arXiv subjects

Rafael L. Delgado

Publications and source records attributed to Rafael L. Delgado.

At least 19 recordsLinked to original sources

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.

hep-ph↗

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).

hep-ph↗

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).

hep-ph↗

arXiv2023

Static Energy in ($2+1+1$)-Flavor Lattice QCD: Scale Setting and Charm Effects

We present results for the static energy in ($2+1+1$)-flavor QCD over a wide range of lattice spacings and several quark masses, including the physical quark mass, with ensembles of lattice-gauge-field configurations made available by the MILC Collaboration. We obtain results for the static energy out to distances of nearly $1$~fm, allowing us to perform a simultaneous determination of the scales $r_{1}$ and $r_{0}$, as well as the string tension $σ$. For the smallest three lattice spacings we also determine the scale $r_{2}$. Our results for $r_{0}/r_{1}$ and $r_{0}\sqrtσ$ agree with published ($2+1$)-flavor results. However, our result for $r_{1}/r_{2}$ differs significantly from the value obtained in the ($2+1$)-flavor case, which is most likely due to the effect of the charm quark. We also report results for $r_{0}$, $r_{1}$, and $r_{2}$ in~fm, with the former two being slightly lower than published ($2+1$)-flavor results. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest two lattices with the previously published ($2+1$)-flavor QCD results at similar lattice spacing. We find that for $r > 0.2$~fm our results on the static energy agree with the ($2+1$)-flavor result, implying the decoupling of the charm quark for these distances. For smaller distances, on the other hand, we find that the effect of the dynamical charm quark is noticeable. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects. This is the first time that the decoupling of the charm quark is observed and quantitatively analyzed on lattice data of the static energy.

hep-lat↗

arXiv2023

Seeking for resonances in unitarized one-loop graviton-graviton scattering

Some effective field theories exhibit dynamical resonances that, when properly included, mitigate their bad behaviour at high energies. Unitarization of the partial wave amplitudes is the preferred method to unveil such resonances. Interpreting the Einstein-Hilbert theory in the spirit of effective Lagrangians, we implement the Inverse Amplitude Method and unitarize the one-loop level graviton-graviton scattering in pure gravity. Due to the presence of infrared divergences, the analysis requires a careful treatment of the infrared region and the introduction of infrared regulators, carefully selected in order to fulfil perturbative unitarity. No evidence of any graviball is found, in contradiction with a recent study.

hep-th↗

arXiv2022

Charm mass effects in the static energy computed in 2+1+1 flavor lattice QCD

We report our analysis for the static energy in (2+1+1)-flavor QCD over a wide range of lattice spacings and several quark masses. We obtain results for the static energy out to distances of nearly 1 fm, allowing us to perform a simultaneous determination of the lattice scales $r_2$, $r_1$ and $r_0$ as well as the string tension, $σ$. While our results for ${r_0}/{r_1}$ and $r_0$ $\sqrtσ$ agree with published (2+1)-flavor results, our result for ${r_1}/{r_2}$ differs significantly from the value obtained in the (2+1)-flavor case, likely due to the effect of the charm quark. We study in detail the effect of the charm quark on the static energy by comparing our results on the finest lattices with the previously published (2+1)-flavor QCD results at similar lattice spacing. The lattice results agree well with the two-loop perturbative expression of the static energy incorporating finite charm mass effects.

hep-lat↗

arXiv2022

QuantumFDTD -- A computational framework for the relativistic Schrödinger equation

We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schrödinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground, first, and second excited states. We (a) include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for the non-relativistic case. All the three new kinetic terms are computed using Fast Fourier Transform (FFT). We release the resulting code as version 3 of quantumfdtd. Finally, the code now supports arbitrary external file-based potentials and the option to project out distinct parity eigenstates from the solutions. Our goal is quark models used for phenomenological descriptions of QCD bound states, described by the three-dimensional Schrödinger equation. However, we target any field where solving either the non-relativistic or the relativistic three-dimensional Schrödinger equation is required.

hep-ph↗

arXiv2022

Unitarized one-loop graviton-graviton scattering

In this work we interpret the Einstein-Hilbert (EH) Lagrangian of gravitation as the first term of a low-energy effective theory similar to those considered in the chiral Lagrangian approach to low-energy hadron physics or the electroweak chiral Lagragians describing the symmetry breaking sector of the Standard Model (SM). Starting from the one-loop computation of the elastic graviton-graviton scattering amplitude by Dunbar and Norridge, we unitarize the IR regularized partial waves by using the Inverse Amplitude Method (IAM). This method enlarges the regime of applicability of the perturbative results to higher energies of the order of the Plank scale $M_P$ and allows for the possibility of poles in the second Riemann which have the natural interpretation of dynamical resonances. In this work we look for these possible resonances for the $++++$ and $ -- -$ helicity channels and the $J=0$, $2$ and $4$ partial waves.

