Belle Experiment At LHCb Finds No Evidence Of Lepton Flavor Universality Violations

Executive Summary: No New Physics

A compilation of all of the Belle collaboration data to date shows no statistically significant evidence of lepton flavor universality violations in B meson decays, which are prohibited by the Standard Model. Evidence of anomalies from earlier data with a smaller sample size has grown less significant as more data has been collected.

This doesn't quite, by itself, but the nail in the coffin of this hint of beyond the Standard Model physics, but it comes close. Upcoming work by a successor Belle II collaboration, measuring the previously anomalous quantities to greater precision, will be more definitive.

One Small Anomaly In Something Else Was Seen

There was one modest statistical tension in the latest Belle data between a Standard Model expectation that is distinct from a lepton universality violation, which is that there would be no semi-leptonic decays of B mesons to kaons with a muon-electron mix, rather than a lepton and anti-lepton of the same flavor as expected, out of four channels tested, with no signal in the other three channels of semi-leptonic B meson decays studied. 

But given look elsewhere effects, the marginal strength of the signal near the boundary of what the experiment can detect (the best fit to its frequency was one per 20 million events in one decay channel), and the small absolute number of events involved, this result is not very notable and is probably just a statistical fluke. 

Unlike the lepton universality violations looked for in the new study, there was no statistically significant evidence of this anomaly from prior experiments at Belle or in other collaborations before the study was done, further heightening the look elsewhere effect impact on its significant. This and a lack of replication casts doubt about the reality of this marginally statistically significant tension with the Standard Model. 

Background

In the Standard Model of Particle Physics, electrons, muons and tau leptons should have exactly the same properties apart from their masses, something called "lepton flavor universality" subject to distinctions to slight to measure caused by interactions in intermediate loops of decays and interactions with oscillating neutrinos whose different types do not behave identically (with their differences described by the PMNS matrix).

One of the hottest areas of fundamental physics in recent years has been the detection of anomalies in B meson decays (a B meson is a two valence quark particle in which at least one of the valence quarks is a b quark) into leptons, that seems to deviation from lepton universality. Individually, none of these anomalies is significant enough to amount to a discovery of new physics, although it is possible (although challenging) to imagine new physics that could explains the anomalies seen in multiple channels which start to look very significant if they are all evidence of the same new physics phenomena. 

A Headache Avoided

This new result from Belle is reassuring, because previously observed anomalies were hard to explain. This is because the decays in which the anomalies were observed are generally believed to arise from a process (W boson decays) that are shared with many other kinds of decays where larger data sets have shown no evidence for the same anomaly, and the Standard Model process assumed to be at work in B meson decays otherwise comes very close to accurately explaining the B meson decays that were observed (e.g. it predicted the overall number of decays accurately).

Lepton universality violations are not seen in W boson decays at the LHC, are not found in tau lepton decays or pion decays (also here), and are not found in anti-B meson and D* meson decays or in Z boson decays, even though all of those examples involve the same kind of weak force decay believed to be involved in B meson decays.

If the old lepton universality anomaly was real, something very big had to have been wrong with our understanding of hadron decays in the Standard Model, even though the Standard Model works basically perfectly in all other hadron decay contexts.

But you would expect statistical flukes (possibly amplified by understated systemic errors) to be seen in early B meson decays data, if they are seen anywhere. This is because the high energies necessary to create B mesons means that the data sets for these decays are the smallest of the various decays where lepton universality could be studied. So the fact that there was an early anomaly in early B meson decay data that has faded as more data has been collected, makes sense.

If the lepton flavor universality violation anomaly seen in prior studies was a real "new physics" effect, it should have gotten stronger, not weaker, as the size of the data set increased. 

The New Results In Detail

A new pre-print is entitled "Test of lepton family universality and search for lepton and baryon number violation at Belle" (and incidentally follows the desirable practice of listing only the corresponding author the the collaboration as authors, rather than comprehensively listing every scientist in the collaboration individually).

The Lepton Flavor Universality Violation Measurement 

The headline result is its test of lepton flavor universality. This updated result analyzes: "the results obtained from a multidimensional fit performed on the full Υ(4𝑆) data sample of Belle. . . .  Following four channels are studied: 𝐵 + → 𝐾+ 𝑒 + 𝑒 − , 𝐵 + → 𝐾+𝜇 +𝜇 − , 𝐵 0 → 𝐾 0 𝑆 𝑒 + 𝑒 − , and 𝐵 0 → 𝐾 0 𝑆 𝜇 +𝜇 − based on 711 fb−1 Υ(4𝑆) data corresponding to 772 × 10^6 𝐵𝐵 events."

