# Symmetry responsible for equality of masses of particles

During my studies of basic particle physics the following question came up. What symmetry is responsible for equality of masses of particles and their antiparticles? In particular, is this symmetry known to be broken in some physical situation?

Discussion in Equality of masses of particle and antiparticle suggests that it is CPT symmetry and therefore not broken, but I don't really know QFT so I don't want to rely on my limited understanding.

• C is charge symmetry, basically $Cx$ -> $x^-$ . – Arif Burhan Apr 8 '16 at 20:43

Naively, suppose you have a field F in your theory. If you look for the mass term of the field F in the Lagrangian it appears like -L $\supset$ $m^2$ $\bar{F}F$, which is invariant under the charge operator C, i.e., -$L^c$ $\supset$ $m^2$ $F^\dagger$$C^\dagger$$\gamma^0$$C$$F$ = $m^2$ $F^\dagger$$\gamma^0$$F$ =$m^2$ $\bar{F}F$ = -L, which means that the same mass term is valid for the antiparticle $\bar{F}$ and therefore particles and antiparticles share the same mass value.