A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

Threshold neutral pion photoproduction off the tri-nucleon to O(q4)

We calculate the electromagnetic neutral pion production off tri-nucleon bound states (³H, ³He) at threshold in chiral nuclear effective field theory to fourth order in the standard heavy baryon counting. We show that the fourth-order two-nucleon corrections to the S-wave multipoles at threshold are very small. This implies that a precise measurement of the S-wave cross section for neutral pion production off ³He allows for a stringent test of the chiral perturbation theory prediction for the S-wave electric multipole $E_{0+}^{\pi^0 n}$ .     

On the charge structure of high-energy multiple production

Correlations between neutral and charged particles produced in high-energy collisions are studied. The associated average multiplicity 〈n₀〉_n and the associated moment (f₂⁰⁰) are expressed in terms of the Mueller moments. An isospin analysis of the pion - pion correlations is performed with the help of Mueller-Regge techniques. From this analysis, the slope of 〈n₀〉_n? is predicted to be asymptotically about 0.75. This asymptotic limit should be approached already at ISR energies. Finally, predictions are given for the associated moment (f₂⁰⁰)_n?, and the importance of the measurements of this quantity is emphasized.     

Neutral-pion correlations. Test of production models

The observed increase of the average number of neutral pions, 〈n_o〉_n?, as a function of the number of charged pions produced in high-energy experiments, can be accounted for by several theoretical models. We analyze the basic trends of the models and find that in the region where 〈n_o〉_n? increases, the π⁰ multiplicity distribution is mainly determined by the isospin properties of the pion clusters and is insensitive to the overall multiplicity distribution. We calculate the values of f_2,n?⁰, the correlation parameter of two π⁰ for a given number of π^?, and show how its measurement can provide a clear test of the different production models.     

MO analysis of the high statistics Belle results on γ γ→π + π −, π 0 π 0 with chiral constraints

We reconsider Muskhelishvili–Omnès (MO) dispersive representations of photon–photon scattering to two pions, motivated by the very high statistics results recently released by the Belle collaboration for charged as well as neutral pion pairs and also by recent progress in the determination of the low-energy π π scattering amplitude. Applicability of this formalism is extended beyond 1 GeV by taking into account inelasticity due to  $K\bar{K}$ . A modified MO representation is derived which has the advantage that all polynomial ambiguities are collected into the subtraction constants and have simple relations to pion polarizabilities. It is obtained by treating differently the exactly known QED Born term and the other components of the left-hand cut. These components are approximated by a sum over resonances. All resonances up to spin two and masses up to ?1.3 GeV are included. The tensor contributions to the left-hand cut are found to be numerically important. We perform fits to the data imposing chiral constraints, in particular, using a model independent sum-rule result on the p ⁶ chiral coupling c ₃₄. Such theoretical constraints are necessary because the experimental errors are dominantly systematic. Results on further p ⁶ couplings and pion dipole and quadrupole polarizabilities are then derived from the fit. The relevance of the new data for distinguishing between two possible scenarios of isospin breaking in the f ₀(980) region is discussed.     

Two-pion production in photon-photon collisions

We calculate within chiral perturbation theory the cross section for γγ→π⁰π⁰ and γγ→π⁺π⁻ to next-to-leading order. The first process only depends on the one-loop contributions and forms a test of chiral perturbation theory. We also calculate the pion electromagnetic form factor and compare it to recent data.     

A chiral theory of nucleons

We present arguments that QCD at low momenta is reduced to a simple theory given by a path integral over pion fields and quarks which obtain dynamical mass owing to chiral symmetry breaking. The dimensional quantities of this low-momenta theory are fixed through the Λ_QCD parameter. The effective chiral lagrangian is given by a quark determinant in a background chiral field. Its properties are investigated both for slowly and rapidly varying pion fields. Though it satisfies requirements known from theory and phenomenology, it does not possess non-trivial soliton solutions. However we show that, at large N_c, nucleons correspond not to the local minimum of the effective chiral lagrangian but to a minimum of a more subtle quantity. In general, different functionals of the chiral field should be minimized, depending on the baryon charge of the system.We obtain a quantitative picture of nucleons as localized states of “constituent” quarks bound by a self-consistent pion field. Its properties, such as electromagnetic form factors, etc., are investigated in detail. We get very reasonable numerical values for the nucleon static properties.     

QCD with Chiral Chemical Vector: Models Versus Lattices

A formation of Local Parity Breaking (LPB) in central heavy-ion collisions (HIC) at high energies is discussed. LPB in the fireball can be produced by a difference between the number densities of right- and left-handed chiral fermions (Chiral Imbalance) which is implemented by a chiral (axial) chemical potential. Based on the effective meson Lagrangian motivated by QCD in the chiral medium the properties of light scalar and pseudoscalar mesons (π, a₀) are analyzed. It is found that exotic decays of scalar mesons arise as a result of mixing of π and a₀ vacuum states in the presence of chiral imbalance. The pion electromagnetic formfactor obtains a parity-odd supplement which generates a photon polarization asymmetry in pion polarizability. We believe that the above-mentioned properties of LPB can be revealed in experiments on LHC, RHIC, CBM FAIR and NICA accelerators.     

