GAUGE INVARIANCE OF THE MUONIUM–ANTIMUONIUM OSCILLATION TIME SCALE AND LIMITS ON RIGHT-HANDED NEUTRINO MASSES

The gauge invariance of the muonium–antimuonium [Formula: see text] oscillation time scale is explicitly demonstrated in the Standard Model modified only by the inclusion of singlet right-handed neutrinos and allowing for general renormalizable interactions. The seesaw mechanism is exploited resulting in three light Majorana neutrinos and three heavy Majorana neutrinos with mass scale MR≫MW. The leading order matrix element contribution to the [Formula: see text] oscillation process is computed in Rξ gauge and shown to be ξ-independent thereby establishing the gauge invariance to this order. Present experimental limits resulting from the non-observation of the oscillation process sets a lower limit on MR roughly of order 600 GeV.

MUONIUM–ANTIMUONIUM OSCILLATIONS AND MASSIVE MAJORANA NEUTRINOS

The electron and muon number violating muonium–antimuonium oscillation process can proceed provided that neutrinos have nonzero masses and mix among the various generations. Modifying the Standard Model only by the inclusion of singlet right-handed neutrino fields and allowing for general neutrino masses and mixings, the leading order matrix element contributing to this process is computed. For the particularly interesting case where the neutrino masses are generated by a seesaw mechanism with a very large Majorana mass MR≫MW, it is found that both the very light and very heavy Majorana neutrinos each give comparable contributions to the oscillation time scale proportional to [Formula: see text]. Present experimental limits set by the non-observation of the oscillation process sets a lower limit on MR of roughly of order 104 GeV.

Quadronium and quantum electrodynamics

The composite-particle scenario is a phenomenology that can organize the data of the "sharp lepton problem" posed by heavy-ion and (β+ + atom) studies. It hypothesizes a new composite particle (of mass ~3mc2) as the source of the observed sharp energy (e+e−) decay pairs. Available data rule out the possibilities that the source is a new elementary particle or that it is a quasi-bound state of (e+e−). Occam's razor therefore currently favors the quadronium structure, Q0 = (e+e+e−e−). Implications of quadronium for high-precision quantum electrodynamics (QED) are considered, and calculated and (or) measured deviations in QED that are sensitive to the existence of Q0 are identified. In particular, for the electron magnetic-moment anomaly, a(e) = (ge − 2)/2, a Q0–pole effects a small correction to the contributions of O(α4), which is therefore small compared to the largest current (theoretical) uncertainty. For photon–photon scattering, Q0 corrects the leading order matrix element, and allows resonant Q0 creation in photon–nucleus scattering. Finally, a Q0 bound state corrects the O(α) correction to the leading 3γ annihilation rate of triplet positronium. Therefore Q0 may contribute significantly to this decay rate, which is currently in a 10σ discrepancy with experiment. A current experimental gap is the lack of corroborative data on the sharp (Γ ≤ 2.1 keV) 330.1 keV electrons reported by Sakai from irradiations of U and Th with β+-decay positrons. A study of these (and (or) their expected partner positrons of the same energy) in collisions of (~3 MeV) beam positrons (or electrons) upon high-Z neutral atoms could fill this gap. Similar studies with positrons of 660–795 keV would test the expectation that recoilless resonance creation of the Q0 source of these pairs is also possible.