To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before

TL;DR

The paper applies extended (beyond) positivity bounds to the Higgs-Dilaton Inflation EFT to constrain its first higher-derivative operators. By analyzing three 2-to-2 scattering channels in the scalar sector and using a decoupled gravity setup, it derives inequalities among the coefficients $A,B,C,D$ in the $1/\Lambda^4$-suppressed operators, depending on the non-minimal couplings $\xi_h$ and $\xi_\chi$. In the HDI regime with $\xi_h \gg \xi_\chi$, the bounds imply $2A+3B \gtrsim \frac{1}{6\pi^2\xi_h^2}\log(E_{\rm UV}/E_{\rm IR})$, $C \gtrsim \frac{1}{192\pi^2\xi_h^2}\log(E_{\rm UV}/E_{\rm IR})$, and $D>0$, which are easily satisfied for phenomenologically relevant values. The results provide a nontrivial consistency check for HDI as a self-contained EFT below the cutoff $\Lambda\sim M_P/\xi_h$, while also highlighting limitations when renormalizable interactions dominate or gravity is dynamically included.

Abstract

We study the consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV completion, we derive constraints on the Wilson coefficients of the first higher order derivative operators. We show that the values allowed by the constraints are consistent with the phenomenological applications of the Higgs-Dilaton model.

Figures (6)

• Figure 1: Integration contours in the complex s plane. We show a pole in $m^2$, being the mass of an arbitrary particle in the spectrum, as well as the pole in $\mu^2$. Left: Integration encircling all IR poles. Right: Equivalent contour in the UV theory.
• Figure 2: Examples of one-loop logarithmically divergent diagrams generating the higher order operators shown in \ref{['eq:higher_order_ops']}. Solid lines represent $\varrho$ fields, while dashed lines indicate $\phi$ fields.
• Figure 3: Schematic representation of the internal channels contributing to the cross section in the right hand side of the bound \ref{['eq:beyond_positivity_bound']} for the $\varrho\phi \rightarrow \varrho\phi$ process. Solid lines correspond to $\varrho$, while dashed lines indicate $\phi$.
• Figure 4: Plot of the lowest allowed value of $L_0=2A+3B$ as a function of $\xi_h$ and $\xi_\chi$. Note that both the rhs of the bound and the cut-off scale $\Lambda$ are functions of the non-minimal couplings. Level lines show different values of $L_0$. The rectangular region indicates the typical values for HDI couplings ($\xi_h \sim 10^3 -10^5$, $\xi_\chi\lesssim 10^{-3}$).
• Figure 5: Schematic representation of the internal channels contributing to the cross section for the $\varrho\varrho \rightarrow \varrho\varrho$ process.