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NASA NTRS1986

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator

The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.

Norbury, J. W.↗
DOE OSTI2023

Threshold charmonium photoproduction with GlueX

Exclusive charmonium photoproduction near threshold opens the door for studying the gluonic properties of the proton: gluonic GPDs, anomalous contribution to the mass of the proton, gravitational form factors, the mass radius of the proton. However, such an ambitious program requires precise measurements to validate the theoretical assumptions that relate the experimental results to the above quantities. The first total cross-section measurements of near-threshold exclusive J/? photoproduction (?p?J/?p) by the GlueX collaboration sparked remarkable theoretical interest, however had limited statistics. We will report new total cross-section results based on more than a four-fold increase in statistics. Even more, due to the full acceptance of the GlueX experiment for this reaction, we will present first measurements of the differential cross-sections over the whole near-threshold kinematic region. Such measurements enable more general conclusions about the reaction mechanism when compared to a wide range of theoretical predictions including GPD calculations and models with open-charm intermediate states.

Pentchev, Lubomir↗
DOE OSTI2023

Study of exclusive photoproduction of charmonium in ultra-peripheral lead-lead collisions

The cross-sections of exclusive (coherent) photoproduction J/ψ and ψ(2S) mesons in ultra-peripheral PbPb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV are measured using a data sample corresponding to an integrated luminosity of 228 ± 10 µb -1 , collected by the LHCb experiment in 2018. The differential cross-sections are measured separately as a function of transverse momentum and rapidity in the nucleus-nucleus centre-of-mass frame for J/ψ and ψ(2S) mesons. The integrated cross-sections are measured to be $σ^{coh}_{J/ψ}$ = 5.965 ± 0.059 ± 0.232 ± 0.262 mb and $σ^{coh}_{ψ(2S)}$ = 0.923 ± 0.086 ± 0.028 ± 0.040 mb, where the first listed uncertainty is statistical, the second systematic and the third due to the luminosity determination. The cross-section ratio is measured to be $σ^{coh}_{ψ(2S)}$/$σ^{coh}_{J/ψ}$ = 0.155 ± 0.014 ± 0.003, where the first uncertainty is statistical and the second is systematic. These results are compatible with theoretical predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Photon-odderon interference in exclusive χ c charmonium production at the Electron-Ion Collider

Exclusive C = + 1 scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a C -odd t -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 d a b c J + a J + b J + c at moderate x , and is not affected by small- x QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer | t | ∼ 1 GeV 2 where the cross section for χ c J production exceeds that for pure photon exchange by up to a factor of 4. Exclusive χ c J 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 χ c J events per month at the Electron-Ion Collider design luminosity. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Observation of the Charmonium Decay η c → γ γ in J / ψ → γ η c

Using ( 2712.4 ± 14.3 ) × 10 6 ψ ( 3686 ) events collected with the BESIII detector at the BEPCII collider, the decay η c → γ γ in J / ψ → γ η c is observed. We determine the product branching fraction B ( J / ψ → γ η c ) × B ( η c → γ γ ) = ( 5.23 ± 0.2 6 stat ± 0.3 0 syst ) × 10 − 6 . This result is consistent with the lattice QCD calculation ( 5.34 ± 0.16 ) × 10 − 6 from HPQCD in 2023. By using the world-average values of B ( J / ψ → γ η c ) and the total decay width of η c , the partial decay width Γ ( η c → γ γ ) is determined to be ( 11.30 ± 0.5 6 stat ± 0.6 6 syst ± 1.1 4 ref ) keV , which deviates from the corresponding world-average value by 3.4 σ . Published by the American Physical Society 2025

Ablikim, M.↗
DOE OSTI2024

Charmonium Transport in Heavy-Ion Collisions at the LHC

We provide an update on our semi-classical transport approach for quarkonium production in high-energy heavy-ion collisions, focusing on 𝐽/𝜓 and 𝜓(2𝑆) mesons in 5.02 TeV Pb-Pb collisions at the Large Hadron Collider (LHC) at both forward and mid-rapidity. In particular, we employ the most recent charm-production cross sections reported in pp collisions, which are pivotal for the magnitude of the regeneration contribution, and their modifications due to cold-nuclear-matter (CNM) effects. Multi-differential observables are calculated in terms of nuclear modification factors as a function of centrality, transverse momentum, and rapidity, including the contributions from feeddown from bottom hadron decays. For our predictions for 𝜓(2𝑆) production, the mechanism of sequential regeneration relative to the more strongly bound 𝐽/𝜓 meson plays an important role in interpreting recent ALICE data.

