Thoughts on RK

The hashtag #CautiouslyExcited is trending on Twitter, in spite of the raging plague. The updated RK measurement in LHCb has made a big splash and has been covered by every news outlet.  RK measures the ratio of the B->Kμμ and B->Kee decay probabilities, which the Standard Model predicts to be very close to one. Using all the data collected so far, LHCb instead finds RK = 0.846 with the error of 0.044. This is the same central value and 30% smaller error compared to their 2019 result based on half of the data.  Mathematically speaking, the update does not much change the global picture of the B-meson anomalies. However, it has an important psychological impact, which goes beyond the PR story of crossing the 3 sigma threshold. Let me explain why. 

For the last few decades, every deviation from the Standard Model prediction in a particle collider experiment would mean one of these 3 things:    

1. Statistical fluctuation. 
2. Flawed theory prediction. 
3. Experimental screw-up.   

In the case of RK, the option 2. is not a worry.  Yes, flavor physics is a swamp full of snake pits, however in the RK ratio the dangerous hadronic uncertainties cancel out to a large extent, so that precise theoretical predictions are possible.  Before March 23 the biggest worry was option 1.  Indeed, 2-3 sigma fluctuations happen all the time at the LHC, due to a huge number of measurements being taken.  However, you expect statistical fluctuations to decrease in significance as more data is collected.  This is what seems to be happening to the sister RD anomaly, and the earlier history of RK was not very encouraging either (in the 2019 update the significance neither increased nor decreased).  The fact that, this time, the significance of the RK anomaly increased, more or less as you would expect it to assuming it is a genuine new physics signal, makes it unlikely that it is merely a statistical fluctuation.  This is the main reason for the excitement you may perceive among particle physicists these days. 

On the other hand,  option 3. remains a possibility.  In their analysis,  LHCb reconstructed 3850 B->Kμμ decays vs. 1640 B->Kee decays, but from that they concluded that decays to muons are less probable than those to electrons. This is because one has to take into account the different reconstruction efficiencies for muons and electrons. An estimate of that efficiency is the most difficult ingredient of the measurement,  and the LHCb folks have spent many nights of heavy drinking worrying about it. Of course, they have made multiple cross-checks and are quite confident that there is no mistake but... there will always be a shadow of a doubt until RK is confirmed by an independent experiment. Fortunately for everyone, a verification will be provided by the Belle-II experiment, probably in 3-4 years from now. Only when Belle-II sees the same thing we will breathe a sigh of relief and put all our money on option

4. Physics beyond the Standard Model 

From that point of view explaining the RK measurement is trivial.  All we need is to add a new kind of interaction between b- and s-quarks and muons to the Standard Model Lagrangian.  For example, this 4-fermion contact term will do: 

where Q3=(t,b), Q2=(c,s), L2=(νμ,μ). The Standard Model won't let you have this interaction because it violates one of its founding principles: renormalizability.  But we know that the Standard Model is just an effective theory, and that non-renormalizable interactions must exist in nature, even if they are very suppressed so as to be unobservable most of the time.  In particular, neutrino oscillations are best explained by certain dimension-5 non-renormalizable interactions.  RK may be the first evidence that also dimension-6 non-renormalizable interactions exist in nature.  The nice thing is that the interaction term above 1) does not violate any existing experimental constraints,  2) explains not only RK but also some other 2-3 sigma tensions in the data (RK*, P5'),  and 3) fits well with some smaller 1-2 sigma effects (Bs->μμ, RpK,...). The existence of a simple theoretical explanation and a consistent pattern in the data is the other element that prompts cautious optimism.  

The LHC run-3 is coming soon, and with it more data on RK.  In the shorter perspective (less than a year?) there will be other important updates (RK*, RpK) and new observables (Rϕ , RK*+) probing the same physics. Finally something to wait for.