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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?

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