Astronomy & Astrophysics↗
DOE OSTI2025

Shining a Light on the Nucleus: Photonuclear Measurements from Correlations to Charmonium

The atomic nucleus is comprised of a collection of nucleons (protons and neutrons), which are bound together by the nucleon-nucleon (NN) interaction that originates from Quantum Chromodynamics (QCD). While most nucleons experience the force from the rest of the nu- cleus as a single net “mean-field” interaction that binds them relatively weakly, a small but impactful fraction are in configurations called “Short-Range Correlations” (SRCs), in which they pair with another nucleon at very short distance to experience strong interactions, sig- nificant binding, and high momentum. Hard, high-energy scattering reactions in which an SRC pair is broken apart, knocking both nucleons out of the nucleus, provide the ability to probe the details of these SRC configurations in the nucleus. Previous measurements have had limited statistics and kinematic reach, and the theoretical tools available were in- sufficient to draw quantitative conclusions regarding the ground-state properties of SRCs. The studies described in this thesis represent the first global analysis of SRC breakup mea- surements in order to present a unified picture of SRCs within light- to medium-size nuclei. This includes the use of a novel theoretical framework, the Generalized Contact Formalism, which connects scattering cross-section measurements and the ground-state properties of the SRC pair, to quantitatively interpret a variety of electron-scattering measurements. This is brought to culmination by a report on the first measurement of SRC pairs via the use of hard meson photoproduction reactions, which, despite differing significantly from the me- chanics of electron-scattering, is well-described under a common framework, pointing to a consistent and universal picture of SRCs across reaction channels. I also report on the first measurement of J/¿ photoproduction in the near- and below-threshold kinematic region, giving the first insights to the gluonic structure of bound nucleons in the large-x “valence” region and providing constraints on a gluonic “EMC effect”. In addition to these studies, I provide details on the search for Primakoff production of axion-like particles using the pho- toproduction data taken for this experiment, and I conclude by describing studies of nucleon spin structure measurements that will be performed at the forthcoming U.S. Electron-Ion Collider.

Pybus, Jackson↗
DOE OSTI2021

Centrality dependence of J /ψ and ψ (2S) production and nuclear modification in p-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 8 . 16 TeV

The inclusive production of the J/ ψ and ψ (2S) charmonium states is studied as a function of centrality in p-Pb collisions at a centre-of-mass energy per nucleon pair \( \sqrt{s_{\mathrm{NN}}} \) = 8 . 16 TeV at the LHC. The measurement is performed in the dimuon decay channel with the ALICE apparatus in the centre-of-mass rapidity intervals – 4 . 46 < y cms < – 2 . 96 (Pb-going direction) and 2 . 03 < y cms < 3 . 53 (p-going direction), down to zero transverse momentum ( p T ). The J/ ψ and ψ (2S) production cross sections are evaluated as a function of the collision centrality, estimated through the energy deposited in the zero degree calorimeter located in the Pb-going direction. The p T -differential J/ ψ production cross section is measured at backward and forward rapidity for several centrality classes, together with the corresponding average \( \left\langle {p}_{\mathrm{T}}\right\rangle \) and \( \left\langle {p}_{\mathrm{T}}^2\right\rangle \) values. The nuclear effects affecting the production of both charmonium states are studied using the nuclear modification factor. In the p-going direction, a suppression of the production of both charmonium states is observed, which seems to increase from peripheral to central collisions. In the Pb-going direction, however, the centrality dependence is different for the two states: the nuclear modification factor of the J/ ψ increases from below unity in peripheral collisions to above unity in central collisions, while for the ψ (2S) it stays below or consistent with unity for all centralities with no significant centrality dependence. The results are compared with measurements in p-Pb collisions at \( \sqrt{s_{\mathrm{NN}}} \) = 5 . 02 TeV and no significant dependence on the energy of the collision is observed. Finally, the results are compared with theoretical models implementing various nuclear matter effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Cross section measurements of the $e^+e^–$ → $D^{*+}D^{*–}$ and $e^+e^–$ → $D^{*+}D^{–}$ processes at center-of-mass energies from 4.085 to 4.600 GeV

