Showing 1–50 of 72 results for author: de Elvira, J R

Isospin-breaking in the $ππ$ scattering amplitude I: Effects due to the pion mass difference

Authors: Gilberto Colangelo, Martina Cottini, Jacobo Ruiz de Elvira

Abstract: This is the first of a series of papers devoted to a detailed analysis of isospin-breaking effects in the $ππ$ scattering amplitude and the vector form factor of the pion. Isospin breaking originates from the mass difference between up and down quarks and from electromagnetic effects. The latter can be further split into effects due to the pion-mass difference and the remaining virtual and real ph… ▽ More This is the first of a series of papers devoted to a detailed analysis of isospin-breaking effects in the $ππ$ scattering amplitude and the vector form factor of the pion. Isospin breaking originates from the mass difference between up and down quarks and from electromagnetic effects. The latter can be further split into effects due to the pion-mass difference and the remaining virtual and real photonic effects. In this paper, we derive the modifications to the Roy equations for $ππ$ scattering due to the mass difference between the charged and the neutral pion. We solve the equations numerically after matching them to the chiral representation of the $ππ$ scattering amplitude evaluated in the same approximation, which is also provided. Numerical results are presented and discussed in detail. △ Less

Submitted 11 November, 2025; originally announced November 2025.

Comments: 46 pages, 8 figures

Report number: IPARCOS-UCM-25-059

Nucleon mass: trace anomaly and $σ$-terms

Authors: Martin Hoferichter, Jacobo Ruiz de Elvira

Abstract: We give a pedagogical introduction to the origin of the mass of the nucleon. We first review the trace anomaly of the energy-momentum tensor, which generates most of the nucleon mass via the gluon fields and thus contributes even in the case of vanishing quark masses. We then discuss the contributions to the nucleon mass that do originate from the Higgs mechanism via the quark masses, reviewing th… ▽ More We give a pedagogical introduction to the origin of the mass of the nucleon. We first review the trace anomaly of the energy-momentum tensor, which generates most of the nucleon mass via the gluon fields and thus contributes even in the case of vanishing quark masses. We then discuss the contributions to the nucleon mass that do originate from the Higgs mechanism via the quark masses, reviewing the current status of nucleon $σ$-terms that encode the corresponding matrix elements. △ Less

Submitted 16 September, 2025; v1 submitted 30 June, 2025; originally announced June 2025.

Comments: 12 pages, 1 figure, version to be published in the Encyclopedia of Particle Physics

The anomalous magnetic moment of the muon in the Standard Model: an update

Authors: R. Aliberti, T. Aoyama, E. Balzani, A. Bashir, G. Benton, J. Bijnens, V. Biloshytskyi, T. Blum, D. Boito, M. Bruno, E. Budassi, S. Burri, L. Cappiello, C. M. Carloni Calame, M. Cè, V. Cirigliano, D. A. Clarke, G. Colangelo, L. Cotrozzi, M. Cottini, I. Danilkin, M. Davier, M. Della Morte, A. Denig, C. DeTar , et al. (210 additional authors not shown)

Abstract: We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_μ$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light s… ▽ More We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_μ$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\toπ^+π^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_μ^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_μ^\text{exp} - a_μ^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor. △ Less

Submitted 11 September, 2025; v1 submitted 27 May, 2025; originally announced May 2025.

Comments: 188 pages, 83 figures; $a_μ^\text{exp}$ updated to final result of the Fermilab experiment, SM prediction unchanged; journal version

Report number: CERN-TH-2025-101, FERMILAB-PUB-25-0344-T, INT-PUB-25-015, IPARCOS-UCM-25-029, KEK Preprint 2025-22, LTH 1403, MITP-25-037, UWThPh 2025-15, ZU-TH 37/25

Journal ref: Phys. Rept. 1143 (2025) 1-158

Kaon Physics: A Cornerstone for Future Discoveries

Authors: Jason Aebischer, Atakan Tugberk Akmete, Riccardo Aliberti, Wolfgang Altmannshofer, Fabio Ambrosino, Roberto Ammendola, Antonella Antonelli, Giuseppina Anzivino, Saiyad Ashanujjaman, Laura Bandiera, Damir Becirevic, Véronique Bernard, Johannes Bernhard, Cristina Biino, Johan Bijnens, Monika Blanke, Brigitte Bloch-Devaux, Marzia Bordone, Peter Boyle, Alexandru Mario Bragadireanu, Francesco Brizioli, Joachim Brod, Andrzej J. Buras, Dario Buttazzo, Nicola Canale , et al. (131 additional authors not shown)

Abstract: The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This docume… ▽ More The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This document highlights the compelling physics case, with emphasis on exciting new opportunities for advancing kaon physics not only in Europe but also on a global stage. As an important player in the future of HEP, the kaon programme promises to drive transformative breakthroughs, inviting exploration at the forefront of scientific discovery. △ Less

Submitted 28 March, 2025; originally announced March 2025.

Comments: 10 pages, one figure, submitted to the European Strategy for Particle Physics Update

The role of chiral symmetry and the non-ordinary $κ/K^*_0(700)$ nature in $π^\pm K_S$ femtoscopic correlations

Authors: Miguel Albaladejo, Alejandro Canoa, Juan Nieves, Jose Ramón Peláez, Enrique Ruiz-Arriola, Jacobo Ruiz de Elvira

Abstract: We show that the use of realistic $πK$ interactions, obtained from a dispersive analysis of scattering data, as well as relativistic corrections, are essential to describe recently observed $π^\pm K_S$ femtoscopic correlations. We demonstrate that the spontaneous chiral symmetry breaking dynamics and the non-ordinary features of the $κ/K^*_0(700)$ resonance, together with large cancellations betwe… ▽ More We show that the use of realistic $πK$ interactions, obtained from a dispersive analysis of scattering data, as well as relativistic corrections, are essential to describe recently observed $π^\pm K_S$ femtoscopic correlations. We demonstrate that the spontaneous chiral symmetry breaking dynamics and the non-ordinary features of the $κ/K^*_0(700)$ resonance, together with large cancellations between isospin channels, produce a large suppression of $π^\pm K_S$ femtoscopic correlations compared to widely used models. Within an improved version of the standard on-shell factorization formalism, we illustrate that compensating for this interaction suppression leads to source radii smaller than 1 fm, contrary to usual expectations, as well as larger correlation strengths. The relation between these two parameters cannot be accommodated within naive models describing the nature of the resonances. This may raise concerns about the applicability of popular but too simple approaches for systems with light mesons. However, the correlation-suppression effects we demonstrate here will be relevant in any formalism, and substantial corrections may be expected for other femtoscopic systems involving light mesons. △ Less

Submitted 26 May, 2025; v1 submitted 25 March, 2025; originally announced March 2025.

