Low-energy Pion Research Articles

Low-energy pions in nuclear matter and ππ photoproduction within a BUU transport model

A description of the low-energy scattering of pions and nuclei within a BUU transport model is presented. Implementing different scenarios of medium modifications, the mean free path of pions in nuclear matter at low momenta and pion absorption reactions on nuclei have been studied and compared to data and to results obtained via quantum-mechanical scattering theory. We show that even in a regime of a long pionic wavelength the semi-classical transport model is still a reliable framework for pion kinetic energies greater than ≈ 20-30MeV. Results are presented on π-absorption cross-sections in the regime of 10 MeV ⩽ T π kin ⩽ 130MeV and on photon-induced ππ production at incident beam energies of 400-500MeV.

Formula omitted]–nuclear bound states in a dynamical model

A comprehensive data base of K − –atom level shifts and widths is re-analyzed in order to study the density dependence of the K ¯ –nuclear optical potential. Significant departure from a t eff ρ form is found only for ρ ( r ) / ρ 0 ≲ 0.2 and extrapolation to nuclear-matter density ρ 0 yields an attractive potential, about 170 MeV deep. Partial restoration of chiral symmetry compatible with pionic atoms and low-energy pion–nuclear data plays no role at the relevant low-density regime, but this effect is not ruled out at densities of order ρ 0 and beyond. K ¯ –nuclear bound states are generated across the periodic table self consistently, using a relativistic mean-field model Lagrangian which couples the K ¯ to the scalar and vector meson fields mediating the nuclear interactions. The reduced phase space available for K ¯ absorption from these bound states is taken into account by adding an energy-dependent imaginary term which underlies the corresponding K ¯ –nuclear level widths, with a strength required by fits to the atomic data. Substantial polarization of the core nucleus is found for light nuclei, and the binding energies and widths calculated in this dynamical model differ appreciably from those calculated for a static nucleus. A wide range of binding energies is spanned by varying the K ¯ couplings to the meson fields. Our calculations provide a lower limit of Γ K ¯ = 50 ± 10 MeV on the width of nuclear bound states for K ¯ -binding energy in the range B K ¯ ∼ 100 – 200 MeV . Comments are made on the interpretation of the FINUDA experiment at DAΦNE which claimed evidence for deeply bound K − p p states in light nuclei.

Low-energy pions in nuclear matter and ππ photoproduction within a BUU transport model

In the present paper we investigate a method to describe low-energy scattering events of pions and nuclei within a Boltzmann-Uehling-Uhlenbeck (BUU) transport model. Implementing different scenarios of medium modifications, we studied the mean free path of pions in nuclear matter at low momenta and compared pion absorption simulations to data. Pursuing these studies we have shown, that also in a regime of a long pionic wave length the semi-classical BUU model still generates reasonable results. We present results on pi-induced events in the regime of 10 MeV < Tkin < 130 MeV and photo-induced pi pi production at incident beam energies of 400-460 MeV.

Multiplicity correlations of intermediate-mass fragments with pions and fast protons in 12C + 197Au

Low-energy pi+ (E < 35 MeV) from 12C+197Au collisions at incident energies from 300 to 1800 MeV per nucleon were detected with the Si-Si(Li)-CsI(Tl) calibration telescopes of the INDRA multidetector. The inclusive angular distributions are approximately isotropic, consistent with multiple rescattering in the target spectator. The multiplicity correlations of the low-energy pions and of energetic protons (E > 150 MeV) with intermediate-mass fragments were determined from the measured coincidence data. The deduced correlation functions 1 + R \approx 1.3 for inclusive event samples reflect the strong correlations evident from the common impact-parameter dependence of the considered multiplicities. For narrow impact-parameter bins (based on charged-particle multiplicity), the correlation functions are close to unity and do not indicate strong additional correlations. Only for pions at high particle multiplicities (central collisions) a weak anticorrelation is observed, probably due to a limited competition between these emissions. Overall, the results are consistent with the equilibrium assumption made in statistical multifragmentation scenarios. Predictions obtained with intranuclear cascade models coupled to the Statistical Multifragmentation Model are in good agreement with the experimental data.

Axial form factor of the nucleon in the perturbative chiral quark model

We apply the perturbative chiral quark model (PCQM) at one loop to analyse the axial form factor of the nucleon. This chiral quark model is based on an effective Lagrangian, where baryons are described by relativistic valence quarks and a perturbative cloud of Goldstone bosons as dictated by chiral symmetry. We apply the formalism to obtain analytical expressions for the axial form factor of the nucleon, which is given in terms of fundamental parameters of low-energy pion–nucleon physics (weak pion decay constant, strong pion–nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core).

