phenomenological implications of multiple Higgs boson production from longitudinal vector boson scattering in the context of effective field theories. We find compact representations for effective tree-level amplitudes with up to four final state Higgs bosons. Total cross sections are then computed for scenarios relevant at the LHC in which we find the general Higgs Effective Theory (HEFT) prediction avoids the heavy suppression observed in Standard Model Effective Field Theory (SMEFT).

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arXiv2024

Redefining Higgs interactions at the TeV scale

We present a field redefinition that simplifies the Higgs Effective Field Theory Lagrangian for the Electroweak Symmetry Breaking Sector. This simplification produces the same on-shell scattering amplitudes while greatly reducing the number of contributing Feynman diagrams for $ωω\to n\times h$ processes (which approximate the $W_LW_L\to n\times h$ amplitudes at the TeV scale by means of the Equivalence Theorem).

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arXiv2023

Flow Oriented Perturbation Theory

Flow Oriented Perturbation Theory (FOPT) is a novel approach to Feynman diagrams based on the coordinate (position) space description of Quantum Field Theories (QFT). FOPT offers interesting features regarding the computation of higher-loop Feynman amplitudes such as combinatorial and canonical Feynman rules, explicit infrared singularity factorization on a per-diagram level and the potential to have manifest cancellation of real and virtual singularities. In these proceedings we briefly summarize the derivation of FOPT and present its Feynman rules for covariant diagrams, S-matrix elements and cut diagrams in massless scalar QFT, supported by examples. We then discuss the extension of FOPT to massless fermion fields and indicate steps towards the treatment of massive lines in arbitrary dimensions.

hep-th↗
arXiv2023

Analytical Quantum Field methods in Particle Physics

In this thesis we deal with different aspects of quantum field theory, particularly in non-perturbative but also perturbative regimes, applied to the intellectual construction that is the Standard Model for Particle Physics (SM), but also its extension via effective theories. We have developed the following practical contributions in different subfields of Particle Physics: qualitatively assessing why the SM has those specific symmetries, explaining the $^3P_0$ mechanism of meson decay from fundamental Quantum Chromodynamics (QCD) calculations, experimentally distinguishing Effective Theories of the Electroweak sector beyond the SM in accelerators, extrapolating LHC data (low energies) to possible resonant regions of new physics (high energies) with controlled uncertainties and studying precision calculations of QCD (high energies) in coordinate space.

hep-ph↗
arXiv2023

SMEFT is falsifiable through multi-Higgs measurements (even in the absence of new light particles)

From the embedding of the Standard Model Effective Field Theory (SMEFT) in the more general Higgs Effective Field Theory (HEFT), we expose correlations among the coefficients of the latter that, if found to be violated in future data, would lead to the experimental falsification of the SMEFT framework. These are derived from the necessary symmetric point of HEFT and analyticity of the SMEFT Lagrangian that allows the construction of the SMEFT expansion, as laid out by other groups, and properties at that point of the Higgs-flare function $\mathcal{F}(h)$ coupling Goldstone and Higgs bosons, of the Higgs potential $V(h)$ and of the Higgs-top quark coupling function $\mathcal{G}(h)$.

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arXiv2023

Split gluon masses in $SU(N)\times SU(M)$ theories

We extend a known mass-gap equation for pure gluodynamics in global colour models (formulated in equal time quantization in Coulomb gauge) to one in which gluons split into two sets which may have different masses. If the theory is $SU(N)\times SU(M)$ with gluons in both groups having identical couplings (as suggested by Grand Unification arguments at large scales) it is immediate to see that different masses are generated for each subgroup. This global symmetry is not broken, but the split masses erase accidental symmetries that might be present due to the two couplings being the same at the large scale, such as $SU(N\times M)$ or similar. We also numerically explore a couple of low-dimensional examples of simple Lie groups, but in spite of the system having a form that would seem to allow spontaneous symmetry breaking, it is not triggered for these groups whose algebra has no ideal, and the dispersion relations for the various gluons converge to the same form.