Comments: 5 pages, 5 figures. v2: minor edits to match journal version

Report number: IPARCOS-UCM-25-020

Journal ref: Phys.Lett.B 866 (2025) 139552

Description of femtoscopic correlations with realistic pion-kaon interactions: the $κ/K^*_0(700)$ case

Authors: A. Canoa, M. Albaladejo, J. Nieves, J. R. Peláez, E. Ruiz Arriola, J. Ruiz de Elvira

Abstract: In this work, we show how $π^+ K_S$ femtoscopic correlations, recently reported by ALICE collaboration in $ pp $ collisions, can be well described taking into account relativistic corrections and using realistic $ πK $ interactions. These are obtained from a dispersive analysis of scattering data, which provides an accurate and model-independent description of the $ κ/K^*_0(700) $ resonance pole.… ▽ More In this work, we show how $π^+ K_S$ femtoscopic correlations, recently reported by ALICE collaboration in $ pp $ collisions, can be well described taking into account relativistic corrections and using realistic $ πK $ interactions. These are obtained from a dispersive analysis of scattering data, which provides an accurate and model-independent description of the $ κ/K^*_0(700) $ resonance pole. The chiral symmetry suppression of the $ πK $ interactions at low energies and the non-ordinary features of the $ κ/K^*_0(700) $ seem to suggest that the $ π^+ K_S $ source radius might be surprisingly smaller than for other hadronic processes when using the standard and simple Lednicky-Lyuboshits factorization approximation. △ Less

Submitted 20 January, 2025; originally announced January 2025.

Comments: 6 pages, 3 figures. To appear in the Proceedings of QNP2024

Improving $ππ$ dispersive analyses and resonance determination with Forward Dispersion Relations

Authors: P. Rabán, J. R. Peláez, J. Ruiz de Elvira

Abstract: We present preliminary results of an improved pion-pion scattering dispersive analysis that includes: a refined treatment of inelasticities, the introduction of G-waves, the extension of Forward Dispersion Relations as constraints up to 1.6 GeV, and data description up to roughly 1.8 GeV. Additionally, we impose Roy-like dispersion relations. As a result, we obtain three reliable solutions corresp… ▽ More We present preliminary results of an improved pion-pion scattering dispersive analysis that includes: a refined treatment of inelasticities, the introduction of G-waves, the extension of Forward Dispersion Relations as constraints up to 1.6 GeV, and data description up to roughly 1.8 GeV. Additionally, we impose Roy-like dispersion relations. As a result, we obtain three reliable solutions corresponding to three different datasets. From the Forward Dispersion Relation output, we extract resonance pole parameters in a parameterization-independent way using continued fractions. △ Less

Submitted 23 December, 2024; originally announced December 2024.

Comments: 6 pages, 3 figures

Global parametrizations of $ππ$ scattering with dispersive constraints: Beyond the S0 wave

Authors: J. R. Peláez, P. Rabán, J. Ruiz de Elvira

Abstract: We provide new global parametrizations of $ππ\to ππ$ scattering for the S2, P, D, F, and G partial waves up to at least 1.8 GeV, easy to implement for phenomenological use. With earlier S0-wave parametrizations, slightly updated here, they reproduce previous partial wave dispersion analyses up to the $πω$ threshold. In addition, these new parametrizations have improved their description of recent… ▽ More We provide new global parametrizations of $ππ\to ππ$ scattering for the S2, P, D, F, and G partial waves up to at least 1.8 GeV, easy to implement for phenomenological use. With earlier S0-wave parametrizations, slightly updated here, they reproduce previous partial wave dispersion analyses up to the $πω$ threshold. In addition, these new parametrizations have improved their description of recent P-wave data, the inelasticity in various waves, and their fulfillment of Roy-like and forward dispersion relations. The latter now test very high partial waves and have an improved matching with the Regge regime, extending those with P-wave contributions up to 1.6 GeV. Above 1.6 GeV and up to 1.8 GeV, or sometimes somewhat beyond, the parametrizations are simple unconstrained fits to data. △ Less

Submitted 4 April, 2025; v1 submitted 19 December, 2024; originally announced December 2024.

Comments: 37 pages, 20 figures. v2: matches published version in Phys. Rev. D

Report number: IPARCOS-UCM-24-062

Journal ref: Phys. Rev. D 111, 074003 (2025)

Effective Lagrangians and thermal resonances under extreme conditions

Authors: Andrea Vioque Rodríguez, Angel Gómez Nicola, Jacobo Ruiz de Elvira

Abstract: We analyze various problems related to the physics of hadrons under extreme conditions of temperature and chemical potentials. On the one hand, we show that the thermal resonances $f_0(500)$ and $K_0^*(700)$, generated in the framework of Unitarized Chiral Perturbation Theory $ππ$ and $Kπ$ scattering at finite temperature, play an essential role concerning chiral and $U(1)_A$ restoration. On the o… ▽ More We analyze various problems related to the physics of hadrons under extreme conditions of temperature and chemical potentials. On the one hand, we show that the thermal resonances $f_0(500)$ and $K_0^*(700)$, generated in the framework of Unitarized Chiral Perturbation Theory $ππ$ and $Kπ$ scattering at finite temperature, play an essential role concerning chiral and $U(1)_A$ restoration. On the other hand, a low-energy effective Lagrangian has been constructed within ChPT at non-zero chemical potential, which we discuss here for an axial chemical potential. △ Less

Submitted 12 December, 2024; originally announced December 2024.

Comments: 6 pages, 4 figures. Proceedings of the 10th International Conference on Quarks and Nuclear Physics (QNP2024)

Report number: IPARCOS-UCM-24-061

Nucleon resonance parameters from Roy-Steiner equations

Authors: Martin Hoferichter, Jacobo Ruiz de Elvira, Bastian Kubis, Ulf-G. Meißner

Abstract: A reliable determination of the pole parameters and residues of nucleon resonances is notoriously challenging, given the required analytic continuation into the complex plane. We provide a comprehensive analysis of such resonance parameters accessible with Roy-Steiner equations for pion-nucleon scattering - a set of partial-wave dispersion relations that combines the constraints from analyticity,… ▽ More A reliable determination of the pole parameters and residues of nucleon resonances is notoriously challenging, given the required analytic continuation into the complex plane. We provide a comprehensive analysis of such resonance parameters accessible with Roy-Steiner equations for pion-nucleon scattering - a set of partial-wave dispersion relations that combines the constraints from analyticity, unitarity, and crossing symmetry - most prominently of the $Δ(1232)$ resonance. Further, we study the Roper, $N(1440)$, resonance, which lies beyond the strict domain of validity, in comparison to Padé approximants, comment on the role of subthreshold singularities in the $S$-wave, and determine the residues of the $f_0(500)$, $ρ(770)$, and $f_0(980)$ resonances in the $t$-channel process $ππ\to\bar NN$. The latter allows us to test - for the first time fully model independently in terms of the respective residues - universality of the $ρ(770)$ couplings and the Goldberger-Treiman relation expected if the scalars behaved as dilatons, in both cases revealing large deviations from the narrow-resonance limit. △ Less

Submitted 9 May, 2024; v1 submitted 22 December, 2023; originally announced December 2023.

