Scouring meson decays for true muonium

Abstract

Rare meson decay experiments promise to measure branching ratios as small as 10 −13 . This presents an opportunity to discover the µ + µ − bound state true muonium. We consider a set of possible channels, all with branching ratios above ∼ 10 −11 . For the electromagnetic decays η/η → (µ + µ − )γ, theoretical and phenomenological form factors F η/η γγ * (Q 2 ) allow predictions of BR(η → (µ + µ − )γ) ∼ 4.8 × 10 −10 and BR(η → (µ + µ − )γ) ∼ 3.7 × 10 −11 at the 5% level. Discussion of experimental prospects and potential backgrounds are made.

Discovering true muonium at LHCb

“…The former is in agreement with the LHCb inelastic cross-section measurement [41], while the latter correctly predicts the low mass limit of the LHCb inclusive µ + µ − dark photon search [39]. Given that BR(η → γ TM) = 4.8 × 10 −10 [22], which agrees well with Eq. ( 7) using the differential η → γe + e − shape from Pythia, the signal cross section in the fiducial volume is…”

“…While searches for long-lived particles typically focus on new BSM states [26], TM is an example of a SM long-lived particle that can be searched for at LHCb. Predictions of the mass and lifetime at higher order than those derived here are available [22,27]; however, it is unlikely that LHCb will be sensitive to these higher order corrections.…”

“…However, both of these methods are statistically limited with potentially large backgrounds and are not expected to have discovery potential. The proposed RedTop [21,22] experiment at Fermilab is designed to produce a large flux of η mesons, and using the methods outlined in this work, might also be sensitive to TM. Searching for a TM γ final state from e + e − collisions has also been proposed [23], which may be accessible to Belle II.…”

Alternative implementation of atomic form factors

“…Many mechanisms for the production of dimuonium have been proposed in the literature. Dimuonium can be formed in fixed-target experiments [5][6][7][8][9], in electron-positron collisions [1,[10][11][12], in elementary particle decays [13][14][15][16][17][18][19], in a quark-gluon plasma [20,21], in relativistic heavy ion collisions [21][22][23], in an astrophysical context [24], or in experiments with ultra-slow muon beams [25,26].…”