Pion-Nucleon Scattering in Kadyshevsky Formalism: I Meson Exchange Sector

In a series of two papers we present the theoretical results of $\pi N$/meson-baryon scattering in the Kadyshevsky formalism. In this paper the results are given for meson exchange diagrams. On the formal side we show, by means of an example, how general couplings, i.e. couplings containing multiple derivatives and/or higher spin fields, should be treated. We do this by introducing and applying the Takahashi-Umezawa and the Gross-Jackiw method. For practical purposes we introduce the $\bar{P}$ method. We also show how the Takashashi-Umezawa method can be derived using the theory of Bogoliubov and collaborators and the Gross-Jackiw method is also used to study the $n$-dependence of the Kadyshevsky integral equation. Last but not least we present the second quantization procedure of the quasi particle in Kadyshevsky formalism.Comment: 29 page

Harmonic Sums and Mellin Transforms up to two-loop Order

A systematic study is performed on the finite harmonic sums up to level four. These sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ of the momentum fraction $x$ emerging in the quantities of massless QED and QCD up to two--loop order, as the unpolarized and polarized splitting functions, coefficient functions, and hard scattering cross sections for space and time-like momentum transfer. The finite harmonic sums are calculated explicitly in the linear representation. Algebraic relations connecting these sums are derived to obtain representations based on a reduced set of basic functions. The Mellin transforms of all the corresponding Nielsen functions are calculated.Comment: 44 pages Latex, contract number adde

Role of retardation in 3-D relativistic equations

Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been used within the framework of $\phi^2\sigma$ coupling to study the role of energy dependence and non-locality when the two-body potential is the sum of $\sigma$-exchange and crossed $\sigma$ exchange. The results show that non-locality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.Comment: 17 pages, RevTeX; 8 figures. Accepted for publication in Phys. Rev. C56 (Nov. 97

Nucleon-Nucleon Interaction: A Typical/Concise Review

Nearly a recent century of work is divided to Nucleon-Nucleon (NN) interaction issue. We review some overall perspectives of NN interaction with a brief discussion about deuteron, general structure and symmetries of NN Lagrangian as well as equations of motion and solutions. Meanwhile, the main NN interaction models, as frameworks to build NN potentials, are reviewed concisely. We try to include and study almost all well-known potentials in a similar way, discuss more on various commonly used plain forms for two-nucleon interaction with an emphasis on the phenomenological and meson-exchange potentials as well as the constituent-quark potentials and new ones based on chiral effective field theory and working in coordinate-space mostly. The potentials are constructed in a way that fit NN scattering data, phase shifts, and are also compared in this way usually. An extra goal of this study is to start comparing various potentials forms in a unified manner. So, we also comment on the advantages and disadvantages of the models and potentials partly with reference to some relevant works and probable future studies.Comment: 85 pages, 5 figures, than the previous v3 edition, minor changes, and typos fixe

Pertinent Dirac structure for QCD sum rules of meson-baryon coupling constants

Using general baryon interpolating fields $J_B$ for $B= N, \Xi, \Sigma,$ without derivative, we study QCD sum rules for meson-baryon couplings and their dependence on Dirac structures for the two-point correlation function with a meson i\int d^4x e^{iqx} \bra 0|{\rm T}[J_B(x)\bar{J}_B(0)] |{\cal M}(p)\ket. Three distinct Dirac structures are compared: $i\gamma_5$, i\gamma_5\fslash{p}, and $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ structures. From the dependence of the OPE on general baryon interpolating fields, we propose criteria for choosing an appropriate Dirac structure for the coupling sum rules. The $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ sum rules satisfy the criteria while the $i\gamma_5$ sum rules beyond the chiral limit do not. For the i\gamma_5\fslash{p} sum rules, the large continuum contributions prohibit reliable prediction for the couplings. Thus, the $\gamma_5\sigma_{\mu\nu}q^\mu p^\nu$ structure seems pertinent for realistic predictions. In the SU(3) limit, we identify the OPE terms responsible for the $F/D$ ratio. We then study the dependence of the ratio on the baryon interpolating fields. We conclude the ratio $F/D \sim 0.6-0.8$ for appropriate choice of the interpolating fields.Comment: To be published in Phys.Rev.C ; 21 pages,8 figures, revtex ; references are adde

