Research

Yuxun Guo, Feng Yuan and Wenbin Zhao, Bayesian Inferring Nucleon’s Gravitation Form Factors via Near-threshold J/ψ Photoproduction, to appear in Physical Review Letters, [arXiv:2501.10532 [hep-ph]].

With Bayesian inference, we investigate the impact of recent near-threshold J/ψ production measurements by the J/ψ 007 experiment and GlueX collaboration on the extraction of proton’s gravitational form factors. We apply the generalized parton distribution framework at the next-to-leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative Cq(t) and Cg(t) are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.

Figure: the average proton mass and scalar radii with parameters sampled from their posterior distributions as compared to the lattice result.

Xiaohui Liu , Werner Vogelsang, Feng Yuan, and Hua Xing Zhu, Universality in the Near-Side Energy-Energy Correlator, Phys. Rev. Lett. 134, 151901 – Published 17 April, 2025

We investigate the energy-energy correlator (EEC) of hadrons produced on the same side in e+e- annihilation or in leading jets in proton-proton collisions. We observe a remarkable universality of the correlator. Using a non-perturbative transverse momentum dependent (TMD) fragmentation function to model the transition from the ``free-hadron" region to the perturbative collinear region, we are able to describe the near-side shapes and peaks over a wide range of energy for both the e+e- annihilation and the proton-proton jet substructure measurements in terms of just two parameters. We present further predictions for the ratio of the projected three-point energy correlator to the EEC. The excellent agreement between our calculations and the experimental data may provide new insights into the role of non-perturbative physics for EECs, and suggests the possibility of exploring non-perturbative TMDs using theoretical tools developed for the energy correlators.

This observation unveils the universal behavior of hadronization in jet when the pair of hadrons are close to each other. The results will play an important role in the study of the hot QCD matter effects of EEC in jet in heavy ion collisisons as well.

Figure: Comparison between the universal TMD model predictions (curves) and the ALICE measurements extracted from ALICE, S. Acharya et al., (2024), 2409.12687. Solid and dashed lines refer to quark and gluon jets, respectively.

Yuxun Guo , Xiaohui Liu , Feng Yuan, and Hua Xing Zhu, Long-Range Azimuthal Correlation, Entanglement, and Bell Inequality Violation by Spinning Gluons at the Large Hadron Collider, Science Partner Journal, Research, Vol 2025, Article ID: 0552, Published 5 Feb 2025

The newly developed concept of the nucleon energy–energy correlator (NEEC) for the gluon sector is applied to investigate the long-range azimuthal angular correlations in proton–proton collisions at the Large Hadron Collider. The spinning gluon in these collisions will introduce substantial nonzero cos(2ϕ) asymmetries in both Higgs boson and top quark pair productions, where ϕ is the azimuthal angle between the forward and backward energy correlators in the NEEC observables. The genesis of the cos(2ϕ) correlation lies in the intricate quantum entanglement. Owing to the substantial cos(2ϕ) effect, the NEEC observable in Higgs boson and ttbar production emerges as a pivotal avenue for delving into quantum entanglement and scrutinizing the Bell inequality at high-energy colliders.

Figures: (upper) Nucleon energy–energy correlator measurements in proton–proton collisions at the Large Hadron Collider. Energy deposits in the forward directions of both incoming hadron beams with polar angles θa,b and azimuthal angles ϕa,b. (lower) Violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality in Higgs (red) and top pair (blue) production at the LHC. Quark jet tagging (dashed lines) substantially enhances the significance

Paul Caucal, Edmond Iancu, A. H. Mueller, and Feng Yuan, Jet definition and transverse-momentum–dependent factorization in semi-inclusive deep-inelastic scattering, Phys. Rev. Lett. 134, 061903 – Published 12 February, 2025

Using the colour dipole picture of Deep Inelastic Scattering (DIS) and the Colour Glass Condensate effective theory, we study semi-inclusive jet production in DIS at small x in the limit where the photon virtuality 𝑄2 is much larger than the transverse momentum squared 𝑃T2 of the produced jet. In this limit, the cross-section is dominated by aligned jet configurations, that is, quark-antiquark pairs in which one of the fermions — the would-be struck quark in the Breit frame — carries most of the longitudinal momentum of the virtual photon. We show that physically meaningful jet definitions in DIS are such that the effective axis of the jet sourced by the struck quark is controlled by its virtuality rather than by its transverse momentum. For such jet definitions, we show that the next-to-leading order cross-section admits factorisation in terms of the (sea) quark transverse momentum dependent distribution, which in turn satisfies a universal DGLAP and Sudakov evolution.

