Collins asymmetries in inclusive charged $KK$ and $K\pi$ pairs produced in $e^{+}{e}^{-}$ annihilation

We present measurements of Collins asymmetries in the inclusive process $e^{+}{e}^{-}\to h_1{h}_{2}X$, $h_1{h}_2=KK$, $K\pi$, $\pi \pi$, at the center-of-mass energy of 10.6 GeV, using a data sample of $468{\mathrm{fb}}^{-1}$ collected by the BABAR experiment at the PEP-II $B$ factory at SLAC National Accelerator Center. Considering hadrons in opposite thrust hemispheres of hadronic events, we observe clear azimuthal asymmetries in the ratio of unlike sign to like sign, and unlike sign to all charged $h_1{h}_2$ pairs, which increase with hadron energies. The $K\pi$ asymmetries are similar to those measured for the $\pi \pi$ pairs, whereas those measured for high-energy $KK$ pairs are, in general, larger.

Figure 1

Thrust reference frame (RF12). The azimuthal angles ${\varphi }_1$ and ${\varphi }_2$ are the angles between the scattering plane and the transverse hadron momenta ${\mathbf{p}}_{t1(t2)}$ around the thrust axis $\widehat{\mathbf{n}}$. The polar angle ${\theta }_{\mathrm{th}}$ is the angle between $\widehat{\mathbf{n}}$ and the beam axis. Note that the difference between ${\mathbf{p}}_{t1(t2)}$ and ${\mathbf{P}}_{hT}$ is that the latter is calculated with respect to the $q\overline{q}$ axis.

Figure 2

Distributions of normalized yields (left plot) for unlike ($U$), like ($L$), and any charge combination ($C$) of $KK$ pairs, and their double ratios (right plot) in RF12.

Figure 3

Correction factors for the dilution of the asymmetry due to the difference between the thrust and the $q\overline{q}$ axis. The open (full) markers, triangles and circles, refer to the $U/L$ and $U/C$ double ratios in the RF12 (RF0) frame, respectively. The 16 ($z_1$, $z_2$) bins are shown on the $x$ axis: in each interval between the dashed lines, $z_1$ is chosen in the following ranges: [0.15, 0.2], [0.2, 0.3], [0.3, 0.5], and [0.5, 0.9], while within each interval the points correspond to the four bins in $z_2$.

Figure 4

Comparison of $U/L$ (top) and $U/C$ (bottom) Collins asymmetries in RF12 (left) and RF0 (right) for $KK$, $K\pi$, and $\pi \pi$ pairs. The statistical and systematic uncertainties are represented by the bars and the bands around the points, respectively. The 16 $(z_1,z_2)$ bins are shown on the $x$ axis: in each interval between the dashed lines, $z_1$ is chosen in the following ranges: [0.15, 0.2], [0.2, 0.3], [0.3, 0.5], and [0.5, 0.9], while within each interval the points correspond to the four bins in $z_2$.