Hadronic vacuum polarization: Comparing lattice QCD and data-driven results in systematically improvable ways Article Swipe
M. Davier
,
Z. Fodor
,
Antoine Gérardin
,
Laurent Lellouch
,
B. Malaescu
,
Finn M. Stokes
,
Kálman Szabó
,
Bálint Tóth
,
Lukas Varnhorst
,
Z. Zhang
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1103/physrevd.109.076019
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1103/physrevd.109.076019
The precision with which hadronic vacuum polarization (HVP) is obtained determines how accurately important observables, such as the muon anomalous magnetic moment aμ or the low-energy running of the electromagnetic coupling α, are predicted. The two most precise approaches for determining HVP are dispersive relations combined with e+e−→hadrons cross section data and lattice QCD. However, the results obtained in these two approaches display significant tensions, whose origins are not understood. Here we present a framework that sheds light on this issue and—if the two approaches can be reconciled—allows them to be combined. Via this framework, we test the hypothesis that the tensions can be explained by modifying the R-ratio in different intervals of center-of-mass energy s. As ingredients, we consider observables that have been precisely determined in both approaches. These are the leading hadronic contributions to aμ, to the so-called intermediate window observable, and to the running of α between spacelike virtualities 1 and 10 GeV2 (for which only a preliminary lattice result exists). Our tests take into account all uncertainties and correlations, as well as uncertainties on uncertainties in the lattice results. For instance, using this framework we show that results obtained in the two approaches can be made to agree, for all three observables, by modifying the ρ peak in the experimental spectrum. More specifically, we show that this requires a common ∼5% increase in the contributions of the peak to each of the three observables. This result is robust against the presence or absence of the running of α in the comparison. However, such an increase is much larger than the uncertainties on the measured R-ratio. We also discuss a variety of generalizations of the methods used here, as well as the limits in the information that can be extracted from the R-ratio via a finite set of observables. Published by the American Physical Society 2024
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physrevd.109.076019
- http://link.aps.org/pdf/10.1103/PhysRevD.109.076019
- OA Status
- hybrid
- Cited By
- 17
- References
- 130
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4395012018
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4395012018Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1103/physrevd.109.076019Digital Object Identifier
- Title
-
Hadronic vacuum polarization: Comparing lattice QCD and data-driven results in systematically improvable waysWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-04-22Full publication date if available
- Authors
-
M. Davier, Z. Fodor, Antoine Gérardin, Laurent Lellouch, B. Malaescu, Finn M. Stokes, Kálman Szabó, Bálint Tóth, Lukas Varnhorst, Z. ZhangList of authors in order
- Landing page
-
https://doi.org/10.1103/physrevd.109.076019Publisher landing page
- PDF URL
-
https://link.aps.org/pdf/10.1103/PhysRevD.109.076019Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://link.aps.org/pdf/10.1103/PhysRevD.109.076019Direct OA link when available
- Concepts
-
Physics, Hadron, Observable, Particle physics, Muon, Anomalous magnetic dipole moment, Lattice QCD, Vacuum polarization, Lattice (music), Quantum chromodynamics, Lattice field theory, Polarization (electrochemistry), Quantum mechanics, Chemistry, Physical chemistry, AcousticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
17Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 9, 2024: 6, 2023: 2Per-year citation counts (last 5 years)
- References (count)
-
130Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4395012018 |
|---|---|
| doi | https://doi.org/10.1103/physrevd.109.076019 |
| ids.doi | https://doi.org/10.1103/physrevd.109.076019 |
| ids.openalex | https://openalex.org/W4395012018 |
| fwci | 9.31710213 |
| type | article |
| title | Hadronic vacuum polarization: Comparing lattice QCD and data-driven results in systematically improvable ways |
| awards[0].id | https://openalex.org/G7959018463 |
| awards[0].funder_id | https://openalex.org/F4320309911 |
| awards[0].display_name | |
| awards[0].funder_award_id | BMBF-05P21PXFCA |
| awards[0].funder_display_name | Aix-Marseille Université |
| awards[1].id | https://openalex.org/G3919108682 |
| awards[1].funder_id | https://openalex.org/F4320309911 |
| awards[1].display_name | |
| awards[1].funder_award_id | NW21-024-A |
| awards[1].funder_display_name | Aix-Marseille Université |
| awards[2].id | https://openalex.org/G5559139127 |
| awards[2].funder_id | https://openalex.org/F4320320883 |
| awards[2].display_name | |
| awards[2].funder_award_id | ANR-22-CE31-0011 |
| awards[2].funder_display_name | Agence Nationale de la Recherche |
| awards[3].id | https://openalex.org/G6611414040 |
| awards[3].funder_id | https://openalex.org/F4320309911 |
| awards[3].display_name | |
| awards[3].funder_award_id | ERC-MUON |
| awards[3].funder_display_name | Aix-Marseille Université |
| awards[4].id | https://openalex.org/G5547716027 |
| awards[4].funder_id | https://openalex.org/F4320331625 |
| awards[4].display_name | |
| awards[4].funder_award_id | 502275 |
| awards[4].funder_display_name | Gauss Centre for Supercomputing |
| awards[5].id | https://openalex.org/G1883808964 |
| awards[5].funder_id | https://openalex.org/F4320309911 |
| awards[5].display_name | |
| awards[5].funder_award_id | AMX-18-ACE-005 |
| awards[5].funder_display_name | Aix-Marseille Université |
| biblio.issue | 7 |
| biblio.volume | 109 |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10048 |
| topics[0].field.id | https://openalex.org/fields/31 |
| topics[0].field.display_name | Physics and Astronomy |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/3106 |
| topics[0].subfield.display_name | Nuclear and High Energy Physics |
| topics[0].display_name | Particle physics theoretical and experimental studies |
| topics[1].id | https://openalex.org/T10224 |
| topics[1].field.id | https://openalex.org/fields/31 |
| topics[1].field.display_name | Physics and Astronomy |
| topics[1].score | 0.9991000294685364 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/3106 |
