Three-pion contribution to hadronic vacuum polarization

Hoferichter, Martