Another Anomaly Bites The Dust (Not A Muon g-2 Experiment Blog Post)

Background

In modern physics, experimental anomalies are almost always due to boring methodological issues, rather than "new physics." This case is no exception. 

(Also, for physics fans who aren't paying close attention, this IS NOT the big muon g-2 experiment result paper that everyone in the high energy physics world has been waiting for for the past fifteen years. That paper is due out about one to six weeks from now.)

Lots of anomalous experimental results show up involving muons, in part, because the reveal with the hard certainty of experimental measurements, flaws in previous work done with electrons which due to their lower mass are often much less precise.

The Cosmic Ray Muon Excess Anomaly

One such anomaly had been an apparently excess of muons in the debris showers of high energy cosmic rays (which, despite the misleading name, are mostly very fast moving microscopic particles of matter rather than photons). Scientists have been seeing 10-100% more muons than predicted by their Standard Model physics motivated models in the fallout from ultrahigh energy cosmic rays (in other words there is a deficit in the number of muons predicted in simulations).

A new paper from a large collaboration of scientists, however, establishes that the muon excess was illusory and mostly flowed from a small but accumulating error in the number of muons predicted to be present in simulations used to established the predicted number of muons, rather than experimental error or new physics.

So, another intriguing anomaly that might have pointed to beyond the Standard Model physics has disappeared.

Significance

In a nutshell, this matters a lot because it implies that there are probably no new high energy physics phenomena beyond the Standard Model of Particle Physics at energy scales far beyond those we have any hope of probing a new particle colliders in our lifetimes, or even in the lifetimes of our great grandchildren.

It tends to confirm that we have entered a large range of energy scales in which there is a new physics "desert". 

We are very likely in what high energy physics experimentalists sometimes call "the nightmare scenario" in which there is nothing new out there in terms of fundamental physics for them to discover in the course of their careers. 

Sure, they can measure physical constants with greater precision and explore the precisely way that ephemeral exotic particles that form only at extremely high energies form and decay in ways that are profoundly difficult to calculate from first principles. But if we are in the nightmare scenario, then the basic laws of physics formulated in the late 1970s and early 1980s are all that is out there that we have any ability to observe for the foreseeable future.

We may be entering a period in high energy physics akin to the period in the physics of gravity and the laws of motion between 1687 when Newton formulated the law of gravity and law basic laws of classical mechanics in physics, and the second decade of the 20th century when General Relativity, Special Relativity and quantum mechanics were developed (Einstein played a pivotal role in all three of these developments, by the way), about 230 years later, or the roughly 50 years between the development of Maxwell's equations in 1862, and the formulation of quantum mechanics, in the physics of electromagnetism (those two fields combined were the whole of fundamental physics at the dawn of the 20th century).

In contrast, we are quite unlikely to be in the period of flourishing scientific advancement from about 1912 to about 2012 (when the Higgs boson was discovered) that marked the development of Special Relativity, General Relativity, quantum physics, the physics of the strong and weak forces, and modern cosmology (although prospects for break throughs in understanding dark matter and dark energy phenomena in the next two or three decades, and in the "non-fundamental" physics of complex systems, are much brighter than the prospects of new high energy physics at energy scales we can probe with experiments and astronomy observations).

The Large Hadron Collider is the most powerful controlled high energy physics experiment in the world of all time. The peak energies of the events that it studies are on the order of 10^13 eV (10 TeV). The multi-billion dollar colliders that scientists are considering building for the next generation of high energy physics experiments would have peak energies on the order of 10^14 eV (100 TeV).

An ultra high energy cosmic ray produced naturally by massive stars and black holes elsewhere in the Universe that happen to end up in our atmosphere, by definition, have energies of at least 10^18 eV (1,000,000 TeV), about 100,000 times more energy than the most energetic interactions at the LHC and about 10,000 times more energy than the most energetic interactions expected at a next generation particle collider.

If the Standard Model of Particle Physics is flawed in some way that needs to be explained by new physics beyond the Standard Model in slight ways at energies ten times what we have observed at particle colliders so far, these deviations from the Standard Model expectation ought to be much greater at energies 100,000 times what we have observed at particle colliders so far.

