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Chiral extrapolation of hadronic vacuum polarization and isospin-breaking corrections
High Energy Physics - Phenomenology · Submitted 21 Oct 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections.
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The abstract, sentence by sentence
By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the $\bar K K$ channel, which are enhanced due to the proximity of the $\bar K K$ threshold and the $\phi$ resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. | background 1.00 | 0.12 | 0.03 | asserted 1.00 |
| s1 | Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. | method 0.97 | 0.25 | 0.04 | asserted 0.57 |
| s2 | In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. | method 0.86 | 0.42 | 0.05 | asserted 0.69 |
| s3 | As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. | contribution 0.94 | 0.93 | 0.08 | asserted 0.94 |
| s4 | In particular, we include IB effects in the $\bar K K$ channel, which are enhanced due to the proximity of the $\bar K K$ threshold and the $\phi$ resonance. | contribution 0.96 | 0.86 | 0.04 | asserted 0.99 |
| s5 | The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections. | interpretation 0.86 | 0.88 | 0.81 | hedged possibility 0.91 |
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The paper
Original abstract
By far the biggest contribution to hadronic vacuum polarization (HVP) arises from the two-pion channel. Its quark-mass dependence can be evaluated by combining dispersion relations with chiral perturbation theory, providing guidance on the functional form of chiral extrapolations, or even interpolations around the physical point. In addition, the approach allows one to estimate in a controlled way the isospin-breaking (IB) corrections that arise from the pion mass difference. As an application, we present an updated estimate of phenomenological expectations for electromagnetic and strong IB corrections to the HVP contribution to the anomalous magnetic moment of the muon. In particular, we include IB effects in the $\bar K K$ channel, which are enhanced due to the proximity of the $\bar K K$ threshold and the $\phi$ resonance. The resulting estimates make it unlikely that the current tension between lattice-QCD and data-driven evaluations of the HVP contribution is caused by IB corrections.
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References
How the literature uses it
5 arXiv papers cite this in 7 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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We conclude that the tensions between lattice QCD and $e^+e^-$ data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.
A phenomenological estimate of isospin breaking in hadronic vacuum polarization · 0.99
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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For pions, this conversion is implemented through adding the correction $Δa_μ(π^+π^-)$ to the results obtained at the isospin-symmetric point, thereby accounting for the corresponding pion mass shift effect on HVP [ref] : a_μ(π^+π^-)|_phys = a_μ(π^+π^-)|_iso-sym+Δa_μ(π^+π^-).
Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_\mu$ · Conversion from isospin-symmetric to physical world with pions · 0.88
Compares with it 2 papers
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Within the VMD model for HVP, given by Eq. [ref], we obtain Δa_μ(π^+π^-)≃-7.95×10^-10, which is in good agreement with the corresponding result $-7.67(94)×10^-10$ reported in Refs. [ref] , where chiral extrapolation within unitarized ChPT up to NNLO order was employed.
Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_\mu$ · Conversion from isospin-symmetric to physical world with pions · 0.99
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The sum of the dominant IB effects from $2π$, $K̅ K$, and the radiative channels $π^0γ$, $ηγ$ [ref] agrees reasonably well with Ref. [ref] , but in the context of strong IB a larger result was observed, more in line with an inclusive estimate from chiral perturbation theory (ChPT) [ref] .
Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization · Introduction · 0.90
What it cites · 20 sentences without a confident label
Uses the method or tool of 4 papers
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To obtain the pion-mass dependence of the $ππ$ phase shift and thus $Ω_1^1(s)$ [ref] , we employ the inverse amplitude method (IAM) at one- (NLO) and two-loop (NNLO) order [ref] , with parameters determined from a combined fit to lattice QCD [ref] and phenomenology [ref] .
Quark mass dependence of the pion vector form factor · Pion-mass dependence of the two-pion channel · 0.96
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To obtain the pion-mass dependence of the $ππ$ phase shift and thus $Ω_1^1(s)$ [ref] , we employ the inverse amplitude method (IAM) at one- (NLO) and two-loop (NNLO) order [ref] , with parameters determined from a combined fit to lattice QCD [ref] and phenomenology [ref] .
