# Crossing symmetry violation by passing from proton-proton scattering to proton-antiproton scattering?

The elastic proton-antiproton $$(p \bar p)$$ scattering is a crossing symmetric process of elastic proton-proton $$(pp)$$ scattering. It is known from Regge theory that the elastic $$pp$$ and $$p\bar p$$ scattering amplitudes are the sums of $$C$$-parity $$=+1$$ and $$C$$-parity$$=-1$$ components:

$$A_{pp} = A_{+} + (-A_{-})$$

$$A_{p\bar p} = A_{+} + A_{-}$$

where $$A_{+}$$ denotes the $$C$$-parity $$=+1$$ component and $$A_{-}$$ denotes the $$C$$-parity $$=-1$$ component. The $$C$$-parity $$=-1$$ component has different signs for $$pp$$ and $$p\bar p$$ scatterings. This way the $$C$$-parity $$=-1$$ term results in a difference between the $$pp$$ and $$p\bar p$$ scattering cross-sections. Does this difference lead to the violation of crossing symmetry? Why? Or why not?