{"id":"https://openalex.org/W7223912907","doi":"https://doi.org/10.48550/arxiv.2610.34276","title":"Nucleon polarizabilities revisited: insights from the Bernab\u00e9u-Ericson-Ferro Fontan-Tarrach sum rule","display_name":"Nucleon polarizabilities revisited: insights from the Bernab\u00e9u-Ericson-Ferro Fontan-Tarrach sum rule","publication_year":2026,"publication_date":"2026-10-25","ids":{"openalex":"https://openalex.org/W7223912907","doi":"https://doi.org/10.48550/arxiv.2610.34276"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.34276","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34276","pdf_url":"https://arxiv.org/pdf/2610.34276","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.34276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088364959","display_name":"Xiong-Hui Cao","orcid":"https://orcid.org/0000-0003-1365-7178","observed_orcids":["https://orcid.org/0000-0003-1365-7178"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210125404","display_name":"Institute of Theoretical Physics","ror":"https://ror.org/02xtbq882","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210125404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cao, Xiong-Hui","raw_affiliation_strings":["Institute of Theoretical Physics , Chinese Academy of Sciences , Beijing 100190 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Physics , Chinese Academy of Sciences , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210125404"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100648398","display_name":"Ling-Yun Dai","orcid":"https://orcid.org/0000-0002-5473-323X","observed_orcids":["https://orcid.org/0000-0002-5473-323X"]},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dai, Ling-Yun","raw_affiliation_strings":["Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications , Hunan University , Changsha 410082 , China","School for Theoretical Physics , School of Physics and Electronics , Hunan University , Changsha 410082 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications , Hunan University , Changsha 410082 , China","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School for Theoretical Physics , School of Physics and Electronics , Hunan University , Changsha 410082 , China","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063845753","display_name":"Feng-Kun Guo","orcid":"https://orcid.org/0000-0002-2919-2064","observed_orcids":["https://orcid.org/0000-0002-2919-2064"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210125404","display_name":"Institute of Theoretical Physics","ror":"https://ror.org/02xtbq882","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210125404"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guo, Feng-Kun","raw_affiliation_strings":["Institute of Theoretical Physics , Chinese Academy of Sciences , Beijing 100190 , China","School of Physical Sciences , University of Chinese Academy of Sciences , Beijing 100049 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Physics , Chinese Academy of Sciences , Beijing 100190 , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210125404"]},{"raw_affiliation_string":"School of Physical Sciences , University of Chinese Academy of Sciences , Beijing 100049 , China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"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/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9667999744415283,"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/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9667999744415283,"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/T10093","display_name":"Nuclear physics research studies","score":0.028200000524520874,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.002400000113993883,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nucleon-polarizabilities","display_name":"nucleon polarizabilities","score":0.9919999837875366},{"id":"https://openalex.org/keywords/a0-980-meson","display_name":"a0(980) meson","score":0.7409999966621399}],"concepts":[{"id":"https://openalex.org/C2781235419","wikidata":"https://www.wikidata.org/wiki/Q6086598","display_name":"Isovector","level":3,"score":0.9078999757766724},{"id":"https://openalex.org/C139287275","wikidata":"https://www.wikidata.org/wiki/Q869891","display_name":"Polarizability","level":3,"score":0.801800012588501},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7738999724388123},{"id":"https://openalex.org/C88407732","wikidata":"https://www.wikidata.org/wiki/Q7636898","display_name":"Sum rule in quantum mechanics","level":3,"score":0.7210000157356262},{"id":"https://openalex.org/C172695262","wikidata":"https://www.wikidata.org/wiki/Q102165","display_name":"Nucleon","level":2,"score":0.6037999987602234},{"id":"https://openalex.org/C61203554","wikidata":"https://www.wikidata.org/wiki/Q171516","display_name":"Compton scattering","level":3,"score":0.5541999936103821},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.542900025844574},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.5292999744415283},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C49874194","wikidata":"https://www.wikidata.org/wiki/Q5282045","display_name":"Discrete dipole