On the formalism and upper limits for spin-dependent cross sections in dark matter elastic scattering with nuclei

TL;DR

This paper refines the theoretical framework for calculating spin-dependent dark matter-nucleus scattering, emphasizing the importance of specific nuclear structure functions and exploring experimental limits within supersymmetric models.

Contribution

It identifies the essential nuclear structure function for accurate calculations and clarifies the model-independent approach for setting upper limits on spin-dependent cross sections.

Findings

A single normalized structure function suffices for accurate nuclear physics modeling.

The formalism allows direct translation of experimental limits into supersymmetric parameter space.

Discussion of experimental prospects like COUPP for probing spin-dependent interactions.

Abstract

We revise the spin-dependent neutralino-nucleus elastic scattering comparing the formalisms and approximations found in literature for the momentum transfer dependent structure functions. We argue that one of the normalized structure functions of Divari, Kosmas, Vergados and Skouras is all that one needs to correctly take into account the detailed nuclear physics information provided by shell-model calculations. The factorization of the particle physics degrees of freedom from the nuclear physics momentum dependent structure functions implied by this formalism allows for a better understanding of the so-called model independent method for setting upper limits. We further discuss the possibility of experiments with spin-dependent sensitivity like COUPP to test or set limits on the proton spin-dependent cross section in the framework of the stau co-annihilation region of the constrained minimal supersymmetric standard model. For this model with $A_0 =0$, we provide a fitting formula by which it is possible to convert an upper limit on the spin-independent cross section as a function of the neutralino mass directly into an exclusion plot in the ($m_{1/2}$, $\tan\beta$) plane.