Dynamical light vector mesons in low-energy scattering of Goldstone bosons

We present a study of Goldstone boson scattering based on the flavor SU(3) chiral Lagrangian formulated with vector mesons in the tensor field representation. A coupled-channel computation is confronted with the empirical s- and p-wave phase shifts, where good agreement with the data set is obtained up to about 1.2 GeV. There are two relevant free parameters only, the chiral limit value of the pion decay constant and the coupling constant characterizing the decay of the rho meson into a pair of pions. We apply a recently suggested approach that implements constraints from micro-causality and coupled-channel unitarity. Generalized potentials are obtained from the chiral Lagrangian and are expanded in terms of suitably constructed conformal variables. The partial-wave scattering amplitudes are defined as solutions of non-linear integral equations that are solved by means of an N/D ansatz.     

Pion–Rho Meson Lagrangian in Nuclear Matter

We present an in-medium modified pion and rho meson Lagrangian which describes the pion, rho meson and the corresponding soliton properties in nuclear matter. Within the present approach pion properties in nuclear matter is closely related to the low-energy pion-nucleus scattering phenomenology. We discuss the possible modifications of rho meson properties in nuclear matter.     

π介子和核子在低能的散射

本文讨论了经过減除的π-核子散射色散关系和通常拉格朗日描述及其重整化处理间的关系。指出一次減除可以解释为作用常数的重整化。我们用经过減除的色散关系处理了π-核子S波散射。计算结果指出,π介子和核子间的相互作用应该是赝矢型而不是赝标型的。     

A possibility of a pion-pion scattering experiment

A possibility of a pion-pion collision experiment is discussed. This experiment permits one to perform very precise measurements of the s-wave scattering lengths at isospin state of I = 0 and 2 and a pion energy of 200 MeV-1 GeV. Quark-antiquark condensate, effective Lagrangian theory, and some features of the QCD lattice approach can be tested with very high precision. The text was submitted by the authors in English.     

A study of transverse charge density of pions in relativistic quantum mechanics

The transverse charge density of pions is calculated based on relativistic quantum mechanics, where the pion is regarded as a quark-antiquark bound state. Corrections from the two spin-1/2 constituents and from the wave function of a quark and antiquark inside the bound system are discussed. The calculated results are compared to the results with a realistic effective Lagrangian approach as well as to that with a simple covariant model where the pion is regarded as a composite system with two scalar particles.     

W-parity, octet dominance and the breaking of chiral symmetry

It is shown that W-invariance together with octet dominance restricts the SU(3) × SU(3) symmetry breaking Lagrangian to the representations (3, ) ( ,3), (6, ) ( ,6), (8,8) and (1,8) (8,1). In a nonlinear model, this Lagrangian predicts that the T = 2, S-wave π-π scattering length is zero; and when fitted to the empirical pion and K-meson masses, it predicts a T = 0 scattering length of 0.26m_π⁻¹. Compared with the (3, ) ( ,3) model, this model gives a larger (by a factor 8/3) nucleon σ-term, in agreement with recent calculations.     

Scattering of negative pions on helium

Differential cross sections for negative pion scattering on ⁴He have been measured at five pion kinetic energies between 110 and 260 MeV in the angular range from 5° to 180°. Total cross sections have also been measured at eleven energies between 67 and 285 MeV. The differential cross sections have been fitted with a phenomenological expression for the nuclear scattering amplitude. Conventional phase shifts have been reconstructed starting from the parameters of the fits.     

The power of effective field theories in nuclei: The deuteron,NN scattering and electroweak processes

We show how effectively effective quantum field theories work in nuclear physics. Using the physically transparent cut-off regularization, we study the simplest nuclear systems of two nucleons for both bound and scattering states at a momentum scale much less than the pion mass. We consider all the static properties of the deuteron, the two-nucleon scattering phase-shifts, the n + p → d + γ process at thermal energy and the solar proton fusion process p + p → d + e⁺ + ν_e, and we demonstrate that these are all described with great accuracy in the expansion to the next-to-leading order. We explore how a “new” degree of freedom enters in an effective theory by turning on and off the role of the pion in the Lagrangian.     

Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

THE EFFECT OF PION CONDENSATION IN HIGH ENERGY PROTON-NUCLEUS SCATTERING

According to the prediction made by A.B. Migda, a pion condensate should already be present in ordinary finite nuclei, We have studied the effect of pion condensate in high energy proton-nucleus scattering by using the Glauber multiple scattering theory, A calculation has been performed for P-⁴⁰Ca elastic scattering at the incident energy of 1 GeV and compared with the data available. The results strongly indicate that pion condensate does not have an adequate, opportunity to manifest itself in high energy proton-nucleus scattering, at least so for small angle scattering.     

QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

π-π scattering in a hot pion gas at URHIC-conditions

Pion-pion scattering in a hot pion environment is considered. In medium effects considerably diminish the pion — pion scattering rates in the σ — and ρ — meson channels at temperatures and chemical potential of the pion gas close tom _π     

π-Nucleus scattering in the Lee model

The scattering operator of a “pion” on two “nucleons” is evaluated in the Lee model and is shown to be identical to the results of Watson's multiple scattering theory.     

Chiral symmetry restoration and parity mixing

We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study the modifications in the nuclear medium of the coupling constants of the axial current, namely the pion decay constant and the nucleonic axial one due to the requirements of chiral symmetry. We express the renormalizations in terms of the local scalar pion density. The latter also governs the quark condensate evolution and we discuss the link between this evolution and the renormalizations. In the case of the nucleon axial coupling constant this renormalization corresponds to a new type of pion exchange currents, with two exchanged pions. We give an estimate for the resulting quenching. Although moderate it helps explaining the quenching experimentally observed.     

Intermediate Energy Pion-20Ne Elastic Scattering in the α+16O Model of 20Ne

We present an analysis of π-²⁰Ne elastic scattering at intermediate energy basing on the α+¹⁶O model of the ²⁰Ne nucleus and in the framework of Glauber multiple scattering theory. Satisfactory agreement with the general features of the experimental data of pion elastic scattering on the neighboring 4N-type nuclei is obtained without any free parameters. Compared with the experimental angular distributions of pion elastic scattering on ¹²C, ¹⁶O, ²⁴Mg, and ²⁸Si nuclei, the diffractive patterns and the positions of the dips and peaks in the angular distributions of π-²⁰Ne elastic scattering are reasonably predicted by the calculations.     

Binding effects in pion-nucleus scattering

The pion nucleus optical potential is evaluated for a pion scattered by a nucleon bound in a potential well. Total cross sections for π-¹⁶O scattering are computed supposing an S-wave separable two body interaction. The comparison with impulse and static approximations shows that they are not justified in a resonance region.     

Modeling of a microscopic optical pion-nucleon potential at energies in the (3, 3)-resonance region and nuclear-matter effect on the pion-nucleon amplitude

Differential cross sections for elastic pion scattering on a number of nuclei at energies between 130 and 290 MeV are calculated. For this purpose, use is made of a microscopic optical pion-nucleus potential that was obtained on the basis of the Glauber theory of high-energy scattering and which is determined by the density distribution of pointlike target nucleons and by the pion-nucleon scattering amplitude. The calculation of the cross sections in question is based on solving the respective relativistic wave equation. Three parameters of the pion-nucleon amplitude are fitted in performing a comparison with experimental data. These are the total cross section for pion-nucleon scattering, the ratio of the real to the imaginary part of the forward pion-nucleon scattering amplitude, and the slope parameter. The resulting values of these parameters are then compared with their counterparts for scattering on free nucleons. The character of nuclear-matter-induced changes in these parameters is studied.     

The composite electron

In this paper, the electron is considered a bound state of a neutrino and a negative pion. A model Lagrangian density that combines weak and electromagnetic interactions gives rise to equations of motion that define such a state. In this model, the muon is a bound state of an antineutrino and a negative pion, which explains why it cannot decay into an electron and a photon. The decay of unstable particles is reduced to pair creation plus particle recombination. The neutral pion is described by an interference between the charged-pion states. Several variations of the model are also presented.