Short answer is that I suspect the physics is not new, but something related to something we think we qualitatively know, but we don't really know how to bound the computational errors correctly in a complicated system.
AFAIK, the QED computation techniques that are used to compute bound state of a proton (often modified ordered pertubation methods) aren't particularly convergent so many shortcuts are taken (e.g., use orders of different quantities like non-relativistic velocity, etc). By using a muon and a proton (instead of an electron and a proton), we are essentially replacing something we know more about (the electron) with something we know less about (muon), to try and compute something about something we don't know much about (the proton). Since we don't know much about protons yet, I believe most computations of the bound state are currently just assuming things about them (charge is a point source, nothing about quarks). I haven't read the paper yet, so it's hard to know what they are doing in the QED corrections.
Maybe there is a slight chance that this simplistic system (muon+proton) can macroscopically exhibit something that hints that QCD confinement inside a proton or muon isn't perfect (e.g, the heavy quarks sortof show themselves in a way that we can measure) which would be some interesting new gluon physics that is currently beyond our particle collider reach. But in some ways this might just show us that the QED based adjustments we are making aren't good enough for the real system and we need some even harder to dream up QCD adjustments and it's hard to say that this would definitly be new physics, but perhaps just new math on old QCD physics....
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/xtDCerTWBhE/story01.htm
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