Ultra-Planckian quark and gluon scattering in agravity

TL;DR

This work investigates graviton-mediated scattering of quarks and gluons within agravity, a renormalizable, scale-free quadratic gravity framework, in the ultra-Planckian regime characterized by $s=(p_1+p_2)^2$ with $s$ much larger than mass scales. By deriving the QCD-agravity Lagrangian and linearized propagators, the authors compute tree-level amplitudes for $gg\to gg$, $gg\to q\bar{q}$, $gq\to gq$, and $qq\to qq$, showing that all amplitudes scale as $|\mathcal{M}|^2 \propto 1/s$ at high energies, consistent with UV completeness. They analyze IR behavior, noting forward divergences in massless cases which are regulated by quark masses, and extract a finite UV piece in the forward limit after subtracting the IR term; positivity of $|\mathcal{M}|^2$ is found to hold in the regime $f_2 \ll f_0$, supporting perturbative unitarity. Overall, the results reinforce agravity as a perturbatively unitary and UV-complete extension of GR, exhibiting universal high-energy gravitational scattering features that parallel earlier photon-scattering findings.

Abstract

We investigate tree-level scattering processes involving quarks ($q$) and gluons ($g$) mediated by graviton exchange in the framework of Agravity, a dimensionless and renormalizable theory of quadratic quantum gravity. Focusing on the ultra-Planckian regime, characterized by the Mandelstam variable $s = (p_1 + p_2)^2$, which corresponds to the total energy squared in the center-of-momentum frame, being much larger than any particle mass scale, we compute the squared amplitudes and analyze the differential cross sections for the processes $gg \to gg$, $gg \to q\bar{q}$, $gq \to gq$, and $qq \to qq$. We demonstrate that all amplitudes scale as $1/s$ at high energies, in agreement with expectations for a UV-complete theory of gravity. In addition, we explore the issue of unitarity in the presence of higher-derivative ghost modes by analyzing the positivity properties of the squared amplitudes. While IR divergences appear in the forward scattering of massless particles, we show that these are regularized by finite quark masses. Our findings support the viability of Agravity as a perturbatively unitary and UV-complete extension of general relativity, capable of consistently describing gravitational interactions among elementary matter fields at trans-Planckian energies.

Figures (4)

• Figure 1: The agravity mediated $gg\rightarrow gg$ scattering. The curly and dashed lines represent the gluon and graviton propagators, respectively.
• Figure 2: The agravity mediated $gg\rightarrow t\bar{t}$ scattering. The continuous lines represents the quark (antiquark) propagator.
• Figure 3: The agravity mediated $gt\rightarrow gt$ scattering.
• Figure 4: The agravity mediated $tt\rightarrow tt$ scattering.