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Measurement of Azimuthal Modulations in the Cross-Section of Di-Pion Pairs in Di-Jet Production from Electron-Positron Annihilation

We present an extraction of azimuthal correlations between two pairs of charged pions detected in opposite jets from electron-positron annihilation. These correlations may arise from the dependence of the di-pion fragmentation on the polarization of the parent quark in the process $e^+e^- \rightarrow q \bar{q}$. Due to the correlation of the quark polarizations, the cross-section of di-pion pair production, in which the pion pairs are detected in opposite jets in a dijet event, exhibits a modulation in the azimuthal angles of the planes containing the hadron pairs with respect to the production plane. The measurement of this modulation allows access to combinations of fragmentation functions that are sensitive to the quark's transverse polarization and helicity. Within our uncertainties we do not observe a significant signal from the previously unmeasured helicity dependent fragmentation function $G_1^\perp$. This measurement uses a dataset of 938~fb$^{-1}$ collected by the Belle experiment at or near $\sqrt{s}\approx10.58$ GeV.