| topics[1].subfield.display_name | Nuclear and High Energy Physics |
| topics[1].display_name | Quantum Chromodynamics and Particle Interactions |
| topics[2].id | https://openalex.org/T10527 |
| topics[2].field.id | https://openalex.org/fields/31 |
| topics[2].field.display_name | Physics and Astronomy |
| topics[2].score | 0.9976000189781189 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/3106 |
| topics[2].subfield.display_name | Nuclear and High Energy Physics |
| topics[2].display_name | High-Energy Particle Collisions Research |
| funders[0].id | https://openalex.org/F4320309911 |
| funders[0].ror | https://ror.org/035xkbk20 |
| funders[0].display_name | Aix-Marseille Université |
| funders[1].id | https://openalex.org/F4320320883 |
| funders[1].ror | https://ror.org/00rbzpz17 |
| funders[1].display_name | Agence Nationale de la Recherche |
| funders[2].id | https://openalex.org/F4320321752 |
| funders[2].ror | https://ror.org/02nv7yv05 |
| funders[2].display_name | Forschungszentrum Jülich |
| funders[3].id | https://openalex.org/F4320331625 |
| funders[3].ror | https://ror.org/0585fsj26 |
| funders[3].display_name | Gauss Centre for Supercomputing |
| funders[4].id | https://openalex.org/F4320336863 |
| funders[4].ror | https://ror.org/05558nw16 |
| funders[4].display_name | Leibniz-Rechenzentrum |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C121332964 |
| concepts[0].level | 0 |
| concepts[0].score | 0.8895647525787354 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[0].display_name | Physics |
| concepts[1].id | https://openalex.org/C19694890 |
| concepts[1].level | 2 |
| concepts[1].score | 0.8268041610717773 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q101667 |
| concepts[1].display_name | Hadron |
| concepts[2].id | https://openalex.org/C32848918 |
| concepts[2].level | 2 |
| concepts[2].score | 0.8065460920333862 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q845789 |
| concepts[2].display_name | Observable |
| concepts[3].id | https://openalex.org/C109214941 |
| concepts[3].level | 1 |
| concepts[3].score | 0.7692867517471313 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q18334 |
| concepts[3].display_name | Particle physics |
| concepts[4].id | https://openalex.org/C205334942 |
| concepts[4].level | 2 |
| concepts[4].score | 0.7152851819992065 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q3151 |
| concepts[4].display_name | Muon |
| concepts[5].id | https://openalex.org/C139455999 |
| concepts[5].level | 3 |
| concepts[5].score | 0.6840130090713501 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q771367 |
| concepts[5].display_name | Anomalous magnetic dipole moment |
| concepts[6].id | https://openalex.org/C3909970 |
| concepts[6].level | 3 |
| concepts[6].score | 0.6152851581573486 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q6166044 |
| concepts[6].display_name | Lattice QCD |
| concepts[7].id | https://openalex.org/C2780154664 |
| concepts[7].level | 2 |
| concepts[7].score | 0.5930728912353516 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1886497 |
| concepts[7].display_name | Vacuum polarization |
| concepts[8].id | https://openalex.org/C2781204021 |
| concepts[8].level | 2 |
| concepts[8].score | 0.5607408285140991 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q6497091 |
| concepts[8].display_name | Lattice (music) |
| concepts[9].id | https://openalex.org/C117137515 |
| concepts[9].level | 2 |
| concepts[9].score | 0.4957354962825775 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q238170 |
| concepts[9].display_name | Quantum chromodynamics |
| concepts[10].id | https://openalex.org/C42238305 |
| concepts[10].level | 3 |
| concepts[10].score | 0.4536634087562561 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q5370778 |
| concepts[10].display_name | Lattice field theory |
| concepts[11].id | https://openalex.org/C205049153 |
| concepts[11].level | 2 |
| concepts[11].score | 0.4319629967212677 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q2698605 |
| concepts[11].display_name | Polarization (electrochemistry) |
| concepts[12].id | https://openalex.org/C62520636 |
| concepts[12].level | 1 |
| concepts[12].score | 0.19505926966667175 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[12].display_name | Quantum mechanics |
| concepts[13].id | https://openalex.org/C185592680 |
| concepts[13].level | 0 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q2329 |
| concepts[13].display_name | Chemistry |
| concepts[14].id | https://openalex.org/C147789679 |
| concepts[14].level | 1 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q11372 |
| concepts[14].display_name | Physical chemistry |
| concepts[15].id | https://openalex.org/C24890656 |
| concepts[15].level | 1 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q82811 |
| concepts[15].display_name | Acoustics |
| keywords[0].id | https://openalex.org/keywords/physics |
| keywords[0].score | 0.8895647525787354 |
| keywords[0].display_name | Physics |
| keywords[1].id | https://openalex.org/keywords/hadron |
| keywords[1].score | 0.8268041610717773 |
| keywords[1].display_name | Hadron |
| keywords[2].id | https://openalex.org/keywords/observable |
| keywords[2].score | 0.8065460920333862 |
| keywords[2].display_name | Observable |
| keywords[3].id | https://openalex.org/keywords/particle-physics |
| keywords[3].score | 0.7692867517471313 |
| keywords[3].display_name | Particle physics |
| keywords[4].id | https://openalex.org/keywords/muon |
| keywords[4].score | 0.7152851819992065 |
| keywords[4].display_name | Muon |
| keywords[5].id | https://openalex.org/keywords/anomalous-magnetic-dipole-moment |
| keywords[5].score | 0.6840130090713501 |
| keywords[5].display_name | Anomalous magnetic dipole moment |
| keywords[6].id | https://openalex.org/keywords/lattice-qcd |
| keywords[6].score | 0.6152851581573486 |
| keywords[6].display_name | Lattice QCD |
| keywords[7].id | https://openalex.org/keywords/vacuum-polarization |
| keywords[7].score | 0.5930728912353516 |
| keywords[7].display_name | Vacuum polarization |
| keywords[8].id | https://openalex.org/keywords/lattice |
| keywords[8].score | 0.5607408285140991 |
| keywords[8].display_name | Lattice (music) |
| keywords[9].id | https://openalex.org/keywords/quantum-chromodynamics |
| keywords[9].score | 0.4957354962825775 |
| keywords[9].display_name | Quantum chromodynamics |
| keywords[10].id | https://openalex.org/keywords/lattice-field-theory |
| keywords[10].score | 0.4536634087562561 |
