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Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization


Colangelo, Gilberto; Hoferichter, Martin; Kubis, Bastian; Stoffer, Peter (2022). Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization. Journal of High Energy Physics, 2022(10):32-51.

Abstract

Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the ρ(770) and ω(782) resonances. This particular IB contribution to the pion vector form factor and thus the line shape in e$^{+}$e$^{−}$→ π$^{+}$π$^{−}$ can be described by the residue at the ω pole — the ρ-ω mixing parameter ϵ$_{ω}$. Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels π$^{0}$γ, ππγ, ηγ can induce a small phase, whose size we estimate as δ$_{ϵ}$ = 3.5(1.0)° by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the e$^{+}$e$^{−}$→ π$^{+}$π$^{−}$ data base and study the consequences for the two-pion HVP contribution to the anomalous magnetic moment of the muon, its IB part due to ρ-ω mixing, and the mass of the ω resonance. We find that the global fit does prefer a non-vanishing value of δ$_{ϵ}$ = 4.5(1.2)°, close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the ρ-ω region.

Abstract

Isospin-breaking (IB) effects in the two-pion contribution to hadronic vacuum polarization (HVP) can be resonantly enhanced, if related to the interference of the ρ(770) and ω(782) resonances. This particular IB contribution to the pion vector form factor and thus the line shape in e$^{+}$e$^{−}$→ π$^{+}$π$^{−}$ can be described by the residue at the ω pole — the ρ-ω mixing parameter ϵ$_{ω}$. Here, we argue that while in general analyticity requires this parameter to be real, the radiative channels π$^{0}$γ, ππγ, ηγ can induce a small phase, whose size we estimate as δ$_{ϵ}$ = 3.5(1.0)° by using a narrow-width approximation for the intermediate-state vector mesons. We then perform fits to the e$^{+}$e$^{−}$→ π$^{+}$π$^{−}$ data base and study the consequences for the two-pion HVP contribution to the anomalous magnetic moment of the muon, its IB part due to ρ-ω mixing, and the mass of the ω resonance. We find that the global fit does prefer a non-vanishing value of δ$_{ϵ}$ = 4.5(1.2)°, close to the narrow-resonance expectation, but with a large spread among the data sets, indicating systematic differences in the ρ-ω region.

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Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Uncontrolled Keywords:Nuclear and High Energy Physics
Language:English
Date:5 October 2022
Deposited On:07 Feb 2023 19:17
Last Modified:28 Jun 2024 01:38
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/jhep10(2022)032
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)