arXiv subjects

Pilar Hernández

Publications and source records attributed to Pilar Hernández.

At least 19 recordsLinked to original sources

arXiv2025

The $ππ$ scattering amplitude at large $N_\text{c}$

We study the scaling of meson-meson scattering amplitudes with the number of colors, $N_\text{c}$. We use lattice calculations in a theory with $N_\text{f}=4$ degenerate flavors, with $N_\text{c}=3-6$ and pion mass $M_π\approx 560$ MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb: the $T_{cs0}^0(2900)$, $T_{c\bar{s}0}^{++}(2900)$, $T_{c\bar{s}0}^0(2900)$ and $T_{c\bar{s}1}^0(2900)$ states. Finite-volume energies are extracted using a large set of operators, containing two-particle operators with the form of two pions or two vector mesons, and local tetraquark operators. The resulting energy spectra is used to constrain the infinite-volume scattering amplitude by means of Lüscher's quantization condition. We consider polynomial parametrizations of the phase shift, as well as one-loop chiral perturbation theory (ChPT) predictions. We find that our lattice results follow the expected $N_\text{c}$ scaling and are sensitive to subleading $N_\text{c}$ corrections. In addition, we constrain the scaling of different combinations of low-energy constants from matching to large $N_\text{c}$ ChPT. The results for the channel corresponding to a $(π^+ D^+_s - K^+ D^+)$ state show evidence of a virtual bound state with energy $E_\text{virtual}=1.63(10)M_π$ for $N_\text{c}=3$, while this pole disappears at $N_\text{c}>3$. This may be connected to the exotic states found in experiment.

hep-lat↗

arXiv2025

Chiral and isospin breaking in the two-flavor Schwinger Model

The Schwinger model with two massive fermions is a nontrivial theory for which no analytical solution is known. The strong coupling limit of the theory allows for different semiclassical approximations to extract properties of its low-lying spectrum. In particular, analytical results exist for the fermion condensate, the fermion mass dependence of the pseudoscalar meson mass or its decay constant. These approximations, nonetheless, are not able to quantitatively predict isospin breaking effects in the light spectrum, for example. In this paper we use lattice simulations to test various analytical predictions, and study isospin breaking effects from nondegenerate quark masses. We also introduce a low-energy effective field theory based on a nonlinear $σ$ model with a dilaton field, which leads to the correct fermion mass dependence of the pion mass, the correct $σ$-to-$π$ mass ratio and a prediction of the isospin breaking effects, which we test numerically.

hep-lat↗

arXiv2025

Neutrino Theory in the Precision Era

This document summarises discussions on future directions in theoretical neutrino physics, which are the outcome of a neutrino theory workshop held at CERN in February 2025. The starting point is the realisation that neutrino physics offers unique opportunities to address some of the most fundamental questions in physics. This motivates a vigorous experimental programme which the theory community fully supports. \textbf{A strong effort in theoretical neutrino physics is paramount to optimally take advantage of upcoming neutrino experiments and to explore the synergies with other areas of particle, astroparticle, and nuclear physics, as well as cosmology.} Progress on the theory side has the potential to significantly boost the physics reach of experiments, as well as go well beyond their original scope. Strong collaboration between theory and experiment is essential in the precision era. To foster such collaboration, \textbf{we propose to establish a CERN Neutrino Physics Centre.} Taking inspiration from the highly successful LHC Physics Center at Fermilab, the CERN Neutrino Physics Centre would be the European hub of the neutrino community, covering experimental and theoretical activities.

hep-ph↗

arXiv2025

Results on meson-meson scattering at large $N_\text{c}$

We present results on the large $N_\text{c}$ scaling of meson-meson scattering amplitudes. We work in a theory with $N_\text{f}=4$ degenerate quark flavors and run lattice simulations with $N_\text{c}=3-6$ and pion mass $M_π\approx 590$ MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb. Finite-volume energies are extracted using a large set of operators, containing two-particle operators corresponding to two pions or two vector mesons, and local tetraquark operators. Using Lüscher's quantization condition, we constrain the infinite-volume scattering amplitudes and investigate subleading $N_\text{c}$ corrections to the large $N_\text{c}$ limit. For one of the channels, we find indications of a virtual bound state at $N_\text{c}=3$, which may be related to one of the aforementioned exotic states.

hep-lat↗

arXiv2024

Progress in meson-meson scattering at large $N_\text{c}$

We study the large $N_\text{c}$ scaling of meson-meson scattering amplitudes in a theory with $N_\text{f}=4$ degenerate quark flavors. We focus on two different scattering channels, one having the same quantum numbers as some recently found tetraquark states at LHCb. Using Lüscher's formalism, we study the $N_\text{c}$ dependence of the scattering phase shift and investigate the presence of exotic resonances in the scattering amplitude. We analyze the impact of including two-vector-meson and tetraquark-like operators to extract the finite-volume energies.