| keywords[10].display_name | Lattice field theory |
| keywords[11].id | https://openalex.org/keywords/polarization |
| keywords[11].score | 0.4319629967212677 |
| keywords[11].display_name | Polarization (electrochemistry) |
| keywords[12].id | https://openalex.org/keywords/quantum-mechanics |
| keywords[12].score | 0.19505926966667175 |
| keywords[12].display_name | Quantum mechanics |
| language | en |
| locations[0].id | doi:10.1103/physrevd.109.076019 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210238307 |
| locations[0].source.issn | 2470-0010, 2470-0029, 2470-0037 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 2470-0010 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Physical review. D/Physical review. D. |
| locations[0].source.host_organization | https://openalex.org/P4310320261 |
| locations[0].source.host_organization_name | American Physical Society |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320261 |
| locations[0].source.host_organization_lineage_names | American Physical Society |
| locations[0].license | cc-by |
| locations[0].pdf_url | http://link.aps.org/pdf/10.1103/PhysRevD.109.076019 |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Physical Review D |
| locations[0].landing_page_url | https://doi.org/10.1103/physrevd.109.076019 |
| locations[1].id | pmh:oai:HAL:hal-04181885v1 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306402512 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| locations[1].source.host_organization | https://openalex.org/I1294671590 |
| locations[1].source.host_organization_name | Centre National de la Recherche Scientifique |
| locations[1].source.host_organization_lineage | https://openalex.org/I1294671590 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | Journal articles |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | Physical Review D, 2024, 109 (7), pp.076019. ⟨10.1103/PhysRevD.109.076019⟩ |
| locations[1].landing_page_url | https://hal.science/hal-04181885 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5070030327 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-0337-1013 |
| authorships[0].author.display_name | M. Davier |
| authorships[0].countries | FR |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I1294671590, https://openalex.org/I277688954, https://openalex.org/I4210133362, https://openalex.org/I4210134832 |
| authorships[0].affiliations[0].raw_affiliation_string | IJCLab, Université Paris-Saclay et CNRS/IN2P3, F-91405 Orsay, France |
| authorships[0].institutions[0].id | https://openalex.org/I1294671590 |
| authorships[0].institutions[0].ror | https://ror.org/02feahw73 |
| authorships[0].institutions[0].type | government |
| authorships[0].institutions[0].lineage | https://openalex.org/I1294671590 |
| authorships[0].institutions[0].country_code | FR |
| authorships[0].institutions[0].display_name | Centre National de la Recherche Scientifique |
| authorships[0].institutions[1].id | https://openalex.org/I4210133362 |
| authorships[0].institutions[1].ror | https://ror.org/03fd77x13 |
| authorships[0].institutions[1].type | facility |
| authorships[0].institutions[1].lineage | https://openalex.org/I1294671590, https://openalex.org/I4210133362 |
| authorships[0].institutions[1].country_code | FR |
| authorships[0].institutions[1].display_name | Institut National de Physique Nucléaire et de Physique des Particules |
| authorships[0].institutions[2].id | https://openalex.org/I4210134832 |
| authorships[0].institutions[2].ror | https://ror.org/03gc1p724 |
| authorships[0].institutions[2].type | facility |
| authorships[0].institutions[2].lineage | https://openalex.org/I1294671590, https://openalex.org/I1294671590, https://openalex.org/I204730241, https://openalex.org/I277688954, https://openalex.org/I4210133362, https://openalex.org/I4210134832 |
| authorships[0].institutions[2].country_code | FR |
| authorships[0].institutions[2].display_name | Laboratoire de Physique des 2 Infinis Irène Joliot-Curie |
| authorships[0].institutions[3].id | https://openalex.org/I277688954 |
| authorships[0].institutions[3].ror | https://ror.org/03xjwb503 |
| authorships[0].institutions[3].type | education |
| authorships[0].institutions[3].lineage | https://openalex.org/I277688954 |
| authorships[0].institutions[3].country_code | FR |
| authorships[0].institutions[3].display_name | Université Paris-Saclay |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Michel Davier |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | IJCLab, Université Paris-Saclay et CNRS/IN2P3, F-91405 Orsay, France |
| authorships[1].author.id | https://openalex.org/A5072744830 |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Z. Fodor |
| authorships[1].countries | DE, HU, US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I106118109 |
| authorships[1].affiliations[0].raw_affiliation_string | Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary |
| authorships[1].affiliations[1].institution_ids | https://openalex.org/I130769515 |
| authorships[1].affiliations[1].raw_affiliation_string | Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA |
| authorships[1].affiliations[2].institution_ids | https://openalex.org/I171892758 |
| authorships[1].affiliations[2].raw_affiliation_string | Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany |
| authorships[1].affiliations[3].institution_ids | https://openalex.org/I167360494 |
| authorships[1].affiliations[3].raw_affiliation_string | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany |
| authorships[1].institutions[0].id | https://openalex.org/I171892758 |
| authorships[1].institutions[0].ror | https://ror.org/02nv7yv05 |
| authorships[1].institutions[0].type | facility |
| authorships[1].institutions[0].lineage | https://openalex.org/I1305996414, https://openalex.org/I171892758 |
| authorships[1].institutions[0].country_code | DE |
| authorships[1].institutions[0].display_name | Forschungszentrum Jülich |
| authorships[1].institutions[1].id | https://openalex.org/I167360494 |
| authorships[1].institutions[1].ror | https://ror.org/00613ak93 |
| authorships[1].institutions[1].type | education |
| authorships[1].institutions[1].lineage | https://openalex.org/I167360494 |
| authorships[1].institutions[1].country_code | DE |
| authorships[1].institutions[1].display_name | University of Wuppertal |
| authorships[1].institutions[2].id | https://openalex.org/I106118109 |
| authorships[1].institutions[2].ror | https://ror.org/01jsq2704 |
