Modeling dihadron fragmentation functions

TL;DR

This work develops a spectator-model for dihadron fragmentation into π+π− X at M_h ≲ 1.3 GeV, deriving leading-twist DiFFs via s- and p-wave decompositions and incorporating resonances. The unpolarized function D1_oo is fixed by fitting to PYTHIA output tuned to HERMES kinematics, enabling predictions for polarized DiFFs D1_ll, D1_ol, and H1_ot and for the transversity–based SSA A_UT^{sin(φ_R+φ_S)} in SIDIS. Using multiple transversity models, the study predicts observable SSA magnitudes (~10% at HERMES, smaller at COMPASS) and highlights the role of interference between s- and p-waves, with signs and magnitude constrained by data. The results offer a framework to extract the nucleon transversity distribution from two-hadron SIDIS and guide future measurements (e.g., BELLE) while acknowledging modeling limitations and the need for final experimental data.

Abstract

We present a model for dihadron fragmentation functions, describing the fragmentation of a quark into two unpolarized hadrons. We tune the parameters of our model to the output of the PYTHIA event generator for two-hadron semi-inclusive production in deep inelastic scattering at HERMES. Once the parameters of the model are fixed, we make predictions for other unknown fragmentation functions and for a single-spin asymmetry in the azimuthal distribution of pi+ pi- pairs in semi-inclusive deep inelastic scattering on a transversely polarized target at HERMES and COMPASS. Such asymmetry could be used to measure the quark transversity distribution function.

Figures (10)

• Figure 1: Angles involved in the measurement of the transverse single-spin asymmetry in deep-inelastic production of two hadrons in the current region.
• Figure 2: Semi-inclusive dihadron counts in bins of $M_h$ from the PYTHIA event generator Sjostrand:2000wi tuned for HERMES Liebing:2004us. The thick solid line represents the sum of all channels. The thin solid line represents the sum of channels 2,3, and 4 described in the text. The dashed line represents the sum of channels 5 and 6 (which are excluded in our model). The gray line is the difference between the total and the sum of all channels 2 to 6 and is assumed to represent channel 1.
• Figure 3: Diagrammatic representation of the correlation function $\Delta$ in the spectator model.
• Figure 4: Semi-inclusive dihadron counts from the PYTHIA event generator Sjostrand:2000wi tuned for HERMES Liebing:2004us and results of the fit (a) as a function of $M_h$, (b) as a function of $z$. Solid line: $p$-wave contribution; dashed line: $s$-wave contribution; dotted line: sum of the two. The contributions of the $\eta$ and $K^0$ have been excluded.
• Figure 5: Model prediction for the ratio $D_{1,ll}/ D_{1,oo}$: (a) as a function of $M_h$, (b) as a function of $z$. The dotted lines represent the positivity bounds of Eq. (\ref{['e:posd1ll']}).