{"id":"https://openalex.org/W7220981231","doi":"https://doi.org/10.48550/arxiv.2610.08632","title":"Light bending at two-loop order from scattering amplitudes","display_name":"Light bending at two-loop order from scattering amplitudes","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220981231","doi":"https://doi.org/10.48550/arxiv.2610.08632"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08632","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08632","pdf_url":"https://arxiv.org/pdf/2610.08632","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08632","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100765416","display_name":"Jing Yang","orcid":"https://orcid.org/0000-0002-0929-9980","observed_orcids":["https://orcid.org/0000-0002-0929-9980"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Jing","raw_affiliation_strings":["MOE Key Laboratory of TianQin Mission ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOE Key Laboratory of TianQin Mission ,","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123247256","display_name":"Fa Peng Huang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Fa Peng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.948199987411499,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.948199987411499,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.02669999934732914,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.007699999958276749,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/light-deflection","display_name":"light deflection","score":0.8640000224113464},{"id":"https://openalex.org/keywords/photon-deflection","display_name":"photon deflection","score":0.8019999861717224},{"id":"https://openalex.org/keywords/black-holes","display_name":"black holes","score":0.6959999799728394},{"id":"https://openalex.org/keywords/post-minkowskian-expansion","display_name":"post-Minkowskian expansion","score":0.8830000162124634},{"id":"https://openalex.org/keywords/two-loop-corrections","display_name":"two-loop corrections","score":0.578000009059906},{"id":"https://openalex.org/keywords/scattering-amplitudes","display_name":"scattering amplitudes","score":0.8230000138282776},{"id":"https://openalex.org/keywords/five-point-amplitudes","display_name":"five-point amplitudes","score":0.6830000281333923},{"id":"https://openalex.org/keywords/on-shell-recursion","display_name":"on-shell recursion","score":0.8040000200271606},{"id":"https://openalex.org/keywords/polynomial-division","display_name":"polynomial division","score":0.546999990940094},{"id":"https://openalex.org/keywords/loop-amplitudes","display_name":"loop amplitudes","score":0.5849999785423279}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6352999806404114},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.5060999989509583},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.46810001134872437},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.46000000834465027},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.44780001044273376},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C115304011","wikidata":"https://www.wikidata.org/wiki/Q72755","display_name":"Schwarzschild radius","level":3,"score":0.4088999927043915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40869998931884766},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3993000090122223},{"id":"https://openalex.org/C2781355719","wikidata":"https://www.wikidata.org/wiki/Q2080698","display_name":"Deflection (physics)","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.37450000643730164},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3675999939441681},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.36090001463890076},{"id":"https://openalex.org/C90167683","wikidata":"https://www.wikidata.org/wiki/Q903040","display_name":"Impact parameter","level":2,"score":0.3549000024795532},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.3334999978542328},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3158999979496002},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3154999911785126},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3059000074863434},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.3043000102043152},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C63493438","wikidata":"https://www.wikidata.org/wiki/Q5533988","display_name":"Geodesics in general relativity","level":3,"score":0.2782999873161316},{"id":"https://openalex.org/C140901224","wikidata":"https://www.wikidata.org/wiki/Q409415","display_name":"Airy function","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.26759999990463257},{"id":"https://openalex.org/C37196565","wikidata":"https://www.wikidata.org/wiki/Q4118602","display_name":"Scattering length","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C130295795","wikidata":"https://www.wikidata.org/wiki/Q3550684","display_name":"Unitarity","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08632","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08632","pdf_url":"https://arxiv.org/pdf/2610.08632","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.08632","doi":"https://doi.org/10.48550/arxiv.2610.08632","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08632","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08632","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08632","pdf_url":"https://arxiv.org/pdf/2610.08632","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G8728142562","display_name":null,"funder_award_id":"12475111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321160","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220981231.pdf","grobid_xml":"https://content.openalex.org/works/W7220981231.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1678750707","https://openalex.org/W1991600871","https://openalex.org/W2022359341","https://openalex.org/W2565652095","https://openalex.org/W2578013395","https://openalex.org/W3084247555","https://openalex.org/W4388851564","https://openalex.org/W2624648570","https://openalex.org/W3089601595","https://openalex.org/W7164917922"],"abstract_inverted_index":{"We":[0,25,74],"calculate":[1],"the":[2,28,35,62,69,76,82,87,92,109,112,117,123,127,139,145,153],"conservative":[3,118],"deflection":[4,147],"of":[5,111,122,156],"a":[6,9,15,56,104],"photon":[7,84,105],"by":[8,46],"massive":[10],"spinless":[11],"source,":[12],"such":[13],"as":[14],"black":[16],"hole,":[17],"at":[18,131],"third":[19],"post-Minkowskian":[20],"order":[21],"using":[22],"scattering":[23],"amplitudes.":[24],"work":[26],"in":[27,86,95,169],"heavy-source":[29],"and":[30,33,49,80,143,160],"long-range":[31],"limits":[32],"adopt":[34],"geometric-optics":[36],"approximation.":[37],"The":[38,120,149],"required":[39],"five-point":[40],"photon-graviton":[41],"tree":[42,114],"amplitude":[43],"is":[44,167],"constructed":[45],"on-shell":[47],"recursion":[48],"sewn":[50],"to":[51,108],"three":[52],"scalar-graviton":[53],"vertices":[54],"across":[55],"five-fold":[57],"cut.":[58],"Polynomial":[59],"division":[60],"organizes":[61],"cut":[63],"information":[64],"into":[65],"sixteen":[66,124],"contributions,":[67],"including":[68],"residues":[70],"with":[71,152],"fewer":[72],"propagators.":[73],"perform":[75],"source":[77],"energy":[78],"integrations":[79],"retain":[81],"near-on-shell":[83],"regions":[85],"remaining":[88],"spatial":[89],"integrals.":[90],"Within":[91],"static":[93],"region":[94],"which":[96],"all":[97],"exchanged":[98],"momenta":[99],"are":[100],"soft,":[101],"we":[102],"relate":[103],"pole":[106],"prescription":[107],"subtraction":[110],"cubic":[113],"iteration":[115],"from":[116],"kernel.":[119],"sum":[121],"contributions":[125],"determines":[126],"classical":[128,164],"logarithmic":[129],"term":[130],"two":[132],"loops.":[133],"Its":[134],"transverse":[135],"Fourier":[136],"transform":[137],"gives":[138],"interaction":[140],"radial":[141],"action":[142],"yields":[144],"third-order":[146],"angle.":[148],"result":[150],"agrees":[151],"weak-deflection":[154],"expansion":[155],"Schwarzschild":[157],"null":[158],"geodesics":[159],"demonstrates":[161],"how":[162],"nonlinear":[163],"light":[165],"bending":[166],"encoded":[168],"loop":[170],"amplitudes":[171],"around":[172],"flat":[173],"spacetime.":[174]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}
