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Multiple dispersive bounds. II. Subthreshold branch cuts

Silvano Simula

Ludovico Vittorio

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Phys. Rev. D 113, 074018 – Published 14 April, 2026

DOI: https://doi.org/10.1103/g1q2-3pmq

Abstract

We apply the strategy proposed in the companion paper [Phys. Rev. D 113, 074017 (2026).] for dealing with multiple dispersive bounds, to the case of subthreshold branch cuts, which is a topic addressed extensively in the literature [J. Phys. A 14, 1271 (1980); Phys. Lett. B 380, 376 (1996); Nucl. Phys. B461, 493 (1996); Phys. Rev. D 58, 056001 (1998); Phys. Rev. D 84, 073006 (2011); Phys. Rev. D 90, 074027 (2014); Phys. Rev. D 111, L031501 (2025)]. We consider the simultaneous application of a double dispersive bound as a proper way to take into account unitarity constraints within phenomenological analyses of hadronic form factors in the presence of subthreshold branch cuts. Accordingly, the standard z-expansion of hadronic form factors, commonly referred to as the Boyd-Grinstein-Lebed approach [Nucl. Phys. B461, 493 (1996); Phys. Rev. Lett. 74, 4603 (1995); Phys. Lett. B 353, 306 (1995); Phys. Rev. D 56, 6895 (1997)], is modified by including simultaneously the dispersive bounds related to the pair-production and to the subthreshold regions. For the latter one the effects of above-threshold poles are described through a simple resonance model and the possible choices of the outer function outside the pair-production region are discussed. A detailed numerical analysis of the experimental data or lattice QCD results in the spacelike region for the charged kaon form factor is presented as a direct application of the procedure of double dispersive bound. The comparison with other methodologies present in literature and with the z-expansion based on the single, total dispersive bound clearly shows that the z-expansion including the double dispersive bound provides the most precise extrapolation at large momentum transfer as well as the most stable results with respect to the choice of the outer function outside the pair-production region.

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Multiple dispersive bounds. I. The z expansion

Silvano Simula and Ludovico Vittorio
Phys. Rev. D 113, 074017 (2026)

Article Text

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Phys. Rev. D 113, 074018– Published 14 April, 2026
  • Received 24 September 2025
  • Accepted 23 March 2026
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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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