Figure: Geometric representation of the typical aligned jet configuration at small xBJ in the dipole frame.

Hao-Yu Liu, Xiaohui Liu, Ji-Chen Pan, Feng Yuan, and Hua Xing Zhu,  Nucleon Energy Correlators for the Color Glass Condensate, Phys. Rev. Lett. 130, 181901 (2023)

Small-x gluon saturation has been one of the central focuses in the nuclear physics community in recent years and will be a major research area in the future Electron Ion Collider. We demonstrate the recently proposed nucleon energy-energy correlator (NEEC) fEEC(x,θ) can unveil the gluon saturation in the small-x regime in eA collisions. The novelty of this probe is that it is fully inclusive just like the deep-inelastic scattering (DIS), with no requirements of jets or hadrons but still provides an evident portal to the small-x dynamics through the shape of the θ distribution. We find that the saturation prediction is significantly different from the expectation of the collinear factorization.

Figure: The xB and Q2 measurement in DIS with a forward detector that records the energy flow ∑iEi at the angle θ. The leading contribution is also illustrated where the collinear splitting initiates the DIS process and a daughter parton that hits the detector at θ ≪ 1. The momentum fractions are shown. 

See also: Synopsis from APS Physics, DOE Highlight

Illuminating nucleon-gluon interference via calorimetric asymmetry, Xiao Lin Li, Xiaohui Liu, Feng Yuan, and Hua Xing Zhu, Phys. Rev. D 108, L091502

Yoshitaka Hatta, Bo-Wen Xiao, Feng Yuan, and Jian Zhou, Anisotropy in Dijet Production in Exclusive and Inclusive Processes, Phys. Rev. Lett. 126, 142001 (2021).

We investigate the effect of soft gluon radiations on the azimuthal angle correlation between the total and relative momenta of two jets in inclusive and exclusive dijet processes. We show that the final state effect induces a sizable cos(2ϕ) anisotropy due to gluon emissions near the jet cones. The phenomenological consequences of this observation are discussed for various collider experiments, including diffractive processes in ultraperipheral pA and AA collisions, inclusive and diffractive dijet production at the EIC, and inclusive dijet in pp and AA collisions at the LHC.

figure: Dijet in transverse plane perpendicular to the beam direction at hadron colliders. Their total transverse momentum qT=k1T+k2T  is much smaller than the individual jet momentum  PT=(k1T−k2T)/2. Angular distribution between qT and PT has an anisotropy due to soft gluon radiation associated with the final state jet with a nonzero  ⟨cos(2ϕ)⟩.

Xiangdong Ji, Feng Yuan, Yong Zhao, What we know and what we don’t know about the proton spin after 30 years, Nature Reviews Physics volume 3, 27–38 (2021)

More than three decades ago, the European Muon Collaboration published a surprising result on the spin structure of the proton: the spins of its three quark components account for only a small part of the spin of the proton. Ever since, theoretical and experimental progress has been made in understanding the origins of the proton spin. In this Review, we discuss what has been learned so far, what is still missing and what could be learned from the upcoming experiments, including the Jefferson Lab 12 GeV upgrade and the proposed Electron-Ion Collider. In particular, we focus on first-principles calculations and experimental measurements of the total gluon helicity ΔG, and the quark and gluon orbital angular momenta.

See an editorial and a comment on EIC project in the same issue of Nature Review Physics.

