Pion Nucleon Research Articles

Nucleon resonance parameters from Roy–Steiner equations

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 f0(500), ρ(770), and f0(980) resonances in the t-channel process ππ→N¯N. 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.

Theory of Majorana-Type Heavy Ion Double Charge Exchange Reactions by Pion–Nucleon Isotensor Interactions

The theory of heavy ion double charge exchange (DCE) reactions proceeding by effective rank-2 isotensor interactions is presented. Virtual pion–nucleon charge exchange interactions are investigated as the source for induced isotensor interactions, giving rise to the Majorana DCE (MDCE) reaction mechanism. MDCE is of a generic character, proceeding through pairs of complementary (π±,π∓) reactions in the projectile and target nucleus. The dynamics of the elementary processes is discussed, where the excitation of pion–nucleon resonances are of central importance. Investigations of initial and final state ion–ion interactions show that these effects are acting as vertex renormalizations. In closure approximation, well justified by the finite pion mass, the second-order transition matrix elements reduce to pion potentials and effective two-body isotensor DCE interactions, giving rise also to two-body correlations in either of the participating nuclei. Connections to neutrinoless Majorana double beta decay (MDBD) are elucidated at various levels of the dynamics, from the underlying fundamental electro-weak and QCD scales to the physical scales of nuclear MDBD and MDCE physics. It is pointed out that heavy ion MDCE reactions may also proceed by competing electro-weak charge exchange processes, leading to lepton MDCE by electrons, positrons, and neutrinos.

Isovector Axial Charge and Form Factors of Nucleons from Lattice QCD

A survey of the calculations of the isovector axial vector form factor of the nucleon using lattice QCD is presented. Attention is paid to statistical and systematic uncertainties, in particular those due to excited state contributions. Based on a comparison of results from various collaborations, a case is made that lattice results are consistent within 10%. A similar level of uncertainty is in the axial charge gAu−d, the mean squared axial charge radius ⟨rA2⟩, the induced pseudoscalar charge gP∗, and the pion–nucleon coupling gπNN. Even with the current methodology, a significant reduction in errors is expected over the next few years with higher statistics data on more ensembles closer to the physical point. Lattice QCD results for the form factor GA(Q2) are compatible with those obtained from the recent MINERνA experiment but lie 2–3σ higher than the phenomenological extraction from the old ν–deuterium bubble chamber scattering data for Q2>0.3 GeV2. Current data show that the dipole ansatz does not have enough parameters to fit the form factor over the range 0≤Q2≤1 GeV2, whereas even a z2 truncation of the z expansion or a low order Padé are sufficient. Looking ahead, lattice QCD calculations will provide increasingly precise results over the range 0≤Q2≤1 GeV2, and MINERνA-like experiments will extend the range to Q2∼2 GeV2 or higher. Nevertheless, improvements in lattice methods to (i) further control excited state contributions and (ii) extend the range of Q2 are needed.

Exploring a new approach to hadronic parity violation from lattice QCD

The long-range, parity-odd nucleon interaction generated by single-pion exchange is captured in the parity-odd pion–nucleon coupling hπ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h^{1}_{\\pi }$$\\end{document}. Its calculation in lattice QCD requires the evaluation of four-quark operator nucleon three-point functions. We investigate a new numerical approach to compute hπ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h^{1}_{\\pi }$$\\end{document} based on nucleon matrix elements of parity-even four-quark operators and related to the parity-violating electroweak theory by partial conservation of axial current (PCAC) and chiral perturbation theory. This study is performed with 2+1+1 dynamical flavors of twisted mass fermions at pion mass mπ≈260MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{\\pi } \\approx 260 \\,\ ext {MeV}$$\\end{document} in a lattice box of L≈3fm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L \\approx 3 \\,\ ext {fm}$$\\end{document} and with lattice spacing of a≈0.091fm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a \\approx 0.091 \\,\ ext {fm}$$\\end{document}. From a calculation excluding fermion loop diagrams we find a bare coupling of hπ1=8.08(98)·10-7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h^{1}_{\\pi }= 8.08 \\,(98) \\cdot 10^{-7}$$\\end{document}.

