# FeaturedI B -> s µµ decays: Current status

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1. Apr 13, 2017

### Staff: Mentor

Something curious is going on with these decays. LHCb gives a seminar talk Tuesday next week, a livestream will be available.
Edit: See results discussed starting here

I'll summarize the current status here. I tried to keep most at the advanced (I)-level, but I don't think that always worked. (B)-level summary: We might have found signs of new unexpected physical effects, but the situation is still unclear.

$b \to s \mu^+ \mu^-$ is a rare process in the Standard Model, it involves a flavor-changing neutral current. New physics could introduce a coupling to these particles and alter the frequency or the dynamics of the process. We cannot see isolated quarks of course, so the experiments measure the decays of various B mesons to a hadron containing a strange quark plus the muons, an example is shown in the following image.

An important test is the frequency of these decays ("branching fraction"). To get more precise theoretical predictions, the branching fraction is often compared to the equivent decay with electrons instead of muons. Based on the production processes, the branching ratios for these decays should be nearly identical, only the slightly different phase space leads to a (well-predicted and tiny) difference.

$B^0 \to K^0 \mu \mu$ and $B^+ \to K^* \mu \mu$ -> too low by 2.0 sigma and 2.2 sigma, respectively (the other measurement has been superseded, see the following entry)
$B^+ \to K^+ ll$ -> muons are too rare by 2.6 sigma
$B_s^0 \to \phi ll$ -> muons are too rare by 3 sigma

Individually, all these measurements look like statistical fluctuations. But they all point in the same direction, towards fewer muons.

$B^0 \to K^{*}(\to K^+ \pi^-) \mu \mu$ is a 3-body decay, but due to the quick decay of the $K^*$ 4 particles are produced in total, that makes it interesting to look at the angular distributions. Typically they are studied as function of the invariant mass of the muon pair. Going into all the details would be beyond the scope of this thread (you can read the papers), in summary many parameters are measured. LHCb did the most precise measurement of them so far. One of them, called P'5, shows an interesting deviation at intermediate q-values, see the figure below. How to interpret this?

Wilson coefficients are a set of parameters describing a generic new interaction between four particles via heavy particles. Here is an introduction. LHCb did a fit to these parameters based on the angular analysis of $B^0 \to K^{*}(\to K^+ \pi^-) \mu \mu$. $C_9$ showed a shift of 3.4 standard deviations relative to the SM value. A new spin-1 particle could lead to such a deviation.

This triggered a lot of interest, so other collaborations measured the same decay as well or updated their results for the recent Moriond conference.
Belle result - a similar deviation in P'5, 2.6 sigma
ATLAS result - a similar deviation in P'5, 2 sigma due to the larger uncertainty.
CMS result - no visible deviation, but also with a significant uncertainty

Individually, all these measurements look like statistical fluctuations. But they all point in the same direction, at the same point that is closely linked to $C_9$.

Theorists combined all these results (and a few more with larger uncertainties) to global fits to the Wilson coefficients: Status of the B->K*µ+µ- anomaly after Moriond 2017.
The result? The best fit value for $C_9$ differs from the Standard Model expectation by 4.9 sigma, supported by both the lower number of muons in the decays and the P'5 measurements. Another option is a deviation in both $C_9$ and $C_10$ with opposite sign. This also fits well to the experimental results (with a slightly lower significance), and would correspond to new heavy particles only coupling to left-handed leptons.
LHCb did a similar analysis just based on their own measurements, and got results consistent with the global fit.

Theoretical flavor physics is complicated. It could be that some effects related to QCD were neglected that will turn out to be larger than expected, and explain at least parts of the deviations seen in P'5. It is unlikely that they explain the observed deviations in the decay probabilities, however.

What is next?
There will certainly be more work on the theory side to see how the observed deviations can be explained - either by SM effects or by some plausible new physics model. Personally I am more waiting for updated measurements, either showing this was all a weird statistical fluctuation, or establishing the deviations beyond reasonable doubt. There are deviations inconsistent with plausible new physics models, in this case it is a problem of our understanding of the SM. If the deviations are consistent with new physics models, then these models will make predictions for other measurements. One important example is the rare decay $B_s \to \mu \mu$ - it has the same particles contributing. So far, the uncertainty on its decay frequency is too large to contribute notably in global fits, but that will change soon.

