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<p>We develop the computational framework for gravitational wave-black hole scattering in worldline quantum field theory (WQFT) without spin. Crucially, we prove on general grounds that, in the absence of dissipation, the exponential representation of the <i>S</i>-matrix maps — through a partial-wave transformation — directly onto the scattering phase shift from black hole perturbation theory (BHPT), indicating an exponentiation of the WQFT amplitude itself in partial-wave space. Computing explicitly, we reproduce the BHPT phase shift without spin up to <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>G</mi> <mn>3</mn> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({G}^3\right) \)</EquationSource> </InlineEquation> from WQFT. While this result is expected, it lays the groundwork for higher-precision analyses involving non-minimal effects. Along the way, we outline our efficient diagram generation technique and include a pedagogical discussion on the computation of the required two-loop integrals.</p>

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Gravitational wave scattering in spinless WQFT

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月22日

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  • Yilber Fabian Bautista,
  • Mathias Driesse,
  • Kays Haddad,
  • Gustav Uhre Jakobsen

摘要

We develop the computational framework for gravitational wave-black hole scattering in worldline quantum field theory (WQFT) without spin. Crucially, we prove on general grounds that, in the absence of dissipation, the exponential representation of the S-matrix maps — through a partial-wave transformation — directly onto the scattering phase shift from black hole perturbation theory (BHPT), indicating an exponentiation of the WQFT amplitude itself in partial-wave space. Computing explicitly, we reproduce the BHPT phase shift without spin up to O G 3 \( \mathcal{O}\left({G}^3\right) \) from WQFT. While this result is expected, it lays the groundwork for higher-precision analyses involving non-minimal effects. Along the way, we outline our efficient diagram generation technique and include a pedagogical discussion on the computation of the required two-loop integrals.