At tree level, the spin independent (SI) direct-detection cross section includes effective coupling constant. How to calculate effective coupling constant? There is always a mandelstram variable in it. Do we need to write something for t mandelstram in case of direct detection?
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$\begingroup$ Can you be more specific? Do you have a specific model in mind? Do you have a reference? $\endgroup$– FrodCubeJun 27, 2021 at 13:12
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$\begingroup$ arXiv:1812.05996v1 [hep-ph] 14 Dec 2018, this particular model I am referring to. in eq 13 and eq 14. I am new in DM detection, having difficulty in this area? $\endgroup$– soomo56Jun 27, 2021 at 17:56
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$\begingroup$ Hey, that paper describes what they calculate in their equations leading to their equation 9, no? i.e. take that equation, integrate over all scattering angles, and you get the predicted cross section... $\endgroup$– rflJun 27, 2021 at 21:15
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The coupling constant in theoretical dark matter approaches is, to the best of my knowledge, a free parameter of the system as well as the mass of the particle. What is usually done by the experimentalist is to plot exclusion limits of the cross section with respect to the mass of the particle, depending on the parameters of the detector such as the exposure time, the detecting nucleus load in the detector (see arXiv:astro-ph/0507190 from the CDMS-II collaboration). More fundamentally, the freedom of the coupling constant resides in the intensity with the WIMP interacts with the standard matter (nuclei in most of the experiments). The intensity is governed by the mass of the exchanged boson between them and, of course, by the nature of the interaction. The last is supposed to be a interaction like the weak interaction due to it is the only one that satisfies the astrophysical measurements, nor the strong, neither the electromagnetic interaction. Finally, say that the coupling constant will be fixed once the cross section of the interaction and the mass is measured.
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$\begingroup$ Yes, thats the very good description. I am following this, arXiv:1812.05996v1 [hep-ph] 14 Dec 2018. Here I need to replot fig 1 and 2, where I need formulae in eq 13 and 14. I now am stuck at how to write t mandelstram in mathematica for eq 13 and 14? Can you please share some reference material if you know any, which can help me in deriving equation 14? $\endgroup$– soomo56Jun 27, 2021 at 20:26
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$\begingroup$ I am not familiarised with interactions between a Wimp and Goldstone bosons... I used to work with Wimp-Nucleus interactions. Sorry $\endgroup$– T. ssPJun 27, 2021 at 21:04
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$\begingroup$ This is exactly not the case for the paper referenced by the OP. In contrast, there, the paper's authors calculate a prediction for the WIMP-nucleon cross section based on their model, see their black lines in their plots. $\endgroup$– rflJun 27, 2021 at 21:13
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$\begingroup$ For Wimp Nucleus interactions , how can we calculate the coupling? $\endgroup$– soomo56Jul 9, 2021 at 20:16