Pion-nucleon scattering inside the Mandelstam triangle

We study the third order pion-nucleon scattering amplitude obtained from heavy baryon chiral perturbation theory inside the Mandelstam triangle. We reconstruct the pion-nucleon amplitude in the unphysical region by use of dispersion relations and determine the pertinent low-energy constants by a fit to this amplitude. A detailed comparison with values obtained from phase shift analysis is given. Our analysis leads to a pion-nucleon sigma-term of sigma(0) = 40 MeV based on the Karlsruhe partial wave analysis. We have repeated the same procedure using the latest solution of the VPI group and find a much larger value for sigma(0).Comment: 17 pp, LaTeX2e, 4 fig

A Mean Field Theory of the Chiral Phase Transition

The recent discussions by Koci\'c and Kogut on the nature of the chiral phase transition are reviewed. The mean-field nature of the transition suggested by these authors is supported in random matrix theory by Verbaarschot and Jackson which reproduces many aspects of QCD lattice simulations. In this paper, we point out physical arguments that favor a mean-field transition, not only for zero density and high temperature, but also for finite density. We show, using the Gross-Neveu model in 3 spatial dimensions in mean-field approximation, how the phase transition is constructed. In order to reproduce the lowering of the $\rho=0$, $T=0$ vacuum evaluated in lattice calculations, we introduce {nucleons} rather than constituent quarks in negative energy states, down to a momentum cut-off of $\Lambda$. We also discuss Brown-Rho scaling of the hadron masses in relation to the QCD phase transition, and how this scaling affects the CERES and HELIOS-3 dilepton experiments.Comment: 23 pages, Latex, no figure

Pion-nucleon scattering in chiral perturbation theory II: Fourth order calculation

We analyse elastic-pion nucleon scattering to fourth order in heavy baryon chiral perturbation theory, extending the third order study published in Nucl. Phys. A640 (1998) 199. We use various partial wave analyses to pin down the low-energy constants from data in the physical region. The S-wave scattering lengths are consistent with recent determinations from pionic hydrogen and deuterium. We find an improved description of the P-waves. We also discuss the pion-nucleon sigma term and problems related to the prediction of the subthreshold parameters.Comment: 28 pp, LaTeX2e, uses epsf, 6 figs, better discussion of the convergence issues, accepted for publication in Nuclear Physics

Pion-nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields

We analyze elastic-pion nucleon scattering to third order in the so-called small scale expansion. It is based on an effective Lagrangian including pions, nucleons and deltas as active degrees of freedom and counting external momenta, the pion mass and the nucleon-delta mass splitting as small parameters. The fermion fields are considered as very heavy. We present results for phase shifts, threshold parameters and the sigma term. We discuss the convergence of the approach. A detailed comparison with results obtained in heavy baryon chiral perturbation theory to third and fourth order is also given.Comment: 44 pp, LaTeX2e, uses epsf, 6 fig

The off-Shell Electromagnetic Vertex of the Nucleon in Chiral Perturbation Theory

We study the electromagnetic vertex of a nucleon in next-to-leading order chiral perturbation theory (CPT). We consider the case where one of the nucleons at the $\gamma$NN vertex is off its mass shell. We define relevant measures for the off-shell dependence in the limited kinematical range allowed, and analyze their expansion in the pion mass. The leading nonanalytic contributions are calculated to estimate their size.Comment: 12 pages (LaTeX), 1 figure (available upon request), NIKHEF 93-P

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one loop order do only depend on the remaining four dimension two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to $\Delta$ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes $P_1^-$ and $P_2^+$ as well as the isovector S-wave effective range parameter $b^-$. The one-loop calculation is in good agreement with the data. The difference $P_1^- - P_2^+$ signals chiral loop effects in the $\pi N$ P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.Comment: 19 pp, LaTeX, enlarged and revised version, title changed, minor corrections in section 4, more detailed discussion in section 5, additional results in sec. 6 and the appendix, accepted for publication in Nucl. Phys.

High temperature QCD with three flavors of improved staggered quarks

We present an update of our study of high temperature QCD with three flavors of quarks, using a Symanzik improved gauge action and the Asqtad staggered quark action. Simulations are being carried out on lattices with Nt=4, 6 and 8 for the case of three degenerate quarks with masses less than or equal to the strange quark mass, $m_s$, and on lattices with Nt=6 and 8 for degenerate up and down quarks with masses in the range 0.2 m_s \leq m_{u,d} \leq 0.6 m_s, and the strange quark fixed near its physical value. We also report on first computations of quark number susceptibilities with the Asqtad action. These susceptibilities are of interest because they can be related to event-by-event fluctuations in heavy ion collision experiments. Use of the improved quark action leads to a substantial reduction in lattice artifacts. This can be seen already for free fermions and carries over into our results for QCD.Comment: Lattice2002(Non-zero temperature and density

Three Flavor QCD at High Temperatures

We have continued our study of the phase diagram of high temperature QCD with three flavors of improved staggered quarks. We are performing simulations with three degenerate quarks with masses less than or equal to the strange quark mass m_s and with degenerate up and down quarks with masses m_{u,d} less than the strange quark mass. For the quark masses studied to date, we find a crossover that strengthens as m_{u,d} decreases, rather than a bona fide phase transition. We present new results for the crossover temperature extrapolated to the physical value of m_{u,d}, and for quark number susceptibilities.Comment: Poster presented at Lattice 2004 (non-zero), Fermilab, June 21-26, 2004, 3 pages, 3 figure