Narrow Results

We present the complete azimuthal asymmetries at leading twist in terms of fragmentation functions in dihadron production semi-inclusive electron–positron annihilation process. When the nontrivial $𝜃$ vacuum is taken into consideration, the parity symmetry of quantum chromodynamics is violated. As a consequence of the $local$${𝒫}$-odd effects, ${𝒫}$-odd fragmentation functions would contribute to the azimuthal asymmetries. Azimuthal asymmetry coming from two interference terms with opposite signs vanishes when sum over many events. This symmetry only survives on the event-by-event basis. Azimuthal asymmetry coming from two interference terms with same signs survives and can be measured to extract the ${𝒫}$-odd fragmentation functions. We also present the hadron polarizations.

When tunneling events induced by nontrivial configurations of the quantum chromodynamics gauge fields are taken into consideration, parity violating quantities emerge. Based on this consideration, parity-odd fragmentation functions can be introduced in the high energy reactions. In this paper, we calculate the differential cross-section in terms of both the parity-even and parity-odd fragmentation functions in semi-inclusive electron positron annihilation process. Semi-inclusive implies that not only a vector meson in one jet but also the back-to-back jet is measured in this reaction. According to the differential cross-section, we further calculate the azimuthal asymmetries and hadron polarizations in terms of fragmentation functions. A method of measuring the parity violating effects in the semi-inclusive annihilation process is suggested.

We present the preliminary results of the measurement of the azimuthal asymmetries of two charged pions in the inclusive process $e^{+}{e}^{-}\to \pi \pi X$ in the BESIII experiment. These asymmetries are attributed to the so-called Collins fragmentation function, which depict the behavior of a hadron produced from a transversely polarized quark. This spin-dependent function is an important input for the global analysis of extracting the transversity inside the nucleon. In addition, by comparison with the measured asymmetries at Belle, this measurement provides the first data to explore the $Q^2$ evolution of the spin-dependent fragmentation function. This work is performed based on about 62${\mathrm{\text{pb}}}^{-1}$ data collected with the BESIII detector at BEPCII at $\sqrt{s}$=3.65GeV.

We applied collinear expansion to the semi-inclusive deeply inelastic lepton-nucleon (nucleus) scattering process $e+N(A)\to e+q+X$ with both polarized beam and polarized target up to twist-3, and unpolarized process up to twist-4. The differential cross section and azimuthal asymmetries are expressed in terms of gauge invariant twist-3 and twist-4 TMD parton distribution/correlation functions. Measurements of such azimuthal asymmetries provide methods to study different spin and transverse momentum aspects of the partonic structure of nucleon. We further study the nuclear dependence of azimuthal asymmetries and adopt Gaussian ansatz for TMD distribution/correlation functions to estimat the semi-quantitive behaviour of the nuclear dependence. We predict the A-dependence of azimuthal asymmetries which can be tested in the planned EIC’s.

In the two papers published recently,^{1, 2} we apply collinear expansion to both inclusive ($e^{+}{e}^{-}\to h+X$) and semi-inclusive ($e^{+}{e}^{-}\to h+\bar{q}+X$) hadron production in $e^{+}{e}^{-}$ annihilation to derive a formalism suitable for a systematic study of leading as well as higher twist contributions to fragmentation functions at the tree level. We carry out the calculations for hadrons with spin-0, spin-1/2 as well as spin-1. This proceeding is mainly a summary of these two papers.

The chiral-odd and time reversal-odd transverse momentum dependent (TMD) parton distribution , the so-called Boer-Mulders function, is calculated in the diquark spectator model for both an active up- and down-quark. In particular the signs of and are of interest as they were predicted in other works, and the result of this analysis is consistent with these predictions. Both flavors of the Boer-Mulders function contribute to observables such as the azimuthal cos(2φ) asymmetry in semi-inclusive DIS. Using the results of this analysis for and and recent calculations of the Collins fragmentation function in a similar spectator model, phenomenological predictions for the cos(2φ) asymmetry are presented. In addition, the chiral-odd but time-reversal even TMD is computed in the diquark spectator model, and is used to present predictions for the sin(2φ) single-spin asymmetry for a longitudinally polarized target in SIDIS.

The roles of the Drell-Yan experiments in studying the Transverse-Momentum-Dependent (TMD) parton distributions are discussed. Recent results from the Fermilab E866 experiment on the angular distributions of Drell-Yan dimuons in p + p and p + d at 800 GeV/c are presented. These data are compared with the pion-induced Drell-Yan data, and with models which attribute the cos2ɸ azimuthal distribution to the presence of the transverse-momentum-dependent Boer-Mulders structure function . Constraints on the magnitude of the sea-quark structure functions are obtained. Future prospects for studying the TMDs with Drell-Yan experiments at Fermilab and J-PARC are also discussed.

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x, Q²) = F_L/F_T and/or the azimuthal cos(2φ) asymmetry in deep inelastic lepton-nucleon scattering. Our approach is based on the following observations. First, unlike the production cross sections, the ratio R(x, Q²) = F_L/F_T and the azimuthal cos(2φ) asymmetry in heavy-quark leptoproduction are sufficiently stable, both parametricallly and perturbatively, in a wide region of variables x and Q² within the fixed-flavor-number scheme of QCD. Second, both these quantities, R(x, Q²) = F_L/F_T and cos(2φ) asymmetry, are sensitive to resummation of the mass logarithms of the type α_s In (Q²/m²) within the variable-flavor-number schemes. These two facts together imply that the heavy-quark densities in the nucleon can, in principle, be determined from high-Q² data on the Callan-Gross ratio and/or the azimuthal asymmetry in heavy-quark leptoproduction. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.