Hadrons, superconductor vortices, and cosmological constant

Keh Fei Liu

doi:10.1016/j.physletb.2023.138418

Hadrons, superconductor vortices, and cosmological constant

Keh Fei Liu

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. 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 where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that 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. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.

Original language	English
Article number	138418
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	849
DOIs	https://doi.org/10.1016/j.physletb.2023.138418
State	Published - Feb 2024

Bibliographical note

Publisher Copyright:
© 2023 The Author(s)

Funding

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Keh-Fei Liu reports financial support was provided by University of Kentucky. Keh-Fei Liu reports financial support was provided by US Department of Energy. Keh-Fei Liu reports a relationship with US Department of Energy that includes: funding grants No. DE-SC0013065 and DE-AC05-06OR23177.The author is indebted to P. Boyle, S. Brodsky, V. Burkert, M. Chanowitz, S. Das, T. Draper, A. Dymarsky, W. Gannon, I. Horváth, T. Hatsuda, F. He, Y. Hatta, X. Ji, D.E. Kharzeev, D. Lin, C. Lorcé, A. Metz, Z. Meziani, G. Murthy, J.C. Peng, M. Peshkin, A. Shapere, O.V. Teryaev, B. Wang, Y.B. Yang, and F. Yuan for fruitful discussions. He also thanks T.J. Hou for providing the CT18 data and B. Wang for help with the figures. This work is partially supported by the U.S. DOE Grant No. DE-SC0013065 and No. DE-AC05-06OR23177 which is within the framework of the TMD Topical Collaboration. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This work used Stampede time under the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. We also thank the National Energy Research Scientific Computing Center (NERSC) for providing HPC resources that have contributed to the research results reported within this paper. We acknowledge the facilities of the USQCD Collaboration used for this research in part, which are funded by the Office of Science of the U.S. Department of Energy. The author is indebted to P. Boyle, S. Brodsky, V. Burkert, M. Chanowitz, S. Das, T. Draper, A. Dymarsky, W. Gannon, I. Horváth, T. Hatsuda, F. He, Y. Hatta, X. Ji, D.E. Kharzeev, D. Lin, C. Lorcé, A. Metz, Z. Meziani, G. Murthy, J.C. Peng, M. Peshkin, A. Shapere, O.V. Teryaev, B. Wang, Y.B. Yang, and F. Yuan for fruitful discussions. He also thanks T.J. Hou for providing the CT18 data and B. Wang for help with the figures. This work is partially supported by the U.S. DOE Grant No. DE-SC0013065 and No. DE-AC05-06OR23177 which is within the framework of the TMD Topical Collaboration. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725 . This work used Stampede time under the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575 . We also thank the National Energy Research Scientific Computing Center (NERSC) for providing HPC resources that have contributed to the research results reported within this paper. We acknowledge the facilities of the USQCD Collaboration used for this research in part, which are funded by the Office of Science of the U.S. Department of Energy.

Funders	Funder number
National Energy Research Scientific Computing Center
University of Kentucky
Office of Science Programs
National Science Foundation Arctic Social Science Program	1053575
U.S. Department of Energy	DE-AC05-00OR22725, DE-SC0013065, DE-AC05-06OR23177

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.physletb.2023.138418

Cite this

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title = "Hadrons, superconductor vortices, and cosmological constant",

abstract = "We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. 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 where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that 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. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.",

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AB - We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. 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 where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that 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. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.

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Hadrons, superconductor vortices, and cosmological constant

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