Exclusive J/$\psi$ Detection and Physics with ECCE

Nuclear parton distribution functions (nPDF) describe the behavior of bound partons in the nucleus. Most of the understanding of nPDF comes from fixed-target experiments. Determination of nPDF is through global fits to existing inclusive deep inelastic scattering (DIS) data. Constructing the ratio nPDF/PDF to quantified nuclear modifications is natural, which can cancel many of the theory uncertainties. A ratio below unity is called shadowing, while an enhancement is known as anti-shadowing. Recently a moderate gluon shadowing has been exhibited by J/$\psi$ photoproduction data from LHC [1, 2, 3]. However, little is known about anti-shadowing at $x\sim 0.1$. The realization of the EIC with variable ion beam species will enable measurements of nPDF over a broad range of x and $Q^{2}$. Photoproduction of vector meson via photon-Pomeron fusion is able to cleanly and clearly determine nuclear gluon PDFs at the EIC. With broad x coverage, J/$\psi$ photoproduction can provide precise measurements to deepen our understanding of shadowing and anti-shadowing.

Exclusive photoproduction, which has a large cross section and a simple final state, is projected to play a prominent role in the heavy quarkonia production processes at the EIC. In the reaction, a virtual incident photon fluctuates into a quark-antiquark pair, which scatters elastically off the target and emerges as a real quarkonium. The scattering process occurs via the exchange of a color neutral object, Pomeron, which can be viewed as two gluons with self interaction (gluon ladder) in the language of QCD. Due to the gluonic nature of Pomeron, the exclusive heavy quarkonia photoproduction at EIC can be related to the gluon distributions in the proton and nucleus using perturbative QCD. Furthermore, the distribution of momentum transfer from the target in the process is sensitive to the interaction sites, which provides a powerful tool to probe the spatial distribution of gluon in the nucleus.

Nucleons constitute about 99$\%$ of the mass of the visible universe. In the standard model, Higgs mechanism describes gauge bosons’ “mass” generation. However it can only account for a small fraction of the nucleon mass. The major part comes from the strong interaction that binds quarks and gluons together. Understanding the hadron mass decomposition from strong interaction has become a topic of great interest in QCD. There are two key models [4, 5, 6, 7, 8, 9] for the mass decomposition. One contains a trace anomaly contribution which is quantified by the energy-momentum tensor (EMT), and the other one agrees with an energy decomposition in the rest frame of the system. Recently, there has been sustained interest [10, 11, 12] among the nucleon structure community in determining the anomaly contribution $M_{a}$ as a key to understanding the origin of the proton mass. Specifically, it has been proposed, based on some theorists’ suggestions [13, 14, 15], that $M_{a}$ can be accessed through the forward (t=0) cross section via the exclusive production of heavy quarkonia states such as J/$\psi$ and $\Upsilon$. Heavy quarkonia are of particular interest here because they only couple to gluons, not to light quarks, and are thus sensitive to the gluonic structure of the proton. The trace anomaly is sensitive to the gluon condensate, with sensitivity greatest for production around the threshold.

In this paper, we simulate exclusive J/$\psi$ production using Fun4All framework with the designed ECCE detector system. In the simulation, we utilize eSTARLight model as the event generator for the exclusive photoproduction process. We make a projection of the exclusive J/$\psi$ measurement at ECCE under the designed integrated luminosity of one year running for EIC to give an insight into related fruitful physics opportunities, such as probing the nuclear gluon PDF, spatial distribution and proton mass decomposition. The major goal of this research is to present the detection capability and the physics opportunities which could be achieved with the ECCE detector setup for the exclusive process of J/$\psi$ photoproduction.

The ECCE detector is a cylindrical detector covering $\left|\eta\right|\leq 3.5$ and the full azimuth. ECCE’s tracking and vertexing systems use semiconductor and gaseous tracking detector technologies: Monolithic Active Pixel Sensor (MAPS) based silicon vertex/tracking detector and $\mu$Rwell based gas tracker derived from Gas Electron Multiplier (GEM) technology. According to the simulation of the designed tracking system, the momentum resolution of the central region and beam e-going direction is closed to or better than the requirement of Yellow Report (YR) [16].

For exclusive photoproduction of J/$\psi$, we adopt eSTARLight prediction of the cross section for $ep\rightarrow eJ/\psi p$ process with two minor improvements, detailed in Sec. 3. eSTARLight provides a photo-Pomeron interaction model parameterized by HERA data. In this study, two beam configurations, 5$\times$41 GeV and 10$\times$100 GeV, are used for e+p and e+Au collisions.

The detector response simulation is done by a GEANT4 based package called Fun4All. In this work, the ”Prop.7” detector concept is employed in J/$\psi$ reconstruction via dielectron channel. Single $e^{+}/e^{-}$ Tracking simulation results are shown as Fig. 1. The difference in efficiency between $e^{+}$ and $e^{-}$ at very low $p_{T}$ is due to the initial assumption parameter in the Kalman filter. If the beginning parameter is set to “positron,” negative charge particles will have a low match quality and will likely be rejected.

