Singularity Structure of the Four Point Celestial Leaf Amplitudes
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910656127565824 |
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| author | Mandal, Raju Misra, Sagnik Paul, Partha Roy, Baishali |
| author_facet | Mandal, Raju Misra, Sagnik Paul, Partha Roy, Baishali |
| contents | 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 \textit {simple pole singularity at $ z = \bar z $}, where, $ z,\bar 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_13969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singularity Structure of the Four Point Celestial Leaf Amplitudes Mandal, Raju Misra, Sagnik Paul, Partha Roy, Baishali High Energy Physics - Theory 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 \textit {simple pole singularity at $ z = \bar z $}, where, $ z,\bar 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. |
| title | Singularity Structure of the Four Point Celestial Leaf Amplitudes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.13969 |