Bo-Wen Xiao, Feng Yuan, and Jian Zhou, Momentum Anisotropy of Leptons from Two-Photon Processes in Heavy-Ion Collisions, Phys. Rev. Lett. 125, 232301 (2020)

Di-lepton production in heavy ion collisions has attracted great attention in recent years. It may provide a unique window to explore the electro-magnetic property of the quark-gluon plasma created in these collisions. Experiments from RHIC and LHC have reported a number of interesting phenomena for these di-lepton in various collision configurations, including ultra-peripheral, peripheral, and in some occasions, even the central collisions. Significant Pt-broadening of the total transverse momentum of the lepton pair was observed from ultra-peripheral to central collisions. This can be explained as a final state interaction effects of the lepton pair when they traverse through the medium, see, our previous paper in Phys. Rev. Lett. 122, 132301 (2019). However, this could come from the initial state effects, as indicated by recent studies (Phys.Lett.B 800 (2020) 135089; Phys.Rev.D 102 (2020) 9, 094013). Therefore, the key is to identify/isolate the production mechanism of the lepton pair in the two photon processes. 

In this paper, we carry out an analysis that can help to identify the production mechanism of the lepton pair in heavy ion collisions. In particular, we investigate the azimuthal angular correlation between the lepton transverse momentum P⊥. and the impact parameter b⊥ in noncentral heavy-ion collisions, where the leptons are produced through two-photon scattering. Among the Fourier harmonic coefficients, a significant v4 asymmetry is found for the typical kinematics at RHIC and LHC with a mild dependence on the P⊥, whereas v2 is power suppressed by the lepton mass over P⊥. This unique prediction, if confirmed from the experiments, shall provide crucial information on the production mechanism for the dilepton in two-photon processes. 

upper figure: Illustration of the polarized photon flux associated with a relativistic heavy nucleus moving to the right. The physical polarization of the photon propagating to the right is along the direction of b1⊥  with respect to the center of the nucleus in the transverse plane. Because of this peculiar polarization states for both incoming photons in heavy ion collisions, the resulting lepton pair will have a cos(4ϕ) anisotropy. 

lower figure: Estimates of the cos(4ϕ) asymmetry as the function of b⊥ in Au-Au collisions at √s=200 GeV as an example to show the momentum anisotropy of leptons from two photon processes in heavy ion collision. Similar results exist for the LHC experiments as well. 

Xiaohui Liu, Felix Ringer, Werner Vogelsang, and Feng Yuan, Lepton-Jet Correlations in Deep Inelastic Scattering at the Electron-Ion Collider,  Phys. Rev. Lett. 122, 192003 (2019)

We propose the lepton-jet correlation in deep inelastic scattering as a unique tool for the tomography of nucleons and nuclei at the electron-ion collider (EIC). The azimuthal angular correlation between the final state lepton and jet depends on the transverse momentum dependent quark distributions. We take the example of single transverse spin asymmetries to show the sensitivity to the quark Sivers function. When the correlation is studied in lepton-nucleus collisions, transverse momentum broadening effects can be used to explore cold nuclear matter effects. These features make lepton-jet correlations an important new hard probe at the EIC.

Upper Figure:  The schematic kinematics of lepton-jet correlation at the electron-ion collider.

Lower Figure: PT-broadening effects for the lepton jet azimuthal correlation due to the interaction with cold nuclear matter as a function of Δϕ=|ϕJ−ϕℓ−π| for two typical values of ^qL.

Spencer Klein, A.H. Mueller, Bo-Wen Xiao, Feng Yuan, Acoplanarity of Lepton Pair to Probe the Electromagnetic Property of Quark Matter, Phys. Rev. Lett. 122, 132301 (2019) arXiv:1811.05519 [hep-ph]

We investigate the PT-broadening effects in dilepton production through photon-photon scattering in heavy ion collisions. The QED multiple interaction effects with the medium is found to be consistent with a recent observation of low transverse momentum lepton pair from ATLAS collaboration at the LHC. We further comment on the magnetic effects and point out a number of ways to disentangle these two mechanisms. In particular, the rapidity dependence of the PT-broadening effects provide a unique probe to the magnetic effects.

