Dispersive techniques for low-energy QCD: Pion-pion and pion-kaon scattering

A good understanding of strong interactions at low energies is key in the precision frontier of Particle and Hadron Physics, since most hadronic observables end up in final states involving pions and kaons, the lightest mesons in the Hadron Spectrum. In particular, the pion–pion and pion–kaon scattering lengths are the lowest energy observables for these interactions, and hence a fundamental quantity for understanding hadron interaction at low energies. In this talk we review the current status of their determination. After discussing the predictions expected from chiral symmetry at different orders in the chiral expansion, we review current experimental and lattice determinations. We then focus on the dispersive determination of pion-pion and pion-kaon interactions, based on the analysis of Roy and Roy-Steiner equation, and continue discussing in detail the current tension between the chiral symmetry and dispersive predicition for the pion- kaon scattering lenthgs. We finish this talk providing an explanation of this disagreement

Estudio de las propiedades y naturaleza de las resonancias escalares más ligeras y su relación con la ruptura espontánea de la simetría quiral

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, leída el 01/02/2013. Tesis formato europeo (compendio de artículos)Fac. de Ciencias FísicasTRUEunpu

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 $\bar q \sigma^{\mu\nu} q$, 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.Comment: 7 pages, 3 figures; strangeness input update

Patterns and partners for chiral symmetry restoration

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) x U(1)_A. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members is 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' and the f₀(500)-f₀(980) mesons at O(4) x 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

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

We present an extraction of the pion-nucleon ($\pi N$) scattering lengths from low-energy $\pi N$ 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 $\pi N$ $\sigma$-term, $\sigma_{\pi N}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.Comment: 17 pages, 3 figures; journal versio

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

We present a determination of the pion-nucleon ($\pi N$) $\sigma$-term $\sigma_{\pi N}$ based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent high-precision data from pionic atoms to pin down the $\pi N$ 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 $\sigma_{\pi N}=(59.1\pm 1.9\pm 3.0)$ MeV $=(59.1\pm 3.5)$ MeV, where the first error refers to uncertainties in the $\pi N$ amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.Comment: 6 pages, 1 figure; title changed by journal, version to be published in PR

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 \Delta(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.Comment: 6 pages, 4 tables; version to appear in PR

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

We present an extraction of the pion-nucleon ($\pi N$) scattering lengths from low-energy $\pi N$ 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 $\pi N$ $\sigma$-term, $\sigma_{\pi N}=58(5)$ MeV, in agreement with, albeit less precise than, the determination from pionic atoms.Comment: 17 pages, 3 figures; journal versio