0000000000219024
AUTHOR
Harold W. Fearing
Field transformations and simple models illustrating the impossibility of measuring off-shell effects
In the context of simple models illustrating field transformations in Lagrangian field theories we discuss the impossibility of measuring off-shell effects in nucleon-nucleon bremsstrahlung, Compton scattering, and related processes. To that end we introduce a simple phenomenological Lagrangian describing nucleon-nucleon bremsstrahlung and perform an appropriate change of variables leading to different off-shell behavior in the nucleon-nucleon amplitude as well as the photon-nucleon vertex. As a result we obtain a class of equivalent Lagrangians, generating identical S-matrix elements, of which the original Lagrangian is but one representative. We make use of this property in order to show …
Radiative and non radiative muon capture on the proton in heavy baryon chiral perturbation theory
We have evaluated the amplitude for muon capture by a proton, mu + p --> n + nu, to O(p^3) within the context of heavy baryon chiral perturbation theory (HBChPT) using the new O(p^3) Lagrangian of Ecker and Mojzis (E&M). We obtain expressions for the standard muon capture form factors and determine three of the coefficients of the E&M Lagrangian, namely, b_7, b_{19}, and b_{23}. We describe progress on the next step, a calculation of the radiative muon capture process, mu + p --> n + nu + gamma.
Anomalous chiral perturbation theory meson Lagrangian to orderp6reexamined
We present a revised and extended construction of the mesonic Lagrangian density in chiral perturbation theory (ChPT) at order ${p}^{6}$ in the anomalous (or epsilon) sector, ${\mathcal{L}}_{6,\ensuremath{\epsilon}}.$ After improving several aspects of the strategy we used originally, i.e., a more efficient application of partial integration, the implementation of so-called Bianchi identities, and additional trace relations, we find the new monomial sets to include 24 ${SU(N}_{f}),$ 23 $\mathrm{SU}(3),$ and 5 $\mathrm{SU}(2)$ elements. Furthermore, we introduce 8 supplementary terms due to the extension of the chiral group to ${SU(N}_{f}{)}_{L}\ifmmode\times\else\texttimes\fi{}{SU(N}_{f}{)}…
Compton scattering by a pion and off-shell effects
We consider Compton scattering by a pion in the framework of chiral perturbation theory. We investigate off--shell effects in the s-- and u--channel pole diagrams. For that purpose we perform a field transformation which, in comparison with the standard Gasser and Leutwyler Lagrangian, generates additional terms at order $p^4$ proportional to the lowest--order equation of motion. As a result of the equivalence theorem the two Lagrangians predict the same Compton scattering S--matrix even though they generate different off--shell form factors. We conclude that off--shell effects are not only model--dependent but also representation--dependent.
Radiative pion capture by a nucleon
The differential cross sections for $\pi^- p \to \gamma n$ and $\pi^+ n \to \gamma p$ are computed up to $O(p^3)$ in heavy baryon chiral perturbation theory (HBChPT). The expressions at $O(p)$ and $O(p^2)$ have no free parameters. There are three unknown parameters at $O(p^3)$, low energy constants of the HBChPT Lagrangian, which are determined by fitting to experimental data. Two acceptable fits are obtained, which can be separated by comparing with earlier dispersion relation calculations of the inverse process. Expressions for the multipoles, with emphasis on the p-wave multipoles, are obtained and evaluated at threshold. Generally the results obtained from the best of the two fits are i…
Muon capture by a proton in heavy baryon chiral perturbation theory
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 Mojzis. 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…
Virtual Compton Scattering off Spin-Zero Particles at Low Energies
We discuss the low-energy behavior of the virtual Compton scattering amplitude off a spin-zero target. We first compare various methods of obtaining a low-energy expression based either on the soft-photon approximation or the use of Ward-Takahashi identities. We point out that structure-dependent terms are defined with respect to a low-energy approximation of the pole terms which commonly is separated from the full amplitude. We derive a general expression for the structure-dependent terms in an expansion in terms of the momenta $k_1$ and $k_2$ of the initial and final virtual photon, respectively, up to and including terms of order ${\cal O}(k^4)$. At order ${\cal O}(k^2)$ two terms appear…