Dijets with a large rapidity separation as a probe for large extra dimension gravity in trans-Planckian regime

Dijets with a large rapidity separation between jets serve as a probe for the gravity with large extra dimensions at proton colliders in the trans-Planckian eikonal regime, i. e., when $\sqrt{\hat{s}} \gg M_D \gg \sqrt{-\hat{t}}$. Here, $\hat{s}$ and $\hat{t}$ are the Mandelstam variables of the colliding parton-parton system, and $M_D$ is the Planck mass scale in the space-time with $n_D$ compactified extra dimensions. A relevant observable for this regime may be the cross section of high-mass ($M_{jj}\sim\sqrt{\hat{s}} \gg M_D$) dijet production with jets widely separated in rapidity. Then the standard model (SM) background should be calculated within the next-to-leading logarithmic (NLL) approximation of Lipatov-Fadin-Kuraev-Balitsky (BFKL) formalism of quantum chromodynamics (QCD) suitable for $\sqrt{\hat{s}}\gg\sqrt{\hat{t}}\gg\Lambda_\mathrm{QCD}$. The signal of the large extra dimension gravity alongside the NLL BFKL QCD background are estimated for the high-luminosity Large Hadron Collider (HL-LHC) and future colliders such as FCCpp and CEPC-SppC.