Here is the new physics that could be around the corner

Here is the new physics that could be around the corner

The anomaly in the value of the magnetic moment of muons measured at Fermilab could be an indication of the existence of a force of nature or of particles that we do not yet know. Or, more simply, it could be an error

(Photo: Reidar Hahn / Fermilab) On April 8, the collaboration of physicists of the Muon g-2 experiment, conducted at the Fermilab in Chicago, announced that it had observed an anomaly in the behavior of a particular type of subatomic particles, the muons. The long-awaited statement (the data was collected in 2018 and it took three years to complete the analysis) caused a major shock in the scientific community, since the anomaly, if confirmed, could imply the existence of a new physics not contemplated by the Standard Model of elementary particles, the theoretical framework that contains the description and behavior of all particles currently known to science. The reactions were not long in coming: just a few days after the announcement, over 30 theoretical articles were uploaded on the ArXiv portal (the Cornell University server that hosts the scientific articles before their publication in the journal). , calling into question, among other things, new forces of nature and new particles with exotic names such as fakeons and dark photons.

The protagonists of the story

To bring order to this story we need starting from afar. Muons are elementary particles produced, in nature, by the interaction of cosmic rays with the earth's atmosphere and considered the heavy cousins ​​of electrons: they have the same electric charge (negative), but are 207 times heavier; they are quite unstable, and radioactively decay into electrons and other superlight particles (neutrinos) in just over 2 millionths of a second.

They were discovered in 1936 by Carl David Anderson and Seth Neddermeyer, quite unexpectedly (it is said that physicist Isaac Rabi, Nobel laureate in 1944, commented on the discovery by exclaiming "And who ordered these?" ), and for some time many have minimized its importance, thinking that they would not have had a prominent role in the stage of particle physics. It was not so: among the properties of muons, in fact, there is the so-called gyromagnetic factor, a quantity that is indicated by the letter g and which measures their interaction with an external magnetic field. When they are immersed in a magnetic field, in fact, muons behave like small magnets, which move - or more correctly precede - as the rotation axis of a spinning top would do.

Now, one of the many oddities of quantum mechanics is that relating to the vacuum: in the microscopic world the vacuum is never really empty, but populated by virtual particles that appear and disappear continuously, so that each particle is constantly surrounded by an entourage of other particles, which affects behavior. According to the predictions of the theory, the gyromagnetic factor g of a solitary muon should have a value equal to 2; but since a muon is never alone, the formula must be corrected to take into account its entourage: it is for this reason that the muon's gyromagnetic factor is slightly higher than 2, and it is precisely this phenomenon that gives its name to experiment. Muon g-2 is an attempt to measure the discrepancy of the value of g with respect to the predictions: the magnitude of the deviation of g somehow gives us a measure of what we do not yet know.

The experiments: Brookhaven and Fermilab

Muon g-2, by the way, is not the first experiment to try to measure the value of the muon's magnetic moment. In the seventies an experiment conducted at CERN and led by physicist Emilio Picasso measured the g-2 of the muon with a precision not yet sufficient to search for new physics signals. Then, in 2001, Chris Polly and colleagues, then in force at Brookhaven National Laboratory, tried to do so using the Alternating Gradient Synchrotron, a particle accelerator capable of creating beams of muons and sending them into a ring in which superconducting magnets were placed. . And even at the time, actually, the measured value turned out to be different from the predictions of the Standard Model, but the statistical significance of the result was too low to be able to officially declare a new discovery.

The current experiment has begun in 2018 and went much further, with a more intense photon beam and with the declared goal of collecting a volume of data 20 times higher than in the previous attempt (in the meantime, while the experimentalists were busy with particle accelerators , theorists did not sit idle: in 2020 a group of 170 physicists of the so-called Muon g-2 Theory Initiative recalculated the theoretical value of g, confirming the discrepancy found in Brookhaven).

I results are consistent with those of 2001 and, combined together, allow us to state that the experimental value of g is distant from the theoretical one with a significance of 4.2 sigma, which is equivalent to say that the probability that the measure took place by chance is 1 in 40 thousand. Very low, of course, but still not enough: to make a discovery "beyond reasonable doubt" official, the scientific community, in fact, requires a significance of 5 sigma, corresponding to a probability of error of 1 in 2 million. To get there we will have to wait a little longer: "The result we have just announced", explained Graziano Venanzoni, researcher at the National Institute of Nuclear Physics and co-spokesperson for the experiment, "is related to 6% of the data that will come products. At the moment we have already acquired the data of the second and third runs, performed between 2019 and 2020, and their analysis should be ready in a couple of years. With this new information we expect to reduce the uncertainty by a factor of 2, thus obtaining an even more precise measurement of g ".

