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Jacobo Ruiz de Elvira

Publications and source records attributed to Jacobo Ruiz de Elvira.

36 records · Page 2Linked to original sources
arXiv2022

Chiral extrapolation of hadronic vacuum polarization

We study the pion-mass dependence of the two-pion channel in the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon $a_μ^\text{HVP}$, by using an Omnès representation for the pion vector form factor with the phase shift derived from the inverse-amplitude method (IAM). Our results constrain the dominant isospin-$1$ part of the isospin-symmetric light-quark contribution, and should thus allow one to better control the chiral extrapolation of $a_μ^\text{HVP}$, required for lattice-QCD calculations performed at larger-than-physical pion masses. In particular, the comparison of the one- and two-loop IAM allows us to estimate the associated systematic uncertainties and show that these are under good control.

hep-ph↗
arXiv2021

The role of strangeness in chiral and $U(1)_A$ restoration

We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ($χ_S^κ$, $χ_P^K$) in the isospin 1/2 channel. We show that $χ_S^κ$ develops a maximum above the QCD chiral transition, after which it degenerates with $χ_P^K$. We also obtain $χ_S^κ$ within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $K_0^*(700)$ (or $κ$) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $πK$ scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $χ_S^κ$ dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $m_l/m_s$ ratio that allows one studying $K-κ$ degeneration in the chiral, two-flavor and $SU(3)$ limits. These results provide an alternative sign for $O(4)\times U(1)_A$ restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $U(1)_A$ restoration.

hep-ph↗
arXiv2021

Two-loop analysis of the pion-mass dependence of the $ρ$ meson

Analyzing the pion-mass dependence of $ππ$ scattering phase shifts beyond the low-energy region requires the unitarization of the amplitudes from chiral perturbation theory. In the two-flavor theory, unitarization via the inverse-amplitude method (IAM) can be justified from dispersion relations, which is therefore expected to provide reliable predictions for the pion-mass dependence of results from lattice QCD calculations. In this work, we provide compact analytic expression for the two-loop partial-wave amplitudes for $J=0,1,2$ required for the IAM at subleading order. To analyze the pion-mass dependence of recent lattice QCD results for the $P$-wave, we develop a fit strategy that for the first time allows us to perform stable two-loop IAM fits and assess the chiral convergence of the IAM approach. While the comparison of subsequent orders suggests a breakdown scale not much below the $ρ$ mass, a detailed understanding of the systematic uncertainties of lattice QCD data is critical to obtain acceptable fits, especially at larger pion masses.

hep-ph↗
arXiv2020

Nucleon matrix elements of the antisymmetric quark tensor

If physics beyond the Standard Model enters well above the electroweak scale, its low-energy effects are described by Standard Model Effective Field Theory. Already at dimension six many operators involve the antisymmetric quark tensor $\bar q σ^{μν} q$, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.

hep-ph↗
arXiv2019

Patterns and partners within the QCD phase diagram including strangeness

We review the current situation of the pattern of chiral symmetry restoration. In particular, we analyze partner degeneration for $O(4)$ and $U(1)_A$ symmetries within the context of Ward Identities and Effective Theories. The application of Ward Identities to the thermal scaling of screening masses is also discussed. We present relevant observables for which an Effective Theory description in terms of Chiral Perturbation Theory and its unitarized extension are compatible with lattice data even around the transition region. We pay special attention to the role of strangeness in this context.

hep-ph↗
arXiv2019

Coarse graining hadronic scattering

We show that it makes sense to coarse grain hadronic interactions such as $ππ$ and $πN$ reactions following previous work on NN scattering. Moreover, if the interaction is taken to be given by chiral dynamics at long distances above a given value $r > r_c$ larger than the elementary radii of the interaction hadrons the unknown short distance region $r< r_c$ is characterized by a {\it finite} number of fitting parameters. This number of independent parameters needed for a presumably complete description of scattering data for a CM energy below $\sqrt{s}$ has been found to be given by $N_{\rm Par} = N_S \times N_I \times (p r_c )^2 /2 $ with $N_S$ and $N_I$ the number of spin and isospin channels, and $p$ the CM momentum respectively. Therefore, for an experiment (or sets of experiments) with a total number of data $N_{\rm Dat}$ the number of degrees of freedom involved in a $χ^2$-fit is given by $ν= N_{\rm Dat}-N_{\rm Par}$ and confidence levels can be obtained accordingly by standard means. Namely a $1 σ$ confidence level corresponds to $χ_{\rm min}^2/ν\in (1- \sqrt{2/ν},1+\sqrt{2/ν})$. We discuss the approach for $ππ$ and $πN$ with an eye put on a data selection program and the eventual validation of chiral symmetry.

