Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization
A bstract Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e − → π + π − channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the...
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| Published in | The journal of high energy physics Vol. 2023; no. 8; pp. 208 - 31 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
30.08.2023
Springer Nature B.V Springer Nature SpringerOpen |
| Subjects | |
| Online Access | Get full text |
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| Abstract | A
bstract
Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the
e
+
e
−
→ π
+
π
−
channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for
e
+
e
−
→
3
π
by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and
ρ
–
ω
mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor
η
3
π
that generalizes the analog treatment of virtual and final-state photons in the 2
π
case. The global fit to the
e
+
e
−
→
3
π
data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives
a
μ
3
π
≤
1.8
GeV
=
45.91
53
×
10
−
10
for the total 3
π
contribution to the anomalous magnetic moment of the muon, of which
a
μ
FSR
3
π
=
0.51
1
×
10
−
10
and
a
μ
ρ
−
ω
3
π
=
−
2.68
70
×
10
−
10
can be ascribed to IB. We argue that the resulting cancellation with
ρ
–
ω
mixing in
e
+
e
−
→
2
π
can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters
M
ω
= 782
.
70(3) MeV,
M
ϕ
= 1019
.
21(2) MeV, Γ
ω
= 8
.
71(3) MeV, and Γ
ϕ
= 4
.
27(1) MeV. |
|---|---|
| AbstractList | Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e+e−→ π+π− channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e+e−→ 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e−→ 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives aμ3π≤1.8GeV=45.9153×10−10 for the total 3π contribution to the anomalous magnetic moment of the muon, of which aμFSR3π=0.511×10−10 and aμρ−ω3π=−2.6870×10−10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e+e−→ 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters Mω = 782.70(3) MeV, Mϕ = 1019.21(2) MeV, Γω = 8.71(3) MeV, and Γϕ = 4.27(1) MeV. Abstract Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e − → π + π − channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e − → 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η 3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e + e − → 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives a μ 3 π ≤ 1.8 GeV = 45.91 53 × 10 − 10 $$ {\left.{a}_{\mu}^{3\pi}\right|}_{\le 1.8\ \textrm{GeV}}=45.91(53)\times {10}^{-10} $$ for the total 3π contribution to the anomalous magnetic moment of the muon, of which a μ FSR 3 π = 0.51 1 × 10 − 10 $$ {a}_{\mu}^{\textrm{FSR}}\left[3\pi \right]=0.51(1)\times {10}^{-10} $$ and a μ ρ − ω 3 π = − 2.68 70 × 10 − 10 $$ {a}_{\mu}^{\rho -\omega}\left[3\pi \right]=-2.68(70)\times {10}^{-10} $$ can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e + e − → 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782.70(3) MeV, M ϕ = 1019.21(2) MeV, Γ ω = 8.71(3) MeV, and Γ ϕ = 4.27(1) MeV. Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e+e- → π+π- channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e+e- → 3π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ–ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η3π that generalizes the analog treatment of virtual and final-state photons in the 2π case. The global fit to the e+e- → 3π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives for the total 3π contribution to the anomalous magnetic moment of the muon, of which ${a}^{FSR}_\mu [3\pi]$ = 0.51(1) x 10-10 and ${a}^{\rho - \omega}_\mu [3\pi]$ = -2.68(70) x 10-10 can be ascribed to IB. We argue that the resulting cancellation with ρ–ω mixing in e+e- → 2π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters Mω = 782.70(3) MeV, MΦ = 1019.21(2) MeV, Γω = 8.71(3) MeV, and ΓΦ = 4.27(1) MeV. A bstract Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e − → π + π − channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e − → 3 π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ – ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η 3 π that generalizes the analog treatment of virtual and final-state photons in the 2 π case. The global fit to the e + e − → 3 π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives a μ 3 π ≤ 1.8 GeV = 45.91 53 × 10 − 10 for the total 3 π contribution to the anomalous magnetic moment of the muon, of which a μ FSR 3 π = 0.51 1 × 10 − 10 and a μ ρ − ω 3 π = − 2.68 70 × 10 − 10 can be ascribed to IB. We argue that the resulting cancellation with ρ – ω mixing in e + e − → 2 π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782 . 