Formation of primary particles in stopped pion absorption reactions

The results from analyzing the yields of protons (p), deuterons (d), and tritons (t) formed in the absorption of stopped π^– mesons by intranuclear clusters are presented. The contributions from cluster absorption to the production of hydrogen isotopes in stopped pion absorption reactions are determined. Phenomenological formulas are proposed for describing the mass number (A) dependences of the yields of the primary protons with ～15% precision in the mass number range of 6 < A < 209 (and of the primary deuterons and tritons in the mass number range of 59 < A < 209). Evidence is observed of the constancy of the ratio between the elemental absorption widths for the absorption of pions by pp and pn pairs over the investigated range of mass numbers.     

Reconstructing the freeze-out state in Pb+Pb collisions at 158 <Emphasis Type="Italic">A</Emphasis>GeV/<Emphasis Type="Italic">c</Emphasis><Superscript>a</Superscript>

For a class of analytical parametrizations of the freeze-out state of relativistic heavy ion collisions, we perform a simultaneous analysis of the single-particle m _⊥-spectra and two-particle Bose-Einstein correlations measured in central Pb+Pb collisions at the CERN SPS. The analysis includes a full model parameter scan with χ² confidence levels. A comparison of different transverse density profiles for the particle emission region allows for a quantitative discussion of possible model dependencies of the results. Our fit results suggest a low thermal freeze-out temperature T≈95±15 MeV and a large average transverse flow velocity \(\bar v_ \bot \approx 0.55 \pm 0.07\). Moreover, the fit favours a box-shaped transverse density profile over a Gaussian one. We discuss the origins and the consequences of these results in detail. In order to reproduce the measured pion multiplicity our model requires a positive pion chemical potential. A study of the pion phase-space density indicates μ_π≈60 MeV for T=100 MeV.     

Recent STAR Spin Results and Spin Measurements at RHIC

The STAR experiment provides measurements of single and double-spin asymmetries in longitudinally and transversely polarized p + p collisions at \(\sqrt s \) = 200 and 510 GeV to deepen our understanding on the proton spin structure and dynamics of parton interactions over a wide range of collision energy, momentum and rapidity of the various produced probes. Polarized processes with W^± production allow us to study the spin-flavor structure of the proton. Recent results obtained by STAR on the double longitudinal asymmetry, A_LL, of pion and jet production at \(\sqrt s \) = 200 and 510 GeV, the single longitudinal, A_L, and transverse, A_N, asymmetry of W^± production at \(\sqrt s \) = 510 GeV are overviewed. STAR results on azimuthal single transverse asymmetry of pion in p^↑ + (p, Au) and jet + π^± in p^↑ + p collisions are discussed. The proposed Forward Calorimeter System (FCS) and Forward Tracking System (FTS) upgrades at STAR would significantly improve the capabilities of existing detectors for measurements of observables such as asymmetries of pion, jet, Drell-Yan pairs produced at forward rapidities.     

Relation between the charged and neutral pion–nucleon coupling constants in the Yukawa model

In the Yukawa-model framework for NN forces, a simple relation between the charged and neutral pion–nucleon coupling constants is derived. The relation implies that the charged pion–nucleon constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion–nucleon constant shows a very good agreement with one of the recent measurements. In relative units, the splitting between the charged and neutral pion–nucleon constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.     

Investigation of <Emphasis Type="Italic">pn</Emphasis> correlations in <Superscript>4</Superscript>He<Emphasis Type="Italic">p</Emphasis> interactions at a momentum of 5 GeV/<Emphasis Type="Italic">c</Emphasis>

Proton-neutron correlations in ⁴Hep interactions are studied in an exclusive experiment by using a 2-m bubble chamber exposed to a 5-GeV/c beam of α particles (the kinetic energy of the protons in the nucleus rest frame is T _p = 620 MeV). Data on the production of pn pairs in 4π geometry for three channels, where it is possible to reconstruct the neutron momentum unambiguously, are used to determine the pn correlation function in ⁴Hep interactions. The experimental results are compared with the predictions of a modified Lednicky-Lyuboshitz model. The value obtained for the root-mean-square radius of the pn-emission region is R _pn = 2.1 ± 0.3 fm. The dependence of the correlation function on the modulus of the total momentum of the emitted nucleon pair and on the direction of the momentum transfer is studied. An indication that the emission of a pn pair proceeds predominantly through the production of a virtual deuteron is obtained.     

The Dynamics of Quantum Entanglement and General Quantum Correlations in the Double Tavis-Cumming Model

We study the dynamics of quantum correlations involving entanglement and discord of two pairs of two-level atoms in cavity QED. In the model, two atoms A and C are coupled with a single-mode cavity field via Tavis-Cumming interaction at one location, and the same for B and D at another location. The two locations are connected by the entanglement of the atoms AB and CD while there are no any direct interactions between them. Through comparing the robustness of entanglement and discord of the atoms in various initial conditions of cavities, it is shown the discord is more robust than the entanglement and would be useful in quantum information technology.     

