πNN coupling determined beyond the chiral limit

Within the conventional QCD sum rules, we calculate the πNN coupling constant, g _πN, beyond the chiral limit using two-point correlation function with a pion. For this purpose, we consider the Dirac structure, iγ₅, at m _π ² order in the expansion of the correlator in terms of the pion momentum. For a consistent treatment of the sum rule, we include the linear terms in quark mass as they constitute the same chiral order as m _π ². In this sum rule, we obtain g _πN= 13.3 ± 1.2, which is very close to the empirical πNN coupling. This demonstrates that going beyond the chiral limit is crucial in determining the coupling. Received: 8 July 1999 / Revised version: 20 August 1999     

Pion-mass dependence of three-nucleon observables

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the ¹ S ₀ scattering length and effective range, the deuteron binding energy, the ³ S ₁ effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse ³ S ₁ and ¹ S ₀ scattering lengths vanishing at m _π ^crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m _π in the region between the physical pion mass and m _π = m _π ^crit .     

Partially conserved axial-vector current inS-matrix theory

Mandelstam’s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm _π andm _ϱ as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionmϱ²−mπ²=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurements of the photon-pion transition form factor F _πγγ*(Q ²), which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exist two asymptotic regimes for the pion transition form factor. One regime with the asymptotic behavior F _πγ*γ(Q ²) ∼ 1/Q ² corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as F _πγ*γ(Q ²) ∼ ln(Q ²)/Q ². Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.     

Cross-sections for low-energy πgamma; reactions

We review the cross-sections for low-energy π^-γ reactions in the framework of chiral perturbation theory. Charged-pion Compton scattering, π^-γ → π^-γ , is considered up to one-loop order where the pion's internal structure enters through the difference of the electric and magnetic pion polarizability, α_π - β_π . The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction π^-γ → π^-π⁰ serves as a test of the QCD chiral anomaly (via the γ3π -coupling constant F _γ3π . Furthermore, we calculate the total cross-sections for neutral and charged pion-pair production, π^-γ → π^-π⁰π⁰ and π^-γ → π^-π⁺π^- , which are governed by the chiral ππ -interaction. Finally, we investigate the radiative (correction) process π^-γ → π^-γγ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the π^- Primakoff scattering events with photons in the final state.     

Roy–Steiner equations for <Emphasis Type="Italic">γγ</Emphasis>→<Emphasis Type="Italic">ππ</Emphasis>

Starting from hyperbolic dispersion relations, we derive a system of Roy–Steiner equations for pion Compton scattering that respects analyticity, unitarity, gauge invariance, and crossing symmetry. It thus maintains all symmetries of the underlying quantum field theory. To suppress the dependence of observables on high-energy input, we also consider once- and twice-subtracted versions of the equations, and identify the subtraction constants with dipole and quadrupole pion polarizabilities. Based on the assumption of Mandelstam analyticity, we determine the kinematic range in which the equations are valid. As an application, we consider the resolution of the γγ→ππ partial waves by a Muskhelishvili–Omnès representation with finite matching point. We find a sum rule for the isospin-two S-wave, which, together with chiral constraints, produces an improved prediction for the charged-pion quadrupole polarizability (a₂-b₂)^p±=(15.3±3.7)×10^-4(\alpha_{2}-\beta_{2})^{\pi^{\pm}}=(15.3\pm3.7)\times 10^{-4} fm⁵. We investigate the prediction of our dispersion relations for the two-photon coupling of the σ-resonance Γ _σγγ . The twice-subtracted version predicts a correlation between this width and the isospin-zero pion polarizabilities, which is largely independent of the high-energy input used in the equations. Using this correlation, the chiral perturbation theory results for pion polarizabilities, and our new sum rule, we find Γ _σγγ =(1.7±0.4) keV.     

Phase structure of the linear sigma model with the standard symmetry breaking term

The linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied by means of the Cornwal–Jackiw–Tomboulis (CJT) effective potential calculated in the improved Hartree–Fock (HF) approximation, where the Goldstone theorem and the thermodynamic consistency are respected. It results that in the chiral limit, for μ=0 the chiral phase transition is second order as expected from the general universality arguments, and for μ≠0 the phase diagram for the pion condensation in the (T,μ) plane exhibits a tricritical point which is crossover from first-order to second-order phase transitions. In the physical world, where the chiral symmetry is explicitly broken, the pion condensation occurs at μ=m _π , the pion mass in vacuum, and its phase diagram is basically in agreement with those found from the chiral perturbation theory. The chiral symmetry gets restored at high values of T for fixed μ and of μ for fixed T.     

Tests of the final-state radiation model at DAFNE near <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>-</Superscript> threshold

Effects due to the non-pointlike behaviour of pions in the process e ⁺ e ^-→π ⁺ π ^- γ can arise for hard photons in the final state. By means of a Monte Carlo event generator, which also includes the contribution of the direct decay φ→π ⁺ π ^- γ, we estimate these effects in the framework of the resonance perturbation theory. We consider angular cuts used in the KLOE analysis of the pion form factor at threshold. A method to reveal the effects of the non-pointlike behaviour of pions in a model-independent way is proposed.     

Can we get deeper inside the pion at the LHC?

