The Role of α_1(1260) in π~-p→α_1~-(1260)p and π~-p → π~-ρ~0p Reactions Near Threshold

We report on a theoretical study of the π~-ρ→α1(1260)p and π~-ρ→π~-ρ~0p reactions near threshold within an effective Lagrangian approach.The production process is described by t-channel ρ~0 meson exchange.For the π~-ρ→π~- ρ~0p reaction,the final π~-ρ~0 results from the decay of the α1(1260) resonance,which is assumed as a dynamically generated state from the K* K and ρπ coupled channel interactions.We calculate the total cross section of the π~-ρ→α1(1260)p reaction.It is shown that,with the coupling constant of the α1(1260) to ρπ channel obtained from the chiral unitary theory and a cut off parameter Δρ~1.5 GeV in the form factors,the experimental measurement can be reproduced.Furthermore,the total and differential cross sections of π~p→α1(1260)p→π~ρ~0p reaction are evaluated,and it is expected that our model calculations can be tested by future experiments.These reactions are important for the study of the α1(1260) resonance and would provide further constraints on the properties of the α1(1260) state.     

Study of theK + K − π+ π− system centrally produced in the reactions π+ p→π+(K + K − π+ π−)p andpp→p(K + K − π+ π−)p at 85 GeV/c

The reactions π⁺ p→π⁺(K ⁺ K ^? π⁺ π^? p andpp→p(K ⁺ K ^? π⁺ π^?)p where the (K ⁺ K ^? π⁺ π^?) system is centrally produced have been studied at 85 GeV/c. 48% of the final state proceeds through single or double vector meson resonant production i.e.,K ^*0(890) (37%), ? (4%),ρ ⁰ (7%). Evidence is found for associatedK ^*0 (890) \(\bar K\) ^*o (890) production (6.4±1.1%) with a cross section ten times higher than that found for associated ? ? production in the same experiment.     

Δ(1232) axial charge and form factors from lattice QCD

We present the first calculation on the Δ axial?vector and pseudoscalar form factors using lattice QCD. Two Goldberger-Treiman relations are derived and examined. A combined chiral fit is performed to the nucleon axial charge, N to Δ axial transition coupling constant and Δ axial charge.     

Study of fermilab data for the reaction π−p → π0n

Fermilab data for the angular distribution measurements of the reaction ^–p ⁰n are investigated and it is shown that a good fit with experiment is obtained by using a simple Regge pole model with phenomenological residue functions. The energy dependence in this case is found to be different from that for the d/dt data obtained at Serpukhov.Work supported by the Pakistan Science Foundation under contract No. P-PU-PHY(11/1).     

Radiative π0 photoproduction on protons in the Δ+ (1232) region

The reaction γp → pπ ⁰γ′ has been measured with the Crystal Ball/TAPS detectors using the energy-tagged photon beam at the electron accelerator facility MAMI-B. Energy and angular differential cross-sections for the emitted photon γ′ and angular differential cross-sections for the π⁰ have been determined with high statistics in the energy range of the Δ⁺ (1232)-resonance. Cross-sections and the ratio of the cross-section to the nonradiative process γp → pπ ⁰ are compared to theoretical reaction models, having the anomalous magnetic moment κ _Δ as free parameter. As the shape of the experimental distributions is not reproduced in detail by the model calculations, currently no extraction of κ _Δ is feasible.     

用Hartree-Fock方法研究Δ(1232)在原子核内的束缚问题

本工作用Hartree-Fock方法研究了核子共振态Δ(1232)在⁴He、¹²C和¹⁶O系统中能否被束缚问题. 核子-核子与核子-Δ粒子之间的相互作用势均采用单玻色子交换势. 计算结果表明, Δ粒子只在⁴He系统中可被束缚, 在¹²C和¹⁶O系统中均不被束缚.     

