Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.     

Measurement of elastic J/ψ photoproduction at HERA

The reaction γ p → J/ψ p has been studied in ep interactions using the ZEUS detector at HERA. The cross section for elastic J/ψ photoproduction has been measured as a function of the photon-proton centre of mass energy W in the range 40 < W < 140 GeV at a median photon virtuality Q ² of 5 × 10^?5 GeV². The photoproduction cross section, σ_{γp→ J/ψp}, is observed to rise steeply with W. A fit to the data presented in this paper to determine the parameter δ in the form σ_{γp→ J/ψp} α W ^δ yields the value δ = 0.92±0.14±0.10. The differential cross section dσ/d ¦t¦is presented over the range ¦t¦< 1.0 GeV² where t is the square of the four-momentum exchanged at the proton vertex. dσ/d ¦t¦falls exponentially with a slope parameter of $4.6pm 0.4_{-0.6}^{+0.4} {? GeV}^{-2}$. The measured decay angular distributions are consistent with s-channel helicity conservation.     

Binding effects in the optical potential of pionic atoms

We calculate the contribution from nucleon binding to the coefficient Re B₀ in the optical potential of pionic atoms. The relevant Feynman graphs are deduced for nuclear matter. They depend on off-shell values for pion-nucleon scattering lengths a_πN and for the nucleon-binding potential V_NA. Off-shell effects are found to be very important: A pole model for a_πN, extrapolated off-shell, increases binding effects by a factor of three over the use of on-shell values. Two simple models are proposed for the off-shell continuation of V_NA. One leads to attractive, the other to repulsive contributions to Re B₀.     

A density expansion of the pion-nucleus optical potential. II. Second order terms

The second order terms in a density expansion of the pion optical potential V_opt are evaluated quantitatively. The coefficients of these terms are proportional to various combinations of on- and off-shell nucleon-nucleon T-matrices, averaged over the distribution of two nucleon relative momenta in the Fermi sea. The on-shell contributions can be obtained directly from experimental phase shifts, but the calculation of the off-shell-parts requires a model for the nucleon-nucleon potential. We consider a number of realistic local and nonlocal, separable potentials which fit nucleon-nucleon phase shifts, in order to study the variations in V_opt which arise from differences in the off-shell behavior of T. We find absorptive (imaginary) and dispersive (real) contributions to V_opt which are of comparable magnitude. The dispersive part, which leads to a real energy shift associated with the two nucleon absorptive process, has not been previously estimated quantitatively. We compare our results to empirical potentials obtained by fitting energy level shifts and widths in pi-mesic atoms, as well as theoretical estimates based on threshold cross sections for the processes π + N + N ? N + N.     

Valence and nonvalence vertex functions for timelike and spacelike nucleon form factors within light-front dynamics

A unified model for spacelike and timelike hadron form factors within light-front dynamics successfully applied to the pion is extended to the nucleon to study the role of valence and nonvalence vertex functions. Preliminary results for ?10(GeV/c)² ≤ q ² ≤ 10(GeV/c)² are presented.     

动量空间中能质子-12C弹性散射截面和自旋量的研究

在KMT理论框架下，应用微观的动量空间一级光学势，包括了库仑修正，自旋关联，NN振幅反对称，离壳效应，核子反冲和结合能转换，Lorentz不变的角变换.在整个中能区域系统地计算了质子-¹²C弹性散射微分截面和自旋观测量，并与实验数据及Glauber理论框架下或已有的其他理论计算结果做了比较，其结果显示，在200—1000MeV，该理论与实验结论符合程度较好.     

Light-cone structure of vertex functions for composite fields

Vertex functions for composite fields are defined in a model field theory both on and off mass shell. Light-cone dominance at large momentum transfer is shown to hold, by the compositeness assumption, for the off-shell vertex function. On the other hand, it is in general untrue that the elastic form factor probes light-like distances between the constituents inside the nucleon. The relevant light-cone singularity (in the relative space-time separation x) is less important in this case than the large x₀ behaviour of the wave function at fixed x². It is found however that, under some conditions, the light-cone singularity determines the large x₀ behaviour of the wave function, and therefore the large q² behaviour of the form factor. For composite particles described by a Bethe-Salpeter equation, this result is equivalent to the known fact that at large q² the form factor depends on the binding interaction at small distances. A relation similar to that of Drell-Yan-West is finally established between the asymptotic behaviour of the elastic form factor and the threshold behaviour of the absorptive part of the vertex scaling function.     

