Charge conjugation and time reversal in the SM

[Einj]

Hi everyone. I have a doubt on charge conjugation symmetry. Consider the Standard Model lagrangian with just the gauge and the fermionic part (no Higgs and no Yukawa). This is invariant under $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_Y$. Moreover, as any other field theory, it is $CPT$ invariant.

Since, however $P$ is clearly violated by the asymmetry in the left-right fields we know that $CT$ must be violated too.

What can we say about $C$ and $T$ independently?

 

[AndyW]

I would like to clarify some misconceptions in this post regarding charge conjugation symmetry and its relation to the Standard Model. First of all, the Standard Model Lagrangian is not just invariant under SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_Y, but it also includes the Higgs and Yukawa terms which are crucial for understanding the origin of particle masses. Therefore, it is not accurate to say that the Standard Model Lagrangian does not have a Higgs or Yukawa sector.

Moving on to the main question, it is important to understand that charge conjugation (C) and time reversal (T) are independent symmetries and should not be confused with each other. Charge conjugation refers to the swapping of particles with their corresponding antiparticles, while time reversal refers to reversing the direction of time. In the Standard Model, C is not a fundamental symmetry, meaning that it is not conserved in all interactions. This is due to the fact that the weak interaction violates C-symmetry, as seen in the parity violation in beta decay.

On the other hand, T-symmetry is a fundamental symmetry in the Standard Model, meaning that it is conserved in all interactions. However, this does not mean that T is always conserved in all physical processes. In fact, there are some processes that violate T-symmetry, such as the CP-violation observed in the decays of neutral kaons.

In summary, the Standard Model Lagrangian is not just invariant under SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_Y and it does have a Higgs and Yukawa sector. C and T are independent symmetries in the Standard Model, with C not being a fundamental symmetry and T being a fundamental symmetry that can still be violated in certain processes. I hope this helps clarify any confusion regarding charge conjugation symmetry in the Standard Model.