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Nuclear muon capture on the proton and 3 He within the standard model and beyond

“…In spite of its remarkable precision of 0.4% for the statistical capture rate at λ stat exp = 1496 ± 4 s −1 , whose value is found to be in perfect agreement with the theoretical prediction λ stat theor = 1496 ± 21 s −1 [2,3], the ensuing value for g P , though at exactly the expected level, is still precise to only 19% [13]. One should add however that in terms of the corresponding pseudoscalar nuclear form factor F P (q 2 ) for 3 He, the same experimental result translates [12,14,15,16,17] into a 13% precise test of the prediction based on PCAC, the symmetry which together with CVC has historically been the precusor for the chiral symmetries of QCD. Even though these results are still a long way off the precision reached by the latest theoretical analyses [6,7,8,9], they stand as a clear confirmation of the basic concepts involved in the chiral symmetry aspects of the problem.…”

“…The calculation of |M λ | 2 then proceeds using the trace properties in (14). The advantage of the above approach is that the combinations of form factors and coupling coefficients which are relevant appear from the start, ever before proceeding to the calculation of traces.…”

“…Thus given the inputs discussed in Sect.3.1 except for the value for F P (q 2 1 ), the result (67) implies [12,14,15,16,17] F P (q …”

“…Moreover, given the above issues surrounding the value of g P , as well as the precision of its theoretical prediction, a new effort has been launched [18,14] in order to measure the singlet rate of ordinary muon capture on hydrogen in a gas target (to avoid the complications due to molecular binding effects), hopefully to a precision of 0.5% to 1% 2 . Here again, beyond the initial aim towards the value of g P , this level of precision should also enable tests of the SM.…”

“…[12] for the statistical capture rate and also by illustrating the potential physics reach of some other final state distribution which does not entail a correlation observable except for an initially polarized muonic atom. In Section 4, the same considerations are applied again to the case of capture on the proton, based on the optimistic aim of a 0.5% precision in the result for the singlet capture rate [18,14]. Section 6 then translates some of the limits for physics beyond the SM obtained from the previous considerations, into limits for parameters of some specific models for such physics.…”