Comments: 9 pages, 1 figure; journal version

Report number: IPARCOS-UCM-23-139

Journal ref: Phys. Lett. B 853 (2024) 138698

Thermal hadron resonances and Ward identities: results for the QCD phase diagram

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Andrea Vioque-Rodríguez

Abstract: We review recent work regarding the role of light scalar resonances at finite temperature for chiral symmetry and $U(1)_A$ restoration. The results obtained are based on unitarized Chiral Perturbation Theory and Ward Identities and are directly connected with presently open problems within the QCD phase diagram We review recent work regarding the role of light scalar resonances at finite temperature for chiral symmetry and $U(1)_A$ restoration. The results obtained are based on unitarized Chiral Perturbation Theory and Ward Identities and are directly connected with presently open problems within the QCD phase diagram △ Less

Submitted 21 December, 2023; originally announced December 2023.

Comments: 5 pages, 2 figures. Proceedings of the 20th International Conference on Hadron Spectroscopy and Structure (HADRON2023)

Report number: IPARCOS-UCM-23-137

Comparing phenomenological estimates of dilepton decays of pseudoscalar mesons with lattice QCD

Authors: Bai-Long Hoid, Martin Hoferichter, Jacobo Ruiz de Elvira

Abstract: Dilepton decays of pseudoscalar mesons have been drawing particular interest, thanks to their sensitivity to both the QCD dynamics at low energy and also signals beyond the Standard Model. In this context, we shortly review our recent study on an improved Standard-Model prediction for the rare decay $π^0\to e^+e^-$, and compare it with the first determination on the lattice that predicted also the… ▽ More Dilepton decays of pseudoscalar mesons have been drawing particular interest, thanks to their sensitivity to both the QCD dynamics at low energy and also signals beyond the Standard Model. In this context, we shortly review our recent study on an improved Standard-Model prediction for the rare decay $π^0\to e^+e^-$, and compare it with the first determination on the lattice that predicted also the $π^0\to γγ$ decay width as a byproduct. In addition, we discuss our recent work on $K_L\to\ell^+\ell^-$ decays and its connection to lattice QCD. We comment on the current uncertainty estimates and discuss how they could be improved profiting from future experiments and progress in lattice QCD. △ Less

Submitted 1 December, 2023; originally announced December 2023.

Comments: 7 pages; proceedings of the 40th International Symposium on Lattice Field Theory (LATTICE2023)

Improved Standard-Model prediction for ${K_L\to \ell^+\ell^-}$

Authors: Martin Hoferichter, Bai-Long Hoid, Jacobo Ruiz de Elvira

Abstract: We present a comprehensive calculation of the $K_L\toγ^*γ^*$ form factor in dispersion theory, using input from the leptonic decays $K_L\to\ell^+\ell^-γ$, $K_L\to \ell_1^+\ell_1^-\ell_2^+\ell_2^-$, the hadronic mode $K_L\to π^+π^-γ$, the normalization $K_L\toγγ$, and the matching to asymptotic constraints. As key result we obtain an improved determination of the long-distance contribution to… ▽ More We present a comprehensive calculation of the $K_L\toγ^*γ^*$ form factor in dispersion theory, using input from the leptonic decays $K_L\to\ell^+\ell^-γ$, $K_L\to \ell_1^+\ell_1^-\ell_2^+\ell_2^-$, the hadronic mode $K_L\to π^+π^-γ$, the normalization $K_L\toγγ$, and the matching to asymptotic constraints. As key result we obtain an improved determination of the long-distance contribution to $K_L\to\ell^+\ell^-$, leading to the Standard-Model predictions $\text{Br}[K_L\toμ^+μ^-]=7.44^{+0.41}_{-0.34}\times 10^{-9}$, $\text{Br}[K_L\to e^+e^-]=8.46(37)\times 10^{-12}$, and more stringent limits on physics beyond the Standard Model. We provide a detailed breakdown of the current uncertainty, and delineate how future experiments and the interplay with lattice QCD could help further improve the precision. △ Less

Submitted 15 April, 2024; v1 submitted 26 October, 2023; originally announced October 2023.

Comments: 39 pages, 6 figures; version published in JHEP

Report number: IPARCOS-UCM-23-089

Journal ref: JHEP 04 (2024) 071

A phenomenological estimate of isospin breaking in hadronic vacuum polarization

Authors: Martin Hoferichter, Gilberto Colangelo, Bai-Long Hoid, Bastian Kubis, Jacobo Ruiz de Elvira, Dominic Schuh, Dominik Stamen, Peter Stoffer

Abstract: Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using $e^+e^-\to\text{hadrons}$ cross-section data. In lattice QCD, the dominant isospin-symmetric par… ▽ More Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using $e^+e^-\to\text{hadrons}$ cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the $e^+e^-\to3π$ channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and $e^+e^-$ data therefore cannot be explained by the IB contributions in the lattice-QCD calculations. △ Less

Submitted 18 October, 2023; v1 submitted 5 July, 2023; originally announced July 2023.