In other words, it looked the semi-leptonic decays of two kinds of B mesons, (1) the decay of charged B mesons into a charged kaon and either an electron-positron pair, or a muon-antimuon pair, and (2) the decay of neutral B mesons into a neutral kaon and either an electron-positron pair, or a muon-antimuon pair. In all it analyzed 772 million B meson decays, the complete set of B meson decays from excited Y(4,S) resonances into B meson pairs from the experiment to date.

If the Standard Model is correct, the ratio of semi-leptonic B meson decays to muon-antimuon pairs to semi-leptonic B meson decays to electron-positron pairs (called R(K) should be equal to exactly one, subject only to random statistical errors (since the laws of quantum physics govern probabilities rather than being deterministic), to asymmetries induced from neutrino interaction loops which should be much smaller than the statistical uncertainties, and to systemic experimental measurement errors that are well quantified in heavily used experimental setup.

The results were also segregated into "q squared" bins that reflect the energy scale of the interaction produce the B mesons in each decay. The number of events in each bin has an uncertainty in it because most of the 772 million decays don't involve the semi-leptonic decays a B mesons to kaons studied, and the scientists had to segregate out background events from the decays that they were actually studying, which can't be distinguished with perfect accuracy. In the end, there were only about 275 charged B meson decays and 49 neutral B meson decays in the sample analyzed.

From the fit we obtain 137 ± 14 and 138 ± 15 events in 𝐵 + → 𝐾+𝜇 +𝜇 − and 𝐵 + → 𝐾+ 𝑒 + 𝑒 − decays, respectively. Similarly, the yields for the neutral channels 𝐵 0 → 𝐾 0 𝑆 𝜇 +𝜇 − and 𝐵 0 → 𝐾 0 𝑆 𝑒 + 𝑒 − are 27.3 + 6.6 − 5.8 and 21.8 + 7.0 − 6.1 events. 

These results were consistent with the Standard Model expectation of a ratio of one to one at the two sigma level used to distinguish between normal statistical variation in experiments like this and tensions that are considered anomalies that deviate from the Standard Model expectation. 

The previous data had shown a 2.4 sigma tension with the Standard Model in the neutral kaon decay channel and a 2.5 sigma tension in the charged kaon decay channels studied by Belle.  Moreover, the direction of the deviation from a perfect one to one ratio in the neutral B meson decay where it was stronger in the current study in terms of the deviation of the best fit ratio from one to one (although with more uncertainty) than in the charged B meson decay in the current study, was in the opposite direction of the previous anomalies. The previous data showed too few muon events in neutral B meson decays relative to the electron events, while this study showed too many. 

Another 3.4 sigma tension seen in the prior data was restricted to a somewhat odd ball measurement, that normally wouldn't attract attention, in a narrow energy scale bin, and can be viewed as a physicists version of p-hacking to find a statistical fluke in a way that doesn't properly account for look elsewhere effects. 

This particular study from Belle didn't examine the fourth channel in which a 3.7 sigma tension with the Standard Model was observed in previous data, involving a different kind of semi-leptonic B meson decay than the decays to kaons reviewed in this pre-print.

Semi-Leptonic Mixed Lepton Flavor Decays

The search also looked for semi-leptonic decays to kaons with a mix of electrons and muons which should not happen in the Standard Model. 

The maximum frequency of such decays consistent with observation was constrained by an additional order of magnitude relative to prior studies to not more than parts per 100 million in three of four channels.

But, in the only notable result of the study, there was 3.2 sigma evidence (a result in tension with the Standard Model) of some anomalous decays in the charged B meson to charged kaon together with a muon and a positron channel at an apparent rate of one such decay per 20 billion charged B meson decays, but with considerable uncertainty in the magnitude of the anomaly that at the low end could be very close to zero. Once look elsewhere effects are considered, this results is somewhat less notable.

Baryon Number Violating Tau Decays

Baryon number violating decays in about 841 million tau lepton decays (in which the net number of quarks less antiquarks before and after the decay changes) which are not allowed by the Standard Model, were not observed. Their frequency, if they happen at all, was constrained to be fewer than something on the order of single digit numbers of events per 10 million tau lepton decays.