Our research group is dedicated to advancing our understanding of the fundamental forces and building blocks of the universe. At the heart of our work lies Quantum Chromodynamics (QCD), the theory that explains how quarks and gluons interact through the strong force to form protons, neutrons, and other particles that make up visible matter. This interaction not only governs the structure and stability of atomic nuclei but also plays a key role in shaping the early universe and the extreme conditions found in neutron stars and heavy-ion collisions.

By delving into the intricate dynamics of QCD, we tackle some of the most profound questions in modern physics: How does the mass of visible matter arise? What governs the spin and structure of protons and nuclei? What are the properties of strongly interacting matter?

We utilize modern theoretical tools, such as Soft Collinear Effective Theory (SCET) and QCD factorization, to build rigorous frameworks for understanding high-energy particle collisions, jet phenomena, and the complex behavior of quarks and gluons. These efforts connect directly with experimental programs at the Relativistic Heavy Ion Collider (RHIC), Jefferson Lab, the Large Hadron Collider (LHC), and the future Electron-Ion Collider (EIC).

The EIC, in particular, represents a groundbreaking facility that will allow us to probe the detailed structure of protons and nuclei like never before, uncovering how their mass, spin, momentum, and spatial distributions arise from their fundamental components.

Building on advanced theoretical frameworks, we are also integrating emerging computational methodologies into our research. Quantum computing offers transformative possibilities for addressing real-time dynamics and non-perturbative problems in QCD, while machine learning accelerates progress in modeling complex phenomena, analyzing large datasets, and crafting innovative observables for precision studies. These approaches not only complement our existing techniques but also push the boundaries of theoretical physics.

• Hadron Physics: Quantum imaging of the proton
• QCD Collider Physics: Studying jets, jet substructure, and heavy flavor dynamics
• Gluon Saturation and Heavy Ion Physics: Probing gluon saturation and hard scattering in nuclear collisions
• Quantum Computing for QCD: Exploring QCD with quantum simulations
• Machine Learning in QCD: Advanced data-driven methodologies

Hadron Physics

Our main focus along this direction is the quantum imaging of nucleons, specifically understanding the QCD structure of the nucleon and spin physics. QCD, the theory of strong interactions, describes how elementary particles like quarks and gluons interact with each other and is responsible for how quarks and gluons make up hadrons. While the fundamental laws of QCD are elegantly concise, decoding the structural complexity of protons and neutrons in terms of quarks and gluons governed by those laws remains one of the greatest challenges in physics today. This challenge drives the development of cutting-edge experimental facilities.

Through QCD factorization theorems, theorists can extract the low-energy properties of nucleon structure from experimental data. In recent years, a multidimensional view of nucleon structure has emerged, offering profound new insights into the internal dynamics of QCD. These advancements address questions such as: How do quarks and gluons move in transverse and longitudinal planes? Do they exhibit orbital motion, contributing to orbital angular momentum? What are the quantum correlations between the motion of partons, their spin, and the spin of the nucleon? This research is closely connected to experimental programs at Jefferson Lab, COMPASS, Belle, RHIC, and the future EIC.

Representative publications include:

• Z. B. Kang, K. Lee, D. Y. Shao, and F. Zhao, Probing transverse momentum dependent structures with azimuthal dependence of energy correlators, JHEP 03, 153 (2024).
• M. Alrashed, D. Anderle, Z. B. Kang, J. Terry, and H. Xing, Three-dimensional imaging in nuclei, Phys. Rev. Lett. 129, 242001 (2022).
• M. G. Echevarria, Z. B. Kang, and J. Terry, Global analysis of the Sivers functions at NLO+NNLL in QCD, JHEP 01, 126 (2021).
• Z. B. Kang, K. Lee, and F. Zhao, Polarized jet fragmentation functions, Phys. Lett. B 809, 135756 (2020).
• Z. B. Kang and J. W. Qiu, Evolution of twist-3 multi-parton correlation functions relevant to single transverse-spin asymmetry, Phys. Rev. D 79, 016003 (2009).

QCD Collider Physics

Research in this area focuses on jets, jet substructure, and heavy flavor production, providing valuable insights into QCD dynamics at high energies. By employing perturbative QCD and effective field theory approaches, we study the formation and internal structures of jets originating from quarks and gluons. Collimated jets of hadrons are key observables in high-energy particle interactions, offering a unique window into the partonic structure of the proton and the properties of QCD. Jet substructure measurements, in particular, have become powerful tools for understanding hadronization processes, extracting the strong coupling constant, and probing potential physics beyond the Standard Model (BSM).

Energy-Energy Correlators (EECs) have emerged as a promising theoretical and experimental tool in jet studies. These observables characterize the angular correlations between energy depositions in jets, enabling precise tests of QCD dynamics and allowing for direct comparisons between theoretical predictions and experimental measurements. EECs bridge the gap between perturbative and non-perturbative aspects of jet physics, shedding light on the interplay between parton dynamics and hadronization.

Heavy flavor production, including open heavy flavor mesons and heavy quarkonia, is another central focus. These studies provide critical insights into fragmentation and hadronization mechanisms. Despite decades of research since the discovery of the J/ψ, many aspects of heavy quarkonia production remain challenging to fully understand, making this an ongoing area of investigation. By combining experimental observations with robust theoretical frameworks, our work continues to advance the understanding of QCD dynamics and high-energy phenomena.

