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Chiral symmetry breaking corrections to the pseudoscalar pole contribution of the Hadronic Light-by-Light piece of $a_\mu$
High Energy Physics - Phenomenology · Submitted 3 Dec 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus, we find a total pseudoscalar pole contribution of $a_\mu^{P,HLbL}=(8.47\pm 0.16)\cdot 10^{-10}$ for our best fit (that neglecting the BaBar $\pi^0$ data).
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We have studied the $P\to\gamma^\star\gamma^\star$ form factor in Resonance Chiral Theory, with $P = \pi^0\eta\eta'$, to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading $U(3)$ chiral symmetry breaking terms, obtaining the most general expression for the form factor up to $\mathcal{O}(m_P^2)$. The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike region. Chiral symmetry relations among the transition form factors for $\pi^0,\eta$ and $\eta'$ allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar $\pi^0$ data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of $a_\mu^{P,HLbL}=(8.47\pm 0.16)\cdot 10^{-10}$ for our best fit (that neglecting the BaBar $\pi^0$ data). Also, a preliminary rough estimate of the impact of NLO in $1/N_C$ corrections and higher vector multiplets (asym) enlarges the uncertainty up to $a_\mu^{P,HLbL}=(8.47\pm 0.16_{\rm stat}\pm 0.09_{N_C}{}^{+0.5}_{-0.0_{\rm asym}})10^{-10}$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We have studied the $P\to\gamma^\star\gamma^\star$ form factor in Resonance Chiral Theory, with $P = \pi^0\eta\eta'$, to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. | contribution 0.99 | 0.95 | 0.05 | asserted 0.98 |
| s1 | In this work we allow the leading $U(3)$ chiral symmetry breaking terms, obtaining the most general expression for the form factor up to $\mathcal{O}(m_P^2)$. | method 0.73 | 0.94 | 0.03 | asserted 0.99 |
| s2 | The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. | method 1.00 | 0.88 | 0.03 | asserted 1.00 |
| s3 | Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike region. | method 1.00 | 0.88 | 0.02 | asserted 1.00 |
| s4 | Chiral symmetry relations among the transition form factors for $\pi^0,\eta$ and $\eta'$ allow for a simultaneous fit to experimental data for the three mesons. | method 0.95 | 0.73 | 0.04 | asserted 0.92 |
| s5 | This shows an inconsistency between the BaBar $\pi^0$ data and the rest of the experimental inputs. | result 0.68 | 0.82 | 0.07 | asserted 0.99 |
| s6 | Thus, we find a total pseudoscalar pole contribution of $a_\mu^{P,HLbL}=(8.47\pm 0.16)\cdot 10^{-10}$ for our best fit (that neglecting the BaBar $\pi^0$ data). | result 1.00 | 0.97 | 0.76 | asserted 1.00 |
| s7 | Also, a preliminary rough estimate of the impact of NLO in $1/N_C$ corrections and higher vector multiplets (asym) enlarges the uncertainty up to $a_\mu^{P,HLbL}=(8.47\pm 0.16_{\rm stat}\pm 0.09_{N_C}{}^{+0.5}_{-0.0_{\rm asym}})10^{-10}$. | result 0.77 | 0.89 | 0.20 | hedged possibility 0.67 |
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Original abstract
We have studied the $P\to\gamma^\star\gamma^\star$ form factor in Resonance Chiral Theory, with $P = \pi^0\eta\eta'$, to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading $U(3)$ chiral symmetry breaking terms, obtaining the most general expression for the form factor up to $\mathcal{O}(m_P^2)$. The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike region. Chiral symmetry relations among the transition form factors for $\pi^0,\eta$ and $\eta'$ allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar $\pi^0$ data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of $a_\mu^{P,HLbL}=(8.47\pm 0.16)\cdot 10^{-10}$ for our best fit (that neglecting the BaBar $\pi^0$ data). Also, a preliminary rough estimate of the impact of NLO in $1/N_C$ corrections and higher vector multiplets (asym) enlarges the uncertainty up to $a_\mu^{P,HLbL}=(8.47\pm 0.16_{\rm stat}\pm 0.09_{N_C}{}^{+0.5}_{-0.0_{\rm asym}})10^{-10}$.
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States the same result 2 papers
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Thus, we find a total pseudoscalar pole contribution of $a_\mu^{P,HLbL}=(8.47\pm 0.16)\cdot 10^{-10}$ for our best fit (neglecting the BaBar $\pi^0$ data).
Pseudoscalar pole contribution to the hadronic light-by-light piece of $a_\mu$ · 0.99
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The combination of data, chiral symmetry relations between form-factors and high-energy constraints allows us to determine with improved precision the on-shell $P$-pole contribution to the Hadronic Light-by-Light scattering of the muon anomalous magnetic moment: we obtain $a_{\mu}^{P,HLbL}=(8.47\pm 0.16)\cdot10^{-10}$ for our best fit.
Pseudoscalar pole light-by-light contributions to the muon $(g-2)$ in Resonance Chiral Theory · 0.97
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