Production of neutral and charged pions in the reaction <Superscript>12</Superscript>C(<Emphasis Type="Italic">γ</Emphasis>, <Emphasis Type="Italic">πp</Emphasis>) in the second resonance region

The results are presented that were obtained by investigating the production of pion-proton pairs in the reaction ¹²C(γ, πp). The experiment in question was performed in the second resonance region of photon energy. The results of this measurement are analyzed on the basis of a model that takes into account the processes of single and double quasifree pion photoproduction.     

Absorptive corrections to the reaction γp→nπ in the one pion exchange model with gauge invariant extension

Absorptive corrections have been calculated for photoproduction ofN ^*. Two versions for the uncorrected production amplitude are used. First, the one pion exchange Born approximation in the Coulomb gauge and second, a gauge invariant extension, restricted to the orbital electromagnetic current and to the isospinI=1-amplitude in thet-channel. We found the second restriction to be unimportant. Numerical values for cross sections and decay correlations in the BeV region are given in diagram form. Present day experimental accuracy does not allow to test the effects of absorption.     

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.     

<Emphasis Type="Italic">SU</Emphasis>(2)×<Emphasis Type="Italic">SU</Emphasis>(2) chiral quark model with nonlocal interaction

Masses and interactions of light mesons are described in the framework of the model with the chiral invariant SU(2)×SU(2) four-quark interaction. The nonlocal kernel of the interaction is chosen in the form that ensures the absence of ultraviolet divergences in the Feynman diagrams and poles in the quark propagator. Within this model, we demonstrate that, in the chiral limit, the pion mass equals zero and the Goldberger-Treiman relation is fulfilled. The sigma-meson mass and the widths of strong decays σ → ππ, ρ → νν are estimated.     

Deviation from the standard model in the decay <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">νγ</Emphasis>

A precise investigation of radiative pion decay (π⁺ → e⁺νγ) in a pion beam from the meson factory of the Paul Scherrer Institute (Switzerland) was performed by the PIBETA Collaboration with the aid of the PIBETA detector. This resulted in finding 41 601 events of radiative pion decay in three kinematical regions. The absolute values of the branching ratio for radiative pion decay were determined in each of these regions. To a precision approximately four times higher than that known previously, the ratio of the axial-vector to the vector form factor was found to be γ ≡ F _A /F _V = 0.443 (15), the latter being fixed at F _V = 0.0259. The number of events found in the kinematical region specified by photon energies of E_γ > 55.6 MeV, positron energies of E _e > 20.0 MeV, and angles of θ_{γ, e} > 40° between the momenta of the corresponding particles (B region) was 5233. In region B, the measured branching ratio for radiative pion decay, R_π→evγ(expt) = 11.6(3) × 10^?8, proved to be smaller by eight standard deviations than that which follows from the Standard Model, R_π→evγ (theor) = 14.34(1) × 10^?8.     

On the Production of <Emphasis Type="Italic">J</Emphasis>/ψ-Mesons in Pion–Nucleus Collisions

The processes of J/ψ-mesons production in pion–nucleus collisions are considered. For the determination of the inclusive spectra πA → J/ψX, the model was used which takes into account the energy losses of hard gluons in the interactions of hadron states with the nucleus nucleons. The results of calculations are presented together with the experimental data of NA3 Collaboration on π^–Pt¹⁹⁵ → J/ψX spectra at the incident pions energies of 150 and 280 GeV.     

Quark microscopic picture for vector and pseudoscalar mesons in the nucleon and their quasielastic knockout by high-energy electrons

A technique for projecting a multiquark wave function in the microscopic model of a ³P⁰ scalar fluctuation onto the virtual-decay channels N → N + ρ and N → N + π is formulated (at a more general level for the latter than previously). The amplitude for the electromagnetic transition ρ + γ _T ^* → π in electron-induced quasielastic rho-meson knockout followed by rho-meson conversion to a pion is considered. Theoretical results obtained in this way are contrasted against available experimental data, and reasonable agreement is found for cross-section values. This confirms a universal character of the ³P₀ model. The precision of relevant experiments is as yet insufficient for comparing the momentum distribution of the rho meson from the channel N → N + ρ with its theoretical counterpart.     

Gaussian free field in the background of correlated random clusters,formed by metallic nanoparticles

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T ? T _c . The fractal dimension of iso-potential lines (D _f ), the exponent of the distribution function of the gyration radius (τ _r ), and the loop lengths (τ _l ), and also the exponent of the loop Green function x _l change in terms of T ? T _c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D _f (T) ? D _f (T _c ) ~ 1/√ξ(T), in which ξ(T) is the spin correlation length in the Ising model.     