Formal theory of heavy ion double charge exchange reactions

The theory of heavy ion double charge exchange (DCE) reactions A(Z, N) → A(Z ± 2, N ∓ 2) is recapitulated emphasizing the role of Double Single Charge Exchange (DSCE) and pion-nucleon Majorana DCE (MDCE) reactions. DSCE reactions are of second–order distorted wave character, mediated by isovector nucleon-nucleon (NN) interactions. The DSCE response functions resemble the nuclear matrix elements (NME) of 2ν2β decay. The MDCE process proceeds by a dynamically generated effective rank-2 isotensor interaction, defined by off–shell pion–nucleon DCE scattering. In closure approximation pion potentials and two–nucleon correlations are obtained, similar to the neutrino potentials and the intranuclear exchange of Majorana neutrinos in 0ν2β Majorana double beta decay (MDBD).

Nucleon Sigma Terms with N_{f}=2+1 Flavors of O(a)-Improved Wilson Fermions.

We present a lattice-QCD based analysis of the nucleon sigma terms using gauge ensembles with N_{f}=2+1 flavors of O(a)-improved Wilson fermions, with a complete error budget concerning excited-state contaminations, the chiral interpolation as well as finite-size and lattice spacing effects. We compute the sigma terms determined directly from the matrix elements of the scalar currents. The chiral interpolation is based on SU(3) baryon chiral perturbation theory using the extended on-mass shell renormalization scheme. For the pion nucleon sigma term, we obtain σ_{πN}=(43.7±3.6) MeV, where the error includes our estimate of the aforementioned systematics. The tension with extractions based on dispersion theory persists at the 2.4-σ level. For the strange sigma term, we obtain a nonzero value, σ_{s}=(28.6±9.3) MeV.

Rescattering effects in nucleon-to-meson form factors and application to tau-lepton-induced proton decay

Nucleon decays put extremely stringent bounds on baryon-number-violating interactions. However, in case the corresponding operators involve only τ leptons, the direct two-body decays, e.g., p→π0τ+, are kinematically not allowed and nucleon decay can only proceed via an off-shell τ, leading to p→π0ℓ+νℓν¯τ. To calculate such processes, the momentum dependence of the form factors for nucleon-to-meson transitions, which describe the hadronization of the underlying process at the quark level, is needed. In this work, we point out new isospin and Fierz relations among such proton–kaon matrix elements and calculate the momentum dependence of the nucleon-to-meson form factors from the universal final-state interactions in terms of pion–nucleon or kaon–nucleon scattering phase shifts. We use these results to derive novel limits on the Wilson coefficients of the baryon-number-violating dimension-6 operators involving a τ lepton, which were previously unconstrained.

Theoretical Analysis of Pion–Nucleus Scattering at Energies of the (3,3) Pion–Nucleon Resonance

Theoretical Analysis of Pion–Nucleus Scattering at Energies of the (3,3) Pion–Nucleon Resonance

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

In recent years, a persistent tension between phenomenological and lattice QCD determinations of the pion–nucleon σ-term σπN 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 ΔσπN=3.1(5)MeV when evaluated in chiral perturbation theory with low-energy constants determined from a Roy–Steiner analysis of pion–nucleon scattering as well as σπN 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, σπN=59.0(3.5)MeV, and provide the corresponding set of scalar couplings of the nucleon.

Pion–nucleon sigma term σπNand deeply bound pionic atoms

AbstractWe investigate the possibility of determining the value of the pion–nucleon sigma term σπN precisely by the experimental observables of deeply bound pionic atoms. We discuss the sensitivity of the observables to σπN and take into account the typical errors of up-to-date experiments on deeply bound pionic atoms. We find that the gap in the binding energies and the width of the deeply bound pionic states are good observables for σπN value determination with experimental data. We also discuss the expected difficulties for the accurate determination of the value of σπN due to the correlation between the σ term and the potential parameter in the pion–nucleus optical potential.

