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We calculate the nucleon form factors G A and G P of the isovector axial-vector current and the pion-nucleon form factor G πN in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order O(p 4 ). In addition to the standard treatment including the nucleon and pions, we also consider the axial-vector meson a 1 as an explicit degree of freedom. This is achieved by using the reformulated infrared renormalization scheme. We find that the inclusion of the axial-vector meson effectively results in one additional low-energy coupling constant that we determine by a fit to the data for G A . The inclusion of the axial-vector meson results in an improved description of the experimental data for G A , while the contribution to G P is small.

We calculate the electromagnetic form factors of the nucleon up to fourth order in manifestly Lorentz-invariant chiral perturbation theory with vector mesons as explicit degrees of freedom. A systematic power counting for the renormalized diagrams is implemented using both the extended on-mass-shell renormalization scheme and the reformulated version of infrared regularization. We analyze the electric and magnetic Sachs form factors, G E and G M , and compare our results with the existing data. The inclusion of vector mesons results in a considerably improved description of the form factors. We observe that the most dominant contributions come from tree-level diagrams, while loop corrections with internal vector meson lines are small.

We demonstrate and explicate Bayesian methods for fitting the parameters that encode the impact of short-distance physics on observables in effective field theories (EFTs). We use Bayes' theorem together with the principle of maximum entropy to account for the prior information that these parameters should be natural, i.e. O(1) in appropriate units. Marginalization can then be employed to integrate the resulting probability density function (pdf) over the EFT parameters that are not of specific interest in the fit. We also explore marginalization over the order of the EFT calculation, M , and over the variable, R, that encodes the inherent ambiguity in the notion that these parameters are O(1). This results in a very general formula for the pdf of the EFT parameters of interest given a data set, D. We use this formula and the simpler "augmented χ 2 " in a toy problem for which we generate pseudo-data. These Bayesian methods, when used in combination with the "naturalness prior", facilitate reliable extractions of EFT parameters in cases where χ 2 methods are ambiguous at best. We also examine the problem of extracting the nucleon mass in the chiral limit, M 0 , and the nucleon sigma term, from pseudo-data on the nucleon mass as a function of the pion mass. We find that Bayesian techniques can provide reliable information on M 0 , even if some of the data points used for the extraction lie outside the region of applicability of the EFT.

We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied to multi-loop diagrams with an arbitrary number of particles with arbitrary masses.  2004 Published by Elsevier B.V.

Quantum electrodynamics for ρ mesons is considered. It is shown that, at tree level, the value of the gyromagnetic ratio of the ρ + is fixed to 2 in a self-consistent effective quantum field theory. Further, the mixing parameter of the photon and the neutral vector meson is equal to the ratio of electromagnetic and strong couplings, leading to the mass difference M ρ 0 − M ρ ± ∼ 1 MeV at tree order.PACS numbers: 11.10. Gh, 12.39.Fe The question of the intrinsic magnetic moment of (elementary) particles of arbitrary spin s has been discussed controversially in the literature and is still of great interest. On the one hand, low-energy theorems and the optical theorem require that the gyromagnetic ratio g ≃ 2 for a particle with arbitrary spin s different from zero (at least for particles which do not participate in strong interactions) [1]. On the other hand, general arguments have been given that the minimal coupling leads to 1/s for this quantity [2]. Finally, the investigations of Ref. [3] regarding the theory of charged vector mesons interacting with the electromagnetic field suggested that the gyromagnetic ratio depends on a free parameter, thus allowing it to take any value. Below, we will address this question from the point of view of effective field theory (EFT).In Ref.[4] we have shown how the universal coupling of the ρ meson and the Kawarabayashi-Suzuki-RiadzuddinFayyazuddin (KSRF) relation [5,6] follow from the requirement that chiral perturbation theory of pions, nucleons, and ρ mesons is a consistent EFT. Although EFTs are non-renormalizable in the traditional sense, the general principles of EFT [7] require that all ultraviolet divergences can be absorbed into the redefinition of fields and parameters of the most general Lagrangian [8]. Imposing the renormalizability in this sense one finds that not all parameters of the most general Lagrangian are free but satisfy consistency conditions [9]. In this Letter we will use similar arguments for the effective Lagrangian including, in addition, the interaction with photons to show that the gyromagnetic ratio is fixed to g = 2 at tree level. Furthermore, the mixing parameter of the photon and the neutral vector meson is also fixed and leads to M ρ 0 − M ρ ± ∼ 1 MeV at tree order.We start with the chirally invariant effective Lagrangian including vector mesons in the form given by Weinberg [10], containing all interaction terms which respect Lorentz invariance, the discrete symmetries, and chiral symmetry. The electromagnetic interaction is introduced by adding all terms with photon fields which are allowed by U(1) gauge invariance,Here, B µ is a U(1) gauge vector field, V a µ (a = 1, 2, 3) denote the Cartesian components of an isospin triplet of vector fields, and Ψ is an isospin doublet of nucleon fields with mass m 0 [11]. Furthermore,All fields and coupling constants in Eq. (1) are bare quantities. From the point of view of EFT it is not consistent to consider a minimal coupling only (see, e.g., Ref. [12]). Using symmetry arguments only, c 0 and κ 0...

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