The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\rm f} = 2+1$ lattice QCD · Pion-mass dependence of the two-pion channel · 0.96
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To obtain the pion-mass dependence of the $ππ$ phase shift and thus $Ω_1^1(s)$ [ref] , we employ the inverse amplitude method (IAM) at one- (NLO) and two-loop (NNLO) order [ref] , with parameters determined from a combined fit to lattice QCD [ref] and phenomenology [ref] .
Two-pion contribution to hadronic vacuum polarization · Pion-mass dependence of the two-pion channel · 0.96
Uses data or values from 5 papers
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With mixed higher-order terms $(e^2ϵ_ω)$ small, $≲0.1$, we have [ref] a_μ^HVP[ππ, FSR, Born]=4.24(2), a_μ^HVP[ππ, ρ–ω]=3.68(17).
Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization · $ρ$–$ω$ mixing and final-state radiation · 0.96
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Using the $ϕ$ spectral function from Ref. [ref] and varying the kaon masses according to Eq. [ref], we obtain [equation] so that, due to the resonance enhancement, IB effects as large as $30%$ are observed, and the mixed $(e^2δ)$ contributions come out larger than in the $2π$ channel.
Kaon electromagnetic form factors in dispersion theory · Isospin breaking in the $K̅ K$ channel · 0.96
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Final-state radiation (FSR) is dominated by infrared enhanced effects, see Refs. [ref] for an explicit test in the context of the forward–backward asymmetry, and we will adopt the results from Ref. [ref] obtained under this assumption, supplemented by small dispersive corrections from Ref. [ref] a_μ^HVP[ππγ, non-Born]=0.15_π^+π^-γ+0.03_π^0π^0γ=0.18(4).
Charge asymmetry in $e^+e^-\to \pi^+\pi^-$ process · $ρ$–$ω$ mixing and final-state radiation · 0.83
Compares with 4 papers
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QED corrections to the $R$-ratio are suppressed by $(10^-3)$ [ref] , which implies a correction $≲0.1$ in the HVP integral for the energy range in which perturbative QCD applies.] For the full HVP contribution, both our estimate and the inclusive ChPT determination from Ref. [ref] (with the critical low-energy constant $δC_93^(1)$ extracted from $τ$ decays) indicate a larger $(δ)$ effect, albeit largely consistent within uncertainties.
A ChPT estimate of the strong-isospin-breaking contribution to the anomalous magnetic moment of the muon · Phenomenological estimates of isospin-breaking effects in the HVP contribution · 0.91
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QED corrections to the $R$-ratio are suppressed by $(10^-3)$ [ref] , which implies a correction $≲0.1$ in the HVP integral for the energy range in which perturbative QCD applies.] For the full HVP contribution, both our estimate and the inclusive ChPT determination from Ref. [ref] (with the critical low-energy constant $δC_93^(1)$ extracted from $τ$ decays) indicate a larger $(δ)$ effect, albeit largely consistent within uncertainties.
Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD · Phenomenological estimates of isospin-breaking effects in the HVP contribution · 0.91
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For $(e^2)$ we observe good agreement with Ref. [ref] , which emerges as a result of substantial cancellations among several individually large effects.
Leading hadronic contribution to the muon magnetic moment from lattice QCD · Phenomenological estimates of isospin-breaking effects in the HVP contribution · 1.00
Cites as background 33 papers
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Understanding the tension between data-driven [ref] and lattice-QCD determinations [ref] of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon is of critical importance for the interpretation of the current $4.2σ$ discrepancy between experiment [ref] and the prediction in the Standard Model [ref] , using $e^+e^-→hadrons$ cross-section data for the latter.
Complete Tenth-Order QED Contribution to the Muon g-2 · Introduction · 0.92
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Understanding the tension between data-driven [ref] and lattice-QCD determinations [ref] of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon is of critical importance for the interpretation of the current $4.2σ$ discrepancy between experiment [ref] and the prediction in the Standard Model [ref] , using $e^+e^-→hadrons$ cross-section data for the latter.
The electroweak contributions to (g-2)_\mu\ after the Higgs boson mass measurement · Introduction · 0.92
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Understanding the tension between data-driven [ref] and lattice-QCD determinations [ref] of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon is of critical importance for the interpretation of the current $4.2σ$ discrepancy between experiment [ref] and the prediction in the Standard Model [ref] , using $e^+e^-→hadrons$ cross-section data for the latter.
Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order · Introduction · 0.92
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