| authorships[1].institutions[2].type | education |
| authorships[1].institutions[2].lineage | https://openalex.org/I106118109 |
| authorships[1].institutions[2].country_code | HU |
| authorships[1].institutions[2].display_name | Eötvös Loránd University |
| authorships[1].institutions[3].id | https://openalex.org/I130769515 |
| authorships[1].institutions[3].ror | https://ror.org/04p491231 |
| authorships[1].institutions[3].type | education |
| authorships[1].institutions[3].lineage | https://openalex.org/I130769515 |
| authorships[1].institutions[3].country_code | US |
| authorships[1].institutions[3].display_name | Pennsylvania State University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Zoltán Fodor |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA, Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany, Institute for Theoretical Physics, Eötvös University, H-1117 Budapest, Hungary, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany |
| authorships[2].author.id | https://openalex.org/A5082849672 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-8839-7166 |
| authorships[2].author.display_name | Antoine Gérardin |
| authorships[2].countries | FR |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I1294671590, https://openalex.org/I143002897 |
| authorships[2].affiliations[0].raw_affiliation_string | Aix Marseille Univ, Université de Toulon, CNRS, CPT, IPhU, Marseille, France |
| authorships[2].institutions[0].id | https://openalex.org/I1294671590 |
| authorships[2].institutions[0].ror | https://ror.org/02feahw73 |
| authorships[2].institutions[0].type | government |
| authorships[2].institutions[0].lineage | https://openalex.org/I1294671590 |
| authorships[2].institutions[0].country_code | FR |
| authorships[2].institutions[0].display_name | Centre National de la Recherche Scientifique |
| authorships[2].institutions[1].id | https://openalex.org/I143002897 |
| authorships[2].institutions[1].ror | https://ror.org/02m9kbe37 |
| authorships[2].institutions[1].type | education |
| authorships[2].institutions[1].lineage | https://openalex.org/I143002897 |
| authorships[2].institutions[1].country_code | FR |
| authorships[2].institutions[1].display_name | Université de Toulon |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Antoine Gérardin |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Aix Marseille Univ, Université de Toulon, CNRS, CPT, IPhU, Marseille, France |
| authorships[3].author.id | https://openalex.org/A5085045767 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-0032-6073 |
| authorships[3].author.display_name | Laurent Lellouch |
| authorships[3].countries | FR |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I1294671590, https://openalex.org/I143002897 |
| authorships[3].affiliations[0].raw_affiliation_string | Aix Marseille Univ, Université de Toulon, CNRS, CPT, IPhU, Marseille, France |
| authorships[3].institutions[0].id | https://openalex.org/I1294671590 |
| authorships[3].institutions[0].ror | https://ror.org/02feahw73 |
| authorships[3].institutions[0].type | government |
| authorships[3].institutions[0].lineage | https://openalex.org/I1294671590 |
| authorships[3].institutions[0].country_code | FR |
| authorships[3].institutions[0].display_name | Centre National de la Recherche Scientifique |
| authorships[3].institutions[1].id | https://openalex.org/I143002897 |
| authorships[3].institutions[1].ror | https://ror.org/02m9kbe37 |
| authorships[3].institutions[1].type | education |
| authorships[3].institutions[1].lineage | https://openalex.org/I143002897 |
| authorships[3].institutions[1].country_code | FR |
| authorships[3].institutions[1].display_name | Université de Toulon |
| authorships[3].author_position | middle |
| authorships[3].raw_author_name | Laurent Lellouch |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Aix Marseille Univ, Université de Toulon, CNRS, CPT, IPhU, Marseille, France |
| authorships[4].author.id | https://openalex.org/A5070734925 |
| authorships[4].author.orcid | https://orcid.org/0000-0002-8813-3830 |
| authorships[4].author.display_name | B. Malaescu |
| authorships[4].countries | FR |
| authorships[4].affiliations[0].institution_ids | https://openalex.org/I1294671590, https://openalex.org/I204730241, https://openalex.org/I39804081, https://openalex.org/I4210091437, https://openalex.org/I4210105151 |
| authorships[4].affiliations[0].raw_affiliation_string | LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, 75252, France |
| authorships[4].institutions[0].id | https://openalex.org/I1294671590 |
| authorships[4].institutions[0].ror | https://ror.org/02feahw73 |
| authorships[4].institutions[0].type | government |
| authorships[4].institutions[0].lineage | https://openalex.org/I1294671590 |
| authorships[4].institutions[0].country_code | FR |
| authorships[4].institutions[0].display_name | Centre National de la Recherche Scientifique |
| authorships[4].institutions[1].id | https://openalex.org/I4210105151 |
| authorships[4].institutions[1].ror | https://ror.org/01hg8p552 |
| authorships[4].institutions[1].type | facility |
| authorships[4].institutions[1].lineage | https://openalex.org/I1294671590, https://openalex.org/I1294671590, https://openalex.org/I204730241, https://openalex.org/I39804081, https://openalex.org/I4210105151, https://openalex.org/I4210133362 |
| authorships[4].institutions[1].country_code | FR |
| authorships[4].institutions[1].display_name | Laboratoire de Physique Nucléaire et de Hautes Énergies |
| authorships[4].institutions[2].id | https://openalex.org/I4210091437 |
| authorships[4].institutions[2].ror | https://ror.org/001z21q04 |
| authorships[4].institutions[2].type | other |
| authorships[4].institutions[2].lineage | https://openalex.org/I4210091437 |
| authorships[4].institutions[2].country_code | FR |
| authorships[4].institutions[2].display_name | Sorbonne Paris Cité |
| authorships[4].institutions[3].id | https://openalex.org/I39804081 |
| authorships[4].institutions[3].ror | https://ror.org/02en5vm52 |
| authorships[4].institutions[3].type | education |
| authorships[4].institutions[3].lineage | https://openalex.org/I39804081 |
| authorships[4].institutions[3].country_code | FR |
| authorships[4].institutions[3].display_name | Sorbonne Université |
| authorships[4].institutions[4].id | https://openalex.org/I204730241 |
| authorships[4].institutions[4].ror | https://ror.org/05f82e368 |
| authorships[4].institutions[4].type | education |
| authorships[4].institutions[4].lineage | https://openalex.org/I204730241 |