hep-th↗

arXiv2021

The Relativistic Schrödinger Equation through FFTW3: An Extension of quantumfdtd

In order to solve the time-independent three-dimensional Schrödinger equation, one can transform the time-dependent Schrödinger equation to imaginary time and use a parallelized iterative method to obtain the full three-dimensional eigenstates and eigenvalues on very large lattices. In the case of the non-relativistic Schrödinger equation, there exists a publicly available code called quantumfdtd which implements this algorithm. In this paper, we (a) extend the quantumfdtd code to include the case of the relativistic Schrödinger equation and (b) add two optimized FFT-based kinetic energy terms for non-relativistic cases. The new kinetic energy terms (two non-relativistic and one relativistic) are computed using the parallelized Fast Fourier Transform (FFT) algorithm provided by the FFTW library. The resulting quantumfdtd v3 code, which is publicly released with this paper, is backwards compatible with version 2, supporting explicit finite differences schemes in addition to the new FFT-based schemes. Finally, the original code has been extended so that it supports arbitrary external file-based potentials and the option to project out distinct parity eigenstates from the solutions. Herein, we provide details of the quantumfdtd v3 implementation, comparisons and tests of the three new kinetic energy terms, and code documentation.

hep-ph↗

arXiv2021

The static energy in 2+1+1-flavor QCD

We report on the status of the analysis of the static energy in $2+1+1$-flavor QCD. The static energy is obtained by measuring Wilson line correlators in Coulomb gauge using the HISQ action, yielding the scales $r_{0}/a$, $r_{1}/a$, $r_{2}/a$, their ratios, and the string tension $σr_{i}^{2}$. We put emphasis on the possible effects due to the dynamical charm-quark by comparing the lattice results to continuum results of the static energy with and without a massive flavor at two-loop accuracy. We employ gauge-field ensembles from the HotQCD and MILC Collaborations.

hep-lat↗

arXiv2020

VBSCan Mid-Term Scientific Meeting

This document summarises the talks and discussions happened during the VBSCan Mid-Term Scientific Meeting workshop. The VBSCan COST action is dedicated to the coordinated study of vector boson scattering (VBS) from the phenomenological and experimental point of view, for the best exploitation of the data that will be delivered by existing and future particle colliders.

hep-ph↗

arXiv2019

Resonances in unitarized HEFT at the LHC

Higgs Effective Field Theory (HEFT) is deployed to study elastic vector-boson scattering at the high LHC energies. The interaction is strong over most of the parameter space, with the minimal Standard Model being a remarkable exception. One-loop HEFT complemented with dispersion relations and the Equivalence Theorem leads to two different unitarization methods which produce analytical amplitudes corresponding to different approximate solutions to the dispersion relations: the Inverse Amplitude method (IAM) and the N/D method. The partial waves obtained can show poles in the second Riemann sheet whose natural interpretation is that of dynamical resonances with masses and widths depending on the starting HEFT parameters. Different unitarizations yield qualitatively, and in many cases quantitatively, very similar results. The amplitudes obtained provide realistic resonant and nonresonant cross sections to be compared with and to be used for a proper interpretation of the LHC data.

hep-ph↗

arXiv2018

Collider phenomenology of vector resonances in WZ scattering processes

We study the production of vector resonances at the LHC via $WZ$ scattering processes and explore the sensitivities to these resonances for the expected future LHC luminosities. The electroweak chiral Lagrangian and the Inverse Amplitude Method (IAM) are used for analyzing a dynamically generated vector resonance, whose origin would be the (hypothetically strong) self interactions of the longitudinal gauge bosons, $W_L$ and $Z_L$. We implement the unitarized scattering amplitudes into a single model, the IAM-MC, that has been adapted to MadGraph~5. It is written in terms of the electroweak chiral Lagrangian and an additional effective Proca Lagrangian for the vector resonances, so that it reproduces the resonant behavior of the IAM and allows us to perform a realistic study of signal versus background at the LHC. We focus on the $pp\to WZjj$ channel, discussing first on the potential of the hadronic and semileptonic channels of the final $WZ$, and next exploring in more detail the clearest signals. These are provided by the leptonic decays of the gauge bosons, leading to a final state with $l^+_1l^-_1l^+_2νjj$, $l=e,μ$, having a very distinctive signature, and showing clearly the emergence of the resonances with masses in the range of $1.5$-$2.5\,{\rm TeV}$, which we have explored.

