Remarks on Top-philic $Z^\prime$ Boson Interactions with Nucleons

TL;DR

This paper calculates the effective interaction between nucleons and a top-philic $Z'$ boson, considering mixing effects and contributions from heavy quarks and gluons, to inform dark matter detection cross sections.

Contribution

It provides a detailed computation of the nucleon-$Z'$ vertex including mixing effects and heavy quark contributions, which was not thoroughly addressed before.

Findings

Light quark contributions dominate despite mixing suppression.

Heavy quark and gluon contributions are suppressed at low momentum transfer.

Mixing effects influence the effective nucleon-$Z'$ interaction significantly.

Abstract

This article provides the calculation of an effective vertex function between a nucleon and a $Z^\prime$ boson that couples preferentially to either the top quark or the third generation of fermions, for the purpose of calculating vector-portal dark matter nuclear recoil cross sections. Mixing effects between the new gauge group $U(1)^\prime$ and the Standard Model hypercharge group $U(1)_Y$ are taken into account. Contributions to the $U(1)^\prime$ nucleon current from heavy quarks are quantified using the heavy quark expansion. Also taken into account are contributions from the 1-loop $Z^\prime$-gluon interactions and mixing-induced contributions from the light quarks in the nucleon. We find that, for reasonable values of the $U(1)^\prime$ gauge parameter, contributions from the light quarks dominate despite being mixing-suppressed. It is shown that this holds for most models even if mixing effects do not appear at tree level. Contributions from the heavy quarks and gluons are suppressed by $1/m_Q^2$ and possibly also by momentum in the low momentum transfer limits relevant for dark matter direct detection. We discuss under which conditions the subdominant terms become relevant.