Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory

Abstract

The amplitude for ordinary muon capture on the proton is evaluated, through the first four orders in the expansion parameter, in a manifestly Lorentz invariant form of baryon chiral perturbation theory. Expressions for the low energy constants in terms of physical quantities are obtained in each of the several renormalization schemes which have been proposed for forcing the relativistic approach to obey the same counting rules as obtained in heavy baryon chiral perturbation theory. The advantages and disadvantages of these schemes are discussed, using the muon capture results as an example, with the aim of gaining insight as to which scheme is preferable for practical calculations.

arXiv commentLatex, 25 pages, 5 figures

References in corpus (31)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Axial structure of the nucleon
• Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors
• Renormalization of relativistic baryon chiral perturbation theory and power counting
• The chiral effective pion-nucleon Lagrangian of order p^4
• Low energy analysis of the nucleon electromagnetic form factors
• The form factors of the nucleon at small momentum transfer
• On the pion-nucleon coupling constant
• Pion--Nucleon Scattering in a New Approach to Chiral Perturbation Theory
• Low energy analysis of pi N --> pi N
• Induced pseudoscalar coupling of the proton weak interaction
• Including the $\Delta (1232)$ resonance in baryon chiral perturbation theory
• Neutron beta decay in effective field theory
• Infrared regularization of baryon chiral perturbation theory reformulated
• Muon capture by a proton in heavy baryon chiral perturbation theory
• Electromagnetic form factors of the nucleon in chiral perturbation theory including vector mesons
• Electromagnetic form factors of the nucleon in relativistic baryon chiral perturbation theory
• Infrared regularization with spin-3/2 fields
• Is Heavy Baryon Approach Necessary?
• Ordinary and radiative muon capture on the proton and the pseudoscalar form factor of the nucleon
• Improving the ultraviolet behavior in baryon chiral perturbation theory
• Capture rate and neutron helicity asymmetry for ordinary muon capture on hydrogen
• Radiative pion capture by a nucleon
• Radiative Muon Capture in Heavy Baryon Chiral Perturbation Theory
• Radiative Muon Capture by a Proton in Chiral Perturbation Theory
• Analysis of ordinary and radiative muon capture in liquid hydrogen
• Polarized photons in radiative muon capture
• Charged radiative pion capture on the nucleon in heavy baryon chiral perturbation theory
• Gauge symmetric delta(1232) couplings and the radiative muon capture in hydrogen

Cited by in corpus (19)

• Chiral Perturbation Theory and Baryon Properties
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• Recent developments in SU(3) covariant baryon chiral perturbation theory
• Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory
• Nucleon Form Factors of the Isovector Axial-Vector Current: Situation of Experiments and Theory
• Elastic $\alpha$-${}^{12}$C scattering at low energies in cluster effective field theory
• On the axial-vector form factor of the nucleon and chiral symmetry
• The $S_{E1}$ factor of radiative $\alpha$ capture on ${}^{12}$C in cluster effective field theory
• Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory
• $pp\to pp{\pi }^0$ near threshold in pionless effective theory
• Parity-violating nucleon-nucleon interaction from different approaches
• Cluster effective field theory and nuclear reactions
• Unified model of nucleon elastic form factors and implications for neutrino-oscillation experiments
• Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology
• Fixing effective range parameters in elastic $\alpha$-${}^{12}$C scattering: an impact on resonant $2_4^{+}$ state of ${}^{16}$O and $S_{E2}$ factor of ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O
• Nucleon axial-vector form factor and radius from future neutrino experiments
• The axial-vector form factor of the nucleon in a finite box