Comments: 7 pages, 2 figures; journal version

Report number: PSI-PR-23-22, ZU-TH 32/23, IPARCOS-UCM-23-077

Journal ref: Phys. Rev. Lett. 131, 161905 (2023)

On the role of isospin violation in the pion-nucleon $σ$-term

Authors: Martin Hoferichter, Jacobo Ruiz de Elvira, Bastian Kubis, Ulf-G. Meißner

Abstract: In recent years, a persistent tension between phenomenological and lattice QCD determinations of the pion-nucleon $σ$-term $σ_{πN}$ has developed. In particular, lattice-QCD calculations have matured to the point that isospin-violating effects need to be included. Here, we point out that the standard conventions adopted in both fields are incompatible, with the data-driven extraction based on the… ▽ More In recent years, a persistent tension between phenomenological and lattice QCD determinations of the pion-nucleon $σ$-term $σ_{πN}$ has developed. In particular, lattice-QCD calculations have matured to the point that isospin-violating effects need to be included. Here, we point out that the standard conventions adopted in both fields are incompatible, with the data-driven extraction based on the charged-pion mass, but lattice-QCD conventions relying on the mass of the neutral pion to define the isospin limit. The corresponding correction amounts to $Δσ_{πN}=3.1(5)\,\text{MeV}$ when evaluated in chiral perturbation theory with low-energy constants determined from a Roy-Steiner analysis of pion-nucleon scattering as well as $σ_{πN}$ itself. It reduces the tension with lattice QCD, and should be included in the comparison to phenomenological determinations. We also update the extraction from pionic atoms accounting for the latest measurement of the width of pionic hydrogen, $σ_{πN}=59.0(3.5)\,\text{MeV}$, and provide the corresponding set of scalar couplings of the nucleon. △ Less

Submitted 14 June, 2023; v1 submitted 11 May, 2023; originally announced May 2023.

Comments: 6 pages, 1 figure; journal version

Journal ref: Phys. Lett. B 843 (2023) 138001

The pion-kaon scattering amplitude and the $K^0(700)$ and $K^*(892)$ resonances at finite temperature

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Andrea Vioque-Rodríguez

Abstract: We perform a complete calculation of the pion-kaon scattering amplitude in Chiral Perturbation Theory at finite temperature, paying particular attention to the analytic structure of the amplitude and the main differences with respect to the zero temperature case. We also extend the Inverse Amplitude Method at finite temperature for unequal-mass scattering processes, which allows us to unitarize th… ▽ More We perform a complete calculation of the pion-kaon scattering amplitude in Chiral Perturbation Theory at finite temperature, paying particular attention to the analytic structure of the amplitude and the main differences with respect to the zero temperature case. We also extend the Inverse Amplitude Method at finite temperature for unequal-mass scattering processes, which allows us to unitarize the amplitude and obtain the thermal evolution of the $K_0^*(700)$ and $K^*(892)$ pole parameters. As a direct application of our analysis, we show that the thermal evolution of the $K_0^*(700)$ resonance is crucial to explain the behavior of the scalar susceptibility for isospin $I=1/2$, which in turn, is directly connected with chiral and $U(1)_A$ restoration properties of the QCD phase diagram. △ Less

Submitted 29 August, 2023; v1 submitted 18 April, 2023; originally announced April 2023.

Comments: 23 pages, 11 figures, published in JHEP

Journal ref: JHEP 08 (2023) 148

Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections

Authors: Martin Hoferichter, Gilberto Colangelo, Bai-Long Hoid, Bastian Kubis, Jacobo Ruiz de Elvira, Dominik Stamen, Peter Stoffer

Abstract: By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way… ▽ More By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the $\bar K K$ channel, which are enhanced due to the proximity of the $\bar K K$ threshold and the $φ$ resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections. △ Less

Submitted 21 October, 2022; originally announced October 2022.

Comments: 9 pages, 1 figure; proceedings of the 39th International Symposium on Lattice Field Theory (LATTICE2022)

Journal ref: PoS(LATTICE2022)316

Note on the definitions of branching ratios of overlapping resonances

Authors: V. Burkert, V. Crede, E. Klempt, K. V. Nikonov, J. A. Oller, J. R. Peláez, J. Ruiz de Elvira, A. V. Sarantsev, L. Tiator, U. Thoma, R. Workman

Abstract: Branching ratios for the decay of hadrons with large width or near thresholds depend on their definition. We test different definitions and show that rather different branching ratios can be obtained. For wide resonances and for sequential decays with wide intermediate resonances, integration over the spectral functions is mandatory. The tests are performed exploiting the latest solution of the Bo… ▽ More Branching ratios for the decay of hadrons with large width or near thresholds depend on their definition. We test different definitions and show that rather different branching ratios can be obtained. For wide resonances and for sequential decays with wide intermediate resonances, integration over the spectral functions is mandatory. The tests are performed exploiting the latest solution of the Bonn-Gatchina multi-channel analysis and published values for residues of light scalar mesons. For a resonance overlapping with a threshold, in case its pole lies in a non-adjacent sheet, we show how the total width, needed for the branching ratios, does not correspond to the imaginary part of the pole position. We use the Madrid-Krakow dispersive parameterizations to illustrate this situation with the $f_0(980)$. △ Less

Submitted 12 July, 2023; v1 submitted 18 July, 2022; originally announced July 2022.

Comments: Report, 9 pages (extended to light scalar mesons)

Radiative corrections to the forward-backward asymmetry in $e^+e^-\toπ^+π^-$

Authors: Gilberto Colangelo, Martin Hoferichter, Joachim Monnard, Jacobo Ruiz de Elvira

Abstract: We present a calculation of the $C$-odd radiative corrections to $e^+e^-\to π^+π^-$ in a dispersive formalism, concentrating on the leading pion-pole contribution in the virtual box diagrams. In particular, we show how the effect of a general pion vector form factor in the loop integral can be incorporated in a model-independent way and how the cancellation of infrared singularities proceeds in th… ▽ More We present a calculation of the $C$-odd radiative corrections to $e^+e^-\to π^+π^-$ in a dispersive formalism, concentrating on the leading pion-pole contribution in the virtual box diagrams. In particular, we show how the effect of a general pion vector form factor in the loop integral can be incorporated in a model-independent way and how the cancellation of infrared singularities proceeds in this case. The numerical results, dominated by the infrared enhanced contributions, indicate significant corrections beyond scalar QED, essentially confirming recent findings in generalized vector-meson-dominance models. △ Less

Submitted 26 February, 2025; v1 submitted 7 July, 2022; originally announced July 2022.

Comments: 16 pages, 3 figures; numerical results for the corrections included as supplemental material; corrected treatment of endpoint singularity, including mixed term in real part

Journal ref: JHEP 08, 295 (2022)

The f0(1370) controversy from dispersive meson-meson scattering data analyses

Authors: Jose Ramon Pelaez, Arkaitz Rodas, Jacobo Ruiz de Elvira

Abstract: We establish the existence of the long-debated $f_0(1370)$ resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at $(1245\pm 40)- i\,(300^{+30}_{-70})$ MeV in $ππ$ scattering. We also provide the couplings as well as further checks extrapolating partial… ▽ More We establish the existence of the long-debated $f_0(1370)$ resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at $(1245\pm 40)- i\,(300^{+30}_{-70})$ MeV in $ππ$ scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at $(1380^{+70}_{-60})-i\,(220^{+80}_{-70})$ MeV also appears in the $ππ\to K\bar K$ data analysis with partial-wave dispersion relations. Despite settling its existence, our model-independent dispersive and analytic methods still show a lingering tension between pole parameters from the $ππ$ and $K\bar K$ channels that should be attributed to data. △ Less

Submitted 23 July, 2024; v1 submitted 29 June, 2022; originally announced June 2022.

