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Why do the mass of anti-particles have to be exactly equal to the particles ?

What I learnt from Srednicki Chapter 23 is that to support charge conjugation symmetry (C-symm) of Lagrangian, mass of particle and anti-particle must be same.

My question is "Is charge conjugation symmetry a universal truth -- proven by experiments, or we still can have some Lagrangians (L) which doesn't support C-symm., where changing + charged particles to - charged in L will not mean m+ = m- ?" What would existence of such a theory mean to our world ?

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  • $\begingroup$ C. S. Wu discovered C violation in 1956 but it did not manifest itself as particles and anti-particles with different mass. $\endgroup$
    – Connor Behan
    Commented Jul 24, 2022 at 16:40
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    $\begingroup$ What you are probably looking for is the CPT theorem. $\endgroup$
    – Martino
    Commented Jul 24, 2022 at 17:28
  • $\begingroup$ C is almost maximally violated in the weak interactions. $\endgroup$
    – Cosmas Zachos
    Commented Jul 24, 2022 at 17:40
  • $\begingroup$ For literature, check the Particle Data Group’s reviews of particle properties, and follow the references for comparisons of particle versus antiparticle masses. $\endgroup$
    – rob ♦
    Commented Jul 24, 2022 at 18:10
  • $\begingroup$ a related discussion is in this question physics.stackexchange.com/questions/672048/… . If they were found to be different experimentally, this would affect the lifetimes also. $\endgroup$
    – anna v
    Commented Jul 25, 2022 at 4:00

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