The Born cross sections of the $e^+e^–$ → $D^{*+}D^{*–}$ and $e^+e^–$ → $D^{*+}D^{–}$ processes are measured using $e^+e^–$ collision data collected with the BESIII experiment at center-of-mass energies from 4.085 to 4.600 GeV, corresponding to an integrated luminosity of 15.7 fb -1 . The results are consistent with and more precise than the previous measurements by the Belle, Babar and CLEO collaborations. The measurements are essential for understanding the nature of vector charmonium and charmonium-like states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Study of γ γ → γ ψ ( 2 S ) at Belle

Using 980 fb -1 of data at and around the Υ(nS)(n = 1, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy e+e- collider, the two-photon process γγ → γψ(2S) is studied from the threshold to 4.2 GeV for the first time. Two structures are seen in the invariant mass distribution of γψ(2S): one at M R 1 = 3922.4 ± 6.5 ± 2.0 MeV/c 2 with a width of Γ R 1 = 22 ± 17 ± 4 MeV, and another at M R 2 = 4014.3 ± 4.0 ± 1.5 MeV/c 2 with a width of Γ R 2 = 4 ± 11 ± 6 MeV; the signals are parametrized with the incoherent sum of two Breit- Wigner functions. The first structure is consistent with the X(3915) or the χ c2 (3930), and the local statistical significance is determined to be 3.1σ with the systematic uncertainties included. The second matches none of the known charmonium or charmonium like states, and its global significance is determined to be 2.8σ including the look-elsewhere effect. The production rates are Γ γγ B(R 1 → γψ(2S)) = 9.8 ± 3.6 ± 1.2 eV assuming (J PC , |λ|) = (0 ++ , 0) or 2.0 ± 0.7 ± 0.2 eV with (2 ++ , 2) for the first structure and Γ γγ B(R 2 → γψ(2S)) = 6.2 ± 2.2 ± 0.8 eV with (0 ++ , 0) or 1.2 ± 0.4 ± 0.2 eV with (2 ++ , 2) for the second one. Furthermore, the first errors are statistical and the second systematic, and λ is the helicity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Gravitational form factors of charmonia

We investigate the gravitational form factors of charmonium. Our method is based on a Hamiltonian formalism on the light front known as basis light-front quantization. The charmonium mass spectrum and light-front wave functions were obtained from diagonalizing an effective Hamiltonian that incorporates confinement from holographic QCD and one-gluon exchange interaction from light-front QCD. We proposed a quantum many-body approach to construct the hadronic matrix elements of the energy momentum tensor T + + and T + − , which are used to extract the gravitational form factors A ( Q 2 ) and D ( Q 2 ) . The obtained form factors satisfy the known constraints, e.g., the von Laue condition. From these quantities, we also extract the energy, pressure and light-front energy distributions of the system. We find that hadrons are multilayer systems. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Production of meson molecules in ultraperipheral heavy ion collisons

In this work we present a calculation of exotic charmonium production in ultraperipheral collisions, in which the exotic state is explicitly treated as a meson molecule. Our formalism is general, but we focus on the lightest possible exotic charmonium state: a 𝐷 + ⁢𝐷 − molecular bound state. It was proposed some time ago, and it has been an object of experimental searches. Here we study the production of the open charm pair in the process 𝛾⁢𝛾 → 𝐷 + ⁢𝐷 − . Then we use a prescription to project the free pair |𝐷 + ⁢𝐷 − ⟩ onto a bound state at the amplitude level and compute the cross section of the process 𝛾⁢𝛾 → 𝐵 (where 𝐵 is the bound state). Finally, we convolute this last cross section with the equivalent photon distributions coming from the projectile and target in an ultraperipheral collision and find the 𝐴⁢𝐴 → 𝐴⁢𝐴⁢𝐵 cross section, which, for 𝑃⁢𝑏 −𝑃⁢𝑏 collisions at $\sqrt{s_{NN}}$ =5.02 TeV, is of the order of 3 μ⁢b.