Nucleon resonances in πN→η'N and J/ψ→pη'

We are aiming to study the J/Ψ→Pη' decay in an isobar model and the effective Lagrangian approach on the basis of the coupling constants extracted from the πN→η'N reaction.After a careful exploration of the contributions of the S_(11)(1535),P_(11)(1710),P_(13)(1900),S_(11)(2090) and P_(11)(2100) resonances,we conclude that either a subthreshold resonance or a broad P-wave state in the near threshold range seems to be indispensable to describe the present data of the πN→η'N.Furthermore,at least one broad resonance above η'N threshold is preferred.With this detailed analysis,we give the invariant mass spectrum and Dalitz plot of the J/Ψ→Pη' decay for the purpose of assisting the future detailed partial wave analysis.It is found that the J/Ψ→Pη' data are useful for disentangling the above or below threshold resonant contribution,though it still further needs the differential cross section data ofπN→η'N to realize some of the resonant and non-resonant contribution.     

Description of initial-and final-state-interaction effects for the reaction γp → π−Δ++ in the region of nucleon-resonance excitation

A model has been developed for describing the cross section for the reaction γ_r,v p → π^?Δ⁺⁺ in the energy region of nucleon-resonance excitation, and relevant calculations have been performed. The model takes into account the contribution of all reliably established resonances with masses less than 2 GeV and the contributions of nonresonance mechanisms in the approximation of Born diagrams. On the basis of data on the amplitudes of pion-nucleon interactions, a method has been evolved for phenomenologically describing the coupling of initial and final states with open inelastic channels. Calculations performed in this study represent a first step in developing a method for determining the electromagnetic form factors for nucleon resonances in exclusive reactions of pion-pair production on a nucleon by real and virtual photons.     

The p + p → π+ + d reaction close to threshold at COSY

Differential and total cross sections of the p + p → π⁺ + d reaction close to threshold were measured employing a magnetic spectrograph with track reconstruction, a very thin liquid hydrogen target and an accelerated proton beam with high phase space density. The data resolve a previous discrepancy between the n + p → π⁰ + d and the π⁺ + d → 2p reaction close to threshold indicating that isospin symmetry may be broken in the s-wave part of the cross section.     

T invariance and polarization effects in the reactions p+3He → π++4He and π++4He → p+3He

On the basis of T invariance, it is established that the dependence of the effective cross section for a binary reaction of the a+b → c+d type on the polarization vectors of primary particles a and b determines completely the polarization vectors and spin correlations for the same particles in the inverse reaction c+d → a+b induced by collisions between unpolarized primary particles c and d. By using the formalism of helicity amplitudes, polarization effects are studied in the process p+³He → π⁺+⁴He and in the inverse process π⁺+⁴He → p+³He. It is shown that, in the reaction π⁺+⁴He → p+³He, the spins of the final-state particles (proton and ³He nucleus) are strongly correlated. An expression for the correlation tensor is obtained for arbitrary values of the (p, ³He) emission angle.     

Experimental test of the PCAC hypothesis in the reactionsv μ p→ μ− pπ+ and \bar v_\mu p \to \mu ^ + p\pi ^ - in theΔ(1232) region

Data on the reactionsv _μ p→ μ^? pπ⁺ and \( \bar v_\mu p \to \mu ^ + p\pi ^ - \) in the Δ(1232) region are presented and a test of the PCAC hypothesis, using a modified version of the Adler model, is performed. The analysis is based on 1081 events in the neutrino and on 180 events in the antineutrino reaction, obtained in a bubble chamber experiment with BEBC at CERN. The experimental cross-sections for an invariant hadronic massW<1.4 GeV and an (anti-)neutrino energyE _v ^L >10 GeV are determined to be (0.628±0.059)·10^?38 cm² for the neutrino and (0.168±0.023)·10^?38 cm² for the antineutrino reaction. TheQ ² andW distributions, the density matrix elements of the Δ resonance, and moments of the pion angular distribution are discussed. The data are found to be in good agreement with the Adler model in theQ ² region below 1 GeV². A maximum likelihood fit for the axial massm _A in the axial-vector form factor yields a value ofm _A =1.31±0.12 GeV. At lowQ ² the data confirm the PCAC hypothesis and the discrepancy, formerly observed between the experimental and theoretical cross-sections forv _μ p→ μ^? pπ⁺ at low momentum transfers (Q ²?0.2 GeV²), is understood as being due to inadequate pion ‘off-mass-shell’ corrections.     