Comments: 13 pages, 8 figures. v2 version: improved results for the f0(1370) pole determination in the pipi to KKbar channel, minor amendments, appendices expanded

Report number: JLAB-THY-22-3649

Journal ref: Phys.Rev.Lett.130 (2023) 5, 051902

Thermal hadron resonances in chiral and $U(1)_A$ restoration

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Andrea Vioque-Rodríguez

Abstract: We review recent work on thermal resonances and their connection with chiral symmetry and $U(1)_A$ restoration within the QCD phase diagram. In particular, the $f_0(500)$ and $K_0^* (700)$ states generated from $ππ$ and $πK$ scattering within Unitarized Chiral Perturbation Theory (ChPT) at finite temperature allow one to describe scalar susceptibilities, which combined with Ward Identities yield i… ▽ More We review recent work on thermal resonances and their connection with chiral symmetry and $U(1)_A$ restoration within the QCD phase diagram. In particular, the $f_0(500)$ and $K_0^* (700)$ states generated from $ππ$ and $πK$ scattering within Unitarized Chiral Perturbation Theory (ChPT) at finite temperature allow one to describe scalar susceptibilities, which combined with Ward Identities yield interesting conclusions regarding the interplay between chiral and $U(1)_A$ restoration, key to understand the nature of the transition △ Less

Submitted 4 March, 2022; originally announced March 2022.

Comments: 6 pages, 2 figures, contribution to the proceedings of the 19th International Conference on Hadron Spectroscopy and Structure (HADRON 2021). Accepted for publication in Suplemento de la Revista Mexicana de Física

Chiral Symmetry Restoration, Thermal Resonances and the $U(1)_A$ symmetry

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Andrea Vioque-Rodríguez

Abstract: We discuss recent results regarding the interplay between chiral and $U(1)_A$ symmetry restoration, both from the point of view of Ward Identities relating meson susceptibilities and quark condensates, and from the behaviour of light meson resonances at finite temperature We discuss recent results regarding the interplay between chiral and $U(1)_A$ symmetry restoration, both from the point of view of Ward Identities relating meson susceptibilities and quark condensates, and from the behaviour of light meson resonances at finite temperature △ Less

Submitted 29 November, 2021; originally announced November 2021.

Comments: Proceedings of the "Particles and Nuclei International Conference" (PANIC2021), 5-10 september 2021. 4 pages, 2 figures

Chiral extrapolation of hadronic vacuum polarization

Authors: Gilberto Colangelo, Martin Hoferichter, Bastian Kubis, Malwin Niehus, Jacobo Ruiz de Elvira

Abstract: 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… ▽ More 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. △ Less

Submitted 5 January, 2022; v1 submitted 11 October, 2021; originally announced October 2021.

Comments: 9 pages, 4 figures; journal version; Mathematica implementation included as supplemental material

Journal ref: Phys. Lett. B 825 (2022) 136852

Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $σ/f_0(500)$ and $κ/K_0^*(700)$

Authors: J. R. Peláez, A. Rodas, J. Ruiz de Elvira

Abstract: For several decades, the $σ/f_0(500)$ and $κ/K_0^*(700)$ resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons $σ/f_0(500)$ and $κ/K_0^*(700)$. Gen… ▽ More For several decades, the $σ/f_0(500)$ and $κ/K_0^*(700)$ resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons $σ/f_0(500)$ and $κ/K_0^*(700)$. Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats. △ Less

Submitted 30 June, 2021; v1 submitted 16 January, 2021; originally announced January 2021.

Comments: Invited tutorial-review for European Physical Journal Special Topics. Final version to appear published. Expanded discussions and reference list. 50 pages

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

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Andrea Vioque-Rodríguez, David Álvarez-Herrero

Abstract: 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) a… ▽ More 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. △ Less

Submitted 8 October, 2021; v1 submitted 22 December, 2020; originally announced December 2020.

Comments: 9 pages, 4 figures. Version published in Eur.Phys.J.C

Journal ref: Eur. Phys. J. C 81, 637 (2021)

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

Authors: Malwin Niehus, Martin Hoferichter, Bastian Kubis, Jacobo Ruiz de Elvira

Abstract: 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 fro… ▽ More 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. △ Less

Submitted 15 March, 2021; v1 submitted 9 September, 2020; originally announced September 2020.

Comments: 20 pages, 5 figures; version published in PRL: Appendix E.1 and Bayesian information criterion added; Mathematica notebook with two-loop expressions included as supplementary material

Report number: INT-20-034

Journal ref: Phys. Rev. Lett. 126, 102002 (2021)

Strange Hadron Spectroscopy with Secondary KL Beam in Hall D

Authors: KLF Collaboration, Moskov Amaryan, Mikhail Bashkanov, Sean Dobbs, James Ritman, Justin Stevens, Igor Strakovsky, Shankar Adhikari, Arshak Asaturyan, Alexander Austregesilo, Marouen Baalouch, Vitaly Baturin, Vladimir Berdnikov, Olga Cortes Becerra, Timothy Black, Werner Boeglin, William Briscoe, William Brooks, Volker Burkert, Eugene Chudakov, Geraint Clash, Philip Cole, Volker Crede, Donal Day, Pavel Degtyarenko , et al. (128 additional authors not shown)

Abstract: We propose to create a secondary beam of neutral kaons in Hall D at Jefferson Lab to be used with the GlueX experimental setup for strange hadron spectroscopy. The superior CEBAF electron beam will enable a flux on the order of $1\times 10^4~K_L/sec$, which exceeds the flux of that previously attained at SLAC by three orders of magnitude. The use of a deuteron target will provide first measurement… ▽ More We propose to create a secondary beam of neutral kaons in Hall D at Jefferson Lab to be used with the GlueX experimental setup for strange hadron spectroscopy. The superior CEBAF electron beam will enable a flux on the order of $1\times 10^4~K_L/sec$, which exceeds the flux of that previously attained at SLAC by three orders of magnitude. The use of a deuteron target will provide first measurements ever with neutral kaons on neutrons. The experiment will measure both differential cross sections and self-analyzed polarizations of the produced $Λ$, $Σ$, $Ξ$, and $Ω$ hyperons using the GlueX detector at the Jefferson Lab Hall D. The measurements will span CM $\cosθ$ from $-0.95$ to 0.95 in the range W = 1490 MeV to 2500 MeV. The new data will significantly constrain the partial wave analyses and reduce model-dependent uncertainties in the extraction of the properties and pole positions of the strange hyperon resonances, and establish the orbitally excited multiplets in the spectra of the $Ξ$ and $Ω$ hyperons. Comparison with the corresponding multiplets in the spectra of the charm and bottom hyperons will provide insight into he accuracy of QCD-based calculations over a large range of masses. The proposed facility will have a defining impact in the strange meson sector through measurements of the final state $Kπ$ system up to 2 GeV invariant mass. This will allow the determination of pole positions and widths of all relevant $K^\ast(Kπ)$ $S$-,$P$-,$D$-,$F$-, and $G$-wave resonances, settle the question of the existence or nonexistence of scalar meson $κ/K_0^\ast(700)$ and improve the constrains on their pole parameters. Subsequently improving our knowledge of the low-lying scalar nonet in general. △ Less