Study of the Strong Interaction Among Hadrons with Correlations at the LHC

The strong interaction among hadrons has been measured in the past by scattering experiments. Although this technique has been extremely successful in providing information about the nucleon–nucleon and pion–nucleon interactions, when unstable hadrons are considered the experiments become more challenging. In the last few years, the analysis of correlations in the momentum space for pairs of stable and unstable hadrons measured in pp and p+Pb collisions by the ALICE Collaboration at the LHC has provided a new method to investigate the strong interaction among hadrons. In this article, we review the numerous results recently achieved for hyperon–nucleon, hyperon–hyperon, and kaon–nucleon pairs, which show that this new method opens the possibility of measuring the residual strong interaction of any hadron pair.

Measurement of the tensor analyzing power T20 for the reaction γd → pnπ0

This paper presents new results for the [Formula: see text]-component of the tensor analyzing power of the reaction [Formula: see text] in the photon energy range of [Formula: see text]. The experimental statistics accumulated in 2013 at the VEPP-3 accelerator-storage complex is used. The reaction events are identified by the coincidence registration of the proton and two [Formula: see text]-quanta from the decay of the neutral pion. To determine the [Formula: see text]-component, the asymmetry of the yields with respect to the change of sign of the tensor polarization of the deuterium target is measured. The experimental results are compared with the theoretical calculations in which the MAID 2007 model is used as the elementary pion–nucleon photoproduction amplitude and contributions from the pion–nucleon and nucleon–nucleon rescattering are taken into account.

Topics in light-quark physics

This special issue of the European Journal of Physics: Special Topics entitled Topics in Light Quark Physics collects 8 papers with the intention to discuss problems in physical processes involving the particles (mesons and baryons) comprising the lighter part in the spectrum of strong interactions, though some connections to the heavy-quark sector are also discussed. Active and timely problems in this broad field are introduced and covered by experts who root their contributions in the known aspects at the same time that take us to the frontier of knowledge, while introducing in many instances new techniques for present and future further developments. The nature of the lightest scalar resonances, the hunt for the lightest glueballs, the $$\Lambda (1405)$$ as a paradigmatic example of two-pole resonances, the pion–nucleon sigma term, two- and three-body scattering amplitudes extracted from lattice QCD, the QCD phase diagram, extrapolations in the number of colors of QCD and their use for addressing properties of its spectrum, and new advances to reach renormalized scattering amplitudes with attractive/repulsive singular potentials are all items covered here.

Brief history of the pion–nucleon sigma term

The pion-nucleon sigma term is a quantity involved in many important aspects of particle and nuclear physics. In this review I show its origin and how it is connected to important questions as the origin of mass of the ordinary matter, studies of dark matter detection and nucleosynthesis. I mention the most common methods used to obtain the sigma term, and comment on the extracted values. As it is shown, the accepted value of the sigma term has been moving from relatively low ($\sim 40$ MeV) to larger ones ($\sim 60$ MeV) until today, where this controversy still persist.

Influence of modified light-flavor hadron spectra on particle yields in the statistical hadronization model

Hadron production in relativistic nuclear collisions is well described in the framework of the Statistical Hadronization Model (SHM). We investigate the influence on SHM predictions of hadron mass spectra for light-flavor baryons and mesons modified by the addition of about 500 new states as predicted by lattice QCD and a relativistic quark model. The deterioration of the resulting thermodynamic fit quality obtained for Pb–Pb collision data at sNN=2.76 TeV suggests that the additional states are not suited to be naively used since also interactions among the states as well as non-resonant contributions need to be considered in the SHM approach. Incorporating these effects via the pion nucleon interaction determined from measured phase shifts leads again to excellent reproduction of the experimental data. This is a strong indication that at least the additional nucleon excited states cannot be understood and used as independent resonances.

