We update our previous calculation of <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> photoproduction near threshold [Y. Hatta and D. L. Yang, Phys. Rev. D 98, 074003 (2018)] by incorporating the recent developments in theory and the new experimental data from Ali et al. [the GlueX Collaboration] at Jefferson Laboratory. We then propose to study the near threshold production of <math><mrow><mi>ϒ</mi></mrow></math> and <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> in ultraperipheral <math><mi>p</mi><mi>A</mi></math> collisions at RHIC. These processes are sensitive to the gluon condensate in the proton which is related to the proton mass via the QCD trace anomaly. Our result emphasizes the role of gluons in generating the proton mass.

United States

Yoshitaka Hatta

Abha Rajan

Japan

Di-Lun Yang

Near threshold <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math><mi>ϒ</mi></math> photoproduction at JLab and RHIC

We show that, in dimensional regularization in the minimal subtraction scheme, the QCD trace anomaly can be unambiguously decomposed into two parts coming from the renormalized quark and gluon energy momentum tensors. We carry out this decomposition at the two-loop level. The result can be used to constrain the renormalization group properties of the nucleon’s twist-four gravitational form factor   <math> <msub> <mover> <mi>C</mi> <mo>¯</mo> </mover> <mrow> <mi>q</mi> <mo>,</mo> <mi>g</mi> </mrow> </msub> </math>  $$ {\overline{C}}_{q,g} $$ .

Kazuhiro Tanaka

Quark and gluon contributions to the QCD trace anomaly

We derive new Lorentz invariance and equation of motion relations between twist-three generalized parton distributions (GPDs) and moments in the parton transverse momentum, <math><msub><mi>k</mi><mi>T</mi></msub></math>, of twist-two generalized transverse momentum-dependent distributions (GTMDs), as a function of the parton longitudinal momentum fraction <math><mi>x</mi></math>. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connected to directly measurable twist-three GPDs. Out of 16 possible equation of motion relations that can be written in the <math><mi>T</mi></math>-even sector, we focus on three helicity configurations that can be detected analyzing specific spin asymmetries: two correspond to longitudinal proton polarization and are associated with quark orbital angular momentum and spin-orbit correlations; the third, obtained for transverse proton polarization, is a generalization of the relation obeyed by the <math><msub><mi>g</mi><mn>2</mn></msub></math> structure function. We also exhibit an additional relation connecting the off-forward extension of the Sivers function to an off-forward Qiu-Sterman term.

Michael Engelhardt

Italy

Simonetta Liuti

Lorentz invariance and QCD equation of motion relations for generalized parton distributions and the dynamical origin of proton orbital angular momentum

We argue that due to parity constraints, the helicity combination of the purely momentum space counterparts of the Wigner distributions – the generalized transverse momentum distributions – that describes the configuration of an unpolarized quark in a longitudinally polarized nucleon can enter the deeply virtual Compton scattering amplitude only through matrix elements involving a final state interaction. The relevant matrix elements in turn involve light-cone operators projections in the transverse direction, or they appear in the deeply virtual Compton scattering amplitude at twist three. Orbital angular momentum or the spin structure of the nucleon was a major reason for these various distributions and amplitudes to have been introduced. We show that the twist three contributions associated with orbital angular momentum are related to the target-spin asymmetry in deeply virtual Compton scattering, already measured at HERMES.