Abstract
The present study aimed to explore the behavior of unpolarized fragmentation functions (FFs) of pion in the regions of small momentum fractions z. This study used a novel phenomenological QCD approach in the framework of fractal (or self-similar) behavior of FFs to quantify the small-z region. To this end, a simple parameterization for the pion fractal FFs is considered and small z experimental datasets on single inclusive pion production in electron–positron ($$e^+e^-$$) annihilation (SIA) for the range of $$10.54< Q < 91.28$$ GeV and $$z<0.1$$ are included in this analysis. The estimations of the uncertainty in the present analysis are carried out using the standard “Hessian” approach. In total, considering the overall value of $$\chi ^2/\mathrm{dof}$$ and theory/data comparisons, the results indicate excellent agreements between the experimental datasets and the theory predictions at small momentum fractions z. Finally, we present detailed comparisons between predictions for the relevant small-z observables obtained with various recent models of pion FFs available in literature. Considering the findings presented in this study, we discuss how our knowledge of pion FFs may be improved at small-z by future measurements.
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