Hadron tomography for pion and its gravitational form factors

Generalized parton distributions (GPDs) are three-dimensional structure functions of hadrons, and they can reveal the orbital-angular-momentum contributions to the nucleon spin. Therefore, GPDs are important for solving the proton spin puzzle. The generalized distribution amplitudes (GDAs) are the $s$-$t$ crossed quantities of the GPDs, and the GDAs can be investigated in two-photon process ($\gamma^* \gamma \to h\bar h$) which is accessible at KEKB. The pion GDAs were obtained by analyzing the Belle measurements for $\pi^0 \pi^0$ production in the $e^+ e^-$ collision. From the obtained GDAs, the form factors of energy-momentum tenor were calculated for pion in the timelike region. In order to study the gravitational radii for the pion, the form factors of energy-momentum tenor were obtained in the spacelike region by using the dispersion relation. Then, the mass radius was calculated as 0.32 $\sim$ 0.39 fm and the mechanical radius was also estimated for the pion as 0.82 $\sim$ 0.88 fm by using the spacelike form factors. This is the first finding on gravitational form factors and radii of hadrons from actual experimental measurements. In the near future we can expect more precise measurements of $\gamma^* \gamma \to h\bar h$ as the Belle II started data taking by the higher luminosity Super KEKB, so that the GDAs of other hadrons could be studied as well.Comment: 4 pages, 4 figures, Proceedings of Eighth International Conference on Quarks and Nuclear Physics (QNP2018), November 13-17, 2018, Tsukuba, Japa

Novel relations for twist-3 tensor-polarized fragmentation functions in spin-1 hadrons

There are three types of fragmentation functions (FFs) which are used to describe the twist-3 cross sections of the hard semi-inclusive processes under QCD collinear factorization, and they are called intrinsic, kinematical, and dynamical FFs. In this work, we investigate the theoretical relations among these FFs for a tensor-polarized spin-1 hadron. Three Lorentz-invariance relations (LIRs) are derived by using the identities between the nonlocal quark-quark and quark-gluon-quark operators, which guarantee the frame independence of the twist-3 spin observables. The QCD equation of motion (e.o.m.) relations are also presented for the tensor-polarized FFs. In addition, we also show that the intrinsic and kinematical twist-3 FFs can be decomposed into the contributions of twist-2 FFs and twist-3 three-parton FFs, and the latter are also called dynamical FFs. If one neglects the dynamical FFs, we can obtain relations which are analogous to the Wandzura-Wilczek (WW) relation. Then, the intrinsic and kinematical twist-3 FFs are expressed in terms of the leading-twist ones. Since the FFs of a spin-1 hadron can be measured at various experimental facilities in the near future, these theoretical relations will play an important role in the analysis of the collinear tensor-polarized FFs.Comment: 10 page

3D structure of hadrons by generalized distribution amplitudes and gravitational form factors

Generalized distribution amplitudes (GDAs) are one type of three-dimensional structure functions, and they are related to the generalized distribution functions (GPDs) by the $s$-$t$ crossing of the Mandelstam variables. The GDA studies provide information on three-dimensional tomography of hadrons. The GDAs can be investigated by the two-photon process $\gamma^* \gamma \to h\bar h$, and the GPDs are studied by the deeply virtual Compton scattering $\gamma^* h \to \gamma h$. The GDA studies had been pure theoretical topics, although the GPDs have been experimentally investigated, because there was no available experimental measurement. Recently, the Belle collaboration reported their measurements on the $\gamma^* \gamma \to \pi^0 \pi^0$ differential cross section, so that it became possible to find the GDAs from their measurements. Here, we report our analysis of the Belle data for determining the pion GDAs. From the GDAs, the timelike gravitational form factors $\Theta_1 (s)$ and $\Theta_2 (s)$ can be calculated, which are mechanical (pressure, shear force) and mass (energy) form factors, respectively. They are converted to the spacelike form factors by using the dispersion relation, and then gravitational radii are evaluated for the pion. The mass and mechanical radii are obtained from $\Theta_2$ and $\Theta_1$ as $\sqrt {\langle r^2 \rangle_{\text{mass}}} =0.56 \sim 0.69$ fm and $\sqrt {\langle r^2 \rangle_{\text{mech}}} =1.45 \sim 1.56$ fm, whereas the experimental charge radius is $\sqrt {\langle r^2 \rangle_{\text{charge}}} =0.672 \pm 0.008$ fm for the charged pion. Future developments are expected in this new field to explore gravitational physics in the quark and gluon level.Comment: 6 pages, LaTeX, 1 style file, 8 figure files, Proceedings of the XXV International Workshop on Deep-Inelastic Scattering and Related Subjects, April 3-7, 2017, University of Birmingham, U

Ds1∗(2860)D_{s1}^*(2860) and Ds3∗(2860)D_{s3}^*(2860): Candidates for 1D1D charmed-strange mesons

Newly observed two charmed-strange resonances, $D_{s1}^*(2860)$ and $D_{s3}^*(2860)$, are investigated by calculating their Okubo-Zweig-Iizuka allowed strong decays, which shows that they are suitable candidates for the $1^3D_1$ and $1^3D_3$ states in the charmed-strange meson family. Our study also predicts other main decay modes of $D_{s1}^*(2860)$ and $D_{s3}^*(2860)$, which can be accessible at the future experiment. In addition, the decay behaviors of the spin partners of $D_{s1}^*(2860)$ and $D_{s3}^*(2860)$, i.e., $1D(2^-)$ and $1D^\prime(2^-)$, are predicted in this work, which are still missing at present. Experimental search for the missing $1D(2^-)$ and $1D^\prime(2^-)$ charmed-strange mesons is an intriguing and challenging task for further experiment.Comment: 8 pages, 3 figures and 4 tables. More discussions added and typos corrected. Accepted by Eur. Phys. J.