Experimental determination of the structure function of the pion

It was shown in the preceeding letter that dimuon production by 22 GeV pions proceeds in part through qq? annihilations in agreement with the Drell-Yan model. Using these data we extract the quark distribution function of the pion. Comparison of our structure function with that obtained from data at higher energy reveals differences compatible with the QCD calculations of the Q²-dependence (scale breaking) of the pion structure function.     

Unnatural parity states in nuclei and pion condensation

This is a systematic study to assess a lower limit on the threshold density for pion condensation on the basis of empirical nuclear data. It turns out that the isovector unnatural parity states in ⁴He, ¹⁶O and ⁴⁰Ca, and quantities related to them are best suited for a quantitative test. Assuming for the interactions parameters in the nucleon-hole and Δ-isobar-hole channels g′: = g′_NN = g′_NΔ = g′_ΔΔ, a value g′ = 0.7±0.1 is obtained from the measured energy shifts of unnatural parity states. Taking also into account results by Oset and Rho who obtain g′_ΔΔ = 0.6?0.7 from the observed quenching of Gamov-Teller matrix elements of (A±1) nuclei around ¹⁶O and ⁴⁰Ca, one finds the onset of pion condensation in nuclear matter at densities considerably larger than twice normal nuclear density, if at all. We discuss the work of Migdal et al. who prefer the assumption g′_NΔ = g′_ΔΔ = 0 and obtain lower critical densities. Also the question of (pre)critical behaviour in finite nuclei is investigated in terms of a quantitative example. It is found that a genuine signal for proximity to pion condensation would be the appearance of a strongly collective spin-isospin mode which has, however, not been observed experimentally so far.     

Possibilities of revealing collective pion degrees of freedomin nuclei by means of quasielastic pion knockout by high-energy electrons

The kinematics of quasielastic pion knockout by longitudinal virtual photons in the electroproduction process is presented. The possibility of directly investigating pion momentum distributions in specific channels owing to pole-amplitude dominance is considered. It is shown that, taking into account the final-state interaction of the knock-on pion and the nucleus involved, one can reveal the existence of a pion condensate in nuclei, since the momentum distribution of collective pions has a pronounced maximum at a momentum in excess of 0.3 GeV/c and since the excitation spectrum of the final recoil nucleus is concentrated in the low-energy region E* ≈ K ²/(2AM _N ) ≤ 1 MeV. The picture of pion knockout from meson clouds of individual nucleons is totally different. The analogous rho-mesonmomentum distributions for the process ρ + γT* → π are also presented.     

Neutral pion photoproduction off nucleons revisited

We investigate threshold pion photoproduction in the framework of heavy baryon chiral perturbation theory. We give the expansion of the electric dipole amplitude E ₀₊ to three orders in μ the ratio of the pion to nucleon mass, and show that it is slowly converging. We argue that this observable is not a good testing ground for the chiral dynamics of QCD. In contrast, we exhibit new and fastly converging low-energy theorems in the P-waves which should be used to constrain the data analysis. We also discuss the importance of polarization observables to accurately pin down certain multipoles and give predictions for the reaction γ n → π⁰ n.     

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     

Role of the pion mass in triple-Regge physics

This paper is an extension of the investigations of Abarbanel et al., who examined asymptotic total cross sections in a multiperipheral model and obtained the surprising result that the scale for the cross sections is provided not by μ, the mass of the exchanged pion (as anticipated on geometrical grounds) but by m_V, the central mass of the dominant low energy ππ resonance entering the kernel. In this paper the role of the pion mass in triple-Regge physics is clarified by examining the pion pole dominance model for the triple-Regge couplings g_ijk. It is found that m_V provides the scale for the inclusive link and that for this reason the couplings g_ijk depend very little on the intercept α_k of the exchanged reggeon. In the exclusive links if i = j = pomeron, m_V once again is the only active energy scale, whereas if i = j = R, the reggeons of intercept 0.5 or less, the pion mass enters the couplings g_RRk in an essential way. It is shown that the smallness of μ²/m_V² is responsible for the largeness of the ratios g_RRk/g_PPk. These features of the model, which are in qualitative agreement with experiment, are put to a quantitative test.     

Chirality and its breaking in a new theory of hadrons

We show that in Anisotropic Chromo-Dynamics (ACD), a new approach to the dynamics of coloured, confined quarks, the π-meson is a qq?-bound state very close to the Nambu-Goldstone boson of a spontaneously broken chiral symmetry. We calculate the “current” quark masses and obtain m_u⁽⁰⁾ ≈ m_d⁽⁰⁾ ≈ 18 MeV, and m_s⁽⁰⁾ ≈ 123 Mev, in disagreement with the usual “strong PCAC” Ansatz.     

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.     

Direct conversion of mixed phase into free hadronic gas and transverse pion momenta in ultra-relativistic nuclear collisions

The deflagration model is developed for a physically substantiated situation when free pions are radiated directly from a time-like hypersurface formed by a rarefaction shock wave. It is shown that the shock front and pion collective flow velocities are enhanced in this approach as compared to the standard deflagration model. Exotic regimes are also possible. The stability conditions are investigated and analytic solutions are found. We calculate the pion transverse momentum spectra in ultra-relativistic nuclear collisions and indicate their behavior in the region 0.2 GeV/c<p _⊥<1 Gev/c. The spectra are essentially different in this region depending on whether or not longitudinal collective flows are in a mixed phase.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

High-pT pion production in ππ interactions

Charged pion production in high energy π^-π^- interactions is studied in the p_T region of 1–2 GeV/c. The characteristics of pion production in π^-π^- interactions are compared with those in π^-p and pp interactions. The p_T dependence of pion production in these reactions follows a systematic trend which indicates that high-p_T pion production for ππ interactions as well as for πp and pp interactions proceeds via quark-quark scattering as predicted by QCD.     

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.     

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.     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.     

Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ ₁+λ ₂=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ ₁+λ ₂=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.     

An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory

A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of \(F_{\pi }\) and \(M_{\pi }^2\) in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low-energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.     

The pion radius

The pion radius has been measured by direct scattering of 50 GeV negative pions from stationary electrons in a hydrogen target. We find the square of the radius to be 〈r_π²〉 = (0.61 ± 0.15)fm².     

A study of single pion production in nucleon-nucleon collisions

A pion exchange model for NN pion production from threshold up to about 6 GeV/c is constructed. In contrast to other models of this type the full information from πN scattering is fed in whereby the πN partial waves on- and off-shell are identified with each other. Detailed comparison with the data for both the channels isospin one and zero, reveals that the shapes of angle and momentum distributions are, in general, well reproduced but the overall magnitude comes out too small for p_L ? 1.5 GeV/c. It is argued that this defect may be due to dibaryon resonances. For reaction cross sections their effects are quantitatively estimated.     

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.