Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

Leor Barack; Zvi Bern; Enrico Herrmann; Oliver Long; Julio Parra-Martinez; Radu Roiban; Michael S. Ruf; Chia-Hsien Shen; Mikhail P. Solon; Fei Teng; Mao Zeng

doi:10.1103/PhysRevD.108.024025

Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

Leor Barack, Zvi Bern, Enrico Herrmann, Oliver Long, Julio Parra-Martinez, Radu Roiban, Michael S. Ruf, Chia-Hsien Shen, Mikhail P. Solon, Fei Teng, Mao Zeng

School of Physics and Astronomy

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge Q off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full O(Q2) scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through O(Q2G3). At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones

Original language	English
Article number	024025
Pages (from-to)	1-30
Number of pages	30
Journal	Physical Review D
Volume	108
Issue number	2
Early online date	12 Jul 2023
DOIs	https://doi.org/10.1103/PhysRevD.108.024025
Publication status	Published - 15 Jul 2023

Keywords / Materials (for Non-textual outputs)

hep-th
gr-qc

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10.1103/PhysRevD.108.024025Licence: Creative Commons: Attribution (CC-BY)

https://arxiv.org/abs/2304.09200Licence: Creative Commons: Attribution (CC-BY)

Scattering amplitudes and applications to precision QCD and gravitational waves
Zeng, M.
Other (Learned Society)
1/08/21 → 31/12/25
Project: Research

Cite this

@article{ef022eca1d2f4131a99ecc2f64b7806c,

title = "Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model",

abstract = "We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge Q off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full O(Q2) scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through O(Q2G3). At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones",

keywords = "hep-th, gr-qc",

author = "Leor Barack and Zvi Bern and Enrico Herrmann and Oliver Long and Julio Parra-Martinez and Radu Roiban and Ruf, {Michael S.} and Chia-Hsien Shen and Solon, {Mikhail P.} and Fei Teng and Mao Zeng",

note = "53 pages, 11 figures, 7 tables Funding Information: We thank Misha Ivanov, Rafael Porto, Zihan Zhou for useful discussion. We are especially grateful to Thibault Damour for detailed discussions on the mass polynomiality of the impulse. We would also like to thank Benjamin Leather for providing the code used to generate Fig. . This research was supported in part by the U.S. Department of Energy (DOE) under Grants No. DE-SC0009937, No. DE-SC00019066, No. DE-SC0011632 and No. DE-SC0009919 and in part by the U.S. National Science Foundation under Grant No. NSF PHY-1748958. In relation to the latter support, we thank the Kavli Institute for Theoretical Physics for their hospitality, where this paper was initiated. M. Z.{\textquoteright}s work is supported in part by the U.K. Royal Society through Grant No. URF\R1\20109. J. P.-M. would like to thank the Institut des Hautes {\'E}tudes Scientifiques and the Korea Institute for Advanced Study, for their hospitality while this work was being completed. M. P. S. is supported by the Alfred P. Sloan Foundation. We are also grateful to the Mani L. Bhaumik Institute for Theoretical Physics and the Walter Burke Institute for Theoretical Physics for support. We acknowledge the use of the IRIDIS High-Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. This work makes use of the Black Hole Perturbation Toolkit . Publisher Copyright: {\textcopyright} 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the {"}https://creativecommons.org/licenses/by/4.0/{"}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.",

year = "2023",

month = jul,

day = "15",

doi = "10.1103/PhysRevD.108.024025",

language = "English",

volume = "108",

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TY - JOUR

T1 - Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

AU - Barack, Leor

AU - Bern, Zvi

AU - Herrmann, Enrico

AU - Long, Oliver

AU - Parra-Martinez, Julio

AU - Roiban, Radu

AU - Ruf, Michael S.

AU - Shen, Chia-Hsien

AU - Solon, Mikhail P.

AU - Teng, Fei

AU - Zeng, Mao

N1 - 53 pages, 11 figures, 7 tables Funding Information: We thank Misha Ivanov, Rafael Porto, Zihan Zhou for useful discussion. We are especially grateful to Thibault Damour for detailed discussions on the mass polynomiality of the impulse. We would also like to thank Benjamin Leather for providing the code used to generate Fig. . This research was supported in part by the U.S. Department of Energy (DOE) under Grants No. DE-SC0009937, No. DE-SC00019066, No. DE-SC0011632 and No. DE-SC0009919 and in part by the U.S. National Science Foundation under Grant No. NSF PHY-1748958. In relation to the latter support, we thank the Kavli Institute for Theoretical Physics for their hospitality, where this paper was initiated. M. Z.’s work is supported in part by the U.K. Royal Society through Grant No. URF\R1\20109. J. P.-M. would like to thank the Institut des Hautes Études Scientifiques and the Korea Institute for Advanced Study, for their hospitality while this work was being completed. M. P. S. is supported by the Alfred P. Sloan Foundation. We are also grateful to the Mani L. Bhaumik Institute for Theoretical Physics and the Walter Burke Institute for Theoretical Physics for support. We acknowledge the use of the IRIDIS High-Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. This work makes use of the Black Hole Perturbation Toolkit . Publisher Copyright: © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"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.

PY - 2023/7/15

Y1 - 2023/7/15

N2 - We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge Q off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full O(Q2) scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through O(Q2G3). At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones

AB - We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge Q off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full O(Q2) scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through O(Q2G3). At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones

KW - hep-th

KW - gr-qc

U2 - 10.1103/PhysRevD.108.024025

DO - 10.1103/PhysRevD.108.024025

M3 - Article

SN - 1550-7998

VL - 108

SP - 1

EP - 30

JO - Physical Review D

JF - Physical Review D

IS - 2

M1 - 024025

ER -

Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

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Scattering amplitudes and applications to precision QCD and gravitational waves

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