Annihilation of + \bar p + p → e + + e ? + π0 and + \bar p + p → γ + π0 through an ω-Meson intermediate state

The s-channel annihilation of a proton and an antiproton into a neutral pion and a real or virtual photon followed by lepton pair emission is studied. Such a mechanism is expected to play a role at moderate values of the total energy $ \sqrt s $ , when the pion is emitted in the angular region around 90° in the center-of-mass system. A fair comparison with the existing data is obtained taking scattering and annihilation channels into account. The cross section is calculated and numerical results are given in the kinematical range accessible in the PANDA experiment at FAIR.     

Measurement of the LT-asymmetry in πelectroproduction at the energy of the Δ(1232)-resonance

The reaction p(e, e'p)π⁰ has been studied at Q² = 0.2 (GeV/c)² in the region of W = 1232MeV. From measurements left and right of , cross-section asymmetries ρ_LT have been obtained in forward kinematics ρ_LT( = 20^°) = (- 11.68±2.36_stat±2.36_sys) and backward kinematics ρ_LT( = 160^°) = (12.18±0.27_stat±0.82_sys) π⁰. Multipole ratios {S₁₊ ^* M₁₊}/| M₁₊|² and {S₀₊ ^* M₁₊}/| M₁₊|² were determined in the framework of the MAID2003 model. The results are in agreement with older data. The unusally strong negative {S₀₊ ^* M₁₊}/| M₁₊|² required to bring also the result of Kalleicher et al. in accordance with the rest of the data is almost excluded.     

Study of Fermilab data for the reaction π− p→ηn

Fermilab data for the angular distribution measurements of the reaction ^– p n are investigated and it is shown that a good fit with experiment is obtained by using a simple Regge pole model with phenomenological residue functions. The energy dependence in this case is found to be different from that for the d/dt/ data obtained at Serpukhov.Work supported by the Pakistan Science Foundation under contract No. P-PU-PHY(11/1).     

Collins and sivers effects in p↑p → jet πX: Universality and process dependence

In this paper we briefly review the transverse momentum dependent generalized parton model and its application to the study of azimuthal asymmetries in the distribution of leading hadrons (mainly pions) inside large transverse momentum jets inclusively produced in polarized proton-proton collisions. We put particular emphasis on the phenomenological interest of these observables, in combination with similar asymmetries measured in semi-inclusive deeply inelastic scattering, Drell-Yan processes and e ⁺ e ^? collisions, for the study of the universality properties of the transverse momentum dependent parton distribution and fragmentation functions. We present results for RHIC kinematics at center-of-mass energies √s = 200 and 500 GeV, for central and mainly forward jet rapidities, in particular for the Sivers distribution and the Collins fragmentation function, that are believed to be responsible for many of the largest asymmetries measured in the last years. We also briefly discuss the case of inclusive jet production and recent phenomenological applications of other theoretical approaches, like the colour gauge invariant generalized parton model and the collinear twist-three approach, aiming at clarifying the issues of the universality and process dependence of transverse momentum dependent functions.     

On momentum dependence of the reaction π− p→ωn near threshold

We discuss the near–threshold behavior of the ω production amplitude in the reaction π⁻ p→ωn. In contrast to the results of earlier analyses we find that the averaged squared matrix element of the production amplitude must be a decreasing function of energy in order to describe the existing experimental data. Received: 11 August 1999     

Search for B_c (ns) via the B_c (ns) → B_c (ms) π~+ π~- transition at LHCb and Z~0 factory

It is interesting to study the characteristics of the whole family of B c which contains two different heavy flavors.LHC and the proposed Z 0 factory provide an opportunity because a large database of the B c family will be achieved.B c and its excited states can be identified via their decay modes.As suggested by experimentalists,B-c (ns) → B c +γ is not easy to be clearly measured,instead,the trajectories of π + and π- occurring in the decay of B c (ns) → B c (ms) + π + π( n m ) can be unambiguously identified,thus the measurement seems easier and more reliable;therefore this mode is more favorable at the early running stage of LHCb and the proposed Z 0 factory.In this work,we calculate the rate of B c (ns) → B c (ms) + π + π-in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and Z 0 factory are feasible.