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Resonance sum rules: An application to the square-well potential

Zi-Xi Ou-Yang1,*, Philipp Gubler2,†, Makoto Oka3,2,‡, Guang-Juan Wang4,§, and Jia-Jun Wu1,∥

  • *Contact author: ouyangzixi23@mails.ucas.ac.cn
  • †Contact author: philipp.gubler1@gmail.com
  • ‡Contact author: makoto.oka@riken.jp
  • §Contact author: wgj@post.kek.jp
  • ∥Contact author: wujiajun@ucas.ac.cn
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Phys. Rev. D 112, 114034 – Published 22 December, 2025

DOI: https://doi.org/10.1103/tcln-c924

Abstract

We propose an extension of the QCD sum rules, termed the resonance sum rules, to access resonance poles in the complex energy plane. By strategically introducing a contour in the complex plane and conformal mapping, the method intends to reach resonance poles on the second Riemann sheet. To validate this approach, we apply resonance sum rules to the square-well potential model, for which the pole locations are known. The analysis demonstrates a successful extraction of the pole positions and residues for both the S-wave and P-wave resonances. The results are in good agreement with the analytic solutions, with discrepancies within 5% for the pole positions and 20% for the residues. This framework provides a basis for future applications to realistic hadronic resonances, promising new insights into spectral properties of QCD.

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Phys. Rev. D 112, 114034– Published 22 December, 2025
  • Received 11 October 2025
  • Accepted 4 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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