hep-ph↗
arXiv2018

Coarse graining $ππ$ scattering

We carry out an analysis of $ππ$ scattering in the $IJ=00$, $11$ and $20$ channels in configuration space up to a maximal center-of-mass energy $\sqrt{s}=1.4$ GeV. We separate the interaction into two regions marked by an elementarity radius of the system; namely, a long distance region above which pions can be assumed to interact as elementary particles and a short distance region where many physical effects cannot be disentangled. The long distance interaction is described by chiral dynamics, where a two-pion-exchange potential is identified, computed and compared to lattice calculations. The short distance piece corresponds to a coarse grained description exemplified by a superposition of delta-shell potentials sampling the interaction with the minimal wavelength. We show how the so constructed non-perturbative scattering amplitude complies with the proper analytic structure, allowing for an explicit N/D type decomposition in terms of the corresponding Jost functions and fulfilling dispersion relations without subtractions. We also address renormalization issues in coordinate space and investigate the role of crossing when fitting the scattering amplitudes above and below threshold to Roy-equation results. At higher energies, we show how inelasticities can be described by one single complex and energy dependent parameter. A successful description of the data can be achieved with a minimal number of fitting parameters, suggesting that coarse graining is a viable approach to analyze hadronic processes.

hep-ph↗
arXiv2017

Recent advances on chiral partners and patterns

We review recent results on chiral $SU(2)_L\times SU(2)_R\approx O(4)$ and $U(1)_A$ symmetry restoration in QCD. In particular, we discuss how Ward Identities allow one to derive general results on partner degeneration, which shed light on the distinction between the $O(4)$ and $O(4)\times U(1)_A$ patterns of the chiral transition. For that purpose, susceptibilities associated with the $O(4)$ and $U(1)_A$ symmetries are studied. From this analysis we conclude that in the ideal regime of exact $O(4)$ restoration (formally achieved in the limit of two massless flavours), $U(1)_A$ partners degenerate as well. We also discuss the role of the thermal $f_0(500)$ state to describe thermodynamic observables sensitive to chiral restoration, such as the scalar susceptibility. We pay special attention to the consistency of our results with recent lattice analysis.

hep-ph↗
arXiv2017

Extracting the sigma-term from low-energy pion-nucleon scattering

We present an extraction of the pion-nucleon ($πN$) scattering lengths from low-energy $πN$ scattering, by fitting a representation based on Roy-Steiner equations to the low-energy data base. We show that the resulting values confirm the scattering-length determination from pionic atoms, and discuss the stability of the fit results regarding electromagnetic corrections and experimental normalization uncertainties in detail. Our results provide further evidence for a large $πN$ $σ$-term, $σ_{πN}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.

hep-ph↗
arXiv2016

Chiral Symmetry restoration from the hadronic regime

We discuss recent advances on QCD chiral symmetry restoration at finite temperature, within the theoretical framework of Effective Theories. $U(3)$ Ward Identities are derived between pseudoscalar susceptibilities and quark condensates, allowing to explain the behaviour of lattice meson screening masses. Unitarized interactions and the generated $f_0(500)$ thermal state are showed to play an essential role in the description of the transition through the scalar susceptibility

hep-ph↗
arXiv2016

Remarks on the pion-nucleon sigma-term

The pion-nucleon $σ$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3σ$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.

