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Register a new userAn update of muon capture on hydrogen
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The successful precision measurement of the rate of muon capture on a proton by the MuCap Collaboration allows for a stringent test of the current theoretical understanding of this process. Chiral perturbation theory, which is a low-energy effective field theory that preserves the symmetries and the pattern of symmetry breaking in the underlying theory of QCD, offers a systematic framework for describing $mu p$ capture and provides a basic test of QCD at the hadronic level. We describe how this effective theory with no free parameters reproduces the measured capture rate. A recent study has addressed new sources of uncertainties that were not considered in the previous works, and we review to what extent these uncertainties are now under control. Finally, the rationale for studying muon capture on the deuteron and some recent theoretical developments regarding this process are discussed.
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A simultaneous analysis is made of the measured rates of ordinary muon capture (OMC) and radiative muon capture (RMC) in liquid hydrogen, using theoretical estimates for the relevant atomic capture rates that have been obtained in chiral perturbation theory with the use of the most recent values of the coupling constants. We reexamine the basic formulas for relating the atomic OMC and RMC rates to the liquid-hydrogen OMC and RMC rates, respectively. Although the analysis is significantly influenced by ambiguity in the molecular state population, we can demonstrate that, while the OMC data can be reproduced, the RMC data can be explained only with unrealistic values of the coupling constants; the degree of difficulty becomes even more severe when we try to explain the OMC and RMC data simultaneously.
The muon capture on 3H leading to muonic neutrino and three neutrons in the final state is studied under full inclusion of final state interactions. Predictions for the three-body break-up of 3H are calculated with the AV18 potential, augmented by the Urbana IX three-nucleon force. Our results are based on the single nucleon weak current operator comprising the dominant relativistic corrections. This work is a natural extension of our investigations of the muon capture on 3He leading to 3H or n+d or n+n+p and muonic neutrino in the final state, presented in Phys. Rev. C90, 024001 (2014).
The Quasiparticle Random Phase Approximation (QRPA) is used in evaluation of the total muon capture ratesfor the final nuclei participating in double-beta decay. Several variants of the method are used, depending on the size of the single particle model space used, or treatment of the initial bound muon wave function. The resulting capture rates are all reasonably close to each other. In particular, the variant that appears to be most realistic, results in rates in good agreement with the experimental values. There is no necessity for an empirical quenching of the axial current coupling constant $g_A$. Its standard value $g_A$ = 1.27 seems to be adequate.
The singlet capture rate $Lambda_S$ for the semileptonic weak process $mu+p to n+ u_mu$ has been measured in the MuCap experiment. The novel experimental technique is based on stopping muons in an active target, consisting of a time projection chamber operating with ultra-pure hydrogen. This allows the unambiguous determination of the pseudoscalar form factor $g_P$ of the charged electroweak current of the nucleon. Our first result $g_P(q^2=-0.88 m^2_mu) = 7.3 pm 1.1 $ is consistent with accurate theoretical predictions and constitutes an important test of QCD symmetries. Additional data are being collected with the aim of a three-fold reduction of the experimental uncertainties. Building on the developed advanced techniques, the new MuSun experiment is being planned to measure the muon capture rate on the deuteron to 1.5% precision. This would provide the by far most accurate experimental information on the axial current interacting with the two-nucleon system and determine the low energy constant $L_{1A}$ relevant for solar neutrino reactions. Muon induced atomic and molecular processes represent challenges as well as opportunities for this science program, and their interplay with the main nuclear and weak-interaction physics aspects will be discussed.
The mu + 2H -> nu + n + n, mu + 3He -> nu + 3H, mu + 3He -> nu + n + d and mu + 3He -> nu + n + n + p capture reactions are studied with various realistic potentials under full inclusion of final state interactions. Our results for the two- and three-body break-up of 3He are calculated with a variety of nucleon-nucleon potentials, among which is the AV18 potential, augmented by the Urbana~IX three-nucleon potential. Most of our results are based on the single nucleon weak current operator. As a first step, we have tested our calculation in the case of the mu + 2H -> nu + n + n and mu + 3He -> nu + 3H reactions, for which theoretical predictions obtained in a comparable framework are available. Additionally, we have been able to obtain for the first time a realistic estimate for the total rates of the muon capture reactions on 3He in the break-up channels: 544 1/s and 154 1/s for the n + d and n + n + p channels, respectively. Our results have also been compared with the most recent experimental data, finding a rough agreement for the total capture rates, but failing to reproduce the differential capture rates.
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