approximation","level":3,"score":0.40709999203681946},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.4043000042438507},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C202579712","wikidata":"https://www.wikidata.org/wiki/Q590051","display_name":"Dispersion relation","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3625999987125397},{"id":"https://openalex.org/C187268509","wikidata":"https://www.wikidata.org/wiki/Q1402884","display_name":"Field theory (psychology)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C142199849","wikidata":"https://www.wikidata.org/wiki/Q3027672","display_name":"Inelastic scattering","level":3,"score":0.2985000014305115},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29440000653266907},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.2904999852180481},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2903999984264374},{"id":"https://openalex.org/C185544564","wikidata":"https://www.wikidata.org/wiki/Q81197","display_name":"Nuclear physics","level":1,"score":0.2653000056743622},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.2623000144958496},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C163387558","wikidata":"https://www.wikidata.org/wiki/Q281778","display_name":"Effective field theory","level":2,"score":0.26010000705718994}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.34276","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34276","pdf_url":"https://arxiv.org/pdf/2610.34276","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.2610.34276","doi":"https://doi.org/10.48550/arxiv.2610.34276","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.34276","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.34276","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34276","pdf_url":"https://arxiv.org/pdf/2610.34276","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/G2330016983","display_name":null,"funder_award_id":"12125507","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G328816031","display_name":null,"funder_award_id":"YSBR-101","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G6539477486","display_name":null,"funder_award_id":"12322502","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G7310684046","display_name":null,"funder_award_id":"12335002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7364093867","display_name":null,"funder_award_id":"12322502","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8220555843","display_name":null,"funder_award_id":"12335002","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G8351509261","display_name":null,"funder_award_id":"12447101","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/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223912907.pdf","grobid_xml":"https://content.openalex.org/works/W7223912907.grobid-xml"},"referenced_works_count":126,"referenced_works":["https://openalex.org/W1603547289","https://openalex.org/W1646343881","https://openalex.org/W1765959364","https://openalex.org/W1889988403","https://openalex.org/W1968655425","https://openalex.org/W1969963577","https://openalex.org/W1970309454","https://openalex.org/W1974434453","https://openalex.org/W1974577047","https://openalex.org/W1975052301","https://openalex.org/W1976303696","https://openalex.org/W1976694155","https://openalex.org/W1979407303","https://openalex.org/W1998749407","https://openalex.org/W1999842579","https://openalex.org/W2000003922","https://openalex.org/W2003226227","https://openalex.org/W2004699036","https://openalex.org/W2010535367","https://openalex.org/W2017726463","https://openalex.org/W2023746134","https://openalex.org/W2036884916","https://openalex.org/W2038092595","https://openalex.org/W2041247565","https://openalex.org/W2043189131","https://openalex.org/W2047987730","https://openalex.org/W2051982098","https://openalex.org/W2052046070","https://openalex.org/W2060454650","https://openalex.org/W2060532946","https://openalex.org/W2063646997","https://openalex.org/W2064177603","https://openalex.org/W2065371717","https://openalex.org/W2068898584","https://openalex.org/W2073856020","https://openalex.org/W2077112240","https://openalex.org/W2079209516","https://openalex.org/W2090469945","https://openalex.org/W2093002399","https://openalex.org/W2101417477","https://openalex.org/W2107156744","https://openalex.org/W2109781083","https://openalex.org/W2117443311","https://openalex.org/W2121852180","https://openalex.org/W2145319584","https://openalex.org/W2152687730","https://openalex.org/W2155471440","https://openalex.org/W2158133093","https://openalex.org/W2159551435","https://openalex.org/W2171022493","https://openalex.org/W2195792787","https://openalex.org/W2196285940","https://openalex.org/W2212225773","https://openalex.org/W2217337822","https://openalex.org/W2218525277","https://openalex.org/W2232479151","https://openalex.org/W2248157420","https://openalex.org/W2249011223","https://openalex.org/W2253075695","https://openalex.org/W2277306361","https://openalex.org/W2297063211","https://openalex.org/W2324480597","https://openalex.org/W2339084736","https://openalex.org/W2346837494","https://openalex.org/W2460789525","https://openalex.org/W2567941844","https://openalex.org/W2584421405","https://openalex.org/W2770585261","https://openalex.org/W2771129175","https://openalex.org/W2795948853","https://openalex.org/W2894877457","https://openalex.org/W2895849978","https://openalex.org/W2899128793","https://openalex.org/W2921270860","https://openalex.org/W2949402505","https://openalex.org/W2961569369","https://openalex.org/W3008736484","https://openalex.org/W3013086740","https://openalex.org/W3018321398","https://openalex.org/W3028406153","https://openalex.org/W3034678343","https://openalex.org/W3037134578","https://openalex.org/W3048797623","https://openalex.org/W3088727093","https://openalex.org/W3104012012","https://openalex.org/W3121410195","https://openalex.org/W3126391675","https://openalex.org/W3154865347","https://openalex.org/W3159103535","https://openalex.org/W3168234261","https://openalex.org/W3179735099","https://openalex.org/W3208379825","https://openalex.org/W4220685521","https://openalex.org/W4221158654","https://openalex.org/W4225160990","https://openalex.org/W4281259699","https://openalex.org/W4288102479","https://openalex.org/W4310027024","https://openalex.org/W4311326826","https://openalex.org/W4390060738","https://openalex.org/W4390305815","https://openalex.org/W4391231167","https://openalex.org/W4391376777","https://openalex.org/W4392166579","https://openalex.org/W4399783879","https://openalex.org/W4400480878","https://openalex.org/W4402983682","https://openalex.org/W4403559081","https://openalex.org/W4404649796","https://openalex.org/W4405354825","https://openalex.org/W4407320710","https://openalex.org/W4409994451","https://openalex.org/W4412538645","https://openalex.org/W4413846942","https://openalex.org/W4415488464","https://openalex.org/W4415595081","https://openalex.org/W4415647522","https://openalex.org/W4415728615","https://openalex.org/W4415766391","https://openalex.org/W4416937014","https://openalex.org/W6967088972","https://openalex.org/W7130338054","https://openalex.org/W7134252764","https://openalex.org/W7134907317","https://openalex.org/W7213348628","https://openalex.org/W7216299949"],"related_works":["https://openalex.org/W25936339","https://openalex.org/W2043189131","https://openalex.org/W7213348628","https://openalex.org/W1506426127","https://openalex.org/W2063646997","https://openalex.org/W2961569369","https://openalex.org/W2047987730","https://openalex.org/W2174195479","https://openalex.org/W7100136999","https://openalex.org/W2950789305"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,143,179,182],"complete":[3],"dispersive":[4,60,94,187,210],"evaluation":[5],"of":[6,84,131,146,165,218],"the":[7,14,30,55,89,112,115,122,128,137,147,152,157,174,195,205,219],"Bernab\u00e9u-Ericson-Ferro":[8],"Fontan-Tarrach":[9],"(BEFT)":[10],"sum":[11,159],"rule":[12],"for":[13,96,104],"nucleon":[15],"dipole":[16],"polarizability":[17,56],"difference":[18,57],"$\u03b1_{E1}-\u03b2_{M1}$.":[19],"The":[20,71,124],"analysis":[21],"is":[22,74],"based":[23],"on":[24],"hyperbolic":[25],"dispersion":[26],"relations,":[27],"which":[28],"separate":[29],"$s$-":[31],"and":[32,38,81,109,141,188],"$t$-channel":[33],"contributions":[34],"without":[35],"double":[36],"counting":[37],"are":[39,199],"particularly":[40],"suited":[41],"to":[42,52,66,114,185,216],"backward":[43],"real":[44],"Compton":[45,68],"scattering.":[46],"This":[47],"framework":[48],"makes":[49],"it":[50],"possible":[51],"precisely":[53],"determine":[54],"from":[58,64],"independent":[59,209],"input":[61,95],"rather":[62],"than":[63],"fits":[65],"low-energy":[67],"scattering":[69],"data.":[70],"$s$-channel":[72],"part":[73],"updated":[75],"with":[76,100,121,156,181,212],"modern":[77],"single-pion":[78],"photoproduction":[79],"multipoles":[80],"model":[82],"estimates":[83],"non-$\u03c0N$":[85],"inelastic":[86],"channels.":[87],"For":[88,173,194],"$t$-channel,":[90],"we":[91,110,161],"use":[92],"contemporary":[93],"$\u03b3\u03b3\\to\u03c0\u03c0/K\\bar":[97],"K_{I_t=0}$":[98],"together":[99],"Roy-Steiner":[101],"equation":[102],"solutions":[103],"$\u03c0\u03c0/K\\bar":[105],"K_{I_t=0}\\to":[106],"N\\bar":[107],"N$,":[108],"extend":[111],"calculation":[113],"isovector":[116,149],"$\u03c0\u03b7/K\\bar":[117],"K_{I_t=1}$":[118],"channel":[119,140],"associated":[120],"$a_0(980)$.":[123],"resulting":[125,153],"treatment":[126],"resolves":[127],"long-standing":[129],"puzzle":[130],"earlier":[132],"BEFT":[133,154],"evaluations":[134],"driven":[135],"by":[136],"scalar-isoscalar":[138],"two-pion":[139],"gives":[142],"controlled":[144],"estimate":[145],"subleading":[148],"contribution.":[150],"Combining":[151],"values":[155,177],"Baldin":[158],"rule,":[160],"obtain,":[162],"in":[163],"units":[164],"$10^{-4}\\,\\mathrm{fm}^3$,":[166],"\\[":[167],"\u03b1_{E1}^p=11.17(52),\\quad":[168],"\u03b2_{M1}^p=2.84(52),\\quad":[169],"\u03b1_{E1}^n=12.18(59),\\quad":[170],"\u03b2_{M1}^n=3.03(59).":[171],"\\]":[172],"proton,":[175],"these":[176],"provide":[178],"benchmark":[180,211],"precision":[183],"comparable":[184,215],"state-of-the-art":[186],"chiral":[189],"effective":[190],"field":[191],"theory":[192],"extractions.":[193],"neutron,":[196],"whose":[197],"polarizabilities":[198],"much":[200],"less":[201],"directly":[202],"constrained":[203],"experimentally,":[204],"result":[206],"provides":[207],"an":[208,213],"uncertainty":[214],"that":[217],"proton.":[220]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-28T00:00:00"}