Jet quenching is considered one of the major discoveries in relativistic heavy ion experiments from RHIC at Brookhaven National Laboratory and the LHC at CERN. These phenomena have been well formulated in QCD, where the energy loss and PT -broadening effects are closely related. The parameter qhat has been extracted from various experimental data. Meanwhile, qhat*L describes the typical transverse momentum squared that a parton acquires in the medium of length L. In the last few years, there have been significant progress in understanding the PT -broadening effects in dijet, photon-jet, and hadron-jet productions in heavy ion collisions.

We extend our previous studies on the dijet azimuthal correlation (Phys.Lett. B763 (2016) 208-212) to the di-lepton correlation and focus on two main areas. One is the QED Sudakov effect, where we show that the theory prediction for the UPC events agree very well with data from ATLAS. Second, we investigate the medium effects, including the QED multiple interaction effects similar to the PT -broadening of the QCD jet and the magnetic effects. We also discuss how to disentangle these two mechanisms. 

The comparison of the PT -broadening effects in QCD and QED is of crucial importance to understand the medium property in heavy ion collisions. The lepton’s PT -broadening effects is sensitive to the electromagnetic property of the quark-gluon plasma, whereas the jet PT -broadening effects depends on the strong interaction property. The experimental and theoretical investigations of both phenomena will deepen our understanding of the hot medium created in these collisions. The clear measurements of lepton PT -broadening effects from ATLAS and STAR should stimulate further study on dijet azimuthal correlations in heavy ion collisions.

Upper Figure: Acoplanarity distribution for lepton pair production at mid-rapidity in UPC events at the LHC with a typical kinematics: lepton transverse momentum P⊥ > 4 GeV and pair invariant mass from 10 to 100 GeV. The detailed explanation of different curves is provided in the main text. The total contribution with resummation (solid curve) agrees well with the ATLAS measurement.

Lower Figure: Medium modifications to the acoplanarity distribution, with different values of the effective qL.

Xiangdong Ji, Feng Yuan, and Yong Zhao, Hunting the Gluon Orbital Angular Momentum at the Electron-Ion Collider, Phys. Rev. Lett. 118, (2017), 192004

One of the major goals in hadron physics facilities around the world is to pin down the proton spin decomposition. Among the different components, the gluon OAM is the most elusive contribution. To fully explore the potential on the proton spin puzzle at the EIC, we need to find novel processes and physical observables that are sensitive to the gluon OAM of the proton. This will provide comprehensive picture of the gluon OAM contribution to the proton spin, in particular, from the small-x region. In our recent publications: one and two, we have applied the connection between the parton Wigner distribution and orbital angular momentum (OAM) and investigated the probe of the gluon OAM in hard scattering processes. We have shown that the single longitudinal target-spin asymmetry in the hard diffractive dijet production is very sensitive to the gluon OAM distribution. The associated spin asymmetry leads to a characteristic azimuthal angular correlation between the proton momentum transfer and the relative transverse momentum between the quark- antiquark pair. The first paper  focuses on the moderate-x region, whereas the second paper  discusses nontrivial small-x behavior. These studies opened a new frontier to study the gluon tomography in nucleon. 

Left Figure: Kinematic illustration of the hard exclusive dijet production in deep inelastic scattering which can probe the gluon orbital angular momentum at the EIC

 A.H. Mueller, Bin Wu, Bo-Wen Xiao, Feng Yuan, Probing Transverse Momentum Broadening in Heavy Ion Collisions, Phys.Lett. B763 (2016) 208-212.

We study the dijet azimuthal de-correlation in relativistic heavy ion collisions as an important probe of the transverse momentum broadening effects of a high energy jet traversing the quark-gluon plasma. We take into account both the soft gluon radiation in vacuum associated with the Sudakov logarithms and the jet PT-broadening effects in the QCD medium. We find that the Sudakov effects are dominant at the LHC, while the medium effects can play an important role at RHIC energies. This explains why the LHC experiments have not yet observed sizable PT-broadening effects in the measurement of dijet azimuthal correlations in heavy ion collisions. Future investigations at RHIC will provide a unique opportunity to study the PT-broadening effects and help to pin down the underlying mechanism for jet energy loss in a hot and dense medium.

Left Figure: Comparison between the theory calculations to the dijet azimuthal distribution at the LHC and predictions for RHIC.