On the short-range behavior of neutrino forces beyond the Standard Model: from 1/r5 to 1/r4, 1/r2, and 1/r

Abstract

The exchange of a pair of neutrinos between two objects, seperated by a distance r, leads to a long-range effective potential proportional to 1/r5, assuming massless neutrinos and four-fermion contact interactions. In this paper, we investigate how this known form of neutrino-mediated potentials might be altered if the distance r is sufficiently short, corresponding to a sufficiently large momentum transfer which could invalidate the contact interactions. We consider two possible scenarios to open up the contact interactions by introducing a t-channel or an s-channel mediator. We derive a general formula that is valid to describe the potential in all regimes as long as the external particles remain non-relativistic. In both scenarios, the potential decreases as 1/r5 in the long-range limit as expected. In the short-range limit, the t-channel potential exhibits the Coulomb-like behavior (i.e. proportional to 1/r), while the s-channel potential exhibits 1/r4 and 1/r2 behaviors.

Neutrino forces and the Sommerfeld enhancement

“…We consider two possible UV completions of the contact interaction and calculate the corresponding Sommerfeld enhancement factor in Secs. 3.2 and 3.3, where the short-range behaviour of the neutrino force is 1/r and 1/r 2 , respectively [42]. Then in Sec.…”

“…At shorter scales, the UV completion must be considered. We computed the Sommerfeld enhancement for two potentials valid at short distances recently derived in [42], and saw that the results varied significantly between the different cases. While the enhancement factor is negligible in the s-channel case, the t-channel one can induce an enhancement as large as O(10 4 ).…”

“…The 1/r 5 form remains valid as long as the external fermions are non-relativistic and the momentum transfer between them, q ∼ r −1 , is smaller than the energy scale of the contact interaction. At smaller distances (correspondingly higher momentum transfer), the 1/r 5 form will be modified to 1/r 2 or 1/r, depending on possible ways of opening the contact interaction [42]. In this section, we investigate possible effects of neutrino forces on the Sommerfeld enhancement.…”

“…[42], the effective potential generated in this case contains spin-dependent and spin-independent pieces. For simplicity, we focus on the latter which reads [42]:…”

“…4.1, this scenario gives the correct DM abundance for O(1) gauge coupling, except in the band m Z 2m χ , where there is an s-channel resonance. The neutrino forces arising in the t-channel mediated by the vector boson can be calculated in the same manner as the scalar case in [42]. The resulting potentials have a similar r-dependence to the scalar case, though the spin dependence is different and more complicated.…”