Muon capture on deuteron using local chiral potentials

Abstract

The muon capture reaction ${\mu }^{-}+d\to n+n+{\nu }_{\mu }$ in the doublet hyperfine state is studied using nuclear potentials and consistent currents derived in chiral effective field theory, which are local and expressed in coordinate-space (the so-called Norfolk models). Only the largest contribution due to the ${}^1{S}_0$ $nn$ scattering state is considered. Particular attention is given to the estimate of the theoretical uncertainty, for which four sources have been identified: (i) the model dependence, (ii) the chiral order convergence for the weak nuclear current, (iii) the uncertainty in the single-nucleon axial form factor, and (iv) the numerical technique adopted to solve the bound and scattering $A=2$ systems. This last source of uncertainty has turned out essentially negligible. The ${}^1{S}_0$ doublet muon capture rate ${\Gamma }^D{(}^1{S}_0)$ has been found to be ${\Gamma }^D{(}^1{S}_0)=255.8(0.6)(4.4)(2.9)$ s${}^{-1}$, where the three errors come from the first three sources of uncertainty. The value for ${\Gamma }^D{(}^1{S}_0)$ obtained within this local chiral framework is compared with previous calculations and found in very good agreement.

33 pages, 3 figures

References in corpus (10)

• Chiral effective field theory and nuclear forces
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
• Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
• Muon capture on deuteron and 3He
• Break-up channels in muon capture on 3He
• Comparative study of ${}^6$He $\beta$-decay based on different similarity-renormalization-group evolved chiral interactions

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• Muon capture on the deuteron in chiral effective field theory