We propose a measurement of leading neutrons spectra at LHC in order to extract inclusive π ⁺ p and π ⁺ π ⁺ cross-sections with high p _T jets production. The cross-sections for these processes are simulated with the use of parton distributions in hadrons. In this work we estimate the possibility to extract parton distributions in the pion from the data on these cross-sections and also search for signatures of fundamental differences in the pion and proton structure.     

Novel approach to pion and eta production in proton-proton collisions near threshold

We evaluate the threshold matrix–element for the reaction pp→ppπ⁰ in a fully relativistic Feynman diagrammatic approach. We employ a simple effective range approximation to take care of the S–wave pp final–state interaction. The experimental value for the threshold amplitude A = (2.7 −i0.3) fm⁴ can be reproduced by contributions from tree level chiral (long–range) pion exchange and short–range effects related to vector meson exchanges, with ω-exchange giving the largest individual contribution. Pion loop effects appear to be small. We stress that the commonly used heavy baryon formalism is not applicable in the NN–system above the pion production threshold due to the large external momentum, |p|≃ (Mm _π)^−1/2, with M and m _π the nucleon and the pion mass, respectively. We furthermore investigate the reaction pp→pnπ⁺ near threshold within the same approach. We extract from the data the triplet threshold amplitude as B = (2.8 −i1.5) fm⁴. Its real part can be well understood from (relativistic) tree level meson–exchange diagrams. In addition, we investigate the process pp→ppη near threshold. We use a simple factorization ansatz for the ppη final–state interaction and extract from the data the modulus of the threshold amplitude, |C|= 1.32 fm⁴. With g _ηN= 5.3, this value can be reproduced by (relativistic) tree level meson–exchange diagrams and η–rescattering, whose strength is fixed by the ηN scattering length. We also comment on the recent near threshold data for η^′–production. Received: 27 November 1998     

Chiral symmetry and light resonances in hot and dense matter

We present a study of the π π scattering amplitude in the σ and ρ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral-symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear-density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar–isoscalar channel to account for finite nuclear-density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear-matter and heavy-ion collision experiments, such as ρ mass scaling versus broadening from dilepton spectra and chiral restoration signals in the σ channel. We also elaborate on the molecular nature of π π resonances.     

Relativistic constituent quark model and experiments at JLab

Within the relativistic-quantum-mechanics version developed by the present authors in their previous studies, the pion electromagnetic form factor is calculated in the region of high momentum transfers reached and planned to be reached in experiments at the Thomas Jefferson Laboratory (JLab). An asymptotic expansion was obtained for the pion form factor for Q ² → ∞. This expansion describes well existing experimental values and the results of a QCD simulation of future experiments at JLab. It is shown that the region of experiments at JLab is an asymptotic region for the relativistic constituent quark model and that the behavior of the pion form factor, F _π (Q ²)Q ² = const, can be obtained within this model.     

Pion mass dependence of the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">l</Emphasis>3</Subscript> semileptonic scalar form factor within finite volume

We calculate the scalar semileptonic kaon decay in finite volume at the momentum transfer t _m =(m _K −m _π )², using chiral perturbation theory. At first we obtain the hadronic matrix element to be calculated in finite volume. We then evaluate the finite size effects for two volumes with L=1.83 fm and L=2.73 fm and find that the difference between the finite volume corrections of the two volumes are larger than the difference as quoted in Boyle et al. (Phys. Rev. Lett. 100:141601, 2008). It appears then that the pion masses used for the scalar form factor in ChPT are large which result in large finite volume corrections. If appropriate values for pion mass are used, we believe that the finite size effects estimated in this paper can be useful for lattice data to extrapolate at large lattice size.     

Calculation of the hadron contribution from light-by-light scattering to the anomalous (g-2)<Subscript>μ</Subscript> muon magnetic moment for a nonlocal quark model

The muon contribution to the anomalous magnetic moment from light-by-light scattering diagrams with pion participation is calculated for a nonlocal chiral quark model. For various nonlocal model parameterizations, the contribution makes a _μ ^Had,LbL = 5.1(0.2) 10⁻¹⁰. Later on, we plan to calculate contributions from diagrams with an intermediate scalar meson and quark boxing.     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Aspects of near-threshold neutral pion photoproduction off protons

We investigate near-threshold neutral pion photoproduction off protons to fourth order in heavy-baryon chiral perturbation theory in the light of the new data from MAMI. We show that the unitarity cusp at the secondary π⁺ n threshold is in agreement with expectations from the final-state theorem. We also analyze the fourth-order corrections to the P-wave low-energy theorems and show that potentially large Δ isobar contributions are cancelled by sizeable pion loop effects. This solidifies the parameter-free third-order predictions, which are in good agreement with the data. Received: 25 May 2001 / Accepted: 21 June 2001     

Energy dependence of the delta resonance: Chiral dynamics in action

There is an important connection between the low-energy theorems of QCD and the energy dependence of the Δ resonance in π-N scattering, as well as the closely related γ^* N → N π reaction. The resonance shape is due not only to the strong π-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e., the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral-based models is presented. Correspondence: A. M. Bernstein, Physics Department and Laboratory for Nuclear Science, MIT, Cambridge, MA 02139, USA