| authorships[4].institutions[4].country_code | FR |
| authorships[4].institutions[4].display_name | Université Paris Cité |
| authorships[4].author_position | middle |
| authorships[4].raw_author_name | Bogdan Malaescu |
| authorships[4].is_corresponding | False |
| authorships[4].raw_affiliation_strings | LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, 75252, France |
| authorships[5].author.id | https://openalex.org/A5061218562 |
| authorships[5].author.orcid | https://orcid.org/0000-0003-1763-8847 |
| authorships[5].author.display_name | Finn M. Stokes |
| authorships[5].countries | DE |
| authorships[5].affiliations[0].institution_ids | https://openalex.org/I171892758 |
| authorships[5].affiliations[0].raw_affiliation_string | Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany |
| authorships[5].institutions[0].id | https://openalex.org/I171892758 |
| authorships[5].institutions[0].ror | https://ror.org/02nv7yv05 |
| authorships[5].institutions[0].type | facility |
| authorships[5].institutions[0].lineage | https://openalex.org/I1305996414, https://openalex.org/I171892758 |
| authorships[5].institutions[0].country_code | DE |
| authorships[5].institutions[0].display_name | Forschungszentrum Jülich |
| authorships[5].author_position | middle |
| authorships[5].raw_author_name | Finn M. Stokes |
| authorships[5].is_corresponding | False |
| authorships[5].raw_affiliation_strings | Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany |
| authorships[6].author.id | https://openalex.org/A5103479238 |
| authorships[6].author.orcid | |
| authorships[6].author.display_name | Kálman Szabó |
| authorships[6].countries | DE |
| authorships[6].affiliations[0].institution_ids | https://openalex.org/I171892758 |
| authorships[6].affiliations[0].raw_affiliation_string | Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany |
| authorships[6].affiliations[1].institution_ids | https://openalex.org/I167360494 |
| authorships[6].affiliations[1].raw_affiliation_string | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany |
| authorships[6].institutions[0].id | https://openalex.org/I171892758 |
| authorships[6].institutions[0].ror | https://ror.org/02nv7yv05 |
| authorships[6].institutions[0].type | facility |
| authorships[6].institutions[0].lineage | https://openalex.org/I1305996414, https://openalex.org/I171892758 |
| authorships[6].institutions[0].country_code | DE |
| authorships[6].institutions[0].display_name | Forschungszentrum Jülich |
| authorships[6].institutions[1].id | https://openalex.org/I167360494 |
| authorships[6].institutions[1].ror | https://ror.org/00613ak93 |
| authorships[6].institutions[1].type | education |
| authorships[6].institutions[1].lineage | https://openalex.org/I167360494 |
| authorships[6].institutions[1].country_code | DE |
| authorships[6].institutions[1].display_name | University of Wuppertal |
| authorships[6].author_position | middle |
| authorships[6].raw_author_name | Kálmán K. Szabó |
| authorships[6].is_corresponding | False |
| authorships[6].raw_affiliation_strings | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich, Germany |
| authorships[7].author.id | https://openalex.org/A5100814084 |
| authorships[7].author.orcid | https://orcid.org/0009-0003-3340-2153 |
| authorships[7].author.display_name | Bálint Tóth |
| authorships[7].countries | DE |
| authorships[7].affiliations[0].institution_ids | https://openalex.org/I167360494 |
| authorships[7].affiliations[0].raw_affiliation_string | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany |
| authorships[7].institutions[0].id | https://openalex.org/I167360494 |
| authorships[7].institutions[0].ror | https://ror.org/00613ak93 |
| authorships[7].institutions[0].type | education |
| authorships[7].institutions[0].lineage | https://openalex.org/I167360494 |
| authorships[7].institutions[0].country_code | DE |
| authorships[7].institutions[0].display_name | University of Wuppertal |
| authorships[7].author_position | middle |
| authorships[7].raw_author_name | Balint C. Toth |
| authorships[7].is_corresponding | False |
| authorships[7].raw_affiliation_strings | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany |
| authorships[8].author.id | https://openalex.org/A5107196581 |
| authorships[8].author.orcid | |
| authorships[8].author.display_name | Lukas Varnhorst |
| authorships[8].countries | DE |
| authorships[8].affiliations[0].institution_ids | https://openalex.org/I167360494 |
| authorships[8].affiliations[0].raw_affiliation_string | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany |
| authorships[8].institutions[0].id | https://openalex.org/I167360494 |
| authorships[8].institutions[0].ror | https://ror.org/00613ak93 |
| authorships[8].institutions[0].type | education |
| authorships[8].institutions[0].lineage | https://openalex.org/I167360494 |
| authorships[8].institutions[0].country_code | DE |
| authorships[8].institutions[0].display_name | University of Wuppertal |
| authorships[8].author_position | middle |
| authorships[8].raw_author_name | Lukas Varnhorst |
| authorships[8].is_corresponding | False |
| authorships[8].raw_affiliation_strings | Department of Physics, University of Wuppertal, D-42119 Wuppertal, Germany |
| authorships[9].author.id | https://openalex.org/A5114375150 |
| authorships[9].author.orcid | https://orcid.org/0000-0002-7853-9079 |
| authorships[9].author.display_name | Z. Zhang |
| authorships[9].countries | FR |
| authorships[9].affiliations[0].institution_ids | https://openalex.org/I1294671590, https://openalex.org/I277688954, https://openalex.org/I4210133362, https://openalex.org/I4210134832 |
| authorships[9].affiliations[0].raw_affiliation_string | IJCLab, Université Paris-Saclay et CNRS/IN2P3, F-91405 Orsay, France |
| authorships[9].institutions[0].id | https://openalex.org/I1294671590 |
| authorships[9].institutions[0].ror | https://ror.org/02feahw73 |
| authorships[9].institutions[0].type | government |
| authorships[9].institutions[0].lineage | https://openalex.org/I1294671590 |
| authorships[9].institutions[0].country_code | FR |
| authorships[9].institutions[0].display_name | Centre National de la Recherche Scientifique |
| authorships[9].institutions[1].id | https://openalex.org/I4210133362 |
| authorships[9].institutions[1].ror | https://ror.org/03fd77x13 |
| authorships[9].institutions[1].type | facility |
| authorships[9].institutions[1].lineage | https://openalex.org/I1294671590, https://openalex.org/I4210133362 |
