Two-loop form factors for Dark Matter annihilation to colored Standard Model particles

TL;DR

We address the problem of achieving NLO QCD precision for dark matter annihilation and production into colored Standard Model states in a UV-complete model with a colored scalar mediator. Our approach computes two-loop QCD form factors for the gluon and quark channels, decomposing amplitudes into scalar form factors via a projector, and reducing two-loop integrals to master integrals using IBP, followed by UV renormalization and IR subtraction. The key contributions are analytic expressions for the $gg$ and $q\bar{q}$ form factors with both massive and massless mediators, including the relevant master integrals, suitable for combining with real-emission contributions to obtain full NLO predictions. This work advances precision DM phenomenology at colliders and in relic-density calculations by providing the essential ingredients for NLO QCD predictions of DM production/annihilation cross sections.

Abstract

We investigate a UV-complete model in which the dark matter (DM) particle interacts with gluons through a colored scalar mediator. This framework provides a phenomenologically viable scenario testable at hadron colliders. While mono-jet signatures are relevant for collider searches, zero-jet processes correspond to complete annihilation of Standard Model (SM) particles into DM, contributing to the relic density. In this work, we study dark matter annihilation into SM colored particles, which in our model arises at leading order from loop-induced processes. We compute the relevant two-loop QCD amplitudes for both gluon and quark channels in dark matter production or annihilation. The amplitudes are decomposed into scalar form factors using the projector technique. Using integration-by-parts (IBP) identities, we obtain analytical expressions for the form factors in terms of master integrals. Ultraviolet divergences are removed via counterterm renormalization, yielding UV-finite results. These results would enable predictions for dark matter production or annihilation into SM colored particles at next-to-leading order (NLO) in QCD.

Figures (5)

• Figure 1: Feynman rules for interaction vertices involving dark matter $\chi$, colored mediator $\phi$ and gluons $g$.
• Figure 2: Leading order Feynman diagrams for $\chi \chi^* \rightarrow g g$.
• Figure 3: Leading order Feynman diagrams for $\chi \chi^* \to q \bar{q}$.
• Figure 4: Topmost topologies in $\chi \chi* \rightarrow g g$ , black lines are massless gluons, green lines are massive mediators and thin black lines are dark matter particles.
• Figure 5: Renormalization of $\alpha_s$ coupling, mediator mass $m_\phi$, and $\lambda_d$ coupling to DM.