Within the vast tapestry of the universe, where the microscopic building blocks of matter intertwine with the cosmic dance of galaxies, lies a story of profound discovery. Venture into a realm where the laws of physics as we know them are both challenged and confirmed, where the invisible forces that hold the very fabric of our reality together are brought into the light. This narrative isn’t born from the pages of a science fiction novel but emerges from the cutting-edge explorations at the heart of quantum physics. At this frontier, scientists embark on a rigorous inquiry to understand the origins of particle mass, revealing insights that connect the infinitesimal to the immense, from the atoms in our bodies to the distant stars.

The relentless pursuit to decipher the universe’s smallest building blocks and the enigmatic forces that knit the fabric of reality is a saga that stretches across centuries of scientific inquiry. Within this vast expanse of curiosity and research, a groundbreaking investigation by Professor Keh-Fei Liu from the University of Kentucky, as published in Physics Letters B, stands as a beacon of progress. This pioneering work delves deep into the quantum realm to shed light on the mass and confinement mechanisms of hadrons—subatomic particles that include protons and neutrons, fundamental to the structure of matter. By venturing into the intricate dynamics of quantum chromodynamics (QCD) and drawing parallels with phenomena in superconductivity and cosmology, Professor Liu’s research marks a significant leap in our understanding of the universe’s underlying principles.

At the heart of this investigation is the trace anomaly, an intriguing quantum phenomenon stemming from the breaking of scale symmetry due to quantum effects,. This anomaly is crucial for explaining the mass and confinement of hadrons, ensuring the stability of atomic nuclei. Professor Liu elucidates, “We explore the roles of the trace anomaly in several hadron properties… It is shown that the energy-equilibrium correspondence of hadrons infers an equation of state where the trace anomaly matrix element emerging from the glue condensate in the vacuum gives a negative constant pressure that leads to confinement much like the confinement mechanism for the vortices in type II superconductors.”

Through meticulous analysis and lattice QCD calculations, Professor Liu uncovers that the trace anomaly is overwhelmingly responsible for the mass of protons, with the quarks’ intrinsic masses contributing the rest, about 8%. This revelation not only deepens our grasp of particle physics but also intertwines the fate of the smallest particles with the vast cosmos.

The study further explores the resemblance between the trace anomaly in QCD and the cosmological constant in general relativity. “Both the trace anomaly in the QCD energy-momentum tensor and the cosmological constant in Einstein’s equation are associated with the metric term which contributes to both energy and pressure,” Professor Liu notes, emphasizing the underlying unity between quantum physics and cosmology.

By weaving together insights from the quantum to the cosmic, Professor Liu’s work opens new horizons in our exploration to understand the universe’s fabric. It underscores the pivotal role of the trace anomaly across diverse physical phenomena, offering a unified perspective that bridges gaps across physics disciplines. This research not only enriches our knowledge of the fundamental forces and particles but also paves the way for future explorations at the quantum frontier. Featured Image Legend: The decomposition of the proton energy at rest in terms of the quarks of various flavors  and the gluons as obtained from experiments and lattice calculations at two different energy scales.


Keh-Fei Liu, “Hadrons, Superconductor Vortices, and the Cosmological Constant,” Physics Letters B, 2024.

DOI: https://doi.org/10.1016/j.physletb.2023.138418.


Keh-Fei Liu was born in Beijing and grew up in Taiwan. He obtained his Ph. D. degree from Stony Brook University and has been on the faculty of University of Kentucky until 2023. He is now working at Lawrence Berkeley National Lab.

His major research area is in lattice gauge theory, working on the calculations of nucleon structure, neutron electron dipole moment, neutrino-nucleon scattering and finite density. He is also working on the design of an accelerator based fusion reactor.

He has been given the First Prize Award in Theoretical Physics by the Chinese Academy of Sciences in 1987 and the Alexander von Humboldt Award for Senior Scientist in 1989. He also won the Albert D. and Elizabeth H. Kirwan Memorial Prize in 2018.

He is a fellow of the American Physical Society.