First extraction of valence transversities in a collinear framework

TL;DR

This work delivers the first valence transversity extraction in a collinear framework by exploiting two-hadron SIDIS with DiFFs, constrained by $e^+e^-$ data from Belle to enable flavor separation between $u$ and $d$ quarks. The analysis combines HERMES and COMPASS SIDIS measurements with DiFF inputs and evolves them using LO chiral-odd splitting functions, implementing both Hessian and Monte Carlo error analyses. The resulting $x h_1^{u_v}$ and $x h_1^{d_v}$ are consistent with Collins-effect extractions within uncertainties, and yield tensor charges $\delta q(Q_0^2)$ that are compatible with model and lattice expectations within the explored $x$-range. The study demonstrates the viability of a collinear approach to transversity with DiFFs and motivates future measurements to reduce uncertainties, particularly at low and high $x$.

Abstract

We present an extraction of the valence transversity parton distributions based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets. Recently released data for proton and deuteron targets at HERMES and COMPASS permit a flavor separation of valence transversities. The present extraction is performed in the framework of collinear factorization, where dihadron fragmentation functions are involved. The latter are taken from a previous analysis of electron-positron annihilation measurements.

Figures (4)

• Figure 1: Kinematics of the two-hadron semi-inclusive production. The azimuthal angles $\phi_{R}$ of the dihadron, and $\phi_S$ of the component $\boldsymbol{S}_T$ of the target-polarization, transverse to both the virtual-photon and target-nucleon momenta $\boldsymbol{q}$ and $\boldsymbol{P}$, respectively, are evaluated in the virtual-photon-nucleon center-of-momentum frame.
• Figure 2: The combinations of Eq. (\ref{['e:h1p']}), left panel, and Eq. (\ref{['e:h1D']}), right panel. The squares and triangles are obtained from the COMPASS and HERMES data, respectively (the values are indicated in the last column of Tab. \ref{['t:data']}). The thick solid line indicates the central value of the best-fit result in the standard approach with the flexible scenario (see text). The error band is the outcome of the merging of all the straight lines connecting the statistical error bars of the fit for each experimental point.
• Figure 3: Same observables and data symbols as in the previous figure. The uncertainty band represents in the Monte Carlo approach the selected $68\%$ of all fitting replicas (see text).
• Figure 4: The up (left) and down (right) valence transversities coming from the present analysis evolved to $Q^2=2.4$ GeV$^2$. From top row to bottom, results with the rigid, flexible, and extra-flexible scenarios are shown, respectively. The dark thick solid lines are the Soffer bound. The uncertainty band with solid boundaries is the best fit in the standard approach at $1\sigma$, whose central value is given by the central thick solid line. The uncertainty band with dashed boundaries is the $68\%$ of all fitting replicas obtained in the Monte Carlo approach. As a comparison, the uncertainty band with short-dashed boundaries is the transversity extraction from the Collins effect Anselmino:2008jk.