Microscopics of mesonic degrees of freedom in nucleons and mesons in nuclei: Quasielastic meson knockout by high-energy electrons

The following questions are considered: (i) that of what quasielastic-knockout reactions are; (ii) that of what experience has been gained in measuring, in various channels, the momentum distributions and spectroscopic factors of nucleons and clusters in nuclei and of electrons in atoms, molecules, and solid-state bodies; (iii) that of how it is possible to introduce the concept of quasielastic knockout in the theory of meson-electroproduction processes p(e, e′m)B at beam energies of a few GeV and at moderate values of the square of the virtual-photon 4-momentum, Q ² = 2–4 (GeV/c)²; and (iv) that of how the momentum distributions of mesons in various channels of virtual proton decay, p → B + π, p → B + ρ, and p → Y + K, are predicted on the basis of the microscopic model of a fluctuation of the QCD vacuum in a nucleon. Proposals for relevant experiments are formulated. It is indicated that quasielastic-knockout processes like (e, e′π) provide the best way to study the problem of a scalar pion condensate in nuclei. In conclusion, it is emphasized that quasielastic processes ²H(e, e′p)B involving various spectator baryons B are of great value for determining the composition of multiquark configurations in nucleon-nucleon systems.     

Pion damping width from <Emphasis Type="Italic">SU</Emphasis>(2)×<Emphasis Type="Italic">SU</Emphasis>(2) NJL model

Within the framework of the NJL model, we investigate the modification of the pion damping width in a hot pion gas for temperatures ranging from 0 to 180 MeV. The pion is found to broaden noticeably at T > 60 MeV. Near the chiral phase transition T ～ 180 MeV, the pion width is saturated and amounts to 70 MeV. The main contribution to the width comes from pion-pion collisions. Other contributions are found to be negligibly small.     

Investigation of Rare Pion Decays with the PIBETA Spectrometer

Experimental results on pion decays obtained with the PIBETA spectrometer at the Paul Scherrer Institute (PSI) are reviewed. For pion beta decay π⁺ → π⁰е⁺ν (πβ), a precision measurement of relative probability yields Г(πβ) = [1.036 ± 0.004(stat) ± 0.004(syst) ± 0.003(π⁺→е⁺ν)] × 10^–8, which implies V_ud = 0.9728(30) for the corresponding element of the Cabibbo–Kobayashi–Maskawa mixing matrix. Using a sample of 65 × 10³ events, relative probability of the π⁺→е⁺νγ radiative pion decay (RPD) in the kinematic region of E_γ > 10 MeV and θ_eγ > 40° is measured as B^exp = 73.86(54) × 10^–8. A statistical analysis of measured E_e+ and E_γ distributions for this decay yield the values F_V = 0.0258(17) and F_A = 0.0117(17) for the pion weak formfactors. Assuming that F_V linearly depends on the е⁺ν invariant mass q² as F_V(q²) = F_V(0)(1 + aq²), the slope parameter is extracted as а = 0.10(6). The pion polarizability and neutral-pion lifetime are estimated as α_E = 2.78(10) × 10^–4 fm³ and τ(π⁰) = (8.5 ± 1.1) × 10^–17 s, respectively. The data for decays π⁺→ е⁺ ν and \({\mu ^ + } \to {e^ + }v\bar v\gamma \) have been collected and are being processed. The follow-up PEN experiment aims at reducing the uncertainty on the π⁺ → е⁺ ν relative probability by almost an order of magnitude (to 5 × 10^–4).     

QCD quark distributions in mesons

The valence-quark distributions in the π meson and in transversely and longitudinally polarized ρ mesons in the region of intermediate x are obtained on the basis of generalized QCD sum rules. Power-law corrections up to d=6 are taken into account. The quark distributions in the pion agree with those found from the data on Drell-Yan processes. A comparison of the results for the π and ρ mesons show that polarization effects are very significant and that the distribution functions do not have SU(6) symmetry.     

Observation of coherent <Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> electroproduction on deuterons at large momentum transfer

The first experimental results for the coherent π⁰ electroproduction on a deuteron, e+d → e+d+π⁰, at large momentum transfer, are reported. The experiment was performed at Jefferson Laboratory at an incident electron energy of 4.05 GeV. A large pion production yield has been observed in the kinematical region 1.1<Q²<1.8 GeV², from the threshold to 200-MeV excitation energy in the dπ⁰ system. The Q² dependence is compared with theoretical predictions.     

QCD and hybrid NBD on oscillating moments of multiplicity distributions in lepton-and hadron-initiated reactions

QCD predictions for moments of multiplicity distributions are compared with experimental data on e⁺e^? collisions and their two-NBD fits. Moments of the multiplicity distribution in a two-NBD model for 1.8-TeV pp collisions are considered. Three-NBD model predictions and fits for pp at LHC energies are also discussed. Analytic expressions for moments of hybrid NBD are derived and used to get insight into jet parameters and multicomponent structure of the processes. Interpretation of observed correlations is proposed.