| authorships[9].institutions[1].country_code | FR |
| authorships[9].institutions[1].display_name | Institut National de Physique Nucléaire et de Physique des Particules |
| authorships[9].institutions[2].id | https://openalex.org/I4210134832 |
| authorships[9].institutions[2].ror | https://ror.org/03gc1p724 |
| authorships[9].institutions[2].type | facility |
| authorships[9].institutions[2].lineage | https://openalex.org/I1294671590, https://openalex.org/I1294671590, https://openalex.org/I204730241, https://openalex.org/I277688954, https://openalex.org/I4210133362, https://openalex.org/I4210134832 |
| authorships[9].institutions[2].country_code | FR |
| authorships[9].institutions[2].display_name | Laboratoire de Physique des 2 Infinis Irène Joliot-Curie |
| authorships[9].institutions[3].id | https://openalex.org/I277688954 |
| authorships[9].institutions[3].ror | https://ror.org/03xjwb503 |
| authorships[9].institutions[3].type | education |
| authorships[9].institutions[3].lineage | https://openalex.org/I277688954 |
| authorships[9].institutions[3].country_code | FR |
| authorships[9].institutions[3].display_name | Université Paris-Saclay |
| authorships[9].author_position | last |
| authorships[9].raw_author_name | Zhiqing Zhang |
| authorships[9].is_corresponding | False |
| authorships[9].raw_affiliation_strings | IJCLab, Université Paris-Saclay et CNRS/IN2P3, F-91405 Orsay, France |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | http://link.aps.org/pdf/10.1103/PhysRevD.109.076019 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Hadronic vacuum polarization: Comparing lattice QCD and data-driven results in systematically improvable ways |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10048 |
| primary_topic.field.id | https://openalex.org/fields/31 |
| primary_topic.field.display_name | Physics and Astronomy |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/3106 |
| primary_topic.subfield.display_name | Nuclear and High Energy Physics |
| primary_topic.display_name | Particle physics theoretical and experimental studies |
| related_works | https://openalex.org/W2177060976, https://openalex.org/W2262128987, https://openalex.org/W4229011800, https://openalex.org/W2987166519, https://openalex.org/W1994579311, https://openalex.org/W2068293790, https://openalex.org/W3169399948, https://openalex.org/W1560858917, https://openalex.org/W1983235757, https://openalex.org/W3006644081 |
| cited_by_count | 17 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 9 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 6 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 2 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1103/physrevd.109.076019 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210238307 |
| best_oa_location.source.issn | 2470-0010, 2470-0029, 2470-0037 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 2470-0010 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Physical review. D/Physical review. D. |
| best_oa_location.source.host_organization | https://openalex.org/P4310320261 |
| best_oa_location.source.host_organization_name | American Physical Society |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320261 |
| best_oa_location.source.host_organization_lineage_names | American Physical Society |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | http://link.aps.org/pdf/10.1103/PhysRevD.109.076019 |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Physical Review D |
| best_oa_location.landing_page_url | https://doi.org/10.1103/physrevd.109.076019 |
| primary_location.id | doi:10.1103/physrevd.109.076019 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210238307 |
| primary_location.source.issn | 2470-0010, 2470-0029, 2470-0037 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 2470-0010 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Physical review. D/Physical review. D. |
| primary_location.source.host_organization | https://openalex.org/P4310320261 |
| primary_location.source.host_organization_name | American Physical Society |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320261 |
| primary_location.source.host_organization_lineage_names | American Physical Society |
| primary_location.license | cc-by |
| primary_location.pdf_url | http://link.aps.org/pdf/10.1103/PhysRevD.109.076019 |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Physical Review D |
| primary_location.landing_page_url | https://doi.org/10.1103/physrevd.109.076019 |
| publication_date | 2024-04-22 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W4235490860, https://openalex.org/W2116109970, https://openalex.org/W2964897915, https://openalex.org/W2983995865, https://openalex.org/W3034678343, https://openalex.org/W3070461787, https://openalex.org/W4387706996, https://openalex.org/W2784714858, https://openalex.org/W4283736760, https://openalex.org/W4366442068, https://openalex.org/W4387048335, https://openalex.org/W4317832219, https://openalex.org/W4281891446, https://openalex.org/W2043879367, https://openalex.org/W3011702383, https://openalex.org/W3035911197, https://openalex.org/W3038119807, https://openalex.org/W3079141818, https://openalex.org/W2770617062, https://openalex.org/W4226313694, https://openalex.org/W2083382688, https://openalex.org/W2921200076, https://openalex.org/W4380853483, https://openalex.org/W3105808240, https://openalex.org/W3119079247, https://openalex.org/W4322626349, https://openalex.org/W2249633705, https://openalex.org/W2610161517, https://openalex.org/W2924199860, https://openalex.org/W4387880324, https://openalex.org/W4387702213, https://openalex.org/W3004150385, https://openalex.org/W2065895987, https://openalex.org/W2066480797, https://openalex.org/W2032300563, https://openalex.org/W2119151822, https://openalex.org/W2035538641, https://openalex.org/W3007281907, https://openalex.org/W2595467801, https://openalex.org/W2547725724, https://openalex.org/W2795629793, https://openalex.org/W2999420976, https://openalex.org/W3017380374, https://openalex.org/W3109192736, https://openalex.org/W1981811987, https://openalex.org/W3117733762, https://openalex.org/W4387879921, https://openalex.org/W3185613173, https://openalex.org/W3082949750, https://openalex.org/W4280521403, https://openalex.org/W2943929775, https://openalex.org/W4225510376, https://openalex.org/W4221160824, https://openalex.org/W4304943549, https://openalex.org/W4390790462, https://openalex.org/W2592806569, https://openalex.org/W2910890398, https://openalex.org/W4318995047, https