Submitted 4 March, 2021; v1 submitted 18 August, 2020; originally announced August 2020.

Comments: Final version of the KLF Proposal [C12-19-001] approved by JLab PAC48. The intermediate version of the proposal was posted in arXiv:1707.05284 [hep-ex]. 103 pages, 52 figures, 8 tables, 324 references. Several typos were fixed

Light- and strange-quark mass dependence of the $ρ(770)$ meson revisited

Authors: R. Molina, J. Ruiz de Elvira

Abstract: Recent lattice data on $ππ$-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the st… ▽ More Recent lattice data on $ππ$-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the $ρ(770)$ meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the $ρ(770)$ meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the $ρ(770)$ meson is studied. △ Less

Submitted 28 September, 2020; v1 submitted 27 May, 2020; originally announced May 2020.

Comments: 44 pages, 41 figures, 11 tables

Patterns and partners within the QCD phase diagram including strangeness

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Andrea Vioque-Rodríguez

Abstract: 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 ter… ▽ More 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. △ Less

Submitted 21 October, 2019; originally announced October 2019.

Comments: Proceedings of the Workshop "Strangeness in Quark Matter 2019", 6 pages, 2 figures

Light- and strange-quark mass dependence of the $ρ(770)$ meson properties

Authors: R. Molina, J. Ruiz de Elvira

Abstract: From an analysis of recent ($I=J=1$)-$ππ$-phase-shift and pseudoscalar-meson decay-constant lattice data on two distinct chiral trajectories, where either the sum of the up, down and strange quark masses, or the mass of the strange quark is kept fixed, we extract the light and strange quark mass dependence of the rho meson parameters, and make predictions of those on chiral trajectories which invo… ▽ More From an analysis of recent ($I=J=1$)-$ππ$-phase-shift and pseudoscalar-meson decay-constant lattice data on two distinct chiral trajectories, where either the sum of the up, down and strange quark masses, or the mass of the strange quark is kept fixed, we extract the light and strange quark mass dependence of the rho meson parameters, and make predictions of those on chiral trajectories which involve lighter masses than the physical strange quark mass. We find that the mass of the rho meson can get as light as $700$ MeV for strange quark mass zero at physical pion masses. While the ratio of the couplings to the $ππ$ and $K\bar{K}$ channels is equal to $\sqrt{2}$ at the SU(3) symmetric chiral trajectory. △ Less

Submitted 3 February, 2020; v1 submitted 4 October, 2019; originally announced October 2019.

Comments: Talk given by R. Molina at the Workshop BLED 2019

Global parameterization of $ππ$ scattering up to 2 GeV

Authors: J. R. Pelaez, A. Rodas, J. Ruiz de Elvira

Abstract: We provide global parameterizations of $ππ$ scattering $S0$ and $P$ partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $ππ$, both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.… ▽ More We provide global parameterizations of $ππ$ scattering $S0$ and $P$ partial waves up to roughly 2 GeV for phenomenological use. These parameterizations describe the output and uncertainties of previous partial-wave dispersive analyses of $ππ$, both in the real axis up to 1.12 GeV and in the complex plane within their applicability region, while also fulfilling forward dispersion relations up to 1.43 GeV. Above that energy we just describe the available experimental data. Moreover, the analytic continuations of these global parameterizations also describe accurately the dispersive determinations of the $σ/f_0(500)$, $f_0(980)$ and $ρ(770)$ pole parameters. △ Less

Submitted 17 December, 2019; v1 submitted 30 July, 2019; originally announced July 2019.

Comments: 18 pages, 8 figures

Journal ref: J. Eur. Phys. J. C (2019) 79: 1008

The QCD topological charge and its thermal dependence: the role of the $η'$

Authors: Angel Gómez Nicola, Jacobo Ruiz De Elvira, Andrea Vioque-Rodríguez

Abstract: We analyze the contribution of the $η'(958)$ meson in the first two non-trivial moments of the QCD topological charge distribution, namely, the topological susceptibility and the fourth-order cumulant of the vacuum energy density. We perform our study within U(3) Chiral Perturbation Theory up to next-to-next-to-leading order in the combined chiral and large-$N_c$ expansion. We also describe the te… ▽ More We analyze the contribution of the $η'(958)$ meson in the first two non-trivial moments of the QCD topological charge distribution, namely, the topological susceptibility and the fourth-order cumulant of the vacuum energy density. We perform our study within U(3) Chiral Perturbation Theory up to next-to-next-to-leading order in the combined chiral and large-$N_c$ expansion. We also describe the temperature dependence of these two quantities and compare them with previous analyses in the literature. In particular, we discuss the validity of the thermal scaling of the topological susceptibility with the quark condensate, which is intimately connected with a Ward Identity relating both quantities. We also consider isospin breaking corrections from the vacuum misalignment at leading order in the U(3) framework. △ Less

Submitted 2 November, 2019; v1 submitted 26 July, 2019; originally announced July 2019.

Comments: Version to be published in JHEP. Comments and references added. 20 pages, 5 figures, supplementary material in ancillary files

Coarse graining hadronic scattering

Authors: Enrique Ruiz Arriola, Jacobo Ruiz de Elvira

Abstract: 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} numbe… ▽ More 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. △ Less

Submitted 26 June, 2019; originally announced June 2019.

