Abstract
We compute the inclusive unpolarized dihadron production cross section in the far from back-to-back region of $e^+ e^-$ annihilation in leading order pQCD using existing fragmentation function fits and standard collinear factorization, focusing on the large transverse momentum region where transverse momentum is comparable to the hard scale (the center-of-mass energy). We compare with standard transverse-momentum-dependent (TMD) fragmentation function-based predictions intended for the small transverse momentum region with the aim of testing the expectation that the two types of calculation roughly coincide at intermediate transverse momentum. We find significant tension, within the intermediate transverse momentum region, between calculations done with existing non-perturbative TMD fragmentation functions and collinear factorization calculations if the center-of-mass energy is not extremely large. We argue that $e^+ e^-$ measurements are ideal for resolving this tension and exploring the large-to-small transverse momentum transition, given the typically larger hard scales ($\gtrsim 10$ GeV) of the process as compared with similar scenarios that arise in semi-inclusive deep inelastic scattering and fixed-target Drell-Yan measurements.
Highlights
The annihilation of lepton pairs into hadrons is one of a class of processes notable for being especially clean electromagnetic probes of elementary quark and gluon correlation functions like parton density and fragmentation functions [1]
Within the intermediate transverse momentum region, between calculations done with existing nonperturbative TMD fragmentation functions and collinear factorization calculations if the center-of-mass energy is not extremely large
As one of the simplest processes with nontrivial transverse momentum dependence, dihadron production in eþe− annihilation is ideal for testing theoretical treatments of transverse momentum distributions generally
Summary
The annihilation of lepton pairs into hadrons is one of a class of processes notable for being especially clean electromagnetic probes of elementary quark and gluon correlation functions like parton density and fragmentation functions (pdfs and ffs) [1]. We focus on the last of the lepton-antilepton annihilation regions mentioned in the previous paragraph, wherein pure collinear factorization is expected to be adequate for describing the large deviations from the back-to-back orientation of the hadron pair We view this as a natural starting point for mapping out the regions of the process generally, since it involves only well-established collinear factorization theorems and starts with tree-level perturbation theory calculations. Whether the solution to the difficulties at moderate transverse momentum lies with the collinear treatment or with the phenomenology of TMD functions remains to be seen All of these observations, we argue, provide enhanced motivation for experimental studies of dihadron pair production that probe the intermediate transition region of the transverse momentum dependence.
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