Reanalysis of nuclear spin matrix elements for dark matter spin-dependent scattering

We show how to include in the existing calculations for nuclei other than Xe-129 and Xe-131 the corrections to the isovector coupling arising in chiral effective field theory recently found in Menendez et al. [Phys. Rev. D 86, 103511 (2012)]. The dominant, momentum-independent, two-body current effect can be taken into account by formally redefining the static spin matrix elements < s(p,n)>. By further using the normalized form factor at q not equal 0 built with the one-body level structure functions, we show that the weakly interacting massive particles (WIMP)-nucleus cross section and the upper limits on the WIMP-nucleon cross sections coincide with the ones derived by using the exact functions at the two-body level. We explicitly show it in the case of XENON100 limits on the WIMP-neutron cross section, and we recalculate the limits on the WIMP-proton spin-dependent cross section set by COUPP. We also give practical formulas to obtain < s(p,n)> given the structure functions in the various formalisms and notations existing in the literature. We argue that the standard treatment of the spin-dependent cross section in terms of three independent isospin functions, S-00(q), S-11(q), and S-01(q), is redundant in the sense that the interference function S-01(q) is the double product vertical bar S-01(q)vertical bar = 2 root S-00(q)root S-11(q) even when including the new effective field theory corrections. DOI: 10.1103/PhysRevD.87.075014