Hint of a crack in standard model

20 December 2022

lhc construction.jpeg
A detector of the LHCb experiment under construction.Credit: Brice, Maximilien; CERN

A once-promising hint of new physics from the Large Hadron Collider (LHC), the world’s largest particle accelerator, has melted away, quashing one of physicists’ best hopes for a major discovery.

The apparent anomaly was an unexpected difference between the behaviour of electrons and that of their more-massive cousins, muons, when they arise from the decay of certain particles.

But the latest results from the LHCb experiment at CERN — Europe’s particle-physics laboratory near Geneva, Switzerland, which hosts the LHC — suggest that electrons and muons are produced at the same rate after all.

“My first impression is that the analysis is much more robust than before,” says Florencia Canelli, an experimental particle physicist at the University of Zurich in Switzerland who is a senior member of a separate LHC experiment. It has revealed how a number of surprising subtleties conspired to produce an apparent anomaly, she says.

Renato Quagliani, an LHCb physicist at the Swiss Federal Institute of Technology in Lausanne, reported the results at CERN on 20 December, in a seminar that attracted more than 700 viewers online. The LHCb collaboration also posted two preprints on the arXiv repository1,2.

Unbalanced decay
LHCb first reported a tenuous discrepancy in the production of muons and electrons in 2014. When collisions of protons produced massive particles called B mesons, these quickly decayed. The most frequent decay pattern produced another type of meson, called a kaon, plus pairs of particles and their antiparticles — either an electron and a positron or a muon and an antimuon. The standard model predicted that the two types of pair should occur with roughly the same frequency, but LHCb data suggested that the electron–positron pairs occurred more often.

Particle-physics experiments frequently produce early results that slightly deviate from the standard model, but turn out to be statistical flukes as the experiments collect more data. But that didn’t happen this time. Instead, as time went on, the B-meson anomaly seemed to become more conspicuous, reaching a confidence level known as 3 sigma3 — although it still did not reach the level of significance often used to claim a discovery, which is 5 sigma. A number of related measurements on B mesons also revealed deviations from theoretical predictions based on the standard model of particle physics.

The results reported this week included more data than the previous LHCb measurements of B-meson decays, and a more thorough study of possible confounding factors. The apparent discrepancies in the earlier measurements involving kaons turned out to be caused in part by misidentifying some other particles as electrons, says LHCb spokesperson Chris Parkes, a physicist at the University of Manchester, UK. Although LHC experiments are good at catching muons, electrons are trickier for them to detect.

Refocusing the search
The result is likely to disappoint many theorists who have spent time trying to come up with models that could explain the anomalies. “I’m sure people would have liked us to find a crack in the standard model,” says Parkes, but in the end, “you do the best analysis with the data you have, and you see what nature gives you”, he says. “It’s really how science works.”

Although the latest result had been rumoured for months, its confirmation comes as a surprise, says Gino Isidori, a theoretical physicist at the University of Zurich who was at the CERN talk, because a coherent picture seemed to be emerging from related anomalies. This could have pointed to the existence of previously unseen elementary particles that affect the decay of B mesons. Isidori gives the LHCb collaboration credit for being “honest” in admitting that its previous analyses had problems, but he regrets that it took so long for the collaboration to find the issues.

However, some other anomalies, including some recorded in B-meson decays that do not involve kaons, could still turn out to be real, Isidori adds. “Not all is lost.”

Marcella Bona, an experimental physicist at Queen Mary University of London who is part of yet another LHC experiment, agrees. “It looks like theorists are already thinking about how to console themselves and refocus.”

The remaining hopeful hints of new physics include a measurement that found the mass of a particle called the W boson to be greater than expected, announced in April. But a separate anomaly, also involving muons, could be going away. The muon’s magnetic moment had seemed to be stronger than predicted by the standard model, but the latest theoretical calculations suggest that it is not, after all. Instead, the discrepancy could have originated in miscalculations of the standard model’s predictions.

doi: https://doi.org/10.1038/d41586-022-04545-z

See: https://www.nature.com/articles/d41586-022-04545-z?utm_source=Nature+Briefing&utm_campaign=b8aaa29e9f-briefing-dy-20221221&utm_medium=email&utm_term=0_c9dfd39373-b8aaa29e9f-46554234

Theoretically, muons and electrons are very similar except for their mass, both of them can interact with electromagnetic field. So my question is, why only muons can get to Muon Chambers, or why muons can get to Muon Chambers but not be detected in EM Calorimeter.

Muons can more easily penetrate more material. Typically in most detectors there is a distinguishable pattern between muons and electrons. A clear example would be data from the Super Kamiokande detector where one detects Cerenkov radiation* coming from electrons/muons.

cerenkov muons.jpeg

The "fuzzines" of the right circle means that the light came from an electron which got scattered and emitted a few Bremsstrahlung photons.