Representative publications include:

• Z. B. Kang, A. J. Larkoski, and J. Yang, Towards a Nonperturbative Formulation of the Jet Charge, Phys. Rev. Lett. 130, 151901 (2023).
• Z. B. Kang, K. Lee, X. Liu, and F. Ringer, The groomed and ungroomed jet mass distribution for inclusive jet production at the LHC, JHEP 10, 137 (2018).
• Z. B. Kang, J. W. Qiu, F. Ringer, H. Xing, and H. Zhang, J/ψ production and polarization within a jet, Phys. Rev. Lett. 119, 032001 (2017).
• Z. B. Kang, F. Ringer, and I. Vitev, The semi-inclusive jet function in SCET and small radius resummation for inclusive jet production, JHEP 10, 125 (2016).
• Z. B. Kang, Y. Q. Ma, J. W. Qiu, and G. Sterman, Heavy Quarkonium Production at Collider Energies: Factorization and Evolution, Phys. Rev. D 90, 034006 (2014).

Gluon Saturation and Heavy Ion Physics

Our research explores the extremes of QCD, focusing on gluon saturation and hard scattering in nucleus and heavy ion collisions. Under extreme temperature and density, nuclear matter undergoes a dramatic phase transition into the quark-gluon plasma (QGP), a novel state of matter where quarks and gluons are no longer confined within hadrons. The QGP is believed to have existed a few microseconds after the Big Bang, offering a unique glimpse into the conditions that shaped the early universe. By recreating and studying the QGP in ultra-relativistic heavy ion collisions at RHIC and the LHC, we investigate how strongly interacting matter behaves under such extreme conditions.

In addition to hot nuclear matter, we delve into the enigmatic properties of cold nuclear matter, where partons scatter within dense nuclei. At high parton densities, coherent interactions between gluons lead to a striking phenomenon known as gluon saturation, where the growth of gluon density at small momentum fractions is tamed. This saturation regime is described using the Color Glass Condensate (CGC), a theoretical framework that captures the dynamics of high-density gluonic matter. Understanding gluon saturation not only reveals the underlying dynamics of high-density QCD but also provides crucial insights for interpreting collisions at RHIC, the LHC, and the future EIC.

Representative publications include:

• Z. B. Kang, J. Penttala, F. Zhao and Y. Zhou, Transverse energy-energy correlators in the color-glass condensate at the electron-ion collider, Phys. Rev. D 109, 094012 (2024)
• V. Cheung, Z. B. Kang, F. Salazar and R. Vogt, Direct quarkonium production in DIS from a joint CGC and NRQCD framework, Phys. Rev. D 110, 094039 (2024)
• H. Liu, K. Xie, Z. B. Kang and X. Liu, Single inclusive jet production in pA collisions at NLO in the small-x regime, JHEP 07, 041 (2022)
• Z. B. Kang, F. Ringer and I. Vitev, Inclusive production of small radius jets in heavy-ion collisions, Phys. Lett. B 769, 242 (2017)
• Z. B. Kang, F. Ringer and I. Vitev, Effective field theory approach to open heavy flavor production in heavy-ion collisions, JHEP 03, 146 (2017)

Quantum Computing for QCD

The strong force, as described by QCD, is the most powerful among the fundamental forces, presenting significant computational challenges. Quantum computing offers a novel approach to addressing non-perturbative problems in QCD, such as real-time dynamics and quantum phase transitions. Early models have shown promising results in simulating quantum many-body systems of strongly interacting quarks and gluons. These efforts align with experimental programs at Jefferson Lab, RHIC, LHC, and the future EIC, paving the way for breakthroughs in high-energy nuclear and particle physics.

Our recent efforts in this direction focus on leveraging quantum simulation to address key QCD-related challenges. These include the quantum simulation of chiral phase transitions at finite chemical potential for the Nambu-Jona-Lasinio model in 1+1 dimensions, exploring real-time dynamics in the Schwinger model in 1+1 dimensions, and simulating parton distributions and dynamics in simplified 1+1 dimensional models. These exploratory studies provide valuable insights into the potential of quantum computing to tackle complex QCD phenomena and complement existing theoretical and computational techniques.

Representative publications include:

• K. Ikeda, Z. B. Kang, D. E. Kharzeev, W. Qian and F. Zhao, Real-time chiral dynamics at finite temperature from quantum simulation, JHEP 10, 031 (2024)
• A. M. Czajka, Z. B. Kang, H. Ma and F. Zhao, Quantum simulation of chiral phase transitions, JHEP 08, 209 (2022)

Machine Learning in QCD

Machine learning has emerged as a transformative tool in QCD research. For example, in our global analysis of multi-dimensional parton distributions—such as transverse momentum-dependent parton distributions and fragmentation functions, or the small-x gluon distribution—machine learning enables flexible parametrization of these functions and accelerates the global fitting process. By synthesizing vast experimental datasets, it helps uncover the distribution of quarks and gluons inside nucleons and nuclei. Machine learning also plays a critical role in jet physics. For instance, it facilitates jet classification, aiding in the identification of jets originating from quarks, gluons, Higgs bosons, or top quarks. These advancements improve precision in experimental analyses, facilitating new discoveries in high-energy physics.