Threshold π+ electroproduction at high-momentum transfer: A determination of the nucleon axial vector form factor

Threshold π⁺ electroproduction has been measured at momentum transfers 6k²6 of 0.45, 0.58 and 0.88 (GeV/c)², extending the range of earlier measurements. Using PCAC and current algebra-based models we have deduced the axial vector form factor of the nucleon G_A(k²), and find that the dipole parametrisation is favoured over the monopole. The value of M_A in the dipole parametrisation is, in a weak PCAC model, 0.96 ± 0.03 GeV, in excellent agreement with neutrino measurements. The threshold cross section is also in excellent agreement with the predictions of a fixed-t dispersion relation model.     

Hypercharge annihilation

Aspects of the process K^?p → Λ + pions for K^? mesons of momentum 8.25 GeV/c are examined. It is shown that the hypercharge annihilation process can be effectively separated into off-shell baryon (B?B) and strangeness (K?K) annihilation. Both annihilation regions have many features in common and show strong similarities to on-shell annihilation processes; some differences are also noted.     

Measurement of the azimuthal anisotropy coefficient <Emphasis Type="Italic">v</Emphasis><Subscript>2</Subscript> for the emission of α particles in nucleus-nucleus collisions at energies 1.88–10.6 GeV/nucleon

The azimuthal anisotropy of the emission of α particles in collisions of the ²²Ne, ²⁴Mg, ⁵⁶Fe, and ¹⁹⁷Au nuclei with photoemulsion nuclei has been measured at projectile energies E_pr = 1.88–10.6 GeV/nucleon. The results are compared with similar measurements for protons. It has been found that the ratio of the azimuthal anisotropy coefficients v₂ for α particles and protons is equal to 6 ± 2 at low energies E_pr ≈ 2 GeV/nucleon, whereas these coefficients coincide with each other for energies E_pr ≥ 4 GeV/nucleon. This difference may indicate that, at low projectile energies, α particles are formed predominantly at the early stage of a collective flow. Formation of α particles for E_pr ≥ 4 GeV/nucleon likely occurs at the stage of nuclear matter scattering.     

Relativistic study of the reaction pp → dπ: Formalism and comparison with experiment at Tp = 578 MeV

A detailed relativistic calculation of pp → πd is presented. The leading graph is the exchange of a nucleon and a pion. The πN amplitudes, including off-shell information, are input, together with relativistic dpn and πNN vertex functions. The dominant nucleon spectator term is calculated without uncontrolled approximations, and the relativistic pion antiparticle contribution is evaluated. The single nucleon exchange diagram is added. Higher order rescattering is treated by initial and final state distortion factors. All amplitudes and spin observables are calculated and a detailed comparison with the measured data at 578 MeV is made. The remaining observed discrepancies are traced to the pp spin-triplet waves.     

The πNN vertex function and off-mass-shell πN scattering

We have extended the dispersion relation calculation of the πNN vertex function to include off-shell terms in the πN scattering matrix. These off-shell terms are constrained by the current algebra and PCAC results, and contribute to the $\text{N}\text{N}\text{→ ππ}$ s-wave. As such, they add to the kinematic off-shell effects which Durso, Jackson and VerWest found in the p-terms. The off-shell terms increase the calculated Goldberger-Treiman discrepancy from 0.02 to 0.03, bringing it into agreement with the field theory value of Jones and Scadron (0.035). The calculated discrepancy remains smaller than the experimental value of 0.06±0.01.     

Implications of gauge invariance for pion electroproduction at threshold

We discuss the implications of gauge invariance in the problem of the on-shell extrapolation of the electroproduction low-energy theorems. We show that there is an invariant amplitude which can be evaluated at the Breit threshold either using gauge invariance and on-shell dispersion relations or following the Fubini and Furlan [5] extrapolation method starting from the current-algebra low-energy value of the amplitude. Comparing the two expressions, we find a relation between the electromagnetic pion form factor, F_π (k²), and the axial-vector nucleon form factors, g_A (k²) and h_A (k²).     

