Observation of Transverse Polarization Asymmetries of Charged Pion Pairs in $e^{+}{e}^{-}$ Annihilation near $\sqrt{s}=10.58\mathrm{GeV}$

The interference fragmentation function translates the fragmentation of a quark with a transverse projection of the spin into an azimuthal asymmetry of two final-state hadrons. In $e^{+}{e}^{-}$ annihilation the product of two interference fragmentation functions is measured. We report nonzero asymmetries for pairs of charge-ordered ${\pi }^{+}{\pi }^{-}$ pairs, which indicate a significant interference fragmentation function in this channel. The results are obtained from a $672{\mathrm{fb}}^{-1}$ data sample that contains $711\times {10}^6$ ${\pi }^{+}{\pi }^{-}$ pairs and was collected at and near the ${\rm Y}(4S)$ resonance, with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Figure 1

Azimuthal angle definitions for ${\varphi }_1$ and ${\varphi }_2$ as defined relative to the thrust axis in the CMS.

Figure 2

Relative contributions of various processes for pion pairs as a function of the $8\times 8$ $m_1$, $m_2$ bin number. The closed circles denote light quark-antiquark pair events, inverted triangles—charm events, triangles—charged $B$ meson pairs, open circles—neutral $B$ meson pairs and squares—$\tau$ pairs.

Figure 3

$a_{12}$ modulations for the $9\times 9$ $z_1$, $z_2$ binning as a function of $z_1$ for the $z_2$ bins. The shaded (green) areas correspond to the systematic uncertainties.

Figure 4

$a_{12}$ modulations for the $8\times 8$ $m_1$, $m_2$ binning as a function of $m_2$ for the $m_1$ bins. The shaded (green) areas correspond to the systematic uncertainties.