Velocity power counting for massive-mediator NREFTs

Generalize the NREFT velocity-power-counting analysis to dark-matter systems with a massive mediator, including the regimes in which the mediator-to-dark-matter mass ratio is comparable to or larger than the dark-matter velocity, and determine how the additional mass scale modifies the matching and Sommerfeld-enhancement analysis.

Background

The paper develops the NREFT velocity power counting explicitly for a massless scalar mediator. Introducing a mediator mass adds the dimensionless parameter epsilon_phi = m_phi/m_chi alongside the velocity expansion parameter v, producing multiple possible scale hierarchies and complicating the matching between the ultraviolet quantum field theory and the nonrelativistic effective theory.

The authors restrict their detailed analysis to the massless-mediator case and identify a systematic treatment of massive mediators—including the regimes in which the mediator mass is comparable to or larger than the typical nonrelativistic scales—as an unresolved extension. Such an analysis is also relevant to axial-vector mediator models, whose consistent ultraviolet completions generally require a nonzero mediator mass.

References

This complicates the matching of the NREFT, and we leave a full exploration of the velocity power counting including a mediator mass to future work.

— EFT Approaches to Sommerfeld Enhancement and Bound States in Singular Potentials  (2609.10690 - Bhattacharya et al., 9 Sep 2026) in Section 3.1, subsection “Scalar mediator”

However, a more nuanced computation of the bound states (or their absence) would need an all-order matching computation, which we leave to future work.

— EFT Approaches to Sommerfeld Enhancement and Bound States in Singular Potentials  (2609.10690 - Bhattacharya et al., 9 Sep 2026) in Section 3.4, subsection “Vector, axial vector and pseudo-Goldstone mediators”