Slow proton andΔ ++ production inK + p interactions at 70 GeV/c

The inclusive inelastic processesK ⁺ p→pX ⁺ andK ⁺ p→Δ ⁺⁺ X ⁰ are studied at an incident momentum of 70 GeV/c. The data comes from the Big European Bubble Chamber BEBC filled with hydrogen, exposed to an rf reparatedK ⁺ beam at the CERN SPS accelerator. The inclusive cross section for protons with laboratory momentump _LAB≦1.2 GeV/c is equal to (6.1±0.1) mb. InclusiveΔ ⁺⁺-production is studied for |t _{p, Δ}|<1.0(GeV/c)². Comparisons are made with otherK ⁺ p data and withpp data at 69 GeV/c. Evidence is found for Pomeron exchange at the beam vertex both for slow proton andΔ ⁺⁺-production as well as for absorptive pion exchange at the (p,Δ ⁺⁺) vertex.     

Parametrization of the 1S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.     

Direct photon production from pions and protons at 200 GeV/c

Direct photon production has been studied by an experiment performed with the NA3 spectrometer at CERN, using incident negative and positive beams at 200 GeV/c interacting with an isoscalar Carbon target. Two different triggers have been used; one of them requires the photon conversion. The experiment is sensitive to direct photons produced with 3.0≦P _T ≦6 GeV/c and center-of-mass rapidity ?0.4≦y ^*≦1.2. Inclusive cross sections are given for incident π^± and protons, and compared with second order QCD predictions; finally an estimation of the gluon structure function of the nucleon is given.     

Parametrization of the S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.     

Measurement of the elliptic flux of Z ⩾ 2 charged particles in collisions of relativistic nuclei with photoemulsion nuclei

The azimuthal asymmetry is measured for the emission of Z ≥ 2 particles from the interaction of ²²Ne, ²⁴Mg, ³²S, ⁵⁶Fe, ¹⁹⁷Au, and ²⁰⁷Pb nuclei with photoemulsion nuclei that is induced by semicentral collisions characterized by projectile energies in the range E _pr = 1.88–200 GeV per nucleon and by impact-parameter (b) values in the range 0.12 ≤ b/b _max ≤ 0.70. The results of these measurements are compared with the results of similar measurements for protons. It is found that, at a low energy of E _pr ≈ 2 GeV per nucleon, the ratio of the azimuthal-anisotropy coefficients v ₂ for Z ≥ 2 particles and protons is 6 ± 2, but that, for energies in the region E _pr ≥ 4 GeV per nucleon, the coefficients in question agree with each other. This may suggest that, at low energies, Z ≥ 2 particles are predominantly formed at an early stage of the development of a collective flow. For E _pr ≥ 4 GeV per nucleon, these particles are presumably formed at the stage of nuclear-matter expansion. Other possible explanations for the results of the observation of an elliptic flux of Z ≥ 2 particles are discussed.     

Target fragmentation in proton-nucleus and16O-nucleus reactions at 60 and 200 GeV/nucleon

Target remnants withZ<3 from proton-nucleus and¹⁶O-nucleus reactions at 60 and 200 GeV/nucleon were measured in the angular range from 30° to 160° (?1.7<η<1.3) employing the Plastic Ball detector. The excitation energy of the target spectator matter in central oxygen-induced collisions is found to be high enough to allow for complete disintegration of the target nucleus into fragments withZ<3. The average longitudinal momentum transfer per proton to the target in central collisions is considerably higher in the case of¹⁶O-induced reactions (≈300 MeV/c) than in proton-induced reactions (≈130 MeV/c). The baryon rapidity distributions are roughly in agreement with one-fluid hydrodynamical calculations at 60 GeV/nucleon¹⁶O+Au but are in disagreement at 200 GeV/nucleon, indicating the higher degree of transparency at the higher bombarding energy. Both, the transverse momenta of target spectators and the entropy produced in the target fragmentation region are compared to those attained in head-on collisions of two heavy nuclei at Bevalac energies. They are found to be comparable or do even exceed the values for the participant matter at beam energies of about 1–2 GeV/nucleon.