Soft-core hyperon-nucleon potentials

A new Nijmegen soft-core OBE potential model is presented for the low-energy YN interactions. Besides the results for the fit to the scattering data, which largely defines the model, we also present some applications to hypernuclear systems using the G-matrix method. An important innovation with respect to the original soft-core potential is the assignment of the cut-off masses for the baryon-baryon-meson (BBM) vertices in accordance with broken SU(3)$_F$, which serves to connect the NN and the YN channels. As a novel feature, we allow for medium strong breaking of the coupling constants, using the $^3P_0$ model with a Gell-Mann--Okubo hypercharge breaking for the BBM coupling. We present six hyperon-nucleon potentials which describe the available YN cross section data equally well, but which exhibit some differences on a more detailed level. The differences are constructed such that the models encompass a range of scattering lengths in the $\Sigma N$ and $\Lambda N$ channels. For the scalar-meson mixing angle we obtained values $\theta_S=37$ to 40 degrees, which points to almost ideal mixing angles for the scalar $q\bar{q}$ states. The G-matrix results indicate that the remarkably different spin-spin terms of the six potentials appear specifically in the energy spectra of $\Lambda$ hypernuclei.Comment: 37 pages, 4 figure

What Does Free Space Lambda-Lambda Interaction Predict for Lambda-Lambda Hypernuclei?

Data on Lambda-Lambda hypernuclei provide a unique method to learn details on the strangeness S =-2 sector of the baryon-baryon interaction. From the free space Bonn-Julich potentials, determined from data on baryon-baryon scattering in the S=0,-1 channels, we construct an interaction in the S =-2 sector to describe the experimentally known Lambda-Lambda hypernuclei. After including short--range (Jastrow) and RPA correlations, we find masses for these Lambda-Lambda hypernuclei in a reasonable agreement with data, taking into account theoretical and experimental uncertainties. Thus, we provide a natural extension, at low energies, of the Bonn-Julich OBE potentials to the S =-2 channel.Comment: 4 pages, 2 figures, revtex4 style. Minor changes in conclusions. References updated. Accepted in Phys. Rev. Let

Nuclear equation of state at high density and the properties of neutron stars

We discuss the relativistic nuclear equation of state (EOS) using a relativistic transport model in heavy-ion collisions. From the baryon flow for $Au + Au$ systems at SIS to AGS energies and above we find that the strength of the vector potential has to be reduced moderately at high density or at high relative momenta to describe the flow data at 1-10 A GeV. We use the same dynamical model to calculate the nuclear EOS and then employ this to calculate the gross structure of the neutron star considering the core to be composed of neutrons with an admixture of protons, electrons, muons, sigmas and lambdas at zero temperature. We then discuss these gross properties of neutron stars such as maximum mass and radius in contrast to the observational values.Comment: 17 pages, 5 figures, to be published in Phy. Rev.

The Lambda-Lambda Interaction and ^{6}_{Lambda Lambda}He

An OBE potential model for the ^{1}S_0 S = -2 interaction is analyzed with emphasis on the role of coupling between the Lambda Lambda, N Xi, and Sigma Sigma channels. Singlet scalar exchange, an approximation to two-pion exchange, is significant in all channels; surprisingly, the one-pion exchange component is almost negligible. The size of the channel coupling as a function of the overall strength of the OBE model potential is examined. Implications of the analysis for the binding energy of ^{6}_{Lambda Lambda}He are considered; the new experimental datum may suggest a consistency between the extracted Lambda Lambda matrix element and the relation implied by SU(3) among OBE baryon-baryon interactions. \\Comment: 4 pages brief report to Physical Review

Chiral two-pion exchange and proton-proton partial-wave analysis

The chiral two-pion exchange component of the long-range pp interaction is studied in an energy-dependent partial-wave analysis. We demonstrate its presence and importance, and determine the chiral parameters c_i (i=1,3,4). The values agree well with those obtained from pion-nucleon amplitudes.Comment: 13 pages, no figure