Vacuum polarization test and search for muonhadron interactions from muonic X-rays:: Crystal-spectrometer experiments

Abstract We have measured the wavelengths of the 3 d 5 2 −2 p 3 2 and the 3 d 3 2 -2 p 1 2 X-ray transitions in μ - 24 Mg, - 28 Si and - 31 P with the bent-crystal spectrometer at the SIN muon channel. The X-rays are measured relative to the wavelengths of the 84 keV and the 63 keV γ-rays of 170 Tm and 169 Yb which have recently been calibrated to about 1 ppm. The measured X-ray wavelengths λ exp are compared with theoretical values λ th , as obtained from QED calculations. The relative difference, averaged over all six measured transitions, is λ exp −λ th λ th = (2 ± 8) × 10 −6 This result corresponds to a test of the vacuum polarization effect in QED of (0.6 ± 2.4) × 10 −3 . Assuming the QED calculations to be correct, we can use the result to put limits on additional muon-nucleon interactions (as required by gauge theories). If such an interaction is mediated by a scalar, isoscalar boson with a mass smaller than 1 MeV, the coupling constant is found to be g N g μ 4π = (−4 ± 17) × 10 −9 Alternatively, we can deduce from our experiments the most accurate direct value to date for the negative muon mass, m μ - = 105.65906(91) MeV .