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arXiv2023

Flow-oriented perturbation theory

We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed graphs (digraphs). FOPT is a coordinate space analogue of time-ordered perturbation theory and loop-tree duality, but it has the advantage of having combinatorial and canonical Feynman rules, combined with a simplified $i\varepsilon$ dependence of the resulting integrals. Moreover, we introduce a novel digraph-based representation for the S-matrix. The associated integrals involve the Fourier transform of the flow polytope. Due to this polytope's properties, our S-matrix representation exhibits manifest infrared singularity factorization on a per-diagram level. Our findings reveal an interesting interplay between spurious singularities and Fourier transforms of polytopes.

hep-th↗
arXiv2022

Explicit computation of jet functions in coordinate space

I review the main results leading to Factorization of QCD amplitudes in momentum space and, in view of the analogue results in coordinate space, the one-loop jet function in coordinate space is computed and Landau's equations for the Abelian radiative corrections to it are studied. Furthermore, two of these radiative corrections are reduced in quadrature.

hep-ph↗
arXiv2021

How to predict a new physics scale and its uncertainty with the Inverse Amplitude Method

Effective Field Theories such as HEFT, organized as momentum expansions, are a controllable approximation to strong dynamics only near threshold, as they miss exact elastic unitarity, reducing their predictive power at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory extends their reach to the saturation of unitarity but, generally with unknown systematics. Here I present a brief "handbook" on how to put to use the Inverse Amplitude Method to predict a resonance (associated with a new physics scale in Beyond the Standard Model searches) and more especially on how to control its systematic uncertainties.

hep-ph↗
arXiv2021

Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method

Effective Field Theories (EFTs) constructed as derivative expansions in powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a controllable approximation to strong dynamics as long as the energy of the interacting particles remains small, as they do not respect exact elastic unitarity. This limits their predictive power towards new physics at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory techniques have been devised to extend the reach of the EFT to regimes where partial waves are saturating unitarity, but their uncertainties have hitherto not been addressed thoroughly. Here we take one of the best known of them, the Inverse Amplitude Method (IAM), and carefully following its derivation, we quantify the uncertainty introduced at each step. We compare its hadron ChPT and its electroweak sector Higgs EFT applications. We find that the relative theoretical uncertainty of the IAM at the mass of the first resonance encountered in a partial-wave is of the same order in the counting as the starting uncertainty of the EFT at near-threshold energies, so that its unitarized extension should \textit{a priori} be expected to be reasonably successful. This is so provided a check for zeroes of the partial wave amplitude is carried out and, if they appear near the resonance region, we show how to modify adequately the IAM to take them into account.

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arXiv2020

Assessment of systematic theory uncertainties in IAM unitarization

Effective Field Theories (EFTs) for Goldstone Boson scattering at a low order allow the computation of near--threshold observables in terms of a few coefficients arranged by a counting. As a matter of principle they should make sense up to an energy scale $E\sim 4πF$ but the expansion in powers of momentum violates exact elastic unitarity and renders the derivative expansion unreliable at much lower energies. If new--physics deviations from the Standard Model are found and encoded in low-energy coefficients, perhaps at the LHC, it will be profitable to extend the reach of the EFT to regimes where partial waves are saturating unitarity. The methods known in hadron physics as "Unitarized Chiral Perturbation Theory" extend the EFT up to its nominal reach or up to the first new physics resonance or structure (if found below that energy reach) in the partial wave amplitude, but they usually have unknown uncertainties. We recapitulate our analysis of the systematic theory uncertainties of the well known Inverse Amplitude Method (IAM).

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arXiv2018

Chiral symmetry breaking for fermions charged under large Lie groups

We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Unification scale, extending the Renormalization Group Equations in the perturbative regime to two-loops and matching to the Dyson-Schwinger Equations in the strong coupling regime.

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