Ultra high energy cosmic ray decay observations don't actually increase our power to detect beyond the Standard Model physics by a full five orders of magnitude, because the precision available to us when we observe these natural experiments that can unfold anywhere in the sky with no advanced notice is not nearly as great as what we can observe in the exquisitely controlled, calibrated, and timed events in a particle collider like the LHC, that we can repeat in almost precisely the same way, over and over and over again.

But observations of Ultra High Energy Cosmic Ray decays still give us low resolution access to vastly higher energy regimes than anything we could observe in a man made particle collider in the foreseeable future. 

To the extent that these observations confirm the Standard Model expectations up to a given magnitude of uncertainty when the "wild" events that we can observe is modeled correctly (uncertainties on the order of low single digit percent errors in relative terms), we know that any new physics that could be observed at a future collider have to be smaller than that, after scaling down any proposed tweak to the Standard Model for the effects that would be expected at energy scales 10,000 times smaller.

In particular, results like this one put a huge damper on "just around the corner" predictions for phenomena like new supersymmetric particles at energies of tens or hundreds of TeV in mass, which are legion in the supersymmetry phenomenology literature.

New fundamental particles with masses in the 10,000 TeV or less, and certainly new fundamental particles with masses of 100 TeV or less that might be seen at next generation collider, would almost surely cause the decays of Ultra High Energy Cosmic Rays in Earth's atmosphere to look dramatically different than the Standard Model of Particle Physics predictions which this latest paper instead, tends to confirm.

If one is a Bayesian statistician trying to develop a statistical prior expectation for the probability of finding new physics at a next generation particle collider, this result is almost as important as the new muon anomalous magnetic moment (muon g-2) measurement expected next month.

Both measurements are very general global tests of new physics at energies well beyond the 10^13 eV energies that can be measured at the LHC, but also well below the GUT (grand unified theory) scale of about 10^25 eV which would have existed in the Universe only at the very earliest moments immediately after the Big Bang.  Neither muon g-2 nor Ultra High Energy Cosmic Ray decays can probe physics at the near GUT scale because new physics at those extreme high energies can "decouple" from a "low" energy effective theory like the Standard Model that can actually be probed with experimental evidence and astronomy observations.

Both muon g-2 anomalies and Ultra High Energy Cosmic Ray decay anomalies can tell us (1) if there are any high energy new physics out there (subject to loopholes for multiple kinds of new physics at high energies that exactly cancel each other out in both of these global measures of new physics), and (2) the approximate magnitude of any new physics that we are missing in a global sense if we see anomalies in these observations. 

But because they are global measures influenced by almost all aspects of the Standard Model, if we do see an anomaly, neither of these observations will tell us much about what is causing it. Also the magnitude of an anomaly does not even tell us the absolute magnitude of the new physics we are looking for. Small new physics effects at just around the corner energies would create the same kind of signal as big new physics effects at much higher energies.

The fact that this new study was able to show that muon excesses got more pronounced at each lower energy scale that could be observed was the big tipoff that the cosmic ray muon excess was a product of cumulative error in each iteration of the simulations that were done, rather than actual new physics, which would have been pronounced at higher energies while not getting much bigger at lower energies whose behavior is better understood because it is within, or is closer to, the energy scales that we have already probed with high precision in particle colliders.

The Paper

The paper and its abstract are as follows:

We present the first measurement of the fluctuations in the number of muons in extensive air showers produced by ultra-high energy cosmic rays. We find that the measured fluctuations are in good agreement with predictions from air shower simulations. 

This observation provides new insights into the origin of the previously reported deficit of muons in air shower simulations and constrains models of hadronic interactions at ultra-high energies. Our measurement is compatible with the muon deficit originating from small deviations in the predictions from hadronic interaction models of particle production that accumulate as the showers develop.

The Pierre Auger Collaboration, "Measurement of the fluctuations in the number of muons in extensive air showers with the Pierre Auger Observatory" Accepted for publication in PRL arXiv:2102.07797 [hep-ex] (February 15, 2021).

The introduction from the body text of the paper provides  context for its conclusions that the excess of muons detected relative to the predicted number is due to a flaw in the simulations used to determine the predicted number of muons rather than a flaw in the experimental measurement of the muons created by ultra high energy cosmic rays, or beyond the Standard Model physics.