The kinematic distribution of J/$\psi$ for exclusive photoproduction is initialized by the theoretical calculation from eSTARLight. With this as input, we can obtain J/$\psi$ reconstruction efficiency from the Fun4All package with ECCE detector setup seen in Fig. 2. The efficiency of J/$\psi$ is almost independent of the rapidity and transverse momentum except for the edge area at large forward and backward rapidity. We also study the effect of magnetic field strength and bremsstrahlung energy loss of electron on J/$\psi$ detection, shown as Fig. 3. At very low $p_{T}$ ($0.5<p_{T}<1.0$ GeV/c), the improvement of the acceptance of the lower magnetic field strength accounts for the higher efficiency. While at larger $p_{T}$ ($1.0<p_{T}<2.0$ GeV/c), there is no significant difference between efficiencies of 0.7 Tesla and 1.4 Tesla. The bremsstrahlung energy loss has already been put in tracking performance in the ”Prop.7” concept detector, which constitutes the tail in the reconstructed mass distribution depicted as the right panel in Fig. 3. We scale the mass distribution to unity for the convenience of comparison, and the efficiencies of several mass window cuts are detailed in Table. 1. As expected, the tail effect is more significant for the J/$\psi$ at forward and backward rapidities (larger momentum of decayed electrons than that at central rapidity). With a proper mass cut window, the efficiency loss is minimal, implying that the effect of bremsstrahlung on J/$\psi$ reconstruction with ECCE setup is not significant.

This section presents the theoretical framework of exclusive J/$\psi$ photoproduction in e+p and e+A collisions, which is employed in the simulation. The cross section of exclusive vector meson photoproduction $\sigma(eA\rightarrow eAV)$ is calculated as an integration of photon flux induced by the electron beam and the collision of the virtual photon on the target nucleus. The cross section of exclusive vector meson photoproduction $\sigma(eA\rightarrow eAV)$ is derived by integrating the photon flux caused by the electron beam and the virtual photon collision on the target nucleus, as illustrated in Eq.(1):

where the photon flux can be written as:

The cross section of virtual photon collision on the nucleus can be related to the production cross section with real photon:

where $c_{1}$ and $c_{2}$ are parameters determined by the HERA measurements. $f\left(M_{V}\right)$ is the Breit-Wigner distribution of the vector meson. And the cross section at $Q^{2}=0$ can be calculated by the integration of the forward scattering cross section and the square of the nucleus form factor, revealed as Eq.(4):

where $\frac{d\sigma(\gamma A\rightarrow VA)}{dt}|_{t=0}$ can be determined by $\frac{d\sigma(\gamma p\rightarrow Vp)}{dt}|_{t=0}$ via Glauber approach. The cross section of $\gamma p\rightarrow Vp$ can be parameterized using the world-wide measurements [17]. The framework is almost the same as eSTARLight [18][19], except for two minor improvements. In eSTARLight, the minimum momentum transfer $t_{min}$ is approximated as $t_{min}=((M_{v})^{2}/2k)^{2}$. One can get the minimum of t when the transverse momentum of the produced vector meson is equal to zero. Then true $t_{min}$ can be obtained from energy-momentum conservation of the $\gamma p\rightarrow Vp$ process in the target frame as Eq.(5):

where $P_{z}^{\prime 2}$ is the longitudinal momentum of the final state proton. The photon energy dependence of $t_{min}$ can be found in the upper panel of Fig. 4. The approximation in eSTARLight is proper at high photon energy. However, it would underestimate the magnitude at low values of photon energy, as is the case for our projection at ECCE. Furthermore, in eSTARLight, the parametrization of the $\gamma p\rightarrow Vp$ cross section is only based on high-energy HERA data. The behavior of energy dependency is notably different between the high and low energy ranges, as demonstrated in the lower panel of Fig. 4, which would skew the computations at EIC. With these two improvements, the calculated results of rapidity distribution for exclusive J/$\psi$ photoproduction in e+p and e+A collisions for 5$\times$41 and 10$\times$100 GeV collision energies are shown in Fig. 5. $Q^{2}$ dependence of e+p collision for 5$\times$41 and 10$\times$100 GeV with a rapidity range from $-3$ to 3 is illustrated in Fig. 6.

The raw counts per unit rapidity are shown in Fig. 7 for e+p and e+Au collisions for 10$\times$100 GeV. For the projection results in the following section, we assume the integrated luminosity collected by ECCE is $100fb^{-1}$ for e+p collisions and $10fb^{-1}/A$ for e+Au collisions, where A is the mass number of Au. The figure shows that millions of J/$\psi$s would be observed with the designed ECCE setup, which provides us with plenty of physics opportunities. And $Q^{2}$ dependence of the statistics of e+p collision in 5$\times$41 and 10$\times$100 GeV are shown in Fig. 8. As we can see, most events locate in the low $Q^{2}$ region, especially for $Q^{2}<1$ $GeV^{2}$.

In this paper, we simulate exclusive J/$\psi$ production using Fun4All framework with the designed ECCE detector system at the future EIC. For J/$\psi$ detection, ECCE has good reconstruction efficiency and broad coverage, with large statistics for the designed EIC luminosity. We also demonstrate the capability of ECCE to probe the related physics opportunities for the exclusive J/$\psi$ photoproduction process. For gluon distribution in the proton and nucleus, the projection of the gluon nuclear shadowing effect shows an excellent capability of constraining the nuclear gluon PDF with the exclusive J/$\psi$ forward scattering measurements at ECCE. Benefited from the unprecedented coverage and excellent reconstruction capability, ECCE can provide a strong constraint to the near-threshold production mechanism of the exclusive J/$\psi$ photoproduction process. Furthermore, the projection results of the near-threshold exclusive heavy quarkonia production also show an excellent capability to extract the trace anomaly parameter to precisely determine the nucleon mass decomposition.

X. Li and W. Zha are supported by the National Natural Science Foundation of China (12005220, 12175223) and MOST(2018YFE0104900). The authors would like to thank the ECCE Consortium for performing a full simulation of their detector design, for providing up-to-date information on EIC run conditions, and for suggestions and comments on the manuscript. X. Li and W. Zha would like to thank Y. Zhou for useful suggestions and discussions related to this analysis.