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<p>In this paper, we study the four-point celestial leaf amplitudes of massless scalar and MHV gluon scattering. These leaf amplitudes are non-distributional decompositions of the celestial amplitudes associated with a hyperbolic foliation of the Klein spacetime. Bulk scale invariance imposes constraints on the total conformal weights of the massless scalars or gluons. Using this constraint we show that the four-point leaf amplitudes have a <i>simple pole singularity at z</i> = <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25593_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overline{z} \)</EquationSource> </InlineEquation>, where, <i>z,</i> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25593_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overline{z} \)</EquationSource> </InlineEquation> are two real independent conformal cross ratios. The distributional nature of the four-point celestial amplitudes is recovered by adding the leaf amplitudes in the timelike and spacelike wedges of the spacetime. We also verify that the MHV gluon leaf amplitudes satisfy a set of differential equations previously obtained for celestial MHV gluon amplitudes by considering the soft gluon theorems and the subleading terms in the OPE expansion between two positive helicity gluons.</p>

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Singularity structure of the four point celestial leaf amplitudes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月21日

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  • Raju Mandal,
  • Sagnik Misra,
  • Partha Paul,
  • Baishali Roy

摘要

In this paper, we study the four-point celestial leaf amplitudes of massless scalar and MHV gluon scattering. These leaf amplitudes are non-distributional decompositions of the celestial amplitudes associated with a hyperbolic foliation of the Klein spacetime. Bulk scale invariance imposes constraints on the total conformal weights of the massless scalars or gluons. Using this constraint we show that the four-point leaf amplitudes have a simple pole singularity at z = z ¯ \( \overline{z} \) , where, z, z ¯ \( \overline{z} \) are two real independent conformal cross ratios. The distributional nature of the four-point celestial amplitudes is recovered by adding the leaf amplitudes in the timelike and spacelike wedges of the spacetime. We also verify that the MHV gluon leaf amplitudes satisfy a set of differential equations previously obtained for celestial MHV gluon amplitudes by considering the soft gluon theorems and the subleading terms in the OPE expansion between two positive helicity gluons.