Other (theoretical) calculations

Before illustrating the scenarios opened by the discovery, it is necessary to point out, among the many reactions of the community, that of the Budapest-Marseille-Wuppertal Collaboration (BMW), a collaboration of physicists who have used another method to calculate (theoretically) the interactions of the muon with the magnetic field. As coordinator Zoltan Fodor, of Penn State University explains in The Conversation, the discrepancy between the theoretical and experimental values ​​of g essentially opens up three possibilities: first, it is the theoretical prediction that is not correct; second, it is the experimental value that is not correct; third (the most intriguing), there is a force of nature that we do not yet know. While at Fermilab they concentrated on the second possibility, refining the experimental measure of g, Fodor's team chose to pursue the first path, looking for an alternative way to recalculate the theoretical value of the magnetic moment.

In general , the four interactions we currently know are the gravitational force, the electromagnetic force, the weak interaction, responsible for radioactive decays, and the strong interaction, which holds neutrons and protons together in the nuclei of atoms. Apart from the gravitational force whose contribution is negligible, the other forces contribute to the magnetic moment of the muon: today we know with great precision the contributions that come from the weak interaction and electromagnetism, but calculate the contribution of the strong interaction (the so-called leading order hadronic vacuum polarization) is much more complicated. To do this, physicists have so far used a mixed approach, both theoretical and experimental: they collect data from the collisions between electrons and positrons and use them to measure the contribution of the strong interaction to the muon's magnetic moment.

Fodor and colleagues have developed an alternative approach, very reminiscent of the one used for weather forecasts, in which temperature, wind speed and pressure data collected by aircraft at precise points in the earth's atmosphere are placed in a spatial grid and then used in the equations that predict the evolution of the weather: in the same way, the physicists of the BMW collaboration inserted the basic equations of the strong interaction in a spacetime lattice and used the processors of several supercomputers from all over Europe to calculate the contribution of the strong interaction to the magnetic moment. By doing so, they produced an estimate of g which appears to be consistent with the experimental value measured first at Brookhaven and then at Fermilab. Or at least more consistent than that produced by traditional theoretical models: "If our calculations were correct", Fodor concludes, "the gap between theory and experimental measurements would close, and with him also the possibility of a new physics behind these experiments ". The results of Fodor's group have been published in a letter in Nature.

What new physics do we expect?

It is precisely about this that we first ask Venanzoni for explanations. . “We are extremely happy with all the reactions aroused by our work,” he tells us. “Science works like this, for small continuous advances. The conclusions of our experiment, on which I feel very confident, refer to the standard theory; if a scenario opens in which there are new theoretical predictions, so be it: now the ball passes to the theoretical physicists, who will have to check the calculations and establish which are the most correct ones. In any case, after a couple of years the analysis of the new data should also be ready, with a statistic four times higher than the one we have analyzed today: at that point we could know with greater certainty. We are in a very electrifying phase, in which different scenarios can be opened. ”

Having made all these premises, we finally come to the most interesting question: if the discrepancy were to be confirmed, what new physics could come? What physicists are hoping for is a significant step forward compared to the Standard Model, a very solid theory that however has some limitations: "The Standard Model is a splendid 50-year-old who looks no more than twenty years old", explains Venanzoni, "since almost all his predictions are promptly confirmed by experiments. However, there are still some unclear and problematic aspects. One of these, for example, lies in the fact that the Standard Model presents us with the fundamental constituents of matter in three different families (electron, muon and tau, with the relative neutrinos) which are completely identical if not for mass; these three families also replicate for quarks. In addition, the model also includes the mediators of three of the forces we know (gravity, at this moment, is still excluded) ”. But, adds Venenzoni, “the problem is that the model tells us nothing about why there should be three families: the measurement of g could help to understand why the muon is an exact copy of the electron but with a different mass, why there is a need for its existence in the universe, and if there are other degrees of freedom of the theory in which families can be unified, that is, another perspective in which electrons and muons are the same particle. This is why muons are so important. ”

Standard Model Scheme (Image: Kush / Wikimedia Commons) Another small flaw in the Standard Model is that it does not predict the existence of elusive matter dark and even more elusive dark energy: what are they really? Why do they exist? "This is a very complex problem, and still open," comments the scientist. “Someone tried to explain it through a change in gravity; there may also be new particles, or new forces, whose existence still eludes us. Once again, the answer to all these questions could come from g-2, which in this sense is a kind of probe that leads us to understand the new physics ”. Among all the ideas proposed to explain the observed discrepancy, Venanzoni cites for example supersymmetry, a theory that predicts that each particle has a symmetrical counterpart with a different mass, and the existence of so-called leptoquarks, hypothetical particles that could interact with quarks and leptons. But, at the moment, it is only a matter of hypotheses: while at Fermilab they will analyze the new data, it will be up to the theorists to try to unravel the problem. Which promises to be quite intricate.

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