Factorization of $e^+e^- \to H \, X$ cross section, differential in $z_h$, $P_T$ and thrust, in the $2$-jet limit

TL;DR

This paper develops a factorization scheme for the $e^+e^- o H X$ cross section differential in $z_h$, $P_T$, and thrust, providing all-order perturbative results and comparing favorably with experimental data.

Contribution

It introduces a novel factorization approach for the $e^+e^- o H X$ process that includes transverse momentum dependence and is applicable to global TMD phenomenology.

Findings

All-order perturbative expressions for the cross section are derived.

NLO and NLL accuracy calculations show excellent agreement with BELLE data.

The scheme links TMD functions across different processes, enabling comprehensive TMD studies.

Abstract

Factorizing the cross section for single hadron production in $e^+e^-$ annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the $e^+e^- \to HX$ cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in $z_h$, $P_T$ and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possibility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, $e^+e^- \to H_1 H_2 X$ and $e^+e^- \to HX$ annihilations.