https://doi.org/10.1140/epja/s10050-026-01875-8
Regular Article - Theoretical Physics
Mass and decay-constant evolution of heavy quarkonia and 
states from thermal QCD sum rules
School of Engineering and Architecture, Campus Heidelberg, SRH University of Applied Sciences Heidelberg, Ludwig-Guttmann-Straße 6, 69123, Heidelberg, Germany
a
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Received:
20
November
2025
Accepted:
29
April
2026
Published online:
28
May
2026
Abstract
We analyze the thermal behavior of heavy vector and axial-vector mesons (
, 
, and ) within the finite-temperature QCD sum-rule framework. Using updated PDG-2024 quark masses, modern lattice-informed gluon condensates, and a temperature-dependent continuum threshold constrained by vacuum stability, we compute the evolution of the masses m(T) and decay constants f(T) up to 
. At 
the sum rules are calibrated to reproduce the experimental and LHCb masses and reference decay constants within the expected 
accuracy of a leading-order + 
phenomenological analysis. The subsequent finite-temperature evolution should therefore be interpreted as a calibrated model prediction within this framework rather than as a fully parameter-free determination. Near the critical temperature, the relative suppression follows a clear hierarchy 
, consistent with their binding energies and lattice spectral trends. The predicted 1P–1S splitting for the system, 
, is consistent with the LHCb observation of orbitally excited 
states. The results provide a coherent finite-temperature baseline for future extensions including radiative, higher-dimensional, and width effects.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Communicated by Che-Ming Ko.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
