Calculation of doublet capture rate for muon capture in deuterium within chiral effective field theory

Abstract

The doublet capture rate Λ 1/2 of the negative muon capture in deuterium is calculated employing the nuclear wave functions generated from accurate nucleon-nucleon (NN) potentials constructed at next-to-next-to-next-to-leading order of heavy-baryon chiral perturbation theory and the weak meson exchange current operator derived within the same formalism. All but one of the lowenergy constants that enter the calculation were fixed from pion-nucleon and nucleon-nucleon scattering data. The low-energy constantd R (c D ), which cannot be determined from the purely two-nucleon data, was extracted recently from the triton β-decay and the binding energies of the three-nucleon systems. The calculated values of Λ 1/2 show a rather large spread for the used values of thed R . Precise measurement of Λ 1/2 in the future will not only help to constrain the value ofd R , but also provide a highly nontrivial test of the nuclear chiral EFT framework. Besides, the precise knowledge of the constantd R will allow for consistent calculations of other two-nucleon weak processes, such as proton-proton fusion and solar neutrino scattering on deuterons, which are important for astrophysics.

Precision muon physics

“…Over recent years a number of calculations of Λ D have been performed with increasing sophistication in the EF T framework. The two most recent calculations, which consistently treat the nuclear wavefunctions and the weak operators, were conducted by Marcucci et al [168], yielding 399±3 s −1 , and by Adam et al [169], yielding 383.8-392.4 s −1 .…”

Nuclear axial current operators to fourth order in chiral effective field theory

“…Notice that the theoretical predictions for the doublet capture rate Λ 1/2 show a significant spread, see e.g. [54,55]. Last but not least, the appearance of the same LEC in the leading 3N force and the short-range part of the 2N weak current opens an exciting possibility to perform nontrivial precision tests of chiral EFT in few-nucleon systems by carrying out a simultaneous calculation of nucleon-deuteron scattering, the binding energy, radius and the precisely known half-life of 3 H and the muon capture rates on 2 H and 3 He, accompanied with a careful analysis of the theoretical uncertainties along the lines of Refs.…”

Theoretical studies of muon capture on light nuclei

“…[13] have performed in Ref. [24] a χEFT calculation of Γ D very similar to the one presented in this section and in fact contemporary to it. In this calculation, Γ D has been found in the range 383.8 − 392.4 sec −1 , depending on the χEFT two-nucleon potential used.…”