Question regarding CP violation in the CKM matrix

[jossives]

Could somebody explain how an imaginary phase in some of the CKM matrix elements represents a CP-violation factor?

 

[hamster143]

My theory is a bit rusty but here's the essence of it.

CKM matrix couples gauge bosons, up-type quarks, and down-type quarks. For example, there's a term in the Lagrangian that couples right-handed anti-up with left-handed strange quark, and it is proportional to $$V_{us}$$, its hermitean conjugate couples left-handed up with right-handed anti-strange, and it is proportional to $$V^*_{us}$$. CP transformation flips charges and spins, so the sum of two terms is invariant under CP only if $$V_{us}$$ is real. If you only have two families, you can fiddle with quark phases and redefine their wave functions to absorb all imaginary numbers, but with three families 'i''s will pop up somewhere. It's convenient to pick quark phases so that all elements connecting with the first family (up & down quarks) are real.

 

[sir-pinski]

The CKM matrix is a mathematical representation of the relationships between different quark flavors in the Standard Model of particle physics. It is used to describe the interactions between quarks, which are the fundamental building blocks of matter.

One of the important properties of the CKM matrix is its ability to account for the phenomenon of CP violation. CP violation is a fundamental asymmetry in the behavior of particles and antiparticles, where CP stands for charge conjugation (C) and parity (P). This means that the laws of physics do not behave the same way for particles and their corresponding antiparticles. This was first observed in the decay of neutral kaons in the 1960s and is now a well-established phenomenon in particle physics.

In the CKM matrix, there are three imaginary phases in some of the matrix elements. These phases represent CP-violation factors, which are responsible for the observed asymmetry between particles and antiparticles. These phases are often denoted by the Greek letter δ (delta) and are present in the matrix elements that involve the third generation of quarks (top, bottom, and charm).

The presence of these imaginary phases in the CKM matrix means that the matrix is not symmetric, which is a necessary condition for CP violation to occur. This is because the imaginary part of a complex number represents a rotation in the complex plane, and this rotation breaks the symmetry between particles and antiparticles.

In summary, the imaginary phases in the CKM matrix represent CP-violation factors, which are responsible for the observed asymmetry between particles and antiparticles. These phases are a crucial aspect of the Standard Model and have been confirmed through various experiments, making the CKM matrix an essential tool in understanding the fundamental interactions between particles.