Precision QCD Event Shapes at Hadron Colliders: The Transverse Energy-Energy Correlator in the Back-to-Back Limit

Area of Science:

• High Energy Physics
• Quantum Chromodynamics (QCD)
• Collider Physics

Background:

• The transverse energy-energy correlator (TEEC) is a key observable for studying particle interactions at hadron colliders.
• Precision calculations in Quantum Chromodynamics (QCD) are essential for interpreting experimental results at the Large Hadron Collider (LHC).
• Understanding event shapes like TEEC in the back-to-back (dijet) limit is crucial for probing fundamental physics.

Purpose of the Study:

• To derive and present an operator-based factorization formula for the TEEC in the dijet limit at hadron colliders.
• To provide the first next-to-next-to-leading logarithmic (NNLL) resummation for a dijet event shape observable at the LHC.
• To obtain the first analytic result for a hadron collider dijet soft function at next-to-next-to-leading order (NNLO).

Main Methods:

• Development of an operator-based factorization formula for the TEEC in the dijet limit.
• Incorporation of soft radiation effects using a dijet soft function, calculated to NNLO.
• Numerical evaluation of the TEEC, resummed to NNLL and matched to fixed order at the LHC.

Main Results:

• A novel, symmetric factorization formula for the TEEC in the back-to-back limit was established.
• The dijet soft function was analytically derived to NNLO, leveraging problem symmetries.
• The first NNLL resummation for a dijet event shape at a hadron collider was achieved.

Conclusions:

• The derived factorization formula and NNLL resummation provide a significant advancement for precision studies of QCD at the LHC.
• The theoretical simplicity of the TEEC observable makes it a valuable tool for both experimental data analysis and theoretical investigations of factorization properties.
• This work paves the way for more precise tests of the Standard Model and searches for new physics at the LHC.