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An international collaboration of theoretical physicists, including scientists from Brookhaven national laboratory (BNL, USA) and the RIKEN-BNL Research center (RBRC), has published a new calculation relevant to the search for an explanation for the antimatter preponderance of matter in our Universe.

The collaboration, known as RBC-UKQCD, also includes scientists from CERN (European laboratory of particle physics), Columbia University, the University of Connecticut, the University of Edinburgh, the Massachusetts Institute of technology, the University of Regensburg, and the University of Southampton. They describe their result in an article, physical D D and marked as "editor's suggestion".

Scientists first noticed a small difference in the behavior of matter and antimatter, known as a "CP-symmetry" violation, when studying the decay of subatomic particles called kaons in an experiment that won the Nobel prize at the Brookhaven laboratory in 1963.

Soon after, particle physics was pieced together, and understanding whether the observed CP violation in kaon decays was consistent with the Standard model proved elusive due to the complexity of the required calculations.

The new calculation provides a more accurate prediction of the probability of kaon decay into a pair of electrically charged pions compared to a pair of neutral pions. Understanding these decays and comparing the predictions with more recent experimental measurements made at CERN and the us Department of energy's Fermi National accelerator laboratory gives scientists the opportunity to test the tiny differences between matter and antimatter and find effects that cannot be explained by the Standard model.

The new calculation represents a significant improvement over the group's previous result, Physical Physical Review Letters 2015 2015.

Based on the Standard model, it gives a range of values for the so-called "direct CP symmetry breaking" in kaon decays, which is consistent with the experimentally measured results. This means that the observed CP violation is now, as far as we know, explained by the Standard model, but the uncertainty in the forecast needs to be further improved, since it is also possible to identify any sources of matter / antimatter asymmetry that lie outside of our description of the world by the current theory.

"Even a more accurate theoretical calculation of the Standard model may still go beyond the experimentally measured range. Therefore, it is very important that we continue our progress and Refine our calculations so that we can provide an even more reliable test of our fundamental principles of understanding,” the scientists say.

"The need to distinguish between matter and antimatter is embedded in modern space theory," said Norman Christ of Columbia University. "Our current understanding is that the current universe was created with almost equal amounts of matter and antimatter.

-With the exception of the tiny effects studied here, matter and antimatter must be identical in all respects, apart from the usual options, such as assigning a negative charge to one particle and a positive charge to its antiparticle. Some difference in how these two types of particles work must have tipped the scales in favor of matter over antimatter, " he said.

Any differences in matter and antimatter that have been observed to date are too weak to explain the preponderance of matter in our current Universe.

Finding a significant discrepancy between experimental observation and predictions based on the Standard model could potentially point the way to new mechanisms of particle interaction that are beyond our current understanding – and that scientists hope to find to explain this imbalance.

All experiments that show the difference between matter and antimatter involve particles made up of quarks, subatomic building blocks that bind strongly to form protons, neutrons, and atomic nuclei, as well as less familiar particles such as kaons and pions.

"Each kaon and pion is made up of a quark and an antiquark, surrounded by a cloud of virtual quark-antiquark pairs, and bound together by force carriers called gluons," explained Christopher Kelly of Brookhaven national laboratory.

Therefore, calculations of the behavior of these particles based on the Standard model should include all possible interactions of quarks and gluons, as described in the modern theory of strong interactions, known as quantum chromodynamics (QCD).

In addition, these bound particles move at a speed close to the speed of light. This means that the calculations must also include the principles of relativity and quantum theory, which regulate such particle interactions at speeds close to light.

Because of the huge number of variables involved, this is one of the most complex calculations in all of physics.

The new calculation, performed using the world's fastest supercomputers, allows scientists to more accurately predict the probability of two kaon decay paths and compare these predictions with experimental measurements. Comparative tests for tiny differences between matter and antimatter that could, with even more computing power and other improvements, point to physical phenomena not explained by the Standard model. Courtesy: Brookhaven national laboratory.

Computational problem

To solve this problem, the theorists used a computational approach called lattice QCD, which "places" particles in a four-dimensional space-time lattice (three spatial dimensions plus time).

This lattice allows them to map all possible quantum paths along which the initial kaon decays into two pions. The result becomes more accurate as the number of lattice nodes increases. The scientists noted that the "Feynman integral" for the calculations presented here included the integration of 67 million variables!

These complex calculations were performed using the latest supercomputers. The first part of the work, creating samples or images of the most likely quark and gluon fields, was performed on supercomputers located in the United States, Japan, and the United Kingdom.

The second and most difficult step to extract the actual kaon decay amplitudes was performed at the national computing center for energy research (nersc), at the us Department of energy's Lawrence Berkeley national laboratory.

But using the fastest computers is not enough; these calculations are possible on these computers only when using highly optimized computer programs developed by the authors for calculations.

"The accuracy of our results cannot be significantly increased by simply performing additional calculations," the physicists say.

"Instead, in order to tighten up our verification of the Standard model, we now have to overcome a number of more fundamental theoretical problems. Our collaboration has already made significant progress in solving these problems, as well as improved computational methods. We expect to achieve significantly better results in the next three to five years."

R. Abbott et al, direct violation of CP δ δi = 1/2 in the decay of K → ππ from the standard model, Physical Review D (2020).