Bracketing the direct detection exclusion plot for a WIMP of spin one half in non-relativistic effective theory

Abstract

Assuming a standard Maxwellian velocity distribution for the WIMPs in the halo of our Galaxy we use the null results of an exhaustive set of 9 direct detection experiments to calculate the maximal variation of the exclusion plot for each Wilson coefficient of the most general Galilean–invariant effective Hamiltonian for a WIMP of spin one half due to interferences. We consider 56 Wilson coefficients cip,n and αin,p for WIMP–proton and WIMP–neutron contact interactions Oip,n and the corresponding long range interaction Oip,n/q2, parameterized by a massless propagator 1/q2. For each coupling we provide a different exclusion plot when the following set of operators is allowed to interfere: proton–neutron, i.e. cip–cin or αip–αin; contact–contact or long range–long range, i.e. cip,n–cjp,n or αip,n–αjp,n; contact– long range, i.e. cip,n–αjp,n. For each of the 56 Wilson coefficients cip,n and αjp,n and for the largest number of interfering operators the exclusion plot variation can reach 3 orders of magnitude and reduces to a factor as small as a few for the Wilson coefficients of the effective interactions where the WIMP couples to the nuclear spin, thanks to the combination of experiments using proton-odd and neutron-odd targets. Some of the conservative bounds require an extremely high level of cancellation, putting into question the reliability of the result. We analyze this issue in a systematic way, showing that it affects some of the couplings driven by the operators O1, O3, O11, O12 and O15, especially when interferences among contact and long range interactions are considered.