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 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

Threshold Photo/Electro Pion Production - Working Group Summary

We summarize the pertinent experimental and theoretical developments in the field of pion photo- and electroproduction in the threshold region. We discuss which experiments and which calculations should be done/performed in the future.Comment: plain TeX (macro included), 6pp, summary talk presented at the workshop on "Chiral Dynamics: Theory and Experiments", MIT, July 25-29, 199

The Goldberger -- Treiman Relation, gAg_A and gπNNg_{\pi NN} at T≠0T\neq 0

The Goldberger-Treiman relation is shown to persist in the chiral limit at finite temperatures to order $O(T^2)$. The $T$ dependence of $g_A$ turns out to be the same as for $F_{\pi}$, $g_{A}(T)=g_{A}(0)(1-T^2/12F^2)$, while $g_{\pi NN}$ is temperature independent to this order. The baryon octet ${\cal D}$ and ${\cal F}$ couplings also behave as $F_{\pi}$ if only pions are massless in the pseudoscalar meson octet.Comment: 7p, NSF-ITP-93-145, BUTP-93/27, PUTP-1433, November 199

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

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.

Towards a lattice calculation of the coefficients of the QCD chiral Lagrangian

We discuss a general strategy to compute the coefficients of QCD chiral Lagrangian by using the lattice regularization of QCD with Wilson fermions. This procedure requires the introduction of an effective Lagrangian for lattice QCD as an intermediate step in the calculation. The continuum QCD chiral Lagrangian can be then obtained by expanding the lattice effective Lagrangian in increasing powers of the external momenta. A suitable renormalization procedure is required to account for the chiral symmetry breaking introduced by the Wilson term in the lattice action. In anticipation of a numerical simulation, the lattice effective Lagrangian is computed analytically and investigated in the strong coupling and large $N$ limitComment: Talk presented at LATTICE96(chirality in qcd) , 3 pages, no figures. Latex file with espcrc2 styl

Effective Lagrangians in bound state calculations

In order to investigate specific aspects of bound state calculations in a non-relativistic framework, we consider the energy-levels of a massive scalar particle, which moves in an external field and interacts in addition with a massless scalar particle. The discussion includes the following topics: dimensionally regularized bound-state calculations, ultraviolet finiteness of bound-state observables and their independence of the off-mass-shell behavior of Green functions, non-renormalizable interactions, structure of the non-relativistic two-point function, power counting and matching.Comment: 45 pages, 8 postscript figures, RevTeX styl

Topics in Chiral Perturbation Theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.Comment: 30 pp, TeX, Review talk, Third Workshop on High Energy Particle Physics (WHEPP III), Madras, India, January 1994. 7 figures available upon request. CRN--94/0