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  • Open Access

Pseudogauge ambiguity in the distributions of energy density, pressure, and shear force inside the nucleon

Kenji Fukushima* and Tomoya Uji†

  • *Contact author: fuku@nt.phys.s.u-tokyo.ac.jp
  • †Contact author: uji@nt.phys.s.u-tokyo.ac.jp
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Phys. Rev. D 113, 016025 – Published 30 January, 2026Erratum Phys. Rev. D 113, 099902 (2026)

DOI: https://doi.org/10.1103/mkyh-n8st

Abstract

We study the spatial distributions of pressure, energy density, and shear forces inside the nucleon within the two-flavor Skyrme model including vector mesons. This framework has the advantage that nucleon configurations can be stabilized without the Skyrme term. In contrast to the model without vector mesons, however, we realize that the energy-momentum tensor (EMT) becomes pseudogauge dependent. We explicitly demonstrate that all these distributions differ between the canonical and Belinfante forms of the EMTs. We identify the pseudogauge ambiguity as originating from nonvanishing surface terms associated with spin currents generated by the vector-meson field strength tensors. Furthermore, we show that the pressure and shear-force distributions in the canonical EMT develop singularities at the nucleon center, whereas the corresponding Belinfante distributions remain finite. Finally, we discuss the implications of pseudogauge dependence for extracting the confining force and for constructing the equation of state inside the nucleon.

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Erratum

Erratum: Pseudogauge ambiguity in the distributions of energy density, pressure, and shear force inside the nucleon [Phys. Rev. D 113, 016025 (2026)]

Kenji Fukushima and Tomoya Uji
Phys. Rev. D 113, 099902 (2026)

Article Text

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Phys. Rev. D 113, 016025– Published 30 January, 2026
  • Received 8 October 2025
  • Accepted 7 January 2026
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