skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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.

Authors:
;  [1]
  1. TRIUMF, Vancouver, British Columbia, V6T 2A3 (Canada)
Publication Date:
OSTI Identifier:
20933239
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.75.014025; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CAPTURE; CHIRALITY; LORENTZ INVARIANCE; MUONS; PERTURBATION THEORY; PROTONS; QUANTUM FIELD THEORY; RELATIVISTIC RANGE; RENORMALIZATION

Citation Formats

Ando, Shungichi, and Fearing, Harold W. Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.014025.
Ando, Shungichi, & Fearing, Harold W. Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory. United States. doi:10.1103/PHYSREVD.75.014025.
Ando, Shungichi, and Fearing, Harold W. Mon . "Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory". United States. doi:10.1103/PHYSREVD.75.014025.
@article{osti_20933239,
title = {Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory},
author = {Ando, Shungichi and Fearing, Harold W.},
abstractNote = {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.},
doi = {10.1103/PHYSREVD.75.014025},
journal = {Physical Review. D, Particles Fields},
number = 1,
volume = 75,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • We analyze meson-baryon scattering lengths in the framework of covariant baryon chiral perturbation theory at leading one-loop order. We compute the complete set of matching relations between the dimension-two low-energy constants in the two- and three-flavor formulations of the theory. We derive new two-flavor low-energy theorems for pion-hyperon scattering that can be tested in lattice simulations.
  • We calculate the nucleon form factors G{sub A} and G{sub P} of the isovector axial-vector current and the pion-nucleon form factor G{sub {pi}}{sub N} in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order O(p{sup 4}). In addition to the standard treatment including the nucleon and pions, we also consider the axial-vector meson a{sub 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 formore » G{sub A}. The inclusion of the axial-vector meson results in an improved description of the experimental data for G{sub A}, while the contribution to G{sub P} is small.« less
  • The matrix element for muon capture by a proton is calculated to O(p{sup 3}) within heavy baryon chiral perturbation theory using the new O(p{sup 3}) Lagrangian of Ecker and Moj{hacek z}i{hacek s}. External nucleon fields are renormalized using the appropriate definition of the wave function renormalization factor Z{sub N}. Our expression for Z{sub N} differs somewhat from that found in the 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 standardmore » muon capture form factors are derived and compared to experimental data and we determine three of the coefficients of the Ecker-Moj{hacek z}i{hacek s} Lagrangian, namely, b{sub 7}, b{sub 19}, and b{sub 23}. {copyright} {ital 1997} {ital The American Physical Society}« less
  • The cross section for radiative thermal neutron capture on {sup 3}He ({sup 3}He+n{yields}{sup 4}He+{gamma}; known as the hen reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N{sup 3}LO). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to N{sup 3}LO, the M1 operators contain two low-energy constants, which appear as the coefficients of nonderivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and {sup 3}He,more » we carry out a parameter-free calculation of the hen cross section. The results are in good agreement with the data.« less
  • No abstract prepared.