We study the low energy expansion of the nucleon's electroweak form factors in the framework of an effective chiral Lagrangian including pions, nucleons and the $Delta (1232)$. We work to third order in the so-called small scale expansion and compare the results with the ones previously obtained in the chiral expansion. In addition, these calculations serve as a first exploratory study of renormalization and decoupling within the small scale expansion.Comment: 21 pp, RevTeX, uses epsf, 4 figs, minor corrections, accepted for publication in Nucl.Phys.

We have derived the most general chirally invariant Lagrangian L 6 for the meson sector at order p 6 . The result provides an extension of the standard Gasser-Leutwyler Lagrangian L 4 to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion' terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating p 6 contributions to simple processes. 11.30. Rd, 12.39.Fe

Radiative corrections to the lifetime and angular correlation coefficients of neutron beta-decay are evaluated in effective field theory. We also evaluate the lowest order nucleon recoil corrections, including weak-magnetism. Our results agree with those of the long-range and model-independent part of previous calculations. In an effective theory the model-dependent radiative corrections are replaced by well-defined low-energy constants. The effective field theory allows a systematic evaluation of higher order corrections to our results to the extent that the relevant low-energy constants are known.

The induced pseudoscalar coupling gp is the least well known of the weak coupling constants of the proton's charged-current interaction. Its size is dictated by chiral symmetry arguments, and its measurement represents an important test of quantum chromodynamics at low energies. During the past decade a large body of new data relevant to the coupling gp has been accumulated. This data includes measurements of radiative and non radiative muon capture on targets ranging from hydrogen and few-nucleon systems to complex nuclei. Herein the authors review the theoretical underpinnings of gp, the experimental studies of gp, and the procedures and uncertainties in extracting the coupling from data. Current puzzles are highlighted and future opportunities are discussed.

The matrix element for muon capture by a proton is calculated to O(p 3 ) within heavy baryon chiral perturbation theory using the new O(p 3 ) Lagrangian of Ecker and Mojžiš. External nucleon fields are renormalized using the appropriate definition of the wave function renormalization factor Z N . Our expression for Z N differs somewhat from that found in existing literature, but is the one which is consistent with the Lagrangian we use and the one which ensures, within our approach, the nonrenormalization of the vector coupling as required by the conserved vector current. Expressions for the standard muon capture form factors are derived and compared to experimental data and we determine three of the coefficients of the Ecker -Mojžiš Lagrangian, namely, b 7 , b 19 , and b 23 .Typeset using REVT E X 1