Studying Antimatter Gravity with Muonium

Abstract

The gravitational acceleration of antimatter,ḡ, has yet to be directly measured; an unexpected outcome of its measurement could change our understanding of gravity, the universe, and the possibility of a fifth force. Three avenues are apparent for such a measurement: antihydrogen, positronium, and muonium, the last requiring a precision atom interferometer and novel muonium beam under development. The interferometer and its few-picometer alignment and calibration systems appear feasible. With 100 nm grating pitch, measurements ofḡ to 10%, 1%, or better can be envisioned. These could constitute the first gravitational measurements of leptonic matter, of 2 nd -generation matter, and possibly, of antimatter.And we note that arguments based on absolute gravitational potentials have been critiqued by Nieto and Goldman [2].Atoms 2018, xx, x 2 of 14 on quite general grounds [2]. 2 Such a measurement can be viewed as a test of general relativity or as a search for a fifth force and is of interest from both perspectives.Although the equivalence principle experiments indicate that nuclear binding energy gravitates in the same way as ordinary mass, absent validated models of gravity at a subnuclear scale, it is unclear how the gravitational interactions of virtual matter should be treated. Use of a pure-leptonic atom, such as positronium or muonium, evades these complexities. Moreover, no measurement has yet been made of the gravitational force on second-or third-generation matter or antimatter (although, with some assumptions, stringent limits can be obtained from neutral-meson oscillations, especially for K 0 -K 0 [14]). Since direct gravitational measurements on other higher-generation particles, such as hyperons, τ leptons, and c or b hadrons, appear impractical due to their short lifetimes, muonium may be the only access we have. Recent work [15][16][17] examining a possible standard-model extension emphasizes the importance of second-generation gravitational measurements. Current interest in "fifth force" models [18,19] (stimulated by evident anomalies in the leptonic decays of B mesons) also supports more detailed investigations of muonium.General relativity (GR) is generally taken to predict identical behaviors of antimatter and matter in a gravitational field. With the observation of gravitational waves [20], most of the predictions of GR are now experimentally confirmed. Nevertheless, GR is fundamentally incompatible with quantum mechanics, and the search for a quantum theory of gravity continues [21]. To date, the experimental evidence on which to base such a theory comes from observations of matter-matter and matter-light interactions. In a quantum field theory, matter-matter and matter-antimatter forces can differ -for example, suppressed scalar and vector terms might cancel in matter-matter interactions, but add in matter-antimatter ones [2], leading to small equivalence principle violations. Matter-antimatter measurements could thus play a key role.While most physicists expect that the equivalence principle a...

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