Gravity and the Neutral Currents: Effective Interactions from the Trace Anomaly

TL;DR

This work delivers a complete one-loop analysis of the graviton coupling to two neutral SM gauge bosons via the TVV' vertex, focusing on the trace anomaly as the leading source of EMT breaking. By deriving a rigorous set of Ward and Slavnov-Taylor identities and performing a full DR/on-shell renormalization, the authors decompose the TVV' amplitudes into fermion, gauge, and improvement sectors, uncovering a characteristic massless anomaly pole in each gauge-invariant sector. The results show that, at high energies, the pole exchange dominates the trace part of the amplitudes, with explicit pole residues tied to beta-function coefficients and gauge couplings; the analysis includes the improved EMT essential for conformal coupling and considers external-leg corrections and graviton–Higgs mixing. The findings provide a robust framework for gravity–SM interactions in curved space and have implications for precision collider phenomenology in low-scale gravity scenarios, while laying groundwork for extensions to charged currents and SUSY contexts.

Abstract

We present a complete study of the one graviton-two neutral gauge bosons vertex at 1-loop level in the electroweak theory. This vertex provides the leading contribution to the interaction between the Standard Model and gravity, mediated by the trace anomaly, at first order in the inverse Planck mass and at second order in the electroweak expansion. At the same time, these corrections are significant for precision studies of models with low scale gravity at the LHC. We show, in analogy with previous results in the QED and QCD cases, that the anomalous interaction between gravity and the gauge current of the Standard Model, due to the trace anomaly, is mediated, in each gauge invariant sector, by effective massless scalar degrees of freedom. We derive the Ward and Slavnov-Taylor identities characterizing the vertex. Our analysis includes the contributions from the improvements of the scalar sector, induced by a conformally coupled Higgs sector in curved space.

Figures (18)

• Figure 1: The pole contribution as a collinear exchange of a fermion/antifermion pair (a) and the diagrammatic representation of the anomaly pole (b).
• Figure 2: One-loop loop decomposition of $G_{\mu\nu\alpha\beta}^{AA}(p,q)$ in terms of the amputated function $\Gamma_{\mu\nu\alpha\beta}^{AA}(p,q)$ and of 2-point functions on the external legs.
• Figure 3: One loop decomposition of $G_{\mu\nu\alpha\beta}^{AZ}(p,q)$ in terms of the amputated funtion $\Gamma_{\mu\nu\alpha\beta}^{AZ}(p,q)$ and of the corrections on the external lines.
• Figure 4: Decomposition of $G_{\mu\nu\alpha}^{A\phi}(p,q)$ at 1-loop in terms of the amputated correlator $\Gamma_{\mu\nu\alpha}^{A\phi,\,1}(p,q)$ and of the corrections on the external legs.
• Figure 5: Decomposition of $G_{\mu\nu\alpha\beta}^{ZZ}(p,q)$ in terms of the amputated $\Gamma_{\mu\nu\alpha\beta}^{ZZ}(p,q)$ and of the corrections on the external legs.