# The $B\to K^*\mu^+\mu^-$ anomaly persists

tl;dr The $B\to K^*\mu^+\mu^-$ anomaly is still there, global fit prefers new physics in $C_9$ over SM by $3.7\sigma$, interpretation as hadronic effect not excluded though.

Two years ago the LHCb experiment measured a significant deviation from the Standard Model predictions in one of the angular observables of the $B\to K^*\mu^+\mu^-$ decay (prosaically called $P_5’$). This deviation caused a lot of discussion because it could in principle be a sign of physics beyond the Standard Model, but it has also been speculated that some mundane QCD effect not accounted for in the theoretical predictions for this (and other) observables is responsible for it.

Last year, another tantalizing announcement was made by the same experiment. Apparently, the decay rates of the two modes $B\to K\mu^+\mu^-$ and $B\to Ke^+e^-$ differ by something like 25% (their ratio, called $R_K$, was measured to be around 0.75). This is not possible in the Standard Model where electrons and muons are identical up to their different masses (which play no role in this decay). Interestingly, the two anomalies — dubbed $B\to K^*\mu^+\mu^-$ and $R_K$ anomalies — fit very nicely together if interpreted in terms of physics beyond the Standard Model. However, it was too early to draw a firm conclusion, with the $B\to K^*\mu^+\mu^-$ observables being potentially susceptible to poorly known QCD effects and the $R_K$ observation not being statistically very significant taken on its own.

Today at the conference Rencontres de Moriond in the Italian ski resort of La Thuile in the Aosta valley, one of the most important conferences in high energy physics, Christoph Langenbruch, on behalf of the LHCb collaboration, has presented their updated analysis of $B\to K^*\mu^+\mu^-$ angular observables and has shown that the tension with the Standard Model is still present (see the announcements here and here).

Thanks to the conference organizers as well as the LHCb collaboration, I was given the honour to be one of the theorists to give some initial interpretations of this measurement. Using the analysis developed with Wolfgang Altmannshofer for our recent paper and exploiting the $B\to K^*$ form factors obtained for a project with Roman Zwicky and Aoife Bharucha, in my talk I showed that in a global fit to all available experimental data, a new physics interpretation (in the so-called Wilson coefficient $C_9$, found already after the previous measurement) is preferred over the Standard Model by $3.7\sigma$ and even $4.3\sigma$ if $R_K$ is included.

While this is extremely interesting, unfortunately this is not yet evidence for the presence of “new” physics. It is still possible we are being fooled by an unexpected QCD effect. An interesting check of the QCD vs. new physics hypotheses is to consider the size of the deviation as a function of the invariant mass-squared of the muons, $q^2$. In the following plot, showing the values preferred by the data, a new physics effect would lead to boxes that align horizontally — i.e., no $q^2$ dependence — while a hadronic effect should have a different $q^2$ dependence. Indeed there seems to be an increasing trend when moving from the left towards the $J/\psi$ resonance (indicated by the first vertical gray line). However, at the moment it is fair to say that the situation is not yet conclusive and both hypotheses — new physics or an unexpectedly large hadronic effect — are still valid and both have interesting implications.

In the near future, it will be extremely intersting to see what LHCb has to say on the ratio of $B\to K^*\mu^+\mu^-$ vs. $B\to K^*e^+e^-$ observables. If muons and electrons indeed behave differently, this should have a visible impact there, even using data already taken in 2012 (but not yet analyzed). In the future, more precise measurements of processes like $B_s\to\mu^+\mu^-$ will certainly solve this puzzle.

[Technical comment: don’t be confused by the three different $3.7\sigma$ numbers here. The first ist the significance of the 2013 LHCb anomaly, which used a theory predictions that many (me included) considered as not conservative enough. The second is the significance of the new tension as obtained by LHCb. This is more conservative because it includes an important source of theory uncertainty (charm loops) not considered in the old analysis. The third is the pull of the $C_9$ new physics solution compared to the SM in our global fit. This uses many more processes and observables, while it does not use one of the bins where the tension observed by LHCb is largest, because we consider this bin to be theoretically unreliable. Using it as well, Joaquim Matias presented a pull of more than $4\sigma$ at the conference. In general, the agreement between the analyses presented by him and by me was very good, which is an important consistency check.]