On the analysis of the pion--nucleon σ\sigma--term: The size of the remainder at the Cheng--Dashen point

We calculate the one--loop contributions of order $M_\pi^4$ to the difference $\Delta_R$ between the on--shell pion--nucleon scattering amplitude $\bar{D}^+(0,2M_\pi^2)$ at the Cheng--Dashen point $\nu =0$, $t=2M_\pi^2$ and the scalar form factor $\sigma (2M_\pi^2)$ in the framework of heavy baryon chiral perturbation theory. We proof that to this order $\Delta_R$ contains $no$ chiral logarithms and therefore it vanishes simply as $M_\pi^4$ in the chiral limit. Numerically, we find as an upper limit $\Delta_R \simeq 2\,$MeV.Comment: 7 pp, LaTeX, uses epsf, 1 figure in separate PS fil

The Gluon Propagator on a Large Volume, at β=6.0\beta=6.0

We present the results of a high statistics lattice study of the gluon propagator, in the Landau gauge, at $\beta=6.0$. As suggested by previous studies, we find that, in momentum space, the propagator is well described by the expression $G(k^2)= \Big[ M^2 + Z\cdot k^2(k^2/\Lambda^2)^\eta\Big]^{-1}$. By comparing $G(k^2)$ on different volumes, we obtain a precise determination of the exponent $\eta=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit. The behaviour of $\eta$ and $M^2$ in the continuum limit is not known, and can only be studied by increasing the value of $\beta$.Comment: 21 pages, uuencoded LATEX plus 5 postscript figures. ROME prep. 94/1042, SHEP prep. 93/94-3

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

Technology Across the Curriculum

Raising questions about different courses of technology across the curriculum I first consider some reasons why such programmes are being promoted. This is followed by some general points about integrated studies and a brief analysis of technology, together with a consideration of the main aims of technological education. The paper concludes with a synthesis of the points 'constructed into seven claims for technology across the curriculum models, which are then examined

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