Dijets with a large rapidity separation in the next-to-leading order BFKL formalism for searches of large extra dimensions at colliders

Search for the gravity with large extra dimensions at collider energies is considered in the trans-Planckian eikonal regime, i.e., when $\sqrt{\widehat{s}}\gg M_D\gg \sqrt{-\widehat{t}}$. Here $\widehat{s}$ and $\widehat{t}$ are the Mandelstam variables of colliding parton-parton system and $M_D$ is the Planck mass scale in the space-time with compactified $n_D$ extra dimensions. A relevant observable for this regime may be the cross section of high-mass ($M_{jj}\sim \sqrt{\widehat{s}}\gg M_D$) dijet production with a large rapidity separation. Then the standard model 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 $\sqrt{\widehat{s}}\gg \sqrt{-\widehat{t}}\gg {\mathrm{\Lambda }}_{\mathrm{Q}\mathrm{C}\mathrm{D}}$. In this work the signal of the large extra dimension gravity as well as 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.