Comments: 11 pages, 6 figures. Proceedings of the 9th Chiral Dynamics International Workshop, Durham, NC, USA, 17-21 September, 2018

Chiral and $U(1)_A$ restoration: Ward Identities and effective theories

Authors: A. Gómez Nicola, J. Ruiz de Elvira, A. Vioque-Rodríguez, S. Ferreres-Solé

Abstract: We discuss our recent results regarding chiral and $U(1)_A$ restoration, both from the formal point of view of QCD Ward Identities (WI) and from an Effective Theory analysis provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature. Our results lead to relevant conclusions regarding the behavior of chiral partners (in terms of susceptibilities) in the limit of exact restoration an… ▽ More We discuss our recent results regarding chiral and $U(1)_A$ restoration, both from the formal point of view of QCD Ward Identities (WI) and from an Effective Theory analysis provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature. Our results lead to relevant conclusions regarding the behavior of chiral partners (in terms of susceptibilities) in the limit of exact restoration and provide useful results for lattice analysis. In addition, it helps to understand the temperature dependence of lattice screening masses in terms of quark condensate combinations. The U(3) ChPT calculation supports the conclusions obtained within the WI analysis. Finally, the role of the thermal $f_0(500)$ state in chiral symmetry restoration, regarding the scalar susceptibility, is also discussed. △ Less

Submitted 5 May, 2019; v1 submitted 11 December, 2018; originally announced December 2018.

Comments: Proceedings of XIII Quark Confinement and the Hadron Spectrum. 8 pages, 4 figures. Minor corrections added

Nucleon matrix elements of the antisymmetric quark tensor

Authors: Martin Hoferichter, Bastian Kubis, Jacobo Ruiz de Elvira, Peter Stoffer

Abstract: 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 vecto… ▽ More 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. △ Less

Submitted 8 May, 2020; v1 submitted 27 November, 2018; originally announced November 2018.

Comments: 7 pages, 3 figures; strangeness input updated

Report number: INT-PUB-18-057

Journal ref: Phys. Rev. Lett. 122, 122001 (2019)

Coarse graining $ππ$ scattering

Authors: Jacobo Ruiz de Elvira, Enrique Ruiz Arriola

Abstract: 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 phys… ▽ More 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. △ Less

Submitted 27 July, 2018; originally announced July 2018.

Comments: 27 pages, 13 Figures

Workshop on Pion-Kaon Interactions (PKI2018) Mini-Proceedings. Editors: M. Amaryan, Ulf-G. Meißner, C. Meyer, J. Ritman, and I. Strakovsky

Authors: M. Amaryan, M. Baalouch, G. Colangelo, J. R. de Elvira, D. Epifanov, A. Filippi, B. Grube, V. Ivanov, B. Kubis, P. M. Lo, M. Mai, V. Mathieu, S. Maurizio, C. Morningstar, B. Moussallam, F. Niecknig, B. Pal, A. Palano, J. R. Pelaez, A. Pilloni, A. Rodas, A. Rusetsky, A. Szczepaniak, J. Stevens

Abstract: This volume is a short summary of talks given at the PKI2018 Workshop organized to discuss current status and future prospects of pi-K interactions. The precise data on pi-K interaction will have a strong impact on strange meson spectroscopy and form factors that are important ingredients in the Dalitz plot analysis of a decays of heavy mesons as well as precision measurement of Vus matrix element… ▽ More This volume is a short summary of talks given at the PKI2018 Workshop organized to discuss current status and future prospects of pi-K interactions. The precise data on pi-K interaction will have a strong impact on strange meson spectroscopy and form factors that are important ingredients in the Dalitz plot analysis of a decays of heavy mesons as well as precision measurement of Vus matrix element and therefore on a test of unitarity in the first raw of the CKM matrix. The workshop has combined the efforts of experimentalists, Lattice QCD, and phenomenology communities. Experimental data relevant to the topic of the workshop were presented from the broad range of different collaborations like CLAS, GlueX, COMPASS, BaBar, BELLE, BESIII, VEPP-2000, and LHCb. One of the main goals of this workshop was to outline a need for a new high intensity and high precision secondary KL beam facility at JLab produced with the 12 GeV electron beam of CEBAF accelerator. This workshop is a successor of the workshops Physics with Neutral Kaon Beam at JLab [1] held at JLab, February, 2016; Excited Hyperons in QCD Thermodynamics at Freeze-Out [2] held at JLab, November, 2016; New Opportunities with High-Intensity Photon Sources [3] held at CUA, February, 2017. Further details about the PKI2018 Workshop can be found on the web page of the conference: http://www.jlab.org/conferences/pki2018/ . △ Less

Submitted 17 April, 2018; originally announced April 2018.

Comments: 163 pages

Chiral and $U(1)_A$ restoration for the scalar/pseudoscalar meson nonets

Authors: A. Gómez Nicola, J. Ruiz de Elvira

Abstract: We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Ch… ▽ More We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1)_A$ partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the $I=1/2$ sector, the behavior of $I=0$ mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses. △ Less

Submitted 22 March, 2018; originally announced March 2018.

Comments: 28 pages and 16 figures

Journal ref: Phys. Rev. D 98, 014020 (2018)

Recent advances on chiral partners and patterns

Authors: Angel Gómez Nicola, Jacobo Ruiz de Elvira, Silvia Ferreres-Solé, Andrea Vioque-Rodríguez

Abstract: 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… ▽ More 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. △ Less

Submitted 30 November, 2017; originally announced December 2017.

Comments: 6 pages, 3 figures. Proceedings of Hadron 2017 conference, 25-29 september 2017, Salamanca (Spain)

Calculation of resonances from $K π$ scattering

Authors: A. Rodas, J. R. Pelaez, J. Ruiz de Elvira

Abstract: We present a determination of the mass, width and coupling of the strange resonances appearing in pion-kaon scattering below 1.8 GeV, namely the much debated $K^*_0(800)$ or $κ$, the scalar $K^*_0(1430)$, the $K^*(892)$ and $K^*(1410)$ vectors, the spin-two $K^*_2(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters of each resonance are determined using a direct analytic continuation of… ▽ More We present a determination of the mass, width and coupling of the strange resonances appearing in pion-kaon scattering below 1.8 GeV, namely the much debated $K^*_0(800)$ or $κ$, the scalar $K^*_0(1430)$, the $K^*(892)$ and $K^*(1410)$ vectors, the spin-two $K^*_2(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters of each resonance are determined using a direct analytic continuation of the pion-kaon partial waves by means of Padé approximants, thus avoiding any particular model description of their pole positions and residues, while taking into account the analytic requirements imposed by dispersion relations. △ Less

Submitted 27 November, 2017; originally announced November 2017.

