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Rev. Lett."],"accepted":{"date-parts":[[2026,7,10]]},"abstract":"<jats:p>\n                    Using the worldline quantum field theory formalism, we compute conservative contributions to the scattering angle and impulse for classical black hole scattering at fifth post-Minkowskian and second self-force order. This four-loop calculation involves nonplanar Feynman integrals and requires advanced integration-by-parts reduction, novel differential-equation strategies, and efficient boundary-integral algorithms to solve a system of hundreds of master integrals in four integral families on high-performance computing systems. The resulting function space includes multiple polylogarithms as well as iterated integrals with a\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mi>K<\/a:mi>\n                      <a:mn>3<\/a:mn>\n                    <\/a:math>\n                    period, which generate a spurious velocity divergence at\n                    <c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <c:mi>v<\/c:mi>\n                      <c:mo>\/<\/c:mo>\n                      <c:mi>c<\/c:mi>\n                      <c:mo>=<\/c:mo>\n                      <c:msqrt>\n                        <c:mn>8<\/c:mn>\n                      <\/c:msqrt>\n                      <c:mo>\/<\/c:mo>\n                      <c:mn>3<\/c:mn>\n                    <\/c:math>\n                    ,\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:mi>\u03b3<\/e:mi>\n                      <e:mo>=<\/e:mo>\n                      <e:mn>3<\/e:mn>\n                    <\/e:math>\n                    . This divergence is present in the potential region and must be canceled by contributions from the radiative memory region, while its dimensional-regularization pole should cancel against the radiative tail region. As the standard use of Feynman propagators fails to ensure this cancellation, we instead propose a \u201c(\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:mrow>\n                        <g:mi>\u03b3<\/g:mi>\n                        <g:mo>\u2212<\/g:mo>\n                        <g:mn>3<\/g:mn>\n                      <\/g:mrow>\n                    <\/g:math>\n                    )\u201d conservative prescription that realizes both cancellations, leading to a physically sensible answer. All available low-velocity checks of our result against the post-Newtonian literature are satisfied.\n                  <\/jats:p>","DOI":"10.1103\/4dvk-nglx","type":"journal-article","created":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T17:26:25Z","timestamp":1783704385000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Conservative Black Hole Scattering at Fifth Post-Minkowskian and Second Self-Force Order"],"prefix":"10.1103","volume":"137","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3983-5852","authenticated-orcid":true,"given":"Mathias","family":"Driesse","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01hcx6992","id-type":"ROR","asserted-by":"publisher"}],"name":"Humboldt-Universit\u00e4t zu Berlin"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9743-0442","authenticated-orcid":true,"given":"Gustav Uhre","family":"Jakobsen","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01hcx6992","id-type":"ROR","asserted-by":"publisher"}],"name":"Humboldt-Universit\u00e4t zu Berlin"},{"id":[{"id":"https:\/\/ror.org\/03sry2h30","id-type":"ROR","asserted-by":"publisher"}],"name":"Max Planck Institut f\u00fcr Gravitationsphysik (Albert Einstein Institut)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3070-5717","authenticated-orcid":true,"given":"Gustav","family":"Mogull","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01hcx6992","id-type":"ROR","asserted-by":"publisher"}],"name":"Humboldt-Universit\u00e4t zu Berlin"},{"id":[{"id":"https:\/\/ror.org\/03sry2h30","id-type":"ROR","asserted-by":"publisher"}],"name":"Max Planck Institut f\u00fcr Gravitationsphysik (Albert Einstein Institut)"},{"id":[{"id":"https:\/\/ror.org\/026zzn846","id-type":"ROR","asserted-by":"publisher"}],"name":"Queen Mary University of London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0202-536X","authenticated-orcid":true,"given":"Christoph","family":"Nega","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sry2h30","id-type":"ROR","asserted-by":"publisher"}],"name":"Max Planck Institut f\u00fcr Gravitationsphysik (Albert Einstein Institut)"},{"id":[{"id":"https:\/\/ror.org\/02kkvpp62","id-type":"ROR","asserted-by":"publisher"}],"name":"Technische Universit\u00e4t M\u00fcnchen"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2883-7825","authenticated-orcid":true,"given":"Jan","family":"Plefka","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01hcx6992","id-type":"ROR","asserted-by":"publisher"}],"name":"Humboldt-Universit\u00e4t zu Berlin"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2071-257X","authenticated-orcid":true,"given":"Benjamin","family":"Sauer","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01hcx6992","id-type":"ROR","asserted-by":"publisher"}],"name":"Humboldt-Universit\u00e4t zu Berlin"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3542-2786","authenticated-orcid":true,"given":"Johann","family":"Usovitsch","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01hcx6992","id-type":"ROR","asserted-by":"publisher"}],"name":"Humboldt-Universit\u00e4t zu Berlin"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,8,21]]},"reference":[{"key":"4dvk-nglxCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.061102","type":"journal-article"},{"key":"4dvk-nglxCc2R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.119.161101","type":"journal-article"},{"key":"4dvk-nglxCc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.13.041039","type":"journal-article"},{"key":"4dvk-nglxCc4R1","doi-asserted-by":"publisher","DOI":"10.3847\/2041-8213\/ae2c74","type":"journal-article"},{"key":"4dvk-nglxCc6R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/27\/19\/194002","type":"journal-article"},{"key":"4dvk-nglxCc8R1","doi-asserted-by":"publisher","DOI":"10.12942\/lrr-2014-2","type":"journal-article"},{"key":"4dvk-nglxCc9R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.04.003","type":"journal-article"},{"key":"4dvk-nglxCc10R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/ab12bc","type":"journal-article"},{"key":"4dvk-nglxCc12R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ac8846","type":"journal-article"},{"key":"4dvk-nglxCc13R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ac7a78","type":"journal-article"},{"key":"4dvk-nglxCc14R1","volume-title":"Snowmass 2021","author":"A. 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