hep-ph↗

arXiv2018

Collider production of Electroweak resonances from photon-photon states

We estimate production cross sections for 2-body resonances of the Electroweak Symmetry Breaking sector (in $W_LW_L$ and $Z_LZ_L$ rescattering) from $γγ$ scattering. We employ unitarized Higgs Effective Field Theory amplitudes previously computed coupling the two photon channel to the EWSBS. We work in the Effective Photon Approximation and examine both $e^-e^+$ collisions at energies of order 1-2 TeV (as relevant for future lepton machines) and $pp$ collisions at LHC energies. Dynamically generating a spin-0 resonance around 1.5 TeV (by appropriately choosing the parameters of the effective theory) we find that the differential cross section per unit $s$, $p_t^2$ is of order 0.01 fbarn/TeV$^4$ at the LHC. Injecting a spin-2 resonance around 2 TeV we find an additional factor 100 suppression for $p_t$ up to 200 GeV. The very small cross sections put these $γγ$ processes, though very clean, out of reach of immediate future searches.

hep-ph↗

arXiv2018

Unitarized HEFT for strongly interacting longitudinal electroweak gauge bosons with resonances

Higgs Effective Field Theory can be used to study vector-boson elastic scattering at the high energies relevant for the LHC. For most of the parameter space, the scattering is strongly interacting, with the minimal Standard Model being a remarkable exception. From its one-loop treatment complemented with dispersion relations and the Equivalence Theorem, we derive two different unitarization methods which produce analytical amplitudes corresponding to different approximate solutions to the dispersion relations: the Inverse Amplitude method (IAM) and the N/D method. The partial waves obtained can show poles in the second Riemann sheet whose natural interpretation is that of dynamical resonances with masses and widths a function of the starting HEFT parameters. We compare the different unitarizations and we find that they are qualitatively, and in many cases quantitatively, very similar. However, for different reason it is more interesting to use one of the two methods depending on the particular channel for WW, ZZ, WZ, Zh, Wh or hh scattering. In this note we briefly describe the possible I and J channels for these reactions and give the unitarization method of choice in each case. The amplitudes obtained provide realistic resonant and nonresonant cross sections to be compared with and to be used for a proper interpretation of the LHC data.

hep-ph↗

arXiv2017

Top-antitop production from $W_L^+ W_L^-$ and $Z_L Z_L$ scattering under a strongly-interacting symmetry-breaking sector

By using a Non-linear Electroweak Chiral Lagrangian, including the Higgs, coupled to heavy quarks, and the Equivalence Theorem, we compute (in the regime $M_t^2/v^2\ll\sqrt{s}M_t/v^2\ll s/v^2$) the one-loop amplitudes $W^+W^-\to t\bar t$, $ZZ\to t\bar t$ and $hh\to t\bar t$ (to NLO in the effective theory). We calculate the scalar partial-wave helicity amplitudes which allow us to check unitarity at the perturbative level in both $M_t/v$ and $s/v$. As with growing energy perturbative unitarity deteriorates, we also introduce a new unitarization method with the right analytical behavior on the complex $s$-plane and that can support poles on the second Riemann sheet to describe resonances in terms of the Lagrangian couplings. Thus we have achieved a consistent phenomenological description of any resonant $t\bar t$ production that may be enhanced by a possible strongly interacting Electroweak Symmetry Breaking Sector.

hep-ph↗

arXiv2016

Coupling of $t\bar t$ and $γγ$ with a strongly interacting Electroweak Symmetry Breaking Sector

We report the coupling of an external $γγ$ or $t\bar t$ state to a strongly interacting EWSBS satisfying unitarity. We exploit perturbation theory for those coupling of the external state, whereas the EWSBS is taken as strongly interacting. We use a modified version of the IAM unitarization procedure to model such a strongly interacting regime. The matrix elements $V_LV_L\to V_LV_L$, $V_LV_L\leftrightarrow hh$, $hh\to hh$, $V_LV_L\leftrightarrow\{γγ,t\bar t\}$, and $hh\leftrightarrow\{γγ,t\bar t\}$ are all computed to NLO in perturbation theory with the Nonlinear Effective Field Theory of the EWSBS, within the Equivalence Theorem. This allows us to describe resonances of the electroweak sector that may be found at the LHC and their effect on other channels such as $γγ$ or $t\bar t$ where they may be discovered.

hep-ph↗

arXiv2016

Coupling WW, ZZ unitarized amplitudes to $γγ$ in the TeV region

We define and calculate helicity partial-wave amplitudes for processes linking the Electroweak Symmetry Breaking Sector (EWSBS) to $γγ$, employing (to NLO) the Higgs-EFT (HEFT) extension of the Standard Model and the Equivalence Theorem, while neglecting all particle masses. The resulting amplitudes can be useful in the energy regime ($500\,{\rm GeV}-3\,{\rm TeV}$). We also deal with their unitarization so that resonances of the EWSBS can simultaneously be described in the $γγ$ initial or final states. Our resulting amplitudes satisfy unitarity, perturbatively in $α$, but for all $s$ values. In this way we improve on the HEFT that fails as interactions become stronger with growing $s$ and provide a natural framework for the decay of dynamically generated resonances into $WW$, $ZZ$ and $γγ$ pairs.

hep-ph↗