$CP$-odd form factor in the $HWW$ vertex

The universe is built on a set of fundamental forces that hold matter together and push it apart. For decades, physicists have relied on a single, highly successful theory called the Standard Model to describe these forces and the particles that carry them. At the heart of this theory is a special field that gives mass to other particles, much like how moving through thick water slows you down. The physical proof of this field is a particle known as the Higgs boson, discovered in 2012. Since that discovery, scientists have been busy measuring its properties with extreme precision, checking to see if it behaves exactly as the theory predicts or if it shows signs of something new and unexpected. One of the most important ways to test the theory is to watch how the Higgs boson interacts with other particles, specifically the W bosons, which are the carriers of the weak nuclear force.

A new study by researchers at the Benemérita Universidad Autónoma de Puebla in Mexico takes a closer look at a very subtle interaction between the Higgs boson and these W bosons. In the standard view of particle physics, the Higgs boson can decay into two W bosons, but because of the laws of energy and mass, it is impossible for both W bosons to be fully stable and "real" at the same time during this process. One of them must be a fleeting, virtual particle that exists only for a split second before turning into other matter. The researchers focused on a specific, rare feature of this interaction that involves a property called "parity," which essentially describes how a system looks when reflected in a mirror. While the main forces usually treat left and right the same, certain rare quantum effects can create a slight difference. The team set out to calculate exactly how strong this mirror-breaking effect is within the Standard Model, a question that had not been answered with numbers before.

Using powerful computer simulations to perform complex calculations that involve particles looping in and out of existence, the researchers found that this mirror-breaking effect does exist, but it is incredibly faint. They discovered that the effect is generated only when the two W bosons have different amounts of energy, a condition that is always true in the decay of a Higgs boson. The size of this effect is determined by the loops of other particles, particularly heavy quarks and leptons, that briefly appear inside the interaction. The researchers calculated that the strength of this effect is roughly one part in one hundred thousand. To put this in perspective, if you were trying to detect this signal in a crowd of one hundred thousand people, you would be looking for a single person who is slightly out of step. This value is far too small to be seen with current technology, which can only detect signals that are about ten billion times larger.

Despite being too small to see right now, finding this effect is important because it represents a genuine prediction of the Standard Model. The researchers showed that this tiny signal is not caused by a fundamental violation of symmetry in the laws of physics, but rather by the way particles move and interact in loops. However, because the signal is complex and has a specific mathematical structure, it creates a background noise that cannot be removed. If scientists in the future discover a much larger mirror-breaking effect, they will need to know exactly how big this tiny Standard Model background is to be sure they are seeing something new. The study also looked at how this faint effect might change the way particles fly out from the decay. They found that it creates a very slight preference for particles to move in one direction versus another, or to spin in a specific way. These preferences, known as asymmetries, are also extremely small, with values around one in a million or one in ten million.

The paper concludes that while these effects are real and have been calculated for the first time, they are currently invisible to our most sensitive detectors. The Large Hadron Collider, the massive machine that discovered the Higgs boson, is not yet sensitive enough to measure these tiny deviations. The researchers note that future improvements in how we analyze particle spins and directions might eventually bring us closer to this goal. Until then, this work serves as a crucial map, defining the exact baseline of what the Standard Model predicts. It ensures that when we finally do see a signal that breaks the mirror, we will know for certain that it comes from new physics and not from a calculation we missed. The study confirms that the universe is consistent with its current rules, even in its most subtle and hidden corners.