Sobrinho, F. C.↗
DOE OSTI2025

Self-consistent analysis for the η c → γ γ process

The next-to-next-to-leading-order (NNLO) perturbative QCD (pQCD) predictions for both the decay width and the transition form factor in the η c → γ γ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the η c → γ γ process by applying the principle of maximum conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC renormalization scales are determined by absorbing the nonconformal β -terms that govern the behavior of the QCD running coupling via the renormalization group equation. We obtain the PMC scale Q ⋆ = 4.49 m c for the η c → γ γ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated next-to-next-to-next-to-leading-order and higher-order terms. The resulting value for Γ η c → γ γ is in agreement with the Particle Data Group’s reported value of Γ η c → γ γ = 5.1 ± 0.4 keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to η c → γ γ puzzle and supports the applicability of NRQCD to charmonium processes. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

ψ ( 2 S ) Suppression in Pb-Pb Collisions at the LHC

The production of the ψ ( 2 S ) charmonium state was measured with ALICE in Pb-Pb collisions at s NN = 5.02 TeV , in the dimuon decay channel. A significant signal was observed for the first time at LHC energies down to zero transverse momentum, at forward rapidity ( 2.5 < y < 4 ). The measurement of the ratio of the inclusive production cross sections of the ψ ( 2 S ) and J / ψ resonances is reported as a function of the centrality of the collisions and of transverse momentum, in the region p T < 12 GeV / c . The results are compared with the corresponding measurements in p p collisions, by forming the double ratio [ σ ψ ( 2 S ) / σ J / ψ ] Pb − Pb / [ σ ψ ( 2 S ) / σ J / ψ ] p p . It is found that in Pb-Pb collisions the ψ ( 2 S ) is suppressed by a factor of ∼ 2 with respect to the J / ψ . The ψ ( 2 S ) nuclear modification factor R AA was also obtained as a function of both centrality and p T . The results show that the ψ ( 2 S ) resonance yield is strongly suppressed in Pb-Pb collisions, by a factor of up to ∼ 3 with respect to p p . Comparisons of cross section ratios with previous Super Proton Synchrotron findings by the NA50 experiment and of R AA with higher- p T results at LHC energy are also reported. These results and the corresponding comparisons with calculations of transport and statistical models address questions on the presence and properties of charmonium states in the quark-gluon plasma formed in nuclear collisions at the LHC. © 2024 CERN, for the ALICE Collaboration 2024 CERN

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Studying the hadron structure with PANDA and CLAS using machine learning techniques

The hadron spectroscopy and structure are currently very active fields of research to study the non-perturbative regime of quantum chronodynamics. The first one studies the complex structure of excited hadrons by looking at their decay products, while the latter uses lepton scattering on nucleons. Both methods require reconstruction algorithms with great efficiency and good particle identification and background rejection rates. This work aims to provide these by either improving the existing methods or developing new ones. The first part of this document presents a feasibility study of a predicted hybrid charmonium state for the PANDA experiment. Lattice QCD calculations predict the ground state hybrid charmonium to be a spin exotic with quantum numbers of JP C = 1?+ at a mass of around 4.3 GeV with a width to be around 20 MeV. A machine learning based data analysis scheme is proposed to further improve the signal efficiency and the background reduction, alongside with improvements of the analysis software (PandaRoot), that are vital for this study. These improvements include a reworked clustering algorithm for the electromagnetic calorimeter (EMC) and an optimized monte carlo matching for neutral particles. The second part of this document is about studying the proton structure. A multidimensional study of the structure function ratio Fsin(?)LU /FUU has been performed for K±, based on the measurement of beam-spin asymmetries. It uses the high statistics data recorded with the CLAS12 spectrometer at Jefferson Laboratory. Fsin(?)LU is a twist-3 quantity that provides information about the quark gluon correlations in the proton. This document will present for the first time a simultaneous analysis of two kaon channels over a large kinematic range of z, xB , PT and Q2 with virtualities Q2 ranging from 1 GeV2 up to 8 GeV2 using machine learning techniques for improved particle identification.

Kripko, Aron↗