Calculating Dihadron Fragmentation Functions in the NJL-jet model

The NJL-jet model provides a framework for calculating fragmentation functions without the introduction of ad hoc parameters. We develop the NJL-jet model to investigate dihadron fragmentation functions (DFFs) of the form $D^{h_1 h_2}_q(z_1,z_2)$. Here we studied DFFs for $q \to \{\pi^+ \pi^-\}$, $\{\pi^+ K^-\}$, and $\{K^+ K^-\}$,with $q = u, d, s$. The driving terms, which represent the probability of one of the hadrons being emitted in the first emission step of the quark-jet hadronization picture, dominate the solutions of the DFFs where either $z_1$ or $z_2$ is large, and $z_1$ ($z_2$) is the light-cone momentum fraction of the emitted hadron, $h_1$ ($h_2$). The higher order terms, which represent the probability of neither of the hadrons being emitted in the first emission step of the quark-jet, become more significant as $z_1$ ($z_2$) is lowered. Finally, we present a sample result for QCD evolution of DFFs, that significantly modify the model solutions when evolved to typical hadronic scale of $4 \mathrm{GeV}^2$.