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<p>We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2 → 2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-<i>t</i> dispersion relations emerge as special cases. Within this setting we re-derive the <i>null constraints</i> from a geometric perspective. Finally, we present, for the first time, an explicit extension of Roy-like equations that remain valid at arbitrarily high energies, relying only on the rigorously established analyticity domain of scattering amplitudes.</p>

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A geometric view on crossing-symmetric dispersion relations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • Joan Elias Miró,
  • Andrea Guerrieri,
  • Mehmet Asım Gümüş,
  • Ahmadullah Zahed

摘要

We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2 → 2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geometric perspective. Finally, we present, for the first time, an explicit extension of Roy-like equations that remain valid at arbitrarily high energies, relying only on the rigorously established analyticity domain of scattering amplitudes.