The discrepancy between the LHCb data and the predictions of the Standard Model has increased

The discrepancy between the LHCb data and the predictions of the Standard Model has increased

Fig. one. LHCb detector internals. A curved 1600-ton magnet, whose coils are visible in the picture, separates the trajectories of charged particles and allows us to reconstruct the processes of meson decay. The photo was taken in December 2018 during planned works. Photo from the site

The LHCb collaboration, having completed the processing of all the statistics collected to date, published the long-awaited results on testing lepton universality in rare B-meson decays. Lepton versatility is the cornerstone of the Standard Model, so the hints of a violation of it a few years ago have caused a stir among theorists. The new results confirm the discrepancy; its statistical significance rose to 3.1 standard deviations.

Six or seven years ago, many physicists who studied the world of elementary particles were waiting for the upcoming fundamental discoveries. The first run of the Large Hadron Collider revealed several very curious deviations from the predictions of the Standard Model. Some of them belonged to energies above 1 TeV, and theorists saw in them hints of new heavy particles, which promised a whole fireworks of discoveries. Other deviations concerned the properties of the Higgs boson discovered the day before, which led many physicists to seriously suspect that the Higgs mechanism in our world is not at all as boring as postulated in the Standard Model. Finally, there have been unpredictable deviations in the rare decays of B mesons, well-known particles that have been explored far and wide for decades.

Hardly anyone believed that all these deviations were real; undoubtedly some of them are caused by statistical fluctuations in the small statistics of events. But in the discussions and debates of theorists about these deviations, there was clearly an expectation that it would be worthwhile to push a little, accumulate several times more data, and a New physics beyond the Standard Model would be discovered, the main goal of the Large Hadron Collider would be achieved.

In 2015, the second run of the collider, LHC Run 2, started. The collision energy increased, statistics increased at record rates – and as the incoming data was processed, the experimenters mercilessly closed one deviation after another. By the beginning of 2018, all hints of something unusual in the properties of the Higgs boson and in the high-mass region had disappeared.

However, the deviations in B-meson decays were surprisingly persistent. As the experimental groups – in particular, the LHCb collaboration – processed more and more new data and improved the analytical methodology, the errors decreased, but the deviations from the Standard Model persisted. Moreover, these deviations concerned three types of measurements, which differed greatly both in the processing methods, and in the volume of statistics, and in the errors of theoretical calculations (see details on the page Collider Riddles for 2018). Each of these discrepancies with the predictions of the Standard Model, taken in isolation, did not look like a reinforced concrete discovery; the statistical significance of the deviation was within 2–4 standard deviations. But all these hints, so different in their manifestations, surprisingly did not contradict each other, but, on the contrary, asked for a single explanation: something wrong is happening during the decays of B-mesons into muons. At conferences in 2018, it was the discussion of these anomalies in B-meson decays that became the hottest topic in particle physics (see Moriond 2018 news: anomalies in B-meson decays remain a hot topic, “Elements”, 03/15/2018).

One of these mysteries was the inexplicable violation of lepton universality in the decays of B mesons into K mesons and a lepton pair – or an electron-positron e+e, or muon-anti-muon μ+μ… These are rare decays, with a probability of less than one millionth. This smallness arises because in the framework of the Standard Model there is no particle that would be able to directly transform b-quark inside the B-meson in s-quark inside the K-meson. This process takes place inside the meson in several stages and requires the “help” of heavy virtual particles (Fig. 2). But since the contribution of the Standard Model is so small, then the weak effects of hypothetical New Physics, which cannot be noticed in other decays, can become significant here.

Fig.  2. Schematic representation of the decay of a B-meson into a K-meson and a muon-anti-muon pair

Fig. 2. Schematic representation of the decay of a B meson into a K meson and a muon-anti-muon pair. Transformation b-quark in s-quark occurs in a complex way, and it is possible that new, so far undiscovered particles manifest themselves in it

If the probabilities of each of these decays could be theoretically predicted with high accuracy, then it would be sufficient to compare measurements with calculations. Unfortunately, the theoretical uncertainties in these probabilities are too great due to the fact that it is necessary to calculate the transformation of mesons into each other; this is the eternal misfortune of hadronic physics, and there is no escape from it. but attitude decays is the probability of decay into Kμ+μ divided by the probability of decay into Ke+e – it is predicted quite reliably: after all, in both decays the mesons are the same, and poorly calculated parameters are canceled. This ratio, which is denoted by RK, in the Standard Model is almost equal to one.

