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

Double neutral pion photoproduction at threshold

We consider the chiral expansion of the threshold amplitude for the reaction $\gamma p \to \pi^0 \pi^0 p$ to order ${\cal O}(M_\pi^2)$. We substantiate a claim that this photoproduction channel is significantly enhanced close to threshold due to pion loops. A precise measurement of the corresponding cross sections is called for which allows to test chiral perturbation theory.Comment: 8 pp, LaTe

Threshold Two-Pion Photo- and Electroproduction: More neutrals than expected

We present an exploratory study of two pion photo-- and electroproduction off the nucleon in the threshold region. To calculate the pertinent amplitudes, we make use of heavy baryon chiral perturbation theory. We show that due to finite chiral loops the production cross section for final states with two neutral pions is considerably enhanced. The experimental implications are briefly discussed.Comment: 23pp, plain TeX, 11 figures available upon request, CRN 94/1

Low--Energy Theorems for Weak Pion Production

We derive novel low--energy theorems for single pion production off nucleons through the isovector axial current. We find that the $k^2$-dependence of the multipole $L_{0+}^{(+)}$ at threshold is given by the nucleon scalar form factor, namely $\sigma(k^2-M_\pi^2 ) /(3 \pi M_\pi F_\pi )$. The relation to PCAC results for soft pions including electroweak form factors is also clarified.Comment: 9 pp, TeX, 2 figures available as ps files, CRN 93-5

A detector of small harmonic displacements based on two coupled microwave cavities

The design and test of a detector of small harmonic displacements is presented. The detector is based on the principle of the parametric conversion of power between the resonant modes of two superconducting coupled microwave cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso and Radicati, who, in 1978, suggested that superconducting coupled cavities could be used as sensitive detectors of gravitational waves, and on the work of Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind. They showed that an harmonic modulation of the cavity length l produced an energy transfer between two modes of the cavity, provided that the frequency of the modulation was equal to the frequency difference of the two modes. They achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}. We repeated the Reece, Reiner and Melissinos experiment, and with an improved experimental configuration and better cavity quality, increased the sensitivity to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device are discussed and the experimental technique is explained in detail. Possible future developments, aiming at gravitational waves detection, are also outlined.Comment: 28 pages, 12 eps figures, ReVteX. \tightenlines command added to reduce number of pages. The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://link.aip.org/link/?rs

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 Reaction πN→ππN\pi N \to \pi \pi N at Threshold

We consider the chiral expansion for the reaction $\pi N \to \pi \pi N$ in heavy baryon chiral perturbation theory. To order $M_\pi$ we derive novel low--energy theorems that compare favorably with recent determinations of the total cross sections for $\pi^+ p \to \pi^+ \pi^+ n$ and $\pi^- p \to \pi^0 \pi^0 n$.Comment: 7 pp, LateX (uses epsf.sty), 3 figures appended as ps files (split off as ppnf1.ps,ppnf2.ps,ppnf3.ps), CRN 94/1