Kinematic regions in the e+e− → hX factorized cross section in a 2-jet topology with thrust

Abstract

Factorization theorems allow to separate out the universal, non-perturbative content of the hadronic cross section from its perturbative part, which can be computed in perturbative QCD, up to the desired order. In this paper, we derive a rigorous proof of factorization of the e+e− → hX cross section, sensitive to the transverse momentum of the detected hadron with respect to the thrust axis, in a completely general framework, based on the Collins-Soper-Sterman approach. This procedure naturally leads to a partition of the e+e− → hX kinematics into three different regions, each associated to a different factorization theorem. In one of these regions, which covers the central and widest range, the factorization theorem has a new structure, which shares the features of both TMD and collinear factorization schemes. In the corresponding cross section, the role of the rapidity cut-off is investigated, as its physical meaning becomes increasingly evident. An algorithm to identify these three kinematic regions, based on ratios of observable quantities, is provided.

Snowmass 2021 White Paper: Electron Ion Collider for High Energy Physics

“…A factorization theorem was recently derived in Ref. [231] for e + e − → HX, where the transverse momentum P T of the detected hadron is measured with respect to the thrust axis. Under certain approximations, this cross section can be written as a convolution of a TMD FF with a coefficient that is totally predicted by perturbative QCD and can be interpreted as a partonic cross section [232,233].…”

New tool for kinematic regime estimation in semi-inclusive deep-inelastic scattering

“…This was also reported in Ref. [43], where an algorithm based on region indicator ratios involving both q T /Q and y h was introduced for the study of the e + e − → hX process. Moreover, as the correlation between the rapidity y h and q T /Q is very strong, it will be important to obtain information on y h directly from experimental measurements.…”

Transverse Momentum Dependent Fragmentation Functions from recent BELLE data

“…[24] and Ref. [25], do not find total agreement on the final form of the corresponding factorization theorem. In this paper we will follow the factorization scheme devised in Refs.…”

“…As discussed in Refs. [24,25], the 2-jet final state topology of the above process can occur in three different kinematic configurations or "Regions", denoted Region 1, 2 and 3 in Refs. [24,25], each corresponding to a different factorization theorem.…”

“…[24,25], the 2-jet final state topology of the above process can occur in three different kinematic configurations or "Regions", denoted Region 1, 2 and 3 in Refs. [24,25], each corresponding to a different factorization theorem. These kinematic regions can be defined in terms of the size of the transverse momentum P T of the hadron observed inside the jet cone.…”