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Looking at the process of neutrino-electron scattering $$\nu_\alpha + e^- \rightarrow \nu_\alpha +e^-$$ one finds that the cross section depends on the neutrino flavor $\alpha$.

While muon and Tau (anti-) neutrinos can only scatter via neutral current (Z exchange) scattering on electrons, both electron neutrinos and antineutrinos can interact via neutral and charged currents. Hence both $\nu_e$ and $\overline{\nu} _e$ have a higher cross section than other flavors. However calculating the cross sections of both one finds that the cross section for $\nu_e+e^-\rightarrow\nu_e+e^-$ is larger than the cross section for $\overline{\nu}_e+e^-\rightarrow\overline{\nu}_e+e^-$. While I thought the difference came from the fact that the charged current process is a t-channel process for $\nu_e$ compared to an s-channel process for $\overline{\nu} _e$ which should result in different mandelstam variables appearing in the calculation I was told recently (without a further explanation) that the difference was due to Helicity suppression.

However I do not see how the Helicity of the neutrinos plays a role here...

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** "i tried writing here but i couldn't write the math. actually in the anti electron neutrino as you can see that due to the conservation laws not the helicity states are allowed. every thing is written in the notes that i posted i am just writing here to compelete 30 characters to post my answer." *

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  • $\begingroup$ see the pictures in the link those have he answer of your question. $\endgroup$
    – Waqar Ali
    Dec 6, 2023 at 13:54
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    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$ Dec 6, 2023 at 14:30

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