The dihadron fragmentation function and its evolution

TL;DR

The paper develops a rigorous framework for dihadron fragmentation functions in high-energy e+e- annihilation. It defines the dihadron fragmentation function in an operator formalism using the cut-vertex approach, derives its leading-log DGLAP evolution for the non-singlet quark channel, and demonstrates factorization of the cross section at LO and NLO. By computing NS evolution and solving it numerically with a simple initial condition, the work reveals that dihadron correlations within a jet evolve in a manner akin to single-hadron fragmentation, with additional contributions from independent fragmentation after parton splitting. This provides a foundation for interpreting dihadron observables and for exploring medium-induced modifications in jet environments, with future work extending to singlet evolution and all-orders factorization.

Abstract

Dihadron fragmentation functions and their evolution are studied in the process of $e^+e^-$ annihilation. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) is shown to factorize into a short distance parton cross section and a long distance dihadron fragmentation function. We provide the definition of such a dihadron fragmentation function in terms of parton matrix elements and derive its DGLAP evolution equation at leading log. The evolution equation for the non-singlet quark fragmentation function is solved numerically with a simple ansatz for the initial condition and results are presented for cases of physical interest.

Figures (21)

• Figure 1: Diagrams to be resummed iteratively to obtain the evolution of the fragmentation functions.
• Figure 2: cut-vertex for quark fragmention function at LO.
• Figure 3: The leading order Feynman diagram contributing to the double inclusive fragmentation function.
• Figure 4: The variable transform from $[{p_1}_x,{p_1}_y,{p_1}_z,{p_2}_x,{p_2}_y,{p_2}_z]$ to $[p_1,p_2,q_\perp,\theta_{cm},\phi_{cm},\phi_\perp]$.
• Figure 5: The cut-vertex representation of the dihadron fragmentation function.