Observation of the Naive-$T$-Odd Sivers Effect in Deep-Inelastic Scattering

Azimuthal single-spin asymmetries of leptoproduced pions and charged kaons were measured on a transversely polarized hydrogen target. Evidence for a naive-$T$-odd, transverse-momentum-dependent parton distribution function is deduced from nonvanishing Sivers effects for ${\pi }^{+}$, ${\pi }^0$, and $K^{\pm }$, as well as in the difference of the ${\pi }^{+}$ and ${\pi }^{-}$ cross sections.

Figure 1

Sivers amplitudes for pions, charged kaons, and the pion-difference asymmetry (as denoted in the panels) as functions of $x$, $z$, or $P_{h\perp }$. The systematic uncertainty is given as a band at the bottom of each panel. In addition there is a 7.3% scale uncertainty from the target-polarization measurement.

Figure 2

Sivers amplitudes for ${\pi }^{+}$ (left) and $K^{+}$ (right) as functions of $z$ or $P_{h\perp }$, compared for two different ranges in $Q^2$ (high-$Q^2$ points are slightly shifted horizontally). The corresponding fraction of pions and kaons stemming from exclusive vector mesons, extracted from a Monte Carlo simulation, is provided in the bottom panels.

Figure 3

Sivers amplitudes for ${\pi }^{+}$ (left) and $K^{+}$ (right) as functions of $x$. The $Q^2$ range for each bin was divided into the two regions above and below $⟨Q^2(x_i)⟩$ of that bin. In the bottom the average $Q^2$ values are given for the two $Q^2$ ranges.

Figure 4

Difference of Sivers amplitudes for $K^{+}$ and ${\pi }^{+}$ as functions of $x$ for all $Q^2$ (left), and separated into “low-” and “high-$Q^2$” regions as done for Fig. 3.