Dilaton Interactions and the Anomalous Breaking of Scale Invariance of the Standard Model

TL;DR

The paper analyzes how dilatons couple to Standard Model currents, distinguishing graviscalar and non-gravitational (effective) dilatons and linking their interactions to the conformal anomaly. It provides a detailed one-loop treatment of dilaton–gauge–gauge vertices, establishing that renormalizability in the electroweak sector requires the Higgs to be conformally coupled with $\chi=\tfrac{1}{6}$ and deriving explicit expressions for $\rho\gamma\gamma$, $\rho\gamma Z$, and $\rho ZZ$ amplitudes together with their decay rates. It also treats the off-shell dilaton–gluon–gluon vertex in QCD, showing the anomaly and top-quark contributions shape the $\Gamma(\rho\to gg)$ width. Extending to scale-invariant extensions of the SM, the work identifies an anomaly pole in the $J_DVV$ and $TVV$ correlators, discusses mass corrections via a PCDC-like relation, and explains how infrared coupling of the anomaly pole drives anomaly-enhanced decays, with distinct implications for graviscalars and effective dilatons. The analysis provides a framework where the trace anomaly signals the dynamical content of the SM at high energies, offering guidance for collider phenomenology and searches for dilaton-like states at the LHC.

Abstract

We discuss the main features of dilaton interactions for fundamental and effective dilaton fields. In particular, we elaborate on the various ways in which dilatons can couple to the Standard Model and on the role played by the conformal anomaly as a way to characterize their interactions. In the case of a dilaton derived from a metric compactification (graviscalar), we present the structure of the radiative corrections to its decay into two photons, a photon and a $Z$, two $Z$ gauge bosons and two gluons, together with their renormalization properties. We prove that, in the electroweak sector, the renormalization of the theory is guaranteed only if the Higgs is conformally coupled. For such a dilaton, its coupling to the trace anomaly is quite general, and determines, for instance, an enhancement of its decay rates into two photons and two gluons. We then turn our attention to theories containing a non-gravitational (effective) dilaton, which, in our perturbative analysis, manifests as a pseudo-Nambu Goldstone mode of the dilatation current ($J_D$). The infrared coupling of such a state to the two-photons and to the two-gluons sector, and the corresponding anomaly enhancements of its decay rates in these channels, is critically analyzed.

Figures (5)

• Figure 1: Amplitudes of triangle topology contributing to the $\rho \gamma\gamma$, $\rho \gamma Z$ and $\rho ZZ$ interactions. They include fermion $(F)$, gauge bosons $(B)$ and contributions from the term of improvement (I). Diagrams (a)-(g) contribute to all the three channels while (h)-(k) only in the $\rho ZZ$ case.
• Figure 2: Bubble and tadpole-like diagrams for $\rho \gamma\gamma$$\rho \gamma Z$ and $\rho Z Z$. Amplitudes (l)-(q) contribute only in the $\rho ZZ$ channel.
• Figure 3: External leg corrections. Diagrams (b) and (c) appear only in the $\rho Z Z$ sector.
• Figure 4: QCD vertices at next-to-leading order. In the on-shell gluon case only diagram (a)contributes.
• Figure 5: Exchange of a dilaton pole mediated by the $J_D V V$ correlator.