Researchers find a possible solution to the cosmic ray muon puzzle

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Scientists have a problem with cosmic rays—they produce too many muons at the Earth's surface. Cascades of muons are byproducts of high-energy cosmic rays as they collide with nuclei in the upper atmosphere, and scientists see more muons at Earth's surface than standard physics models predict.

Explaining these excess muons has been a challenge for several years. But now a team of researchers say they can explain the surplus by invoking "gluon condensation" in the first cascade collision. Their work has been published in The Astrophysical Journal.

Every second, millions of high-energy cosmic rays traveling at nearly the speed of light bombard Earth's upper atmosphere, where they collide with atomic nuclei, primarily nitrogen, oxygen and argon. The nuclei explode into a shower of particles, primarily pions, kaons and baryons. These then decay into primarily muons, the heavier copy of the electron. (About 90% of the muons come from decays of pions and kaons.)

These muons suffer only a small energy loss as they proceed through the atmosphere until they reach the surface. (Their ability to reach the surface, despite their lifetime being too short to apparently do so, is triumphally explained by special relativity.) About one muon per square-centimeter reaches the Earth's surface per minute, with an average energy of 4 GeV but a very broad energy spectrum.

Yet, compared to the results of standard physics models derived from particle accelerator experiments such as at the Large Hadron Collider and the Super Proton Synchrotron at CERN, too many muons are observed at the surface. For muon energies between 6 and 16 exa-electronvolts (1.0 to 2.5 joules!), the muon flux is 30% to 60% higher than expected.

"Although the research about the muon puzzle is becoming increasingly detailed," Bingyang Liu and his colleagues from East China Normal University write, "the truth remains elusive, necessitating further investigations."

In tackling the excess problem, the team wrote that they "tend to believe" that the main difference between experiments and theory is the initial collision in air showers—when the high-energy cosmic ray particle first interacts with a nucleus in the atmosphere. (These incoming cosmic rays can have energies as high as the "Oh my God" particle observed in 1991, which had an energy of 320 exa-eV. That's 25 million times the highest accelerator energies created on Earth, 13 TeV at CERN.)

Twenty-five years ago it was proposed that in ultrahigh-energy collisions, as the incoming cosmic ray particle (primarily protons and helium nuclei) collides with hadrons in atmospheric nuclei, the gluon distribution in the hadrons might undergo condensation, forming a gluon condensate. The formation of these gluon condensates would then influence the hadrons subsequently produced, which in turn affects the final muon production.

Hadrons are particles consisting of two or more quarks—examples are the proton and neutron, with three quarks each, and pions and kaons with two quarks. Just as molecules are composed of atoms held together by the electrical force, hadrons are composed of quarks held together by the strong force.

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A photon carries the electrical force between electrically charged electrons and protons in atoms and molecules and is described by the theory of quantum electrodynamics (QED); gluons carry the strong force between quarks and is described by quantum chromodynamics (QCD).

The difference is that, whereas photons have no electrical charge, gluons are charged—charged with the colors of the strong force. (Quarks, of course, also carry one of three types of color charge.) This "nonlinearity" makes states governed by the strong force much more complex than atoms and molecules. Even with the quantum field theory QCD, strong interaction states are very difficult to analyze, model and compute.

We know that accelerated electric charges emit QED radiation (photons), and these will contribute to the hadron cascades from the initial cosmic ray collision. So too, accelerated colored quarks (and gluons themselves) emit QCD radiation (gluons). Unlike the uncharged photons though, the gluons have their own charge and therefore emit further radiation, leading to much bigger particle showers.

Gluon distributions in hadrons may form "gluon condensates." Such high-energy states consist of a large number of gluons at a certain energy level that can generate a number of the constituent quarks of hadrons, making the hadron cascades more effective, and increasing the number of pions and strange quarks, which makeup kaons.

In a reference frame centered on the cascades' center-of-mass, almost all available collision energy is used to produce these pions and kaons, and subsequently produce the final muon that streams to the surface.

The researchers used the gluon condensation model described by QCD to analyze the initial collision of the cascades in an attempt to resolve the muon excess problem.

They found that temporary quark-gluon plasmas can be formed by the high collision energies of gluons; in particular, their theoretical analysis found that the appearance of a quark–gluon plasma leads to an increased number of strange quarks and antistrange quarks.

"The occurrence of the gluon condensate requires a higher collision energy," they wrote, "and we find that it leads to more strange quarks (antiquarks) production than in the quark-gluon plasma conditions."

After a complicated calculation, the team found that the production of strange quark pairs was two to 10 times larger—depending on energy—when beginning with a gluon condensate state than if they began with a quark-gluon plasma state.

They conclude by writing, "In high-energy collision experiments, the existing research suggests that QGP [quark-gluon plasmas] may occur, but considering only the conventional QGP effect cannot solve the muon excess problem in the air shower. We consider that GC [gluon condensate] may occur in extremely high-energy collisions.

"In the GC state, the production of strange quarks will be greatly enhanced," thus leading to more muons at Earth's surface than would otherwise be the case without gluon condensates.

More information: Bingyang Liu et al, Explaining Muon Excess in Cosmic Rays Using the Gluon Condensation Model, The Astrophysical Journal (2024). DOI: 10.3847/1538-4357/ad6b9a

Journal information: Astrophysical Journal

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