There is the LHCb seminar on Tuesday, and we can expect new results. So far the collaboration has shown the results for $B^0 \to K^{*} \mu \mu$ based on Run 1 data (2011-2012), the dataset collected in 2015 to 2016 should have a similar size. They might double their statistics. I expect more big updates in the next two years based on the 2017 and then 2018 datasets, and ATLAS and CMS can improve their measurements as well.

Edit: See results discussed starting here. More branching fractions with missing muons.

There is another related measurement: The ratio of $B^0 \to D^* \tau \nu$ to $B^0 \to D^* \mu \nu$. As the $\tau$ has a large mass, it is smaller than 1: The SM prediction is 0.25. Belle, BaBar and LHCb measured it. All experimental values are higher, with a combined significance of 3.9 sigma. Again fewer muons...

As various 3-5 sigma excesses in the past showed, new physics is always the most unlikely explanation, unless all possible alternatives have been ruled out. It is probably not new physics. But at least it is a promising place to look. And we'll know more next week.

Last edited: Apr 19, 2017
2. Apr 14, 2017

### dukwon

I should say that the result being presented on Tuesday is Run 1 only. We have not shown this particular measurement before.

3. Apr 14, 2017

### ChrisVer

Why would those effects appear in loops and not tree-level decays? (originates from your mention to the BD*τν vs BD*μν excess)...

4. Apr 14, 2017

### Staff: Mentor

If it is a coupling to $b$,$s$,$\mu$,$\mu$: There is no SM tree-level diagram.

In general, processes without SM tree-level mechanism are more promising places to search for new physics as the SM amplitudes are smaller.

@dukwon: A completely new measurement sounds interesting.

5. Apr 14, 2017

### dukwon

There are previous measurements from the B factories, I should add. Their error bars are much larger though.

6. Apr 18, 2017

### dukwon

Well, here are the slides: https://indico.cern.ch/event/580620/attachments/1442409/2226501/cern_2017_04_18.pdf

The quantity being measured is $$R(K^*) \equiv \frac{B^0 \to K^{*0} \mu^+ \mu^-}{B^0 \to K^{*0} e^+ e^-}$$
Results are on slides 32 and 33:
$R(K^*)=0.660^{+0.110}_{-0.070}\pm0.024$ in $q^2 \in [0.045,1.1]\text{ GeV}^2/c^4$ (2.2~2.4σ below SM)
and
$R(K^*)=0.685^{+0.113}_{-0.069}\pm0.047$ in $q^2 \in [1.1,6.0]\text{ GeV}^2/c^4$ (2.4~2.5σ below SM)

Attached is a plot comparing the results to SM predictions:

This result agrees with the B-factory measurements, but their errors were ~30%.

7. Apr 18, 2017

### Staff: Mentor

Ratio of $B^0 \to K^* \mu \mu$ to $B^0 \to K^* ee$.
2.2-2.4 sigma below the different SM predictions in the lowest bin of dilepton invariant mass.
2.4-2.5 sigma below the different SM predictions in the lowest bin of dilepton invariant mass.

Again missing muons...

Edit: dukwon was faster.

5/fb expected in Run 2, together with higher energy and better triggers this could give a 5 times larger dataset. As the analysis is limited by statistics, the uncertainty should reduce by more than a factor 2. If the central value stays the same, it would give a 5 sigma deviation in both bins.

An interesting detail about the electrons:
The LHCb electron energy measurement is mainly based on the tracking system, which means bremsstrahlung emitted before passing the magnet is a problem. LHCb developed a system to add bremsstrahlung photons to the reconstructed electrons. This is different to ATLAS and CMS which mainly rely on their calorimeters.

8. Apr 19, 2017

### Staff: Mentor

@dukwon collected some theory papers that popped up.

Patterns of New Physics in b→sℓ+ℓ− transitions in the light of recent data
Interpreting Hints for Lepton Flavor Universality Violation
Flavour anomalies after the RK∗ measurement
RK and RK∗ beyond the Standard Model
Towards the discovery of new physics with lepton-universality ratios of b→sℓℓ decays
On Flavourful Easter eggs for New Physics hunger and Lepton Flavour Universality violation

Different flavours sorry of the same interpretation: 3.5 to 5 sigma tension with the Standard Model depending on what exactly you consider. Could be explained by a variation of C9, or potentially C9 and C10.

A larger C10 would make the decay Bs -> μμ more frequent, but even the recent LHCb measurement is not yet precise enough to contribute notably to fits.

Leptoquarks are a viable model.
A Z' could explain it.
Even with more precise measurements, if the deviation gets more significant, it will be challenging to figure out what exactly is correct.