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It is "easy" to show that the cross-section of the 2 reactions: $$ (1)~~~\nu_{\mu} + d \to \mu^- + u~~~~~~(2)~~~\bar{\nu}_{\mu} + u \to \mu^+ + d$$ are different. The naive calculation gives a factor $\sigma_1/\sigma_2 = 3$ as shown below. The fact that the figure in the particle data group gives actually almost a factor 2 needs to take into account the ...


The answer is that in general cross section of particles and antiparticles are different. For this case in specific there is one point that Dirac particle have four possible states: due two possible ranges for energy E<0, E>0, and two possible range for helicities h>0 and h<0. In the standard model of particles only the neutrino with h<0 interact ...

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