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Neutrino-Nucleus scattering

Physics Asked on March 24, 2021

For calculating the amplitude of the coherent elastic neutrino-nucleus scattering, I face the problem in finding the coupling constant for the vertex of nuclei and the Z boson.

$$ gamma^mu(g_V-g_A(gamma^5))$$

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In this case if we have a nucleus (A) with Z number of protons and N number of neutrons, how we can we find the value of this coupling constant for this vertex?
Thanks in advance.

One Answer

This thesis (http://compphys.ugent.be/docs/theses/WauthierSamuelThierry_2016-2017.pdf) indicates that the "coupling constant" (i.e. the term attached to the spinors and momentum 4-vectors) is:

$$-frac{G_F}{sqrt{2}}Q_Wg_Lgamma^mu(1-gamma^5)F(q^2)$$

where $F(q^2)$ is the nuclear form factor. So the "coupling constant" is explicitly a function of the momentum transfer in the reaction, and not in a trivial way - nuclear form factors do not come from first principles, and must be measured in experiments.

Answered by probably_someone on March 24, 2021

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