Dyson–Schwinger approach to pion–nucleon scattering using time-ordered perturbation theory

We present a simple description of pion–nucleon (πN) scattering taking into account the full complexity of pion absorption and creation on the nucleon. To do this, we solve Dyson–Schwinger equations within the framework of time-ordered perturbation theory. This enables us to construct partial wave separable πN t matrices that can be useful in models of nuclear processes involving fully dressed nucleons. At the same time, our approach demonstrates features of quantum field theory, such as particle dressing, renormalization, and the use of Dyson–Schwinger equations, in a non-relativistic context that is maximally close to that of quantum mechanics. For this reason, this article may also be of pedagogical interest.

On the Breakdown of Charge Independence and Charge Symmetry of the Pion—Nucleon Coupling Constant

A simple, physically validated, model of charge-independence and charge-symmetry breaking is proposed for the pion-nucleon coupling constant. Within this model, the pion-nucleon coupling constants are assumed to be in direct proportion to the masses of nucleons and pions involved in the interaction. The charge dependence of the pion-nucleon coupling constants and low-energy parameters of nucleon-nucleon scattering in the 1S0 spin-singlet state is studied on the basis of Yukawa’s meson theory. By using the value of $$f_{pp\pi^0}^2=0.0749(7)$$ established reliably for the pseudovector pion-nucleon coupling constant, which characterizes the strength of the nuclear proton-proton interaction, the values of $$f_c^2=0.0802(7)$$ and $$f_0^2=0.0750(7)$$ were calculated for, respectively, the charged and neutral pion-nucleon coupling constants, along with the value of $$f_{nn\pi^0}^2=0.0751(7)$$, which characterizes the strength of the nuclear neutron-neutron interaction. The values calculated for the low-energy parameters of neutron-proton and neutron-neutron scattering with the aid of the above constants agree well with experimental data.

Neutral-Pion Photoproduction on a 7Li Nucleus in the Excitation Region of the First Pion—Nucleon Resonance

In order to explain elastic neutral-pion photoproduction on a 7Li nucleus in the excitation-energy region of the Δ(1232)3/2+ resonance, a new interpretation of coherent pion photoproduction on nuclei featuring two or more shells is proposed with allowance for a special feature of inelastic pion photoproduction on a nucleon. Coherence originating from nucleons of different nuclear shells is retained, while coherence from all of the nucleons is removed, since, after pion production on nucleons from different shells, they cannot cannot be in the same phases because of the difference in the conditions of their residence in the nucleus. Under this assumption, a noncontradictory description of all experimental data is obtained upon additionally including the interaction of Δ isobars in the nucleus that are produced along with neutral pions.

Total hadronic cross sections at high energies in holographic QCD

We present our analysis on high energy hadron–hadron scattering in the framework of the holographic QCD. Combining the Brower–Polchinski–Strassler–Tan Pomeron exchange kernel and gravitational form factors of the involved hadrons which are obtained by using the bottom-up AdS/QCD models in the five-dimensional AdS space, we calculate the total cross sections at high energies. We show that our calculations for the nucleon–nucleon scattering agree with the experimental data including the recent ones taken by the TOTEM collaboration at the LHC. The present framework is applicable to any high energy process, in which the strong interaction can be approximated by the Pomeron exchange. We present the results for the pion–nucleon and pion–pion scattering as examples, which can be obtained without any additional parameter because all the adjustable parameters are fixed via the analysis on the nucleon–nucleon scattering. The resulting total cross section ratios are σtotπN/σtotNN=0.63 and σtotππ/σtotNN=0.45, respectively.

The effective description of non-strange hadrons low-energy electro-weak transitions

Starting with the general principles of global and local symmetries, the effective pion–nucleon lagrangian, essentially nonlinear in the pion field, to describe the non-strange hadrons low-energy electro-weak transitions is developed. We encounter no divergence summarizing properly all the infinite power series in a pion field which occur in the course of treatment. Our consistent approach proves to be relevant in considering the parity violation in pion–nucleon interactions.