On the pion distribution amplitude shape

We argue that the recent BaBar data on γ → π e.m. transition form factor at large photon virtuality supports the idea that pion distribution amplitude (DA) is close to unity with ϕ_π^′(0)/6 ≫ 1 at a normalization point of μ = 0.6–0.8 GeV. Such pion DA can be obtained in the effective chiral quark model. The possible flat shape of the pion DA implies that the standard expansion of the DA in Gegenbauer polynomials can be divergent. On basis of chiral models we predict that the two-pion DA should exhibit anomalous endpoint behaviour for pions in the S-wave and that such feature is absent for higher partial waves. The latter implies that the ρ, f ₂, etc. meson DAs have no anomalous endpoint behaviour. Possible implications of such pion DA for other hard exclusive processes are shortly discussed.     

Hard pions and axial meson exchange current effects in negative muon capture in deuterium

The contribution of the axial meson exchange current effects to the doublet transition rate in the reaction μ^? +d → 2n+ ν_μ is calculated by using the minimal, chiral and approximately gauge invariant Lagrangian model for the A₁ρπ system. The contribution from the ρ-π weak decay process current usually considered is found to be nearly cancelled by that from the A₁ pole graph which is prescribed by the underlying invariance principles. Correct treatment of the N¹ propagator in the N¹ excitation current of the pion range leads to ≈ 30 % suppression of the N¹ effect.     

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM ₀, its value at zero momentum, and by the strong coupling constant α _s and bare quark massm ₀. In the limiting case of no explicit chiral symmetry breaking. i.e.,m ₀=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm ₀, α _s andM ₀ well in step with other estimates. This makes possible a calculation off _π, the pion decay constant, in reasonable agreement with experiment.     

Pion chemical potentials in heavy-ion collisions: relativistic quantum molecular dynamic analysis

In the framework of relativistic quantum molecular dynamics we analyse pion chemical potentials in the hadron system produced in central heavy-ion collisions at the bombarding energiesE _lab/A=(1–2) GeV/nucl. We find that the equilibrium relations hold for chemical potentials of π^?, of π⁰, of π⁺ and pion energy spectra reach local thermal equilibrium. However, there is no chemical equilibrium. The pion chemical potentials are very large and decrease during the expansion stage.     

Low-energy dilation

We study consequences of scale symmetry breaking in the QCD effective SU(2)×SU(2) chiral model. The mass of a pseudo-Goldstone boson dilation is estimated to be M_σ≅1 GeV and the upper bound to its lifetime τ_σ⩽4×10⁻²⁸ s. We also show that the dilation gives a considerable contribution to the pion scalar radius.     

pi-Mesonic decay of hypernuclei and pion wavefunction

The pi-mesonic decay of hypernuclei is studied by using the pion distorted waves which are the solutions of the Klein-Gordon equation with the optical potential. The distortions of the pion waves give rise to significant enhancement of theπ-decay rate compared with the pion free-wave case. Theπ-decay rates are very sensitive to the behavior of the pion wave deep inside the nucleus and therefore to the chosen pion optical potentials. There is a tendency that the enhancement is larger for theπ ^?-decay than for theπ ⁰-decay due to the combined effects of the Coulomb and optical potentials.     

Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.     

Nuclear bound states of ω mesons

Models based on chiral SU(3)_l ⊗ SU(3)_r symmetry and vector meson dominance suggest an attractive potential for the ω meson in a nuclear medium. We discuss the feasibility of producing nuclear bound states of ω mesons using (d, ³He) and pion induced reactions on selected nuclear targets.     

Bag confinement chiral breaking effect on a goldstone pion

We present a model in which the pion is a bound-state Goldstone boson in QCD and then the quarks are confined by a MIT bag-like boundary condition. We depart from the MIT cavity approximation in that we dynamically break chiral symmetry prior to confinement and we confine only in the $\text{q}\text{q}$ relative coordinate, leaving translation invariance in the total coordinate. We find M_π= 120 MeV, and a bag diameter R_π=7 GeV^?1.     

Production of positive pions by neutron-proton collisions

Spectra of positive pions from the processn+p→π ⁺+n+n have been measured for incident neutron energies from 470 MeV to 590 MeV and for laboratory angles up to 20°. The rather broad pion energy spectra and the pronounced anisotropy of the differential cross sections, both indicate an appreciable non-resonant, isoscalar (T=0) contribution to the pion production.