  Fundamental physics could be described as having a muon problem.
Discrepancies between theory and experiment in a number of muonic measurements
($r_P$, $a_\mu$, $H\rightarrow\mu\tau$, $\mathcal{R}_K$, $\mathcal{R}_{D^*}$)
have been observed in the last decade that demand explanation. True muonium,
the bound state of a muon and its antiparticle, has the potential to put strong
constraints on any beyond standard model physics that affects the muon sector.
To study these effects, theoretical predictions and experiment need a, not
unreasonable, precision of 100 MHz. Surprisingly, at this level, QCD and
electroweak corrections become relevant in true muonium as well. Presented here
is a discussion of the novel properties of true muonium from the standard
model, potential discovery methods at near future facilities like DIRAC and
HPS, and its ability to discriminate between a variety of solutions to the muon
problem.
