Figure 1

The experimental data on $A_{12}^{UL}$, $A_{12}^{UC}$ (upper plots) and $A_0^{UL}$ and $A_0^{UC}$ (lower plots), as measured by the Belle Collaboration [12] in unpolarized $e^{+}{e}^{-}\to h_1{h}_{2}X$ processes, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table , obtained by fitting the SIDIS and the $A_{12}$ asymmetries with the standard parametrization; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. 24. Notice that the $A_0^{UL}$ and $A_0^{UC}$ data are not included in the fit and our curves, with the corresponding uncertainties, are simply computed using the parameters of Table .Reuse & Permissions

Figure 2

The experimental data on the SIDIS azimuthal moment $A_{UT}^{\sin ({\varphi }_h+{\varphi }_S)}$, as measured by the COMPASS Collaboration [10] on proton (upper plots) and deuteron (lower plots) targets, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table , obtained by fitting the SIDIS and the $A_{12}$ asymmetries with standard parametrization; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. 24.Reuse & Permissions

Figure 3

The experimental data on the SIDIS azimuthal moment $A_{UT}^{\sin ({\varphi }_h+{\varphi }_S)}$, as measured by the HERMES Collaboration [11], are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table , obtained by fitting the SIDIS and the $A_{12}$ asymmetries with standard parametrization; the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. 24.Reuse & Permissions

Figure 4

Plots of the functions ${\mathcal{N}}_{\mathrm{fav}}^C(z)$ and ${\mathcal{N}}_{\mathrm{dis}}^C(z)$ for the favored and disfavored Collins functions as obtained by using the standard, Eq. (12), and polynomial, Eq. (32), parametrizations. On the left panel we show the results obtained by fitting the SIDIS data together with the $A_{12}$ Belle asymmetries (both with standard and polynomial parametrization), while on the right panel we show the corresponding results obtained by fitting the SIDIS data together with the $A_0$ Belle asymmetries.Reuse & Permissions

Figure 5

The experimental data on $A_0^{UL}$, $A_0^{UC}$ (upper plots) and $A_{12}^{UL}$ and $A_{12}^{UC}$ (lower plots), as measured by the Belle Collaboration [12] in unpolarized $e^{+}{e}^{-}\to h_1{h}_{2}X$ processes, are compared to the curves obtained from our global fit. The solid lines correspond to the parameters given in Table , obtained by fitting the SIDIS and the $A_0$ asymmetries with polynomial parametrization, the shaded areas correspond to the statistical uncertainty on the parameters, as explained in the text and in Ref. 24. Notice that the $A_{12}^{UL}$ and $A_{12}^{UC}$ data are not included in the fit and our curves, with the corresponding uncertainties, are simply computed using the parameters of Table .Reuse & Permissions

Figure 6

The left panel shows (solid red lines) the transversity distribution functions $x{h}_{1q}(x)=x{\Delta }_{T}q(x)$ for $q=u$, $d$, with their uncertainty bands (shaded areas), obtained from the best fit of SIDIS data on $A_{UT}^{\sin ({\varphi }_h+{\varphi }_S)}$ and $e^{+}{e}^{-}$ data on $A_{12}$, adopting the standard parametrization (Table ). Similarly, the right panel shows the corresponding first moment of the favored and disfavored Collins functions, Eq. (33). All results are given at $Q^2=2.41{\mathrm{GeV}}^2$. The corresponding results using the polynomial parametrization, not shown, would almost entirely overlap with those shown here, both for the transversity and the Collins functions. The dashed blue lines show the same quantities as obtained in Ref. 7 using the data then available on $A_{UT}^{\sin ({\varphi }_h+{\varphi }_S)}$ and $A_{12}^{UL}$.Reuse & Permissions

Figure 7

The left panel shows (solid red lines) the transversity distribution functions $x{h}_{1q}(x)=x{\Delta }_{T}q(x)$ for $q=u$, $d$, with their uncertainty bands (shaded areas), obtained from our best fit of SIDIS data on $A_{UT}^{\sin ({\varphi }_h+{\varphi }_S)}$ and $e^{+}{e}^{-}$ data on $A_0$, adopting the polynomial parametrization (Table ). Similarly, the right panel shows the corresponding first moment of the favored and disfavored Collins functions, Eq. (33). All results are given at $Q^2=2.41{\mathrm{GeV}}^2$. The corresponding results using the standard parametrization, not shown, would almost entirely overlap with those shown here for the transversity distribution. The favored Collins function would be smaller and the disfavored one also smaller (i.e., larger in magnitude), with their uncertainty bands still partially overlapping.Reuse & Permissions

Figure 8

The tensor charge $\delta q\equiv {\int }_0^{1}dx[{\Delta }_{T}q(x)-{\Delta }_T\overline{q}(x)]$ for $u$ (left) and $d$ (right) quarks, computed using the transversity distributions obtained from our best fits, Table  (top solid red circles) and Table  (solid red triangles). The gray areas correspond to the statistical uncertainty bands in our extraction. These results are compared with those given in Ref. 7 (number 2), obtained in Ref. 8 (number 10) and computed with lattice [26] (number 5) or model calculations Refs. 27, 28, 29, 30, 31, 32 (respectively, numbers 3, 4 and 6–9).Reuse & Permissions

Figure 9

Estimates, obtained from our global fit, for the azimuthal correlations $A_{12}^{UL}$, $A_{12}^{UC}$, $A_0^{UL}$ and $A_0^{UC}$ in unpolarized $e^{+}{e}^{-}\to h_1{h}_{2}X$ processes at BABAR [25]. The solid lines correspond to the parameters given in Table , obtained by fitting the $A_{12}$ Belle asymmetry; the shaded area corresponds to the uncertainty on these parameters, as explained in the text.Reuse & Permissions

Figure 10

Estimates, obtained from our global fit, for the azimuthal correlations $A_{12}^{UL}$, $A_{12}^{UC}$, $A_0^{UL}$ and $A_0^{UC}$ in unpolarized $e^{+}{e}^{-}\to h_1{h}_{2}X$ processes at BABAR [25]. The solid lines correspond to the parameters given in Table , obtained by fitting the $A_0$ Belle asymmetry; the shaded area corresponds to the uncertainty on these parameters, as explained in the text.Reuse & Permissions