There are at least 3 distinct B-meson anomalies that are currently intriguing:
- A few sigma (2 to 4, depending who you ask) deviation in differential distribution of B → K*μμ decays,
- 2.6 sigma violation of lepton flavor universality in B → Kμμ vs B → Kee decays,
- 3.5 sigma violation of lepton flavor universality, but this time in B → Dτν vs B → Dμν decays.
If both λb and λs are non-zero then a tree-level leptoquark exchange can mediate the b-quark decay b → s μ μ. This contribution adds up to the Standard Model amplitudes mediated by loops of W bosons, and thus affects the B-meson observables. It turns out that the first two anomalies listed above can be fit if the leptoquark mass is in the 1-50 TeV range, depending on the magnitude of λb and λs.
Also the 3rd anomaly above can be easily explained by leptoquarks. One example from this paper is a leptoquark transforming as (3,1,-1/3) and coupling to matter as
There are more kinds of leptoquarks with different charges that allow for Yukawa couplings to matter. Some of them could also explain the 3 sigma discrepancy of the experimentally measured muon anomalous magnetic moment with the Standard Model prediction. Actually, a recent paper says that the (3,1,-1/3) leptoquark discussed above can explain all B-meson and muon g-2 anomalies simultaneously, through a combination of tree-level and loop effects. In any case, this is something to look out for in this and next year's data. If a leptoquark is indeed the culprit for the B → Dτν excess, it should be within reach of the 13 TeV run (for the 1st two anomalies it may well be too heavy to produce at the LHC). The current reach for leptoquarks is up to 1 TeV mass (strongly depending on model details), see e.g. the recent ATLAS and CMS analyses. So far these searches have provoked little public interest, but that may change soon...