Exclusive <math><mi>C</mi><mo>=</mo><mo>+</mo><mn>1</mn></math> scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a <math><mi>C</mi></math>-odd <math><mi>t</mi></math>-channel exchange of a photon or a three-gluon ladder. We derive the expressions for the corresponding amplitudes. The relative phase of the photon vs three-gluon exchange amplitudes is determined by the sign of the light-front matrix element of the eikonal color current operator <math><msup><mi>d</mi><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow></msup><msup><mi>J</mi><mrow><mo>+</mo><mi>a</mi></mrow></msup><msup><mi>J</mi><mrow><mo>+</mo><mi>b</mi></mrow></msup><msup><mi>J</mi><mrow><mo>+</mo><mi>c</mi></mrow></msup></math> at moderate <math><mi>x</mi></math>, and is not affected by small-<math><mi>x</mi></math> QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer <math><mrow><mo>|</mo><mi>t</mi><mo>|</mo><mo>∼</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> where the cross section for <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> production exceeds that for pure photon exchange by up to a factor of 4. Exclusive <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> electroproduction at the high luminosity Electron-Ion Collider occurs with well measurable rates and measurements of these processes should find evidence for the perturbative odderon exchange. We also compute the total electroproduction cross section as a function of energy and provide first estimates of the number of <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> events per month at the Electron-Ion Collider design luminosity.

Croatia

Sanjin Benić

United States

Adrian Dumitru

Abhiram Kaushik

Poland

Leszek Motyka

Tomasz Stebel

Photon-odderon interference in exclusive <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> charmonium production at the Electron-Ion Collider

In a previous publication [Benić et al., Phys. Rev. D 104, 094027 (2021)], we have computed the perturbative QCD contribution to transverse single spin asymmetries (SSAs) in semi-inclusive deep inelastic scattering (SIDIS) involving the <math><msub><mi>g</mi><mi>T</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> distribution. In this paper, we first present a more efficient derivation of the asymmetries which is applicable to both transverse and longitudinal SSAs and correct some inconsistencies in our previous calculation. We then adapt the method to compute transverse SSAs in the Drell-Yan process proportional to <math><msub><mi>g</mi><mi>T</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> and its gluonic counterpart and discuss the crossing symmetry between the results for SIDIS and the Drell-Yan process. Finally, we present numerical results for various asymmetries measurable at the EIC, RHIC, COMPASS, and Fermilab (SpinQuest), including also part of the genuine twist-three corrections to <math><msub><mi>g</mi><mi>T</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> from a recent global analysis. We find that the asymmetries can reach percent-level magnitude, if the kinematics predominantly probes the large-<math><mi>x</mi></math> (valence) region of the polarized proton, but remain at subpercent levels otherwise.

Yoshitaka Hatta

China

Hsiang-nan Li

Perturbative QCD contribution to transverse single spin asymmetries in the Drell-Yan process and SIDIS

We compute exclusive <math><msub><mi>η</mi><mi>c</mi></msub></math> production in high-energy electron-nucleon and electron-nucleus collisions that is sensitive to the odderon. In perturbative QCD the odderon is a <math><mi>C</mi></math>-odd color singlet consisting of at least three <math><mi>t</mi></math>-channel gluons exchanged with the target. By using the Color Glass Condensate effective theory our result describes the odderon exchange at the high-collision energies that would be reached at a future electron-ion collider. The odderon distribution is evolved to small-<math><mi>x</mi></math> using the Balitsky-Kovchegov evolution equation with running coupling corrections. We find that while at low momentum transfers <math><mi>t</mi></math> the cross section off a proton is dominated by the Primakoff process, the odderon becomes relevant at larger momentum transfers of <math><mrow><mo>|</mo><mi>t</mi><mo>|</mo><mo>≥</mo><mn>1.5</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>. We point that the odderon could also be extracted at low-<math><mi>t</mi></math> using neutron targets since the Primakoff component is strongly suppressed. In the case of nuclear targets, the odderon cross section becomes enhanced thanks to the mass number of the nuclear target. The gluon saturation effect induces a shift in the diffractive pattern with respect to the Primakoff process that could be used as a signal for the odderon.

Davor Horvatić

Eric Andreas Vivoda

Exclusive <math><mrow><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> production from small-<math><mi>x</mi></math> evolved Odderon at an electron-ion collider

We compute the transverse single spin asymmetry in forward <math><msup><mi>p</mi><mo>↑</mo></msup><mi>p</mi><mo>→</mo><mi>h</mi><mi>X</mi></math> and <math><msup><mi>p</mi><mo>↑</mo></msup><mi>A</mi><mo>→</mo><mi>h</mi><mi>X</mi></math> collisions from the odderon mechanism originally suggested by Kovchegov and Sievert [Phys. Rev. D 86, 034028 (2012)]. Working in the hybrid approach of the color glass condensate effective theory, we first identify the relevant collinear parton distribution function (PDF) of the transversely polarized proton <math><msup><mi>p</mi><mo>↑</mo></msup></math> as the intrinsic twist-3 <math><msub><mi>g</mi><mi>T</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> distribution. We further argue that the complete polarized cross section also contains contributions from the kinematical and the dynamical twist-3 PDFs, in addition to the intrinsic twist-3 PDF. By restricting to the Wandzura-Wilczek approximation, where the dynamical twist-3 PDFs are dropped, we find that the odderon contribution to the polarized cross section for inclusive hadron production is exactly zero at the next-to-leading order in the strong coupling.