Low energy analyzing powers in pion–proton elastic scattering

Analyzing powers of pion–proton elastic scattering have been measured at PSI with the Low Energy Pion Spectrometer LEPS and a novel polarized scintillator target. Angular distributions between 40 and 120 deg (c.m.) were taken at 45.2, 51.2, 57.2, 68.5, 77.2, and 87.2 MeV incoming pion kinetic energy for π+p scattering, and at 67.3 and 87.2 MeV for π−p scattering. These new measurements constitute a substantial extension of the polarization data base at low energies. Predictions from phase shift analyses are compared with the experimental results, and deviations are observed at low energies.

Pions versus magnons: from QCD to antiferromagnets and quantum Hall ferromagnets

The low-energy dynamics of pions and magnons—the Goldstone bosons of the strong interactions and of magnetism—are analogous in many ways. The electroweak interactions of pions result from gauging an SU(2) L ⊗ U(1) Y symmetry which then breaks to the U(1) em gauge symmetry of electromagnetism. The electromagnetic interactions of magnons arise from gauging not only U(1) em but also the SU(2) s spin rotational symmetry, with the electromagnetic fields E → and B → appearing as non-Abelian vector potentials. Pions couple to electromagnetism through a Goldstone–Wilczek current that represents the baryon number of Skyrmions and gives rise to the decay π 0→ γγ. Similarly, magnons may couple to an analogue of the Goldstone–Wilczek current for baby-Skyrmions which induces a magnon–two-photon vertex. The corresponding analogue of photon–axion conversion is photon–magnon conversion in an external magnetic field. The baryon number violating decay of Skyrmions can be catalyzed by a magnetic monopole via the Callan–Rubakov effect. Similarly, baby-Skyrmion decay can be catalyzed by a charged wire. For more than two flavors, the Wess–Zumino–Witten term enters the low-energy pion theory with a quantized prefactor N c —the number of quark colors. The magnon analogue of this prefactor is the anyon statistics angle θ which need not be quantized.

Pion production in deeply virtual Compton scattering

Using a soft pion theorem based on chiral symmetry and a $\Delta(1232)$ resonance model we propose an estimate for the production cross section of low energy pions in the deeply virtual Compton scattering (DVCS) process. In particular, we express the $e p \to e \gamma \pi N$ processes in terms of generalized parton distributions. We provide estimates of the contamination of the $e p \to e \gamma p$ DVCS observables due to this associated pion production processes when the experimental data are not fully exclusive, for a set of kinematical conditions representative of present or planned experiments at JLab, HERMES and COMPASS.

Lateral distributions of charged particles and muons in EAS at different zenith angles

It is well known that the Yakutsk array experimental data demonstrate spatial EAS changes at energies above 3·10 18 eV. In this paper we present the analysis of these data in the framework of modern quark-gluon string models and discuss different possibilities. We explore specially the role of low energy pions. It should be stressed that the account of such contributions proves to be essential at large distances.

Unitarized pion–nucleon scattering amplitude from inverse amplitude method

In a recent work on low energy pion–nucleon scattering, instead of using chiral perturbation theory (ChPT) amplitude, we started from a pion–nucleon soft-pion result and used elastic unitarity directly as a dynamical constraint to construct first-order unitarity corrected amplitudes. The resulting amplitudes are crossing symmetric but, as the ChPT ones, satisfy only approximate unitarity relation. In the present work, we reconsider our approach and we apply the inverse amplitude method (IAM) in order to access the energy resonance region. We present the resulting S- and P-wave phase shifts that are shown to be in qualitative agreement with experimental data.

Chiral SU(3) symmetry and strangeness

In this paper we review recent progress on the systematic evaluation of the kaon and antikaon spectral functions in dense nuclear matter based on a chiral SU(3) description of the low-energy pion–, kaon– and antikaon–nucleon scattering data.

Probing Chiral Symmetry of Nucleons by Threshold Production

Double meson production of eta and pi mesons in the threshold region is investigated in order to determine chiral properties of the nucleon. The eta can be used as a probe for the negative parity nucleon N* ≡N*(1535), produced in the intermediate state. The coupling of the low energy pion in the final state is then used to extract the sign of the Yukawa coupling, gπN*N*, which distinguishes the two realizations of chiral symmetry, naive and mirror, for the nucleon.

Emission pattern of high-energy pions: A new probe for the early phase of heavy-Ion collisions

The emission pattern of charged pions has been measured in Au+Au collisions at 1 GeV/nucleon incident energy. In peripheral collisions and at target rapidities, high-energy pions are emitted preferentially towards the target spectator matter. In contrast, low-energy pions are emitted predominantly in the opposite direction. The corresponding azimuthal anisotropy is explained by the interaction of pions with projectile and target spectator matter. This interaction with the spectator matter causes an effective shadowing which varies with time during the reaction. Our observations show that high-energy pions stem from the early stage of the collision whereas low-energy pions freeze out later.