Ultra High Energy Cosmic Rays (UHECRs) are particles coming from outer space, with energies exceeding 10^18 eV. They provide the only experimental opportunity to explore particle physics beyond energies reachable by Earth-based accelerators, which go up to cosmic ray energies of 9 × 10^16 eV. 

The Pierre Auger Observatory detects extensive air showers that are initiated by the UHECRs colliding with the nuclei in the atmosphere. Information about UHECRs is extracted using simulations based on hadronic interaction models which rely on extrapolations of accelerator measurements to unexplored regions of phase space, most notably the forward and highest-energy region. In addition, accelerator experiments at the highest energies either probe the interactions between protons or of protons with heavy nuclei, while most interactions within air showers are between pions and light nuclei. 

A further challenge is that the UHECR mass has to be measured despite not being yet completely decoupled from the hadronic uncertainties. The observable with the least dependence on hadronic interactions is the atmospheric depth at which the longitudinal development of the electromagnetic (EM) component of the shower reaches the maximum number of particles, namely Xmax.

In hadronic cascades the energy of each interacting particle is distributed among the secondaries, mostly pions. Neutral pions rapidly decay into two photons feeding a practically decoupled electromagnetic cascade (other resonances decaying into πº’s, electrons and or photons also contribute). Charged pions (and other long lived mesons like kaons) tend to further interact until their individual energies are below a critical value, below which they are more likely to decay. 

Muons, which are products of hadronic decays, are thus predominantly produced in the final shower stages. In sufficiently inclined showers, the pure EM component is absorbed in the atmosphere and the particles that reach the ground (muons and muon decay products) directly sample the muon content, reflecting the hadronic component of the shower. 

Air showers are mainly detected at the Pierre Auger Observatory by the Surface Detector (SD), an array of water-Cherenkov detector stations, and the Fluorescence Detector (FD) consisting of 24 fluorescence telescopes. By selecting the sub-sample of events reconstructed with both the SD and the FD and with zenith angles exceeding 62º, both the muon content and the energy of the shower are simultaneously measured. 

The results obtained indicate that all the simulations underestimate the number of muons in the showers. 

These analyses come with the caveat that they cannot distinguish a muon rescaling from a shift in the absolute energy scale of the FD measurement. However, muon content and energy scale were disentangled in a complementary technique based on showers with zenith angles below 60º. Using the longitudinal profile of the shower in the atmosphere obtained with the FD and the signals at the ground measured with the SD, it was shown that the muonic component still has to be scaled up to match observed data, while no rescaling of the EM component and the FD energy is required. The measurements with the FD also show that both the position of the shower maximum in the atmosphere (Xmax) and the entire shape of the EM shower are well described by the simulations.

At lower energies, down to ∼ 10^17.3 eV, in a measurement using the sub-array of buried scintillators of the Pierre Auger Observatory, a direct count of the muons independent of EM contamination was obtained, which also shows that simulations produce too few muons. 

There is much evidence that all the simulations underpredict the average number of muons in the showers: a comprehensive study of muon number measurements made with different experiments has shown that the muon deficit in simulations starts around ∼ 10^16 eV and steadily increases with energy. Depending on model and experiment, the deficit at ∼ 10^20 eV ranges between tens of percent up to a factor of two. 

The increased statistics obtained at the Pierre Auger Observatory allows us to now take a further step and explore fluctuations in the number of muons between showers, hereinafter referred to as physical fluctuations. The ratio of the physical fluctuations to the average number of muons (relative fluctuations) has been shown to be mostly dominated by the first interaction, rather than the lower energy interactions deeper in the shower development. Here, we exploit the sensitivity of fluctuations to the first-interaction to explore hadronic interactions well above the energies achievable in accelerator experiments.

The paper concludes with the following summary of the study's results:

We have presented for the first time a measurement of the fluctuations in the number of muons in inclined air showers, as a function of the UHECR primary energy. Within the current uncertainties, the relative fluctuations show no discrepancy with respect to the expectation from current high-energy hadronic interaction models and the composition taken from Xmax measurements. 

This agreement between models and data for the fluctuations, combined with the significant deficit in the predicted total number of muons, points to the origin of the models’ muon deficit being a small deficit at every stage of the shower which accumulates along the shower development, rather than a discrepancy in the first interaction. Adjustments to models to address the current muon deficit, must therefore not alter the predicted relative fluctuations.