The point of all this is to show you that just the difference in mass is enough to make the Muon penetrate a lot more material than the electron. This is due to the fact that the (simplified) formulas for Bremsstrahlung** are:




and both are proportional to the acceleration SQUARED! The force applied on both particles from the material in the calorimeter for example is the same (just an E-field), but due to the different masses, the electron has a lot bigger acceleration, thus loses more energy. This of course is simplified, since if you are calculating it precisely you need to take relativistic effects into account, but the intuition is the same.

Muons are about 200 times heavier than electrons; muons are about 100 MeV, whereas electrons are about 0.5 MeV. It follows that whereas an electron is stopped in the ECAL, a muon just ploughs through it and into the muon chamber, as illustrated by this cartoon from this blog post about the muon.

With the usual expressions (e.g. 𝑝=𝑚𝑣p=mv), we find that a muon retains about 99%99% of its initial velocity, 𝑣𝑖vi,


where 𝑣𝑓v is its final velocity and most of the energy loss for muons comes from multiple soft scatterings. An electron, on the other hand, retains none of its velocity, 𝑣𝑓=0vf=0, as in an elastic collision between balls of equal mass, the balls simply 'swap' velocities.

Muons are detected in the electromagnetic calorimeter as charged tracks. They are not identified as muons and go through as possible hadrons: protons, charged kaons, pions . The hadronic calorimeter detects the hadrons by their strong interactions with the material, and the muon detector makes sure that the track going through has only electromagnetic and weak interactions as it has gone through so much hadronic mass without interaction. Thus it is identified as a muon, by exclusion of other possibilities and use of the standard model which has no other charged weakly interacting particles.

See: https://physics.stackexchange.com/questions/355652/whats-the-difference-between-muons-and-electrons-in-experiment

* Cerenkov radiation: is light produced by charged particles when they pass through an optically transparent medium at speeds greater than the speed of light in that medium. Devices sensitive to this particular form of radiation, called Cherenkov detectors, have been used extensively to detect the presence of charged subatomic particlesmoving at high velocities.

Cherenkov radiation, when it is intense, appears as a weak bluish white glow in the pools of water shielding some nuclear reactors. The Cherenkov radiation in cases such as this is caused by electrons from the reactor traveling at speeds greater than the speed of light in water, which is 75 percent of the speed of light in a vacuum. The energetic charged particle traveling through the medium displaces electrons in some of the atoms along its path. The electromagnetic radiation that is emitted by the displaced atomic electrons combines to form a strong electromagnetic wave analogous to the bow wave caused by a power boat traveling faster than the speed of water waves or to the shock wave(sonic boom) produced by an airplane traveling faster than the speed of sound in air. The phenomenon was discovered by the Soviet physicist Pavel A. Cherenkov in 1934 and was explained by Ilya M. Frank and Igor Y. Tamm in 1937.

See: https://www.britannica.com/science/Cherenkov-radiation

** Bremstrallung: from bremsen "to brake" and Strahlung "radiation" or as in Lichtstrallung, or light "waves"; i.e., electromagnetic radiationproduced by a sudden slowing down or deflection of charged particles (especially electrons) passing through matter in the vicinity of the strong electric fields of atomic nuclei. Bremsstrahlung, for example, accounts for continuous X-ray spectra—i.e., that component of X rays the energy of which covers a whole range from a maximum value downward through lower values. In generating bremsstrahlung, some electrons beamed at a metal target in an X-ray tube are brought to rest by one head-on collision with a nucleus and thereby have all their energy of motion converted at once into radiation of maximum energy. Other electrons from the same incident beam come to rest after being deflected many times by the positively charged nuclei. Each deflection gives rise to a pulse of electromagnetic energy, or photon, of less than maximum energy.

Internal Bremsstrahlung arises in the radioactive disintegration process of beta decay, which consists of the production and emission of electrons (or positrons, positive electrons) by unstable atomic nuclei or the capture by nuclei of one of their own orbiting electrons. These electrons, deflected in the vicinity of their own associated nuclei, emit internal bremsstrahlung.

Bremsstrahlung is one of the processes by which cosmic rays dissipate some of their energy in the Earth’s atmosphere. Solar X rays have been attributed to bremsstrahlung generated by fast electrons passing through the matter in the part of the Sun’s atmosphere called the chromosphere.

See: See: https://www.britannica.com/science/bremsstrahlung

The only difference between muons and electrons is that 𝑚𝜇≫𝑚𝑒, so a simple explanation of their different behaviours in detectors, based on this fact, should exist. However, the big difference is in the response to acceleration: electrons generate a lot more Bremstrallung.
Mar 18, 2023
Hint of a Crack in the Standard Model is an intriguing and thought-provoking read. It takes a deep dive into the world of physics and explores the implications of the current theories of the universe. The author does an excellent job of explaining the science behind the theories and how they could be used to explain the recent results from CERN. The book also provides a great overview of the history of particle physics and the development of the Standard Model, as well as a glimpse into the potential future of the field.
A very good, and modern, introduction to the theory of the standard model is given by Matthew D. Schwartz's book 'Quantum field theory and the standard model'. A more in depth book on the dynamics of the standard model is the book 'Dynamics of the standard model' by John F. Donoghue, Eugene Golowich, et al.

These two books are a good place to start.


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