hep-lat↗
arXiv2016

Roy-Steiner-equation analysis of pion-nucleon scattering

We review the structure of Roy-Steiner equations for pion-nucleon scattering, the solution for the partial waves of the t-channel process $ππ\to \bar N N$, as well as the high-accuracy extraction of the pion-nucleon S-wave scattering lengths from data on pionic hydrogen and deuterium. We then proceed to construct solutions for the lowest partial waves of the s-channel process $πN\to πN$ and demonstrate that accurate solutions can be found if the scattering lengths are imposed as constraints. Detailed error estimates of all input quantities in the solution procedure are performed and explicit parameterizations for the resulting low-energy phase shifts as well as results for subthreshold parameters and higher threshold parameters are presented. Furthermore, we discuss the extraction of the pion-nucleon $σ$-term via the Cheng-Dashen low-energy theorem, including the role of isospin-breaking corrections, to obtain a precision determination consistent with all constraints from analyticity, unitarity, crossing symmetry, and pionic-atom data. We perform the matching to chiral perturbation theory in the subthreshold region and detail the consequences for the chiral convergence of the threshold parameters and the nucleon mass.

hep-ph↗
arXiv2016

On the uncertainty estimates of the $σ$-pole determination by Padé approximants

We discuss the determination of the $f_0(500)$ (or $σ$) resonance by analytic continuation through Padé approximants of the $ππ$-scattering amplitude from the physical region to the pole in the complex energy plane. The aim is to analyze the uncertainties of the method, having in view the fact that analytic continuation is an ill-posed problem in the sense of Hadamard. Using as input a class of admissible parameterizations of the scalar-isoscalar $ππ$ partial wave, which satisfy with great accuracy the same set of dispersive constraints, we find that the Roy-type integral representations lead to almost identical pole positions for all of them, while the predictions of the Padé approximants have a larger spread, being sensitive to features of the input parameterization that are not controlled by the dispersive constraints. Our conservative conclusion is that the $σ$-pole determination by Padé approximants is consistent with the prediction of Roy-type equations, but has an uncertainty almost a factor two larger.

hep-ph↗
arXiv2015

Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

nucl-th↗
arXiv2015

High-precision determination of the pion-nucleon $σ$-term from Roy-Steiner equations

We present a determination of the pion-nucleon ($πN$) $σ$-term $σ_{πN}$ based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent high-precision data from pionic atoms to pin down the $πN$ scattering lengths as well as of constraints from analyticity, unitarity, and crossing symmetry in the form of Roy-Steiner equations to perform the extrapolation to the Cheng-Dashen point in a reliable manner. With isospin-violating corrections included both in the scattering lengths and the LET, we obtain $σ_{πN}=(59.1\pm 1.9\pm 3.0)$ MeV $=(59.1\pm 3.5)$ MeV, where the first error refers to uncertainties in the $πN$ amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.

hep-ph↗
arXiv2014

Precise determination of resonance pole parameters through Padé approximants

In this work, we present a precise and model--independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Padé approximants. Precise theoretical parameterizations of pion-pion scattering phase shifts based on once-- and twice-- subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrization the pole positions of the $f_0(500)$ at $\sqrt{s}=(453\pm 15) - i(297 \pm 15)$ MeV, the $ρ(770)$ at $\sqrt{s}=(761.4\pm 1.2)-i(71.8 \pm 1.0)$ MeV, and the pole of the $f_2(1270)$, located at $\sqrt{s}=(1267.3\pm 1.7)-i(95.0\pm 2.3)$ MeV. The couplings of the resonances to two pions are also determined with high precision, obtaining respectively, $3.8\pm 0.4$ GeV, $5.92\pm 0.15$ and $4.41\pm 0.23$ GeV$^{-1}$. Special attention is dedicated to the systematic treatment of the theoretical and statistical uncertainties, together with their comparison with previous determinations.

hep-ph↗
arXiv2011

Fock space expansion of sigma meson in leading-Nc

We examine the leading-Nc behavior of the masses and transition matrix elements of some low-lying, few-particle configurations in QCD. A truncation of the Fock space produces an effective, symmetric Hamiltonian that we diagonalize. The lowest eigenvalue is identified as the sigma meson if the Hamiltonian is chosen to represent the scalar sector. As an application, the coefficients of the Nc powers are then fit to two-loop Unitarized SU(2) Chiral Perturbation Theory results for the sigma mass and width as a function of the number of colors, and we show that those results can be accommodated using the QCD Nc dependence previously derived for matrix elements, without the need for unnatural parameters or fine tunings. Finally, we show a very preliminary good quality fit, estimating the proportion of tetraquark/molecule-like (dominant), q-anti-q-like (subdominant) and exotic-like (marginal) configurations in the sigma.

hep-ph↗