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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msqrt> <a:mover accent="true"> <a:mi>s</a:mi> <a:mo stretchy="false">^</a:mo> </a:mover> </a:msqrt> <a:mo>≫</a:mo> <a:msub> <a:mi>M</a:mi> <a:mi>D</a:mi> </a:msub> <a:mo>≫</a:mo> <a:msqrt> <a:mrow> <a:mo>−</a:mo> <a:mover accent="true"> <a:mi>t</a:mi> <a:mo stretchy="false">^</a:mo> </a:mover> </a:mrow> </a:msqrt> </a:math> . Here <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mover accent="true"> <g:mi>s</g:mi> <g:mo stretchy="false">^</g:mo> </g:mover> </g:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mover accent="true"> <k:mi>t</k:mi> <k:mo stretchy="false">^</k:mo> </k:mover> </k:math> are the Mandelstam variables of colliding parton-parton system and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>M</o:mi> <o:mi>D</o:mi> </o:msub> </o:math> is the Planck mass scale in the space-time with compactified <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>n</q:mi> <q:mi>D</q:mi> </q:msub> </q:math> extra dimensions. A relevant observable for this regime may be the cross section of high-mass ( <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>M</s:mi> <s:mrow> <s:mi>j</s:mi> <s:mi>j</s:mi> </s:mrow> </s:msub> <s:mo>∼</s:mo> <s:msqrt> <s:mover accent="true"> <s:mi>s</s:mi> <s:mo stretchy="false">^</s:mo> </s:mover> </s:msqrt> <s:mo>≫</s:mo> <s:msub> <s:mi>M</s:mi> <s:mi>D</s:mi> </s:msub> </s:math> ) dijet production with a large rapidity separation. Then the standard model background should be calculated within the next-to-leading logarithmic (NLL) approximation of Balitsky-Fadin-Kuraev-Lipatov (BFKL) formalism of quantum chromodynamics (QCD) suitable for <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:msqrt> <w:mrow> <w:mover accent="true"> <w:mrow> <w:mi>s</w:mi> </w:mrow> <w:mrow> <w:mo stretchy="false">^</w:mo> </w:mrow> </w:mover> </w:mrow> </w:msqrt> <w:mo>≫</w:mo> <w:msqrt> <w:mrow> <w:mo>−</w:mo> <w:mover accent="true"> <w:mrow> <w:mi>t</w:mi> </w:mrow> <w:mrow> <w:mo stretchy="false">^</w:mo> </w:mrow> </w:mover> </w:mrow> </w:msqrt> <w:mo>≫</w:mo> <w:msub> <w:mrow> <w:mi mathvariant="normal">Λ</w:mi> </w:mrow> <w:mrow> <w:mi>QCD</w:mi> </w:mrow> </w:msub> </w:mrow> </w:math> . 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.