The unit is not accidental here. Within the Standard Model, a property called lepton universality is postulated. This means that the weak interaction acts in the same way (that is, universally) on leptons of any kind. If some experiment will reliably show that the lepton universality of the weak interaction is violated, then this result cannot be dismissed – nothing else can be changed in the Standard Model, it is completely fixed. Therefore, the reliable difference RK from unity will become a long-awaited discovery of New physics; a discovery, albeit indirect, but worthy of the Nobel Prize.

In 2014, the LHCb collaboration, after analyzing data from the Run 1 session, reported that RK indeed, much less than one: its value turned out to be approximately equal to 0.745 with an error of about 0.1. On the one hand, the difference is significant, by almost a quarter. On the other hand, the error is large: the deviation from unity was approximately 2.6 standard deviations. In 2017, a similar deviation in decay into an excited K * meson was published (Another hint of violation of the Standard Model was found at the LHC, “Elements”, 04/20/2017). This is a different process, with its own subtleties of analysis, but here the relation (it is denoted by RK *) was less than one.

Are these deviations real or is it just another “joke of nature” before us, when the statistical fluctuation confuses physicists? Of course, only new, more accurate experimental results can answer this question. In 2018, the Run 2 dataset session ended, but the LHCb collaboration continued to methodically analyze the data, repeatedly rechecking all possible sources of error.

In 2019, LHCb released a new article on the relation RK (R. Aaij et al., 2019. Search for Lepton-Universality Violation in B+→ K++ Decays). The statistics have grown, the errors have decreased, however, the deviation from unity has also decreased – and as a result, the statistical significance of the deviation from the Standard Model even slightly weakened. One got the feeling that this collider mystery would soon come to naught.

And the other day, after several years of painstaking work, the LHCb collaboration finally presented an analysis of all the statistics of the Run 2 session, which was about twice the sample used in 2019. R valueK turned out to be approximately 0.846 ± 0.044, which differs from unity by 3.1 standard deviations. In fig. 3 shows how the new value compares with the previous ones. It can be seen that, in comparison with the result of 2019, the error has noticeably decreased, but the central value hasn’t moved anywhere… This is a very encouraging signal! Over the past years, experimenters have thoroughly studied their installation and analysis methodology, they know all their weaknesses and errors, they can not only correctly assess them, but also compensate (in the analysis, not just an attitude, but a double attitude was used, see details in the news. another hint of violation of the Standard Model, “Elements”, 20.04.2017), and are also able to reliably control the quality of compensation. In order not to seem that the experimenters specially adjusted the data to the desired result, it is worth emphasizing that the entire analysis technique was debugged and fixed before a new portion of data was added to the analysis.

Fig.  3. Results of testing lepton universality in terms of the ratio RK

Fig. 3. Results of testing lepton universality through the ratio RK according to the data of various experiments: in the BaBar and Belle detectors at the electron-positron colliders and in the LHCb detector on the ever increasing statistics. Black dot with errors – the value of 2021. Vertical dotted line – prediction of the Standard Model. Chart from

An indication of the ever-growing confidence of the experimenters themselves in the reality of the observed deviation is the very formulation of the result: not just a test of lepton universality, but an indication of its violation. Experimenters are usually very conservative in their statements and do not throw such words down the drain. Finally, it is worth noting that a new article has been submitted to the journal Nature physics, which is also not typical for particle physics. And since statistical error still dominates over systematic error, you can be confident that a new run of the collider, LHC Run 3, which starts next year, will further expose the discrepancy with the Standard Model – if it persists, of course. In the long term, you can count on at least a threefold decrease in errors.

How should the deviation be interpreted, if it is real? On this score, theorists already have dozens of hypotheses and models of varying degrees of sophistication. There is no doubt that in the coming days and weeks dozens of new theoretical works will appear with one or another explanation or clarification of past calculations. But the analysis of theoretical interpretations is another story.

In the meantime, judging by the synopsis on the LHCb results page, we will soon find out new LHCb results on other B-meson decays. Hopefully, the discrepancy with the Standard Model will sharpen on several fronts at once and the LHCb detector, unexpectedly for many, will become our flagship in the study of the depths of the microworld.

A source: LHCb Collaboration. Test of lepton universality in beauty-quark decays // arXiv preprint: 2103.11769 [hep-ex]…

See also:

1) Intriguing new result from the LHCb experiment at CERN – short news on the CERN website.
2) Materials of the LHC Seminar at CERN New results on theoretically clean observables in rare B-meson decays from LHCb, March 23, 2021.

Igor Ivanov

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