://openalex.org/W2138649302, https://openalex.org/W2787575645, https://openalex.org/W4311330420, https://openalex.org/W4312337510, https://openalex.org/W2137619955, https://openalex.org/W2165714791, https://openalex.org/W2036897648, https://openalex.org/W2729192571, https://openalex.org/W4391427382, https://openalex.org/W2088805718, https://openalex.org/W3010369246, https://openalex.org/W4224988135, https://openalex.org/W4322619253, https://openalex.org/W4390060501, https://openalex.org/W4391692580, https://openalex.org/W4206236450, https://openalex.org/W4327698784, https://openalex.org/W1532872899, https://openalex.org/W2132162721, https://openalex.org/W1651605877, https://openalex.org/W3202860274, https://openalex.org/W2785694820, https://openalex.org/W4205759316, https://openalex.org/W4390061990, https://openalex.org/W1974697555, https://openalex.org/W1534533008, https://openalex.org/W1484711978, https://openalex.org/W4387776143, https://openalex.org/W2994924297, https://openalex.org/W3108284800, https://openalex.org/W2572659746, https://openalex.org/W1988792587, https://openalex.org/W1968431963, https://openalex.org/W2071360735, https://openalex.org/W2040680703, https://openalex.org/W4388395101, https://openalex.org/W2165739256, https://openalex.org/W2057967338, https://openalex.org/W2174340045, https://openalex.org/W2072605975, https://openalex.org/W1989944623, https://openalex.org/W2101654452, https://openalex.org/W4284674879, https://openalex.org/W2132343497, https://openalex.org/W2625957305, https://openalex.org/W2770040815, https://openalex.org/W2152349224, https://openalex.org/W3182839386, https://openalex.org/W4366279060, https://openalex.org/W1997841560, https://openalex.org/W2162020865, https://openalex.org/W4292583683, https://openalex.org/W3196214551, https://openalex.org/W4379980424, https://openalex.org/W2557851759, https://openalex.org/W2963120226, https://openalex.org/W2156175240, https://openalex.org/W2113859228, https://openalex.org/W2121140421, https://openalex.org/W2950809315, https://openalex.org/W3049342414, https://openalex.org/W3103763899, https://openalex.org/W3105579295, https://openalex.org/W3010774713, https://openalex.org/W3167234302, https://openalex.org/W3142641870, https://openalex.org/W3103399847, https://openalex.org/W4296554603, https://openalex.org/W3104184565, https://openalex.org/W3009759090, https://openalex.org/W3105162519, https://openalex.org/W3101775943 |
| referenced_works_count | 130 |
| abstract_inverted_index.1 | 165 |
| abstract_inverted_index.a | 80, 175, 240, 294, 319 |
| abstract_inverted_index.As | 125 |
| abstract_inverted_index.We | 291 |
| abstract_inverted_index.an | 279 |
| abstract_inverted_index.as | 16, 189, 191, 303, 305 |
| abstract_inverted_index.be | 93, 97, 110, 214, 313 |
| abstract_inverted_index.by | 112, 222, 325 |
| abstract_inverted_index.in | 65, 116, 135, 195, 209, 229, 246, 274, 308 |
| abstract_inverted_index.is | 8, 260, 281 |
| abstract_inverted_index.of | 29, 119, 158, 249, 254, 267, 270, 296, 298, 322 |
| abstract_inverted_index.on | 85, 193, 287 |
| abstract_inverted_index.or | 25, 265 |
| abstract_inverted_index.to | 96, 144, 148, 155, 216, 252 |
| abstract_inverted_index.we | 78, 102, 127, 204, 235 |
| abstract_inverted_index.For | 199 |
| abstract_inverted_index.HVP | 45 |
| abstract_inverted_index.Our | 180 |
| abstract_inverted_index.The | 0, 38 |
| abstract_inverted_index.Via | 99 |
| abstract_inverted_index.all | 185, 219 |
| abstract_inverted_index.and | 58, 154, 166, 187 |
| abstract_inverted_index.are | 36, 46, 74, 139 |
| abstract_inverted_index.can | 92, 109, 213, 312 |
| abstract_inverted_index.for | 43, 218 |
| abstract_inverted_index.how | 11 |
| abstract_inverted_index.not | 75 |
| abstract_inverted_index.set | 321 |
| abstract_inverted_index.the | 17, 26, 30, 62, 89, 104, 107, 114, 140, 149, 156, 196, 210, 224, 230, 247, 250, 255, 263, 268, 275, 285, 288, 299, 306, 309, 316, 326 |
| abstract_inverted_index.two | 39, 67, 90, 211 |
| abstract_inverted_index.via | 318 |
| abstract_inverted_index.(for | 172 |
| abstract_inverted_index.2024 | 330 |
| abstract_inverted_index.Here | 77 |
| abstract_inverted_index.More | 233 |
| abstract_inverted_index.QCD. | 60 |
| abstract_inverted_index.This | 258 |
| abstract_inverted_index.also | 292 |
| abstract_inverted_index.been | 132 |
| abstract_inverted_index.both | 136 |
| abstract_inverted_index.data | 57 |
| abstract_inverted_index.each | 253 |
| abstract_inverted_index.from | 315 |
| abstract_inverted_index.have | 131 |
| abstract_inverted_index.into | 183 |
| abstract_inverted_index.made | 215 |
| abstract_inverted_index.most | 40 |
| abstract_inverted_index.much | 282 |
| abstract_inverted_index.muon | 18 |
| abstract_inverted_index.only | 174 |
| abstract_inverted_index.peak | 228, 251 |
| abstract_inverted_index.show | 205, 236 |
| abstract_inverted_index.such | 15, 278 |
| abstract_inverted_index.take | 182 |
| abstract_inverted_index.test | 103 |
| abstract_inverted_index.than | 284 |
| abstract_inverted_index.that | 82, 106, 130, 206, 237, 311 |
| abstract_inverted_index.them | 95 |
| abstract_inverted_index.this | 86, 100, 202, 238 |
| abstract_inverted_index.used | 301 |
| abstract_inverted_index.well | 190, 304 |
| abstract_inverted_index.with | 2, 50 |
| abstract_inverted_index.(HVP) | 7 |
| abstract_inverted_index.These | 138 |
| abstract_inverted_index.cross | 55 |
| abstract_inverted_index.here, | 302 |
| abstract_inverted_index.issue | 87 |
| abstract_inverted_index.light | 84 |
| abstract_inverted_index.sheds | 83 |
| abstract_inverted_index.tests | 181 |
| abstract_inverted_index.these | 66 |
| abstract_inverted_index.three | 220, 256 |
| abstract_inverted_index.using | 201 |
| abstract_inverted_index.which | 3, 173 |
| abstract_inverted_index.whose | 72 |
| abstract_inverted_index.agree, | 217 |
| abstract_inverted_index.common | 241 |
| abstract_inverted_index.energy | 121 |
| abstract_inverted_index.finite | 320 |
| abstract_inverted_index.larger | 283 |
| abstract_inverted_index.limits | 307 |
| abstract_inverted_index.moment | 21 |
| abstract_inverted_index.result | 178, 259 |
| abstract_inverted_index.robust | 261 |
| abstract_inverted_index.vacuum | 5 |
| abstract_inverted_index.window | 152 |
| abstract_inverted_index.<a:math | 22 |
| abstract_inverted_index.<c:math | 33 |
| abstract_inverted_index.<e:math | 51 |
| abstract_inverted_index.<h:math | 122 |
| abstract_inverted_index.<j:math | 145 |
| abstract_inverted_index.<l:math | 159 |