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.

Unitarity corrections to a low-energy pion–nucleon scattering amplitude

A method is present to unitarize a low energy pion–nucleon scattering amplitude. Starting from a soft-pion result, we have used unitarity directly as a dynamical constraint and constructed amplitudes from their first-order discontinuities. There is no commitment to the existence of resonances, but they can be derived from the general structure of the model. Working with two parameters we determine low energy πN amplitudes. We have fixed the two parameters of the model by fitting the experimental P 33 phase shifts near 90°. Five S- and P-wave phase shifts are then shown to agree qualitatively with experimental data.

On the size of isospin violation in low-energy pion–nucleon scattering

We present an analysis of isospin-breaking effects in threshold pion–nucleon scattering due to the light quark mass difference and the dominant virtual photon effects. We discuss the deviation from various relations, which are exact in the isospin limit. The size of the isospin-violating effects in the relations involving the isovector πN amplitudes is typically of the order of one percent. We also find a new remarkably large effect in an isoscalar triangle relation connecting the charged and neutral pion scattering off protons.

Deconfinement at finite chemical potential

In a confining, renormalisable, Dyson-Schwinger equation model of two-flavour QCD we explore the chemical-potential dependence of the dressed-quark propagator, which provides a means of determining the behaviour of the chiral and deconfinement order parameters, and low-energy pion observables. We find coincident, first order deconfinement and chiral symmetry restoration transitions at \mu_c = 375 MeV. f_\pi is insensitive to \mu until \mu \approx \mu_0 = 0.7 mu_c when it begins to increase rapidly. m_\pi is weakly dependent on \mu, decreasing slowly with \mu and reaching a minimum 6% less than its \mu=0 value at \mu=\mu_0. In a two-flavour free-quark gas at \mu=\mu_c the baryon number density would be approximately 3 \rho_0, where \rho_0=0.16 fm^{-3}; while in such a gas at \mu_0 the density is \rho_0.

Low energy pion reactions

The s-wave amplitude for pion production in pp-collisions has been deduced from a recently updated data set, α 0 = 0.230 ± 0.019 mb. The new number is in agreement with data from pionic deuterium width applying basic symmetries and known ratios, yielding a value b 1 = (−80.5±6.8) × 10 −3 m π for the πN isovector scattering length. A compilation of all results for the isovector scattering length from analysis of data from reactions will real pions yields a new mean value, b 1 = (−87.3±2.4) × 10 −3 m π . The main source of uncertainty seems to be the ratio T = w(π − + d → n + n + γ) w(π − + p → n + γ) which has to be 0.74±0.12 in order to lead to this mean value of b 1.

Evidence for different freeze-out radii of high- and low-energy pions emitted in Au+Au collisions at 1 A·GeV

Abstract Double differential production cross sections of π − and π + mesons and the number of participating protons have been measured in central Au+Au collisions at 1 A·GeV. At low pion energies the π − yield is strongly enhanced over the π + yield. The energy dependence of the π − / π + ratio is assigned to the Coulomb interaction of the charged pions with the protons in the reaction zone. The deduced Coulomb potential increases with increasing pion c.m. energy. This behavior indicates different freeze-out radii for different pion energies in the c.m. frame.

Cross sections, spin observables, and helicity amplitudes of the reaction at the isobar resonance and below

We have calculated the reaction cross sections and spin observables from threshold to the resonance by considering three types of mechanisms; the impulse (absorption) mechanism, rescattering and s-wave rescattering. The effect of final-state interactions has also been included. While traditionally the first two mechanisms have been included within a sound theoretical basis, the s-wave rescattering generally has been treated phenomenologically using a coupling constant fitted to the low-energy pion - nucleon data. Herein, we treat the isovector component of such a pion rescattering process as being mediated by the -exchange. Also, in those absorption mechanisms where the pion enters directly without rescattering, we employ a phenomenological cut-off scaling governed by the nucleon coordinates, since at the pion - nucleon vertex the nucleon itself may be off mass shell. The energy dependence of the total cross section is well explained by the combined effects of the three mechanisms, but we find that this observable is not sensitive enough to give useful insight into fine details of the reaction. We calculated the spin observables of at a variety of energies spanning the resonance, finding such sensitivity to fine details of the calculation that we cannot obtain a complete agreement with the vast experimental data base. A better understanding of the importance of the various aspects of the reaction was obtained when the calculated helicity amplitudes were compared with those extracted via phase-shift analyses of the reaction data.