hep-lat↗

arXiv2023

New bounds on axion-like particles from MicroBooNE

Neutrino experiments lie at the edge of the intensity frontier and therefore can be exploited to search for new light particles weakly coupled to the visible sector. In this work we derive new constraints on axion-like particles (ALPs) using data from the MicroBooNE experiment, from a search for $e^+ e^-$ pairs pointing in the direction of the NuMI absorber. In particular, we consider the addition of higher-dimensional effective operators coupling the ALP to the electroweak gauge bosons. These would induce $K\to πa$ from kaon decay at rest in the NuMI absorber, as well as ALP decays into pairs of leptons or photons. We discuss in detail and compare various results obtained for the decay width $K\rightarrow πa$ in previous literature. For the operator involving the Higgs, MicroBooNE already sets competitive bounds (comparable to those of NA62) for ALP masses between 100 and 200 MeV. We also compute the expected sensitivities from the full NuMI dataset recorded at MicroBooNE. Our results show that a search for a $a\toγγ$ signal may be able to improve over current constraints from beam-dump experiments on the operator involving the ALP coupling to the $W$.

hep-ph↗

arXiv2023

Learning Trivializing Flows in a $ϕ^4$ theory from coarser lattices

The so-called trivializing flows were proposed to speed up Hybrid Monte Carlo simulations, where the Wilson flow was used as an approximation of a trivializing map, a transformation of the gauge fields which trivializes the theory. It was shown that the scaling of the computational costs towards the continuum did not change with respect to HMC. The introduction of machine learning tecniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on solving topology freezing in lattice QCD simulations. In this talk I will present our work in a $ϕ^{4}$ theory using normalizing flows as trivializing flows (given its similarity with the idea of a trivializing map), training from a trivial distribution as well as from coarser lattices, and study its scaling towards the continuum, comparing it with standard HMC.

hep-lat↗

arXiv2023

Learning Trivializing Flows

The recent introduction of Machine Learning techniques, especially Normalizing Flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional Hybrid Monte Carlo (HMC) algorithm. In this work we study a modified HMC algorithm that draws on the seminal work on trivializing flows by Lüscher. Autocorrelations are reduced by sampling from a simpler action that is related to the original action by an invertible mapping realised through Normalizing Flows models with a minimal set of training parameters. We test the algorithm in a $ϕ^{4}$ theory in 2D where we observe reduced autocorrelation times compared with HMC, and demonstrate that the training can be done at small unphysical volumes and used in physical conditions. We also study the scaling of the algorithm towards the continuum limit under various assumptions on the network architecture.

hep-lat↗

arXiv2023

Topological sampling through windings

We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional $U(1)$ gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors$-$winding steps$-$combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the $U(1)$ pure gauge theory, which are known even at finite $β$. We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC$-$leading to significant deviations in topological as well as non-topological quantities$-$the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $L\sim 8 \times 10^3$.

hep-lat↗

arXiv2023

Resonant helicity mixing of electromagnetic waves propagating through matter

Dual scatterers preserve the helicity of an incident field, whereas antidual scatterers flip it completely. In this setting of linear electromagnetic scattering theory, we provide a completely general proof on the non-existence of passive antidual scatterers. However, we show that scatterers fulfilling the refractive index matching condition flip the helicity of the fields very efficiently without being in contradiction with the law of energy conservation. Moreover, we find that this condition is paired with the impedance matching condition in several contexts of electromagnetism and, in particular, within Fresnel's and Mie's scattering problems. Finally, we show that index-matched media induce a resonant helicity mixing on the propagating electromagnetic waves. We reach to this conclusion by identifying that the refractive index matching condition leads to the phenomenon of avoided level-crossing. Our contribution not only closes a historical discussion within the Nanophotonics community, but also opens up new possibilities in the fields of Metamaterials and Particle Physics.

physics.optics↗

arXiv2022

Learning trivializing flows

The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional HMC algorithm. Naive use of normalizing flows has been shown to lead to bad scaling with the volume. In this talk we propose using local normalizing flows at a scale given by the correlation length. Even if naively these transformations have a small acceptance, when combined with the HMC algorithm lead to algorithms with high acceptance, and also with reduced autocorrelation times compared with HMC. Several scaling tests are performed in the $ϕ^{4}$ theory in 2D.

hep-lat↗

arXiv2022

A lattice study of $ππ$ scattering at large $N_\text{c}$

We present the first lattice study of pion-pion scattering with varying number of colors, $N_\text{c}$. We use lattice simulations with four degenerate quark flavors, $N_\text{f}=4$, and $N_\text{c}=3-6$. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, $SS$, and the fully antisymmetric one, $AA$. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for $N_\text{f} \geq 4$. A representative state is $\left( |D_s^+ π^+\rangle - |D^+ K^+\rangle\right)/\sqrt{2}$. Using Lüscher's formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large $N_\text{c}$. For this, we compute the analytical U$(N_\text{f})$ ChPT prediction for two-pion scattering, and use the lattice results to constrain the $N_\text{c}$ scaling of the relevant low-energy couplings.