| abstract_inverted_index.<n:math | 167 |
| abstract_inverted_index.<p:math | 225 |
| abstract_inverted_index.<r:math | 242 |
| abstract_inverted_index.<t:math | 271 |
| abstract_inverted_index.R-ratio | 115, 317 |
| abstract_inverted_index.Society | 329 |
| abstract_inverted_index.absence | 266 |
| abstract_inverted_index.account | 184 |
| abstract_inverted_index.against | 262 |
| abstract_inverted_index.between | 162 |
| abstract_inverted_index.discuss | 293 |
| abstract_inverted_index.display | 69 |
| abstract_inverted_index.lattice | 59, 177, 197 |
| abstract_inverted_index.leading | 141 |
| abstract_inverted_index.methods | 300 |
| abstract_inverted_index.origins | 73 |
| abstract_inverted_index.precise | 41 |
| abstract_inverted_index.present | 79 |
| abstract_inverted_index.results | 63, 207 |
| abstract_inverted_index.running | 28, 157, 269 |
| abstract_inverted_index.section | 56 |
| abstract_inverted_index.variety | 295 |
| abstract_inverted_index.American | 327 |
| abstract_inverted_index.However, | 61, 277 |
| abstract_inverted_index.Physical | 328 |
| abstract_inverted_index.R-ratio. | 290 |
| abstract_inverted_index.and—if | 88 |
| abstract_inverted_index.combined | 49 |
| abstract_inverted_index.consider | 128 |
| abstract_inverted_index.coupling | 32 |
| abstract_inverted_index.exists). | 179 |
| abstract_inverted_index.hadronic | 4, 142 |
| abstract_inverted_index.increase | 245, 280 |
| abstract_inverted_index.magnetic | 20 |
| abstract_inverted_index.measured | 289 |
| abstract_inverted_index.obtained | 9, 64, 208 |
| abstract_inverted_index.presence | 264 |
| abstract_inverted_index.requires | 239 |
| abstract_inverted_index.results. | 198 |
| abstract_inverted_index.tensions | 108 |
| abstract_inverted_index.Published | 324 |
| abstract_inverted_index.anomalous | 19 |
| abstract_inverted_index.combined. | 98 |
| abstract_inverted_index.different | 117 |
| abstract_inverted_index.explained | 111 |
| abstract_inverted_index.extracted | 314 |
| abstract_inverted_index.framework | 81, 203 |
| abstract_inverted_index.important | 13 |
| abstract_inverted_index.instance, | 200 |
| abstract_inverted_index.intervals | 118 |
| abstract_inverted_index.modifying | 113, 223 |
| abstract_inverted_index.precisely | 133 |
| abstract_inverted_index.precision | 1 |
| abstract_inverted_index.relations | 48 |
| abstract_inverted_index.so-called | 150 |
| abstract_inverted_index.spacelike | 163 |
| abstract_inverted_index.spectrum. | 232 |
| abstract_inverted_index.tensions, | 71 |
| abstract_inverted_index.accurately | 12 |
| abstract_inverted_index.approaches | 42, 68, 91, 212 |
| abstract_inverted_index.determined | 134 |
| abstract_inverted_index.determines | 10 |
| abstract_inverted_index.dispersive | 47 |
| abstract_inverted_index.framework, | 101 |
| abstract_inverted_index.hypothesis | 105 |
| abstract_inverted_index.low-energy | 27 |
| abstract_inverted_index.predicted. | 37 |
| abstract_inverted_index.approaches. | 137 |
| abstract_inverted_index.comparison. | 276 |
| abstract_inverted_index.determining | 44 |
| abstract_inverted_index.information | 310 |
| abstract_inverted_index.observable, | 153 |
| abstract_inverted_index.observables | 129 |
| abstract_inverted_index.preliminary | 176 |
| abstract_inverted_index.significant | 70 |
| abstract_inverted_index.understood. | 76 |
| abstract_inverted_index.experimental | 231 |
| abstract_inverted_index.ingredients, | 126 |
| abstract_inverted_index.intermediate | 151 |
| abstract_inverted_index.observables, | 14, 221 |
| abstract_inverted_index.observables. | 257, 323 |
| abstract_inverted_index.polarization | 6 |
| abstract_inverted_index.virtualities | 164 |
| abstract_inverted_index.contributions | 143, 248 |
| abstract_inverted_index.correlations, | 188 |
| abstract_inverted_index.specifically, | 234 |
| abstract_inverted_index.uncertainties | 186, 192, 194, 286 |
| abstract_inverted_index.center-of-mass | 120 |
| abstract_inverted_index.electromagnetic | 31 |
| abstract_inverted_index.generalizations | 297 |
| abstract_inverted_index.</n:mtext><n:mtext> | 170 |
| abstract_inverted_index.reconciled—allows | 94 |
| abstract_inverted_index.display="inline"><l:mi>α</l:mi></l:math> | 161 |
| abstract_inverted_index.display="inline"><n:mn>10</n:mn><n:mtext> | 169 |
| abstract_inverted_index.display="inline"><p:mi>ρ</p:mi></p:math> | 227 |
| abstract_inverted_index.display="inline"><t:mi>α</t:mi></t:math> | 273 |
| abstract_inverted_index.display="inline"><c:mi>α</c:mi></c:math>, | 35 |
| abstract_inverted_index.xmlns:a="http://www.w3.org/1998/Math/MathML" | 23 |
| abstract_inverted_index.xmlns:c="http://www.w3.org/1998/Math/MathML" | 34 |
| abstract_inverted_index.xmlns:e="http://www.w3.org/1998/Math/MathML" | 52 |
| abstract_inverted_index.xmlns:h="http://www.w3.org/1998/Math/MathML" | 123 |
| abstract_inverted_index.xmlns:j="http://www.w3.org/1998/Math/MathML" | 146 |
| abstract_inverted_index.xmlns:l="http://www.w3.org/1998/Math/MathML" | 160 |
| abstract_inverted_index.xmlns:n="http://www.w3.org/1998/Math/MathML" | 168 |
| abstract_inverted_index.xmlns:p="http://www.w3.org/1998/Math/MathML" | 226 |
| abstract_inverted_index.xmlns:r="http://www.w3.org/1998/Math/MathML" | 243 |
| abstract_inverted_index.xmlns:t="http://www.w3.org/1998/Math/MathML" | 272 |
| abstract_inverted_index.display="inline"><h:msqrt><h:mi>s</h:mi></h:msqrt></h:math>. | 124 |
| abstract_inverted_index.display="inline"><r:mo>∼</r:mo><r:mn>5</r:mn><r:mo>%</r:mo></r:math> | 244 |
| abstract_inverted_index.stretchy="false">→</e:mo><e:mtext>hadrons</e:mtext></e:mrow></e:math> | 54 |
| abstract_inverted_index.display="inline"><j:msub><j:mi>a</j:mi><j:mi>μ</j:mi></j:msub></j:math>, | 147 |
| abstract_inverted_index.</n:mtext><n:msup><n:mrow><n:mi>GeV</n:mi></n:mrow><n:mn>2</n:mn></n:msup></n:math> | 171 |
| abstract_inverted_index.display="inline"><a:mrow><a:msub><a:mrow><a:mi>a</a:mi></a:mrow><a:mrow><a:mi>μ</a:mi></a:mrow></a:msub></a:mrow></a:math> | 24 |
| abstract_inverted_index.display="inline"><e:mrow><e:msup><e:mrow><e:mi>e</e:mi></e:mrow><e:mrow><e:mo>+</e:mo></e:mrow></e:msup><e:msup><e:mrow><e:mi>e</e:mi></e:mrow><e:mrow><e:mo>−</e:mo></e:mrow></e:msup><e:mo | 53 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 94 |
| countries_distinct_count | 4 |
| institutions_distinct_count | 10 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.7400000095367432 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile.value | 0.99086399 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |