{"id":"https://openalex.org/W7222654445","doi":"https://doi.org/10.48550/arxiv.2610.20975","title":"The Sill distribution for all partial waves","display_name":"The Sill distribution for all partial waves","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7222654445","doi":"https://doi.org/10.48550/arxiv.2610.20975"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.20975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20975","pdf_url":"https://arxiv.org/pdf/2610.20975","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/2610.20975","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107124383","display_name":"Krzysztof Kyzio\u0142","orcid":"https://orcid.org/0000-0002-9290-3607","observed_orcids":["https://orcid.org/0000-0002-9290-3607"]},"institutions":[{"id":"https://openalex.org/I169495764","display_name":"Jan Kochanowski University","ror":"https://ror.org/00krbh354","country_code":"PL","type":"education","lineage":["https://openalex.org/I169495764"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Kyzio\u0142, Krzysztof","raw_affiliation_strings":["Institute of Physics , Jan Kochanowski University , Kielce , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics , Jan Kochanowski University , Kielce , Poland","institution_ids":["https://openalex.org/I169495764"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135505475","display_name":"Francesco Giacosa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]},{"id":"https://openalex.org/I169495764","display_name":"Jan Kochanowski University","ror":"https://ror.org/00krbh354","country_code":"PL","type":"education","lineage":["https://openalex.org/I169495764"]}],"countries":["DE","PL"],"is_corresponding":false,"raw_author_name":"Giacosa, Francesco","raw_affiliation_strings":["Institute of Physics , Jan Kochanowski University , Kielce , Poland","Institute of Theoretical Physics , Goethe University , Frankfurt am Main , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics , Jan Kochanowski University , Kielce , Poland","institution_ids":["https://openalex.org/I169495764"]},{"raw_affiliation_string":"Institute of Theoretical Physics , Goethe University , Frankfurt am Main , Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.9657999873161316,"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":0.9657999873161316,"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":0.021400000900030136,"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":0.007300000172108412,"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/partial-wave-analysis","display_name":"partial wave analysis","score":0.5090000033378601},{"id":"https://openalex.org/keywords/short-lived-resonances","display_name":"short-lived resonances","score":0.8029999732971191},{"id":"https://openalex.org/keywords/threshold-behavior","display_name":"threshold behavior","score":0.47200000286102295},{"id":"https://openalex.org/keywords/delta-1232-resonance","display_name":"Delta(1232) resonance","score":0.8700000047683716},{"id":"https://openalex.org/keywords/resonance-line-shape","display_name":"resonance line shape","score":0.7639999985694885},{"id":"https://openalex.org/keywords/p-wave-decays","display_name":"P-wave decays","score":0.38199999928474426}],"concepts":[{"id":"https://openalex.org/C40201923","wikidata":"https://www.wikidata.org/wiki/Q830230","display_name":"Sill","level":2,"score":0.8510000109672546},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6216999888420105},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5785999894142151},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5454000234603882},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44020000100135803},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.34540000557899475},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C134222618","wikidata":"https://www.wikidata.org/wiki/Q2713132","display_name":"Mass distribution","level":3,"score":0.31630000472068787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30379998683929443},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C2780550144","wikidata":"https://www.wikidata.org/wiki/Q1156976","display_name":"Excursion","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.27390000224113464},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.25999999046325684},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.20975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20975","pdf_url":"https://arxiv.org/pdf/2610.20975","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.2610.20975","doi":"https://doi.org/10.48550/arxiv.2610.20975","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.20975","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:2610.20975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20975","pdf_url":"https://arxiv.org/pdf/2610.20975","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222654445.pdf","grobid_xml":"https://content.openalex.org/works/W7222654445.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W782139581","https://openalex.org/W1500256440","https://openalex.org/W1593482979","https://openalex.org/W1638111448","https://openalex.org/W1724889751","https://openalex.org/W1862518851","https://openalex.org/W1964664702","https://openalex.org/W1973778620","https://openalex.org/W1974814862","https://openalex.org/W1978449352","https://openalex.org/W1990189003","https://openalex.org/W1993088516","https://openalex.org/W1994993367","https://openalex.org/W2006824787","https://openalex.org/W2022767536","https://openalex.org/W2022955359","https://openalex.org/W2030353222","https://openalex.org/W2043719160","https://openalex.org/W2052643328","https://openalex.org/W2065257265","https://openalex.org/W2071394924","https://openalex.org/W2071735768","https://openalex.org/W2073234783","https://openalex.org/W2074436307","https://openalex.org/W2076642067","https://openalex.org/W2086414247","https://openalex.org/W2087863203","https://openalex.org/W2089949648","https://openalex.org/W2090420909","https://openalex.org/W2093873958","https://openalex.org/W2109264750","https://openalex.org/W2149934264","https://openalex.org/W2166704981","https://openalex.org/W2438562676","https://openalex.org/W2499570793","https://openalex.org/W2517229838","https://openalex.org/W2582717733","https://openalex.org/W2916133289","https://openalex.org/W2921021130","https://openalex.org/W2948814398","https://openalex.org/W2962886726","https://openalex.org/W2971904588","https://openalex.org/W3002905821","https://openalex.org/W3009578594","https://openalex.org/W3047365041","https://openalex.org/W3101418132","https://openalex.org/W3104012012","https://openalex.org/W3175749815","https://openalex.org/W3194718107","https://openalex.org/W3199335028","https://openalex.org/W4200028534","https://openalex.org/W4308457283","https://openalex.org/W4311946192","https://openalex.org/W4383216843","https://openalex.org/W4393212420","https://openalex.org/W4399675980","https://openalex.org/W4401113806","https://openalex.org/W4408763345","https://openalex.org/W4413339074","https://openalex.org/W4415343817","https://openalex.org/W4417199158","https://openalex.org/W7164486650","https://openalex.org/W7172480893"],"related_works":["https://openalex.org/W4387561006","https://openalex.org/W4200028534","https://openalex.org/W7100221991","https://openalex.org/W2095035029","https://openalex.org/W2035657215","https://openalex.org/W2273930551","https://openalex.org/W61188860","https://openalex.org/W139498606","https://openalex.org/W2007391399","https://openalex.org/W7162699370"],"abstract_inverted_index":{"In":[0],"high-energy":[1],"physics,":[2],"short-lived":[3],"resonances":[4],"appearing":[5],"in":[6,75,152],"scattering":[7],"processes":[8],"are":[9,56],"described":[10],"by":[11,158],"energy-dependent":[12],"spectral":[13],"functions.":[14],"The":[15,58,96],"relativistic":[16,23],"Breit--Wigner":[17,28],"distribution":[18,60,91],"(rBW),":[19],"obtained":[20],"as":[21],"a":[22,62,109,120,126],"extension":[24],"of":[25,112,116,130],"the":[26,39,46,52,67,89,113,117,122,131,159],"standard":[27],"form,":[29],"is":[30,80,101,106],"commonly":[31],"employed":[32],"owing":[33],"to":[34,45,65,83,92,136],"its":[35,76,142,148],"simplicity.":[36],"However,":[37],"when":[38],"lower-energy":[40],"threshold":[41,69,99],"lies":[42],"sufficiently":[43],"close":[44],"resonance":[47],"peak,":[48],"sizable":[49],"deviations":[50],"from":[51],"rBW":[53],"line":[54,133],"shape":[55,134],"expected.":[57],"Sill":[59,90,124],"provides":[61,125],"simple":[63,110],"way":[64],"incorporate":[66],"physical":[68],"while":[70,103],"preserving":[71],"exact":[72,104],"normalization,":[73],"but":[74],"original":[77],"formulation":[78],"it":[79],"inherently":[81],"restricted":[82],"$s$-wave":[84],"decays.":[85],"Here,":[86],"we":[87],"extend":[88],"arbitrary":[93],"partial":[94],"waves.":[95],"correct":[97],"$\\ell$-wave":[98],"behaviour":[100],"implemented":[102],"normalization":[105],"retained":[107],"through":[108],"modification":[111],"mass":[114,144],"term":[115],"propagator.":[118],"As":[119],"benchmark,":[121],"$p$-wave":[123],"very":[127],"good":[128],"description":[129],"$\u0394(1232)^{++}$":[132],"up":[135],"1.35":[137],"GeV":[138],"and":[139,145,147],"simultaneously":[140],"reproduces":[141],"on-shell":[143],"width":[146],"complex":[149],"pole":[150],"position,":[151],"agreement":[153],"with":[154],"independent":[155],"determinations":[156],"compiled":[157],"PDG.":[160]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-17T00:00:00"}