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−→ H X cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in zh, PT 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 possi- bility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e−→ H1H2X and e+e−→ H X annihilations.
Highlights
The factorization mechanism, which was first devised by Collins, Soper and Sterman (CSS) for Drell-Yan processes and later proven to work for Semi-Inclusive Deep Inelastic Scattering (SIDIS) [2,3,4,5,6] and e+e− → H1 H2 X ref. [7], cannot be directly applied to e+e− → H X processes
Having only one hadron detected in the final state makes it impossible to cast the cross section in a form that allows to define the Transverse Momentum Dependent parton densities (TMDs) in the conventional way, i.e. by including part of the soft radiation generated in the process inside the TMD itself
The final cross section is written as the convolution of a hard coefficient, which represents the partonic core of the process and is calculable in pQCD at any desired order, with a Transverse Momentum Dependent Fragmentation Function (TMD FF), which carries non-perturbative information and provides a direct probe of the 3D-dynamics of the hadronization mechanism
Summary
We will compute the partonic cross section of e+e− → H X in the 2-jet limit, providing its explicit expression to 1-loop (NLO) precision and its all-order, resummed, formulation. [8], the partonic cross section is the hard part of the factorized full cross section and encodes its short-distance contributions It is fully computable in perturbative QCD as it represents the partonic analogue of the whole process. In the 2-jet limit, the contribution of the fragmenting gluon is strongly suppressed by kinematics (we will present the explicit computation in section 2.1) so that the only relevant contribution is given by the fragmenting fermions. [8], the subtracted and renormalized final state tensor of the partonic cross section is given, order by order in perturbation theory, by: Wjμν, [n], sub(z, τ, τMAX) = Wfμν, [n], unsub( ; z, τ, τMAX)−. We will separately compute the contributions of a fragmenting gluon and a fragmenting fermion, in sections 2.1 and 2.2 respectively
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