Comments: Led parallel talk at the XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017, 25-29 September, 2017.University of Salamanca, Salamanca, Spain. arXiv admin note: text overlap with arXiv:1707.04534

Feynman-Hellmann theorem for resonances and the quest for QCD exotica

Authors: J. Ruiz de Elvira, U. -G. Meißner, A. Rusetsky, G. Schierholz

Abstract: The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data… ▽ More The generalization of the Feynman-Hellmann theorem for resonance states in quantum field theory is derived. On the basis of this theorem, a criterion is proposed to study the possible exotic nature of certain hadronic states emerging in QCD. It is shown that this proposal is supported by explicit calculations in Chiral Perturbation Theory and by large-$N_c$ arguments. Analyzing recent lattice data on the quark mass dependence in the pseudoscalar, vector meson, baryon octet and baryon decuplet sectors, we conclude that, as expected, these are predominately quark-model states, albeit the corrections are non-negligible. △ Less

Submitted 27 June, 2017; originally announced June 2017.

Comments: 26 pages, 2 figures

Journal ref: Eur.Phys.J. C77 (2017) no.10, 659

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

Authors: Jacobo Ruiz de Elvira, Martin Hoferichter, Bastian Kubis, Ulf-G. Meißner

Abstract: 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 normalizati… ▽ More 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. △ Less

Submitted 30 October, 2017; v1 submitted 5 June, 2017; originally announced June 2017.

Comments: 17 pages, 3 figures; journal version

Report number: INT-PUB-17-019

Patterns and partners for chiral symmetry restoration

Authors: A. Gomez Nicola, J. Ruiz de Elvira

Abstract: We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis… ▽ More We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $η$-$η^\prime$ and the $f_0(500)$-$f_0(980)$ mesons at $O(4)\times U(1)_A$ restoration, with a possible range where the pseudoscalar mixing vanishes if the two transitions are well separated. We test our results with lattice data and provide further relevant observables regarding chiral and $U(1)_A$ restoration for future lattice and model analyses. △ Less

Submitted 21 March, 2018; v1 submitted 17 April, 2017; originally announced April 2017.

Comments: 12 pages and 4 figures. Minor clarifications added. Version accepted in Phys. Rev. D

Journal ref: Phys. Rev. D 97, 074016 (2018)

Strange resonance poles from $Kπ$ scattering below 1.8 GeV

Authors: J. R. Peláez, A. Rodas, J. Ruiz de Elvira

Abstract: In this work we present a determination of the mass, width and coupling of the resonances that appear in kaon-pion scattering below 1.8 GeV. These are: the much debated scalar $κ$-meson, nowdays known as $K_0^*(800)$, the scalar $K_0^*(1430)$, the $K^*(892)$ and $K_1^*(1410)$ vectors, the spin-two $K_2^*(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters will be determined from the pol… ▽ More In this work we present a determination of the mass, width and coupling of the resonances that appear in kaon-pion scattering below 1.8 GeV. These are: the much debated scalar $κ$-meson, nowdays known as $K_0^*(800)$, the scalar $K_0^*(1430)$, the $K^*(892)$ and $K_1^*(1410)$ vectors, the spin-two $K_2^*(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters will be determined from the pole associated to each resonance by means of an analytic continuation of the $Kπ$ scattering amplitudes obtained in a recent and precise data analysis constrained with dispersion relations, which were not well satisfied in previous analyses. This analytic continuation will be performed by means of Padé approximants, thus avoiding a particular model for the pole parameterization. We also pay particular attention to the evaluation of uncertainties. △ Less

Submitted 21 February, 2017; v1 submitted 23 December, 2016; originally announced December 2016.

Comments: 13 pages, 12 figures. Accepted version to appear in Eur. Phys. J. C. Clarifications and references added, minor typos corrected

Journal ref: Eur. Phys. J. C (2017) 77: 91

Chiral Symmetry restoration from the hadronic regime

Authors: Angel Gomez Nicola, Santiago Cortes, John Morales, Jacobo Ruiz de Elvira, Ricardo Torres Andres

Abstract: 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 essen… ▽ More 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 △ Less

Submitted 22 November, 2016; originally announced November 2016.

Comments: 10 pages, 9 figures. Proceedings of "XII Quark Confinement and the Hadron Spectrum"

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

Authors: D. Siemens, J. Ruiz de Elvira, E. Epelbaum, M. Hoferichter, H. Krebs, B. Kubis, U. -G. Meißner

Abstract: Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be… ▽ More Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $Δ(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $Δ$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $Δ$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation. △ Less

Submitted 27 April, 2017; v1 submitted 27 October, 2016; originally announced October 2016.

Comments: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal version

Report number: INT-PUB-16-035, NSF-KITP-16-158

Journal ref: Phys.Lett. B770: 27-34, 2017

On the pi pi continuum in the nucleon form factors and the proton radius puzzle

Authors: M. Hoferichter, B. Kubis, J. Ruiz de Elvira, H. -W. Hammer, U. -G. Meißner

Abstract: We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty… ▽ More We present an improved determination of the $ππ$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $ππ\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $ππ$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius. △ Less

Submitted 11 November, 2016; v1 submitted 21 September, 2016; originally announced September 2016.

Comments: 10 pages, 3 figures, spectral functions included as supplementary material; journal version

Report number: INT-PUB-16-031

Remarks on the pion-nucleon sigma-term

Authors: Martin Hoferichter, Jacobo Ruiz de Elvira, Bastian Kubis, Ulf-G. Meißner

Abstract: 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… ▽ More 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. △ Less

Submitted 29 June, 2016; v1 submitted 24 February, 2016; originally announced February 2016.

Comments: 5 pages, 2 figures; version published in PLB

Report number: INT-PUB-16-006

Journal ref: Phys.Lett.B760:74-78,2016

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

Authors: Irinel Caprini, Pere Masjuan, Jacobo Ruiz de Elvira, Juan José Sanz-Cillero

Abstract: 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 ad… ▽ More 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. △ Less

Submitted 5 February, 2016; originally announced February 2016.

Comments: 11 pages, 13 figures

Journal ref: Phys. Rev. D 93, 076004 (2016)

Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

Authors: A. Gomez Nicola, J. Ruiz de Elvira

Abstract: We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the $η$-$η'$ sector and the $U_A(1)$ anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard $SU(3)$ framework for the octet case and combining the use of the $U(3)$ framework and the large-$N_c$ expansion… ▽ More We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the $η$-$η'$ sector and the $U_A(1)$ anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard $SU(3)$ framework for the octet case and combining the use of the $U(3)$ framework and the large-$N_c$ expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of $U(3)$ quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses, which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration. △ Less

Submitted 3 February, 2016; originally announced February 2016.

Comments: 20 pages, 6 figures

Journal ref: JHEP 1603 (2016) 186