hep-lat↗

arXiv2021

Improved topological sampling for lattice gauge theories

Standard sampling algorithms for lattice QCD suffer from topology freezing (or critical slowing down) when approaching the continuum limit, thus leading to poor sampling of the distinct topological sectors. I will present a modified Hamiltonian Monte Carlo (HMC) algorithm that triggers topological sector jumps during the assembly of Markov chain of lattice configurations. We study its performance in the 2D Schwinger model and compare it to alternative methods, such as fixing topology or master field. We then briefly discuss the difficulties of the algorithm in a SU(2) gauge model in 4D.

hep-lat↗

arXiv2021

$ππ$ scattering at Large $N_\text{c}$

We study the Large $N_\text{c}$ scaling of pion-pion scattering amplitudes for $N_\text{f}=4$ degenerate quark flavors. We focus on the standard isospin-2 channel and the adjoint-antisymmetric (AA) representation. The latter only exists for $N_\text{f}\geq 4$ and a representative state is $\frac{1}{\sqrt{2}}(|D_s^+π^+\rangle-|D^+ K^+\rangle)$. We compare the results obtained for two regularizations (Wilson and twisted-mass fermions) and three values of the lattice spacing, and observe significant discretization effects in the AA channel. Finally, we match our results to NLO SU(4) and NNLO U(4) Chiral Perturbation Theory and constrain the $N_\text{c}$ scaling of the relevant low-energy couplings.

hep-lat↗

arXiv2021

The Large $N_c$ limit of QCD on the lattice

We review recent progress in the study of the large $N_c$ limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of ${\mathcal O}(N_c^{-1})$ corrections for values of $N_c\gtrsim 3$. Some concrete examples of the topics we include are tests of large-$N_c$ factorization, the topological susceptibility, the glueball, meson and baryon spectra, the chiral dependence of masses and decay constants, and weak matrix elements related to the $ΔI=1/2$ rule in kaon decays.

hep-lat↗

arXiv2020

Dissecting the $ΔI= 1/2$ rule at large $N_c$

We study the scaling of kaon decay amplitudes with the number of colours, $N_c$, in a theory with four degenerate flavours, $N_f=4$. In this scenario, two current-current operators, $Q^\pm$, mediate $ΔS=1$ transitions, such as the two isospin amplitudes of non-leptonic kaon decays for $K\to (ππ)_{I=0,2}$, $A_0$ and $A_2$. In particular, we concentrate on the simpler $K\toπ$ amplitudes, $A^\pm$, mediated by these two operators. A diagrammatic analysis of the large-$N_c$ scaling of these observables is presented, which demonstrates the anticorrelation of the leading ${\mathcal O}(1/N_c)$ and ${\mathcal O}(N_f/N_c^2)$ corrections in both amplitudes. Using our new $N_f=4$ and previous quenched data, we confirm this expectation and show that these corrections are $naturally$ large and may be at the origin of the $ΔI=1/2$ rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, $g^\pm$, can be determined. A NLO estimate of the $K \to (ππ)_{I=0,2}$ isospin amplitudes can then be derived, which is in good agreement with the experimental value.

hep-lat↗

arXiv2020

New constraints on Heavy Neutral Leptons from Super-Kamiokande data

Heavy neutral leptons are predicted in many extensions of the Standard Model with massive neutrinos. If kinematically accessible, they can be copiously produced from kaon and pion decays in atmospheric showers, and subsequently decay inside large neutrino detectors. We perform a search for these long-lived particles using Super-Kamiokande multi-GeV neutrino data and derive stringent limits on the mixing with electron, muon and tau neutrinos as a function of the long-lived particle mass. We also present the limits on the branching ratio versus lifetime plane, which are helpful in determining the constraints in non-minimal models where the heavy neutral leptons have new interactions with the Standard Model.

hep-ph↗

arXiv2020

Searches for Atmospheric Long-Lived Particles

Long-lived particles are predicted in extensions of the Standard Model that involve relatively light but very weakly interacting sectors. In this paper we consider the possibility that some of these particles are produced in atmospheric cosmic ray showers, and their decay intercepted by neutrino detectors such as IceCube or Super-Kamiokande. We present the methodology and evaluate the sensitivity of these searches in various scenarios, including extensions with heavy neutral leptons in models of massive neutrinos, models with an extra $U(1)$ gauge symmetry, and a combination of both in a $U(1)_{B-L}$ model. Our results are shown as a function of the production rate and the lifetime of the corresponding long-lived particles.

hep-ph↗