70(3) MeV, M ϕ = 1019 . 21(2) MeV, Γ ω = 8 . 71(3) MeV, and Γ ϕ = 4 . 27(1) MeV. Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise from the e + e − → π + π − channel, also IB in the subleading channels can become relevant for a detailed understanding, e.g., of the comparison to lattice QCD. Here, we provide such an analysis for e + e − → 3 π by extending our dispersive description of the process, including estimates of final-state radiation (FSR) and ρ – ω mixing. In particular, we develop a formalism to capture the leading infrared-enhanced effects in terms of a correction factor η 3 π that generalizes the analog treatment of virtual and final-state photons in the 2 π case. The global fit to the e + e − → 3 π data base, subject to constraints from analyticity, unitarity, and the chiral anomaly, gives $$ {\left.{a}_{\mu}^{3\pi}\right|}_{\le 1.8\ \textrm{GeV}}=45.91(53)\times {10}^{-10} $$ a μ 3 π ≤ 1.8 GeV = 45.91 53 × 10 − 10 for the total 3 π contribution to the anomalous magnetic moment of the muon, of which $$ {a}_{\mu}^{\textrm{FSR}}\left[3\pi \right]=0.51(1)\times {10}^{-10} $$ a μ FSR 3 π = 0.51 1 × 10 − 10 and $$ {a}_{\mu}^{\rho -\omega}\left[3\pi \right]=-2.68(70)\times {10}^{-10} $$ a μ ρ − ω 3 π = − 2.68 70 × 10 − 10 can be ascribed to IB. We argue that the resulting cancellation with ρ – ω mixing in e + e − → 2 π can be understood from a narrow-resonance picture, and provide updated values for the vacuum-polarization-subtracted vector-meson parameters M ω = 782 . 70(3) MeV, M ϕ = 1019 . 21(2) MeV, Γ ω = 8 . 71(3) MeV, and Γ ϕ = 4 . 27(1) MeV. |
| ArticleNumber | 208 |
| Author | Hoid, Bai-Long Hoferichter, Martin Schuh, Dominic Kubis, Bastian |
| Author_xml | – sequence: 1 givenname: Martin orcidid: 0000-0003-1113-9377 surname: Hoferichter fullname: Hoferichter, Martin email: hoferichter@itp.unibe.ch organization: Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern – sequence: 2 givenname: Bai-Long orcidid: 0000-0001-9471-1740 surname: Hoid fullname: Hoid, Bai-Long organization: Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern – sequence: 3 givenname: Bastian orcidid: 0000-0002-1541-6581 surname: Kubis fullname: Kubis, Bastian organization: Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn – sequence: 4 givenname: Dominic surname: Schuh fullname: Schuh, Dominic organization: Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn |
| BackLink | https://www.osti.gov/servlets/purl/2418910$$D View this record in Osti.gov |
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| CitedBy_id | crossref_primary_10_1016_j_nuclphysbps_2024_10_002 crossref_primary_10_1103_PhysRevLett_131_161905 crossref_primary_10_1007_JHEP07_2024_276 crossref_primary_10_1103_PhysRevD_109_036010 crossref_primary_10_1103_PhysRevD_110_112005 crossref_primary_10_1103_PhysRevD_109_096007 crossref_primary_10_1140_epjc_s10052_024_12608_w crossref_primary_10_1103_PhysRevLett_133_211906 crossref_primary_10_1007_JHEP04_2024_092 crossref_primary_10_1007_JHEP04_2024_071 crossref_primary_10_1007_JHEP02_2025_121 crossref_primary_10_1007_JHEP08_2024_052 |
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Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant... Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions arise... Abstract Isospin-breaking (IB) effects are required for an evaluation of hadronic vacuum polarization at subpercent precision. While the dominant contributions... |
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| SubjectTerms | Chiral Lagrangian Classical and Quantum Gravitation Elementary Particles High energy physics Magnetic moments Physics Physics and Astronomy PHYSICS OF ELEMENTARY PARTICLES AND FIELDS Pions Polarization Precision QED Quantum chromodynamics Quantum Field Theories Quantum Field Theory Quantum Physics Quarks Radiation Regular Article - Theoretical Physics Relativity Theory String Theory Theoretical physics Vector mesons |
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| Title | Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization |
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