Sensitivity of WIMP bounds on the velocity distribution in the limit of a massless mediator

We discuss the sensitivity of the bounds on the spin-independent (SI) and spin-dependent (SD) WIMP-proton and WIMP-neutron interaction couplings αSI,SDp,n on the WIMP velocity distribution for a massless mediator. We update the bounds in the Standard Halo Model (SHM) for direct detection and the neutrino signal from WIMP annihilation in the Sun (fixing the annihilation channel to bb̅), and set a halo-independent bound for the first time using the single-stream method. In the case of a massless mediator the SHM capture rate in the Sun diverges and is regularized by removing the contribution of WIMPs locked into orbits that extend beyond the Sun-Jupiter distance. We discuss the dependence of the SHM bounds on the Jupiter cut showing that it can be sizeable for αSDp and a WIMP mass mχ exceeding 1 TeV. Our updated SHM bounds show an improvement between about two and three orders of magnitude compared to the previous ones in the literature. Our halo-independent analysis shows that, with the exception of αSDp at large mχ, the relaxation of the bounds compared to the SHM is of the same order of that for contact interactions, i.e. relatively moderate in the low and high WIMP mass regimes and as large as ∼ 102 for mχ ≃ 20 GeV. On the other hand, the exact determination of the relaxation of the bound becomes not reliable for αSDp and mχ ≳ 1 TeV due to the sensitivity of the SHM capture rate in the Sun to the details of the Maxwellian velocity distribution at low incoming WIMP speeds. In contrast, the halo-independent bounds are robust against the details of the velocity distribution including the Jupiter cut and the local escape speed, as expected.