A few days ago I received from my esteemed colleague Massimo Passera, a theorist and an INFN director of research in the Padova section where I also work, a draft of a new article he produced with his colleagues Antonio Masiero and Paride Paradisi, which is relevant to my present interests. The paper discusses what new physics effects could be accessible by the precision measurement of elastic scattering of energetic muons off electrons, in a setup which is being considered at the CERN north area for the determination of the hadronic contribution to the effective electromagnetic coupling (the article has meanwhile being published in the arXiv).
The proposed experiment, aptly called MUonE (Muon on Electron), wants to measure very precisely the elastic scattering reaction when 150 GeV muons are impinged on a fixed target, as the resulting shape of the collision rate, studied as a function of the energy transfer, provides indirect input on the leading systematic uncertainty to the theoretical prediction of the muon g-2 factor, the so-called "anomalous magnetic moment of the muon".
The muon magnetic moment is a very interesting physical quantity, mainly because it has been measured with high precision and its value was found to disagree with its theoretical prediction by almost four standard deviations. So new physics could be responsible. By beating down systematic uncertainties on the theoretical input, which is what MUonE aims to do, one could put the disagreement to more focus, eventually proving that the Standard Model of particle physics misses some piece.
The new article by Passera and collaborators fills a gap in the syllogism that led to propose the MUonE experiment, as it proves that no conceivable new physics effect would interfere with the measurement of the elastic scattering -and the consequent extraction of a more precise theoretical estimate of the muon anomaly- at an experimentally detectable level. So, in a sense, it closes an important loophole in the motivation for the experiment.
What I wish to discuss here, however, is not the MUonE experiment or the new physics that Passera and collaborators studied in detail. In their paper, they also take the care to estimate, in what looks to me as a warm up of their calculation muscles, what is the contribution to the total reaction rate of muons in the MUonE detector due to a Standard Model process which is not new physics nor exotic in any way: weak interactions predict that in rare occurrences, when muons impinge on electrons they will interact by exchanging a weak W boson, thereby producing a muon neutrino and an electron neutrino. They do the exercise and show that the rate of these collisions is, as anybody with some rudiments in particle physics would guess, very, very small.
The prediction is that the cross section of neutrino pair production, for 150 GeV muons such as those MUonE will employ, is two trillionths of the elastic cross section. They soberly conclude in their article that "This process is therefore negligible at the MUonE experiment". As a guy who loves understatements, this made me chuckle!
Neutrinos are basically undetectable in a setup like the one of MUonE, as they traverse it without giving any signal -for that matter, they have a sizable chance of continuing to do so for the next light year of matter they traverse. So experimentally these events amount to "muon in, nothing out". In a setup where the detector is hit by a rate of 13 million muons per second, you quickly realize that such a signature is hardly of any value, both as a signal of the rare electroweak process, or as a background of sorts.
If you need to know the actual number of such interactions, in a year of data taking, I took the pains to do the back of the envelope calculation: we are talking of three and a half muons per year which "vanish" without apparently leaving a trace. Wow. Maybe one day an alien race will be able to detect something like that... We are talking of showering a few trillion muons in a detector and having a rather precise bookkeeping of where they all go!
The new article by Passera and collaborators will be soon available in the arXiv, so if you are interested check it in a few days!