Why do the W bosons transform into each other under a CP transformation?

[spaghetti3451]

I was wondering if someone could may be help me out with understanding why the Higgs boson is CP even.

I was wanting help here from someone to prove that the $W^{\pm}$ bosons transfrom into each other under a CP transformation.

I can't happen to find a simple short argument for why this must be the case.

I can understand that charge conjugation simply flips the sign of the electric charge.

How do you account for parity?

 

[AndyW]

Hello there,

I am happy to help you understand why the Higgs boson is CP even and how the W bosons transform under a CP transformation. Let's start with the Higgs boson.

The Higgs boson is a fundamental particle that is responsible for giving mass to other particles through the Higgs mechanism. It is also known as a scalar particle, which means it has spin 0 and no intrinsic angular momentum. This allows it to have a CP even nature.

To understand why the Higgs boson is CP even, we need to look at how it interacts with other particles. The Higgs boson has a coupling with the W bosons, which are gauge bosons responsible for the weak nuclear force. These couplings are described by the Higgs potential, which is a function of the Higgs field.

Under a CP transformation, the Higgs field and its potential remain unchanged. This means that the Higgs boson will also remain unchanged, making it CP even.

Now, let's move on to the W bosons. As you mentioned, under a charge conjugation transformation, the electric charge of a particle changes sign. This means that the W bosons, which have a non-zero electric charge, will transform into their antiparticles under a charge conjugation transformation.

As for parity, it is a symmetry operation that reflects a system about a mirror plane. In particle physics, it is related to the direction of motion of a particle. For the W bosons, they are left-handed particles, meaning their spin is opposite to their direction of motion. Under a parity transformation, the direction of motion is reversed, but the spin remains the same. This means that the W bosons will transform into their antiparticles, but their spin state will not change.

To summarize, the Higgs boson is CP even because its interactions do not change under a CP transformation. The W bosons transform into their antiparticles under a charge conjugation transformation, and their spin remains unchanged under a parity transformation.

I hope this explanation helps you understand why the Higgs boson is CP even and how the W bosons transform under a CP transformation. Let me know if you have any further questions.