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Feasibility study of true muonium observation with the Belle II existing dataset

Università degli Studi La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy and INFN Sezione di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy

INFN Laboratori Nazionali di Frascati, Via Enrico Fermi 54, 00044 Frascati, Italy

Università degli Studi La Sapienza, Piazzale Aldo Moro 5, 00185 Roma, Italy and Galileo Galilei Institute for Theoretical Physics, Largo Enrico Fermi 2, I-50125 Firenze, Italy

^*Contact author: ruben.gargiulo@uniroma1.it

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Phys. Rev. D 111, 112002 – Published 9 June, 2025

DOI: https://doi.org/10.1103/wbpp-sch4

Abstract

True muonium ( $μ^{+} μ^{-}$ ) is one of the cleanest bound states, being composed only of leptons, along with true tauonium and positronium. Unlike the latter, true muonium and true tauonium have not been observed so far. This article shows that the spin-0 state of true muonium (para-TM), decaying into two photons, can be observed at a discovery level of significance in the dataset already collected by the Belle-II experiment at the $ϒ (4 S)$ peak, with certain assumptions on systematic uncertainties. Para-TM is produced via photon-photon fusion, and its observation is based on the detection of the photon pair resulting from its decay, on top of the continuum background due predominantly to light-by-light scattering. Trigger, acceptance and isolation cuts, along with calorimeter resolution and reconstruction efficiency, are taken into account during the Monte Carlo simulation of both signal and background. In order to separate signal and background, a machine learning method, based on extremely randomized trees, is trained on simulated events. Finally, the expected statistical significance of TM observation is evaluated, taking into account systematic uncertainties in a parametric fashion.

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Phys. Rev. D 111, 112002– Published 9 June, 2025

Vol. 111, Iss. 11 — 1 June 2025

Received 4 April 2025
Accepted 19 May 2025

DOI: https://doi.org/10.1103/wbpp-sch4

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

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Feasibility study of true muonium observation with the Belle II existing dataset

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