Odderon mechanism for transverse single spin asymmetry in the Wandzura-Wilczek approximation

Motivated by a novel origin of transverse single spin asymmetry (SSA) in semi-inclusive deep inelastic scattering (SIDIS) uncovered by some of us, we quantitatively investigate its impact on the theoretical understanding of the mechanism responsible for SSA. This new contribution from the quark-initiated channel first appears in two-loop perturbation theory and involves the <math><msub><mi>g</mi><mi>T</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> distribution. We point out another entirely analogous piece from the gluon-initiated channel proportional to the gluon helicity distribution <math><mi>Δ</mi><mi>G</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>. Both contributions are solely expressed in terms of twist-two polarized parton distribution functions and twist-two fragmentation functions in the Wandzura-Wilczek approximation, such that they can be unambiguously evaluated without introducing free parameters. We make predictions for measurements of the asymmetries <math><msub><mi>A</mi><mrow><mi>U</mi><mi>T</mi></mrow></msub></math> at the future electron-ion collider (EIC), and find that <math><msub><mi>A</mi><mrow><mi>U</mi><mi>T</mi></mrow></msub></math> associated with the <math><mi>sin</mi><mo>(</mo><msub><mi>ϕ</mi><mi>h</mi></msub><mo>−</mo><msub><mi>ϕ</mi><mi>S</mi></msub><mo>)</mo></math>, <math><mi>sin</mi><msub><mi>ϕ</mi><mi>S</mi></msub></math> and <math><mi>sin</mi><mo>(</mo><mn>2</mn><msub><mi>ϕ</mi><mi>h</mi></msub><mo>−</mo><msub><mi>ϕ</mi><mi>S</mi></msub><mo>)</mo></math> harmonics can reach up to 1–2% even at the top EIC energy.

<math><msub><mi>g</mi><mi>T</mi></msub><mo>(</mo><mi>x</mi><mo>)</mo></math> contribution to single spin asymmetries in SIDIS

We present estimates of transverse single-spin asymmetry in prompt photon production in the scattering of low virtuality photons off a polarized proton target and discuss the possibility of using this as a probe to get information about the gluon Sivers function (GSF). Using a generalized parton model (GPM) framework, we estimate the asymmetries at electron-ion collider energy (<math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>140</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>) taking into account both direct and resolved photon processes and find that the dominant contribution, up to 10%, comes from quark Sivers function (QSF) while the contribution from GSF is found to be up to 2%. However, upon taking into account the effects of the process-dependent initial and final state interactions through the color-gauge invariant generalized parton model approach we find that the situation is significantly changed, with near zero contributions from the QSFs and up to a 1% level contribution from the <math><mrow><mi>f</mi></mrow></math>-type GSF. Our results indicate that this process may be useful for distinguishing between GPM and color-gauge invariant generalized parton models and can be used as a good probe of <math><mrow><mi>f</mi></mrow></math>-type GSF.

India

Siddhesh Padval

Rohini M. Godbole

Anuradha Misra

Vaibhav S. Rawoot

Gluon Sivers function and transverse single spin asymmetries in <math><mi>e</mi><mo>+</mo><msup><mi>p</mi><mo>↑</mo></msup><mo>→</mo><mi>γ</mi><mo>+</mo><mi>X</mi></math>

We study the production of prompt photons at the RHIC in the context of a generalized parton model framework, with a view to obtain information on the gluon Sivers function (GSF). At RHIC energy (<math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>), the Compton process <math><mi>g</mi><mi>q</mi><mo>→</mo><mi>γ</mi><mi>q</mi></math> contributes significantly to the production of direct photons at midrapidity and dominates it in the negative (backward) rapidity region. We find that for direct photons, asymmetries of up to 10% are allowed by a maximal gluon Sivers function. However, the asymmetry obtained using existing fits of the GSF available in the literature is negligible. We also estimate the impact that photons produced via fragmentation can have on the signal and find that their inclusion can dilute the asymmetry by between 10% and 50% of the direct photon value. Finally, using the color-gauge invariant generalized parton model (CGI-GPM) approach, we consider the effects of initial-state and final-state interactions which can affect the universality of the Sivers functions in different processes. We find that the inclusion of these effects leads to the size of the gluon contributions being roughly halved. However, in the backward region which we are interested in, the sizes of the quark contributions are suppressed even further, leading to increased dominance of the gluon contributions.

Netherlands

Probing the gluon Sivers function through direct photon production at RHIC

We study the low-virtuality inclusive leptoproduction of open charm, <math><mrow><msup><mrow><mi>p</mi></mrow><mrow><mo>↑</mo></mrow></msup><mi>l</mi><mo>→</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>+</mo><mi>X</mi></mrow></math> as a probe of the gluon Sivers function. We perform the analysis in a generalized parton model framework. At leading order, this process is sensitive only to the gluon content of the proton. Hence any detection of a transverse single-spin asymmetry in this process would be clear indication of a non-zero gluon Sivers function (GSF). Considering COMPASS and a future Electron-Ion Collider (EIC), we present predictions for asymmetry using fits for the GSF available in literature. Predictions for peak asymmetry values lie in the range of 0.8% to 13%. We also present estimates of the upper bound on the asymmetry as obtained with a maximal gluon Sivers function. Further, for the case of the Electron-Ion Collider, we evaluate the asymmetry in the muons decaying from the <math><mi>D</mi></math>-meson and find that the asymmetry is well preserved in the kinematics of the muons. Peak values of the muon asymmetry are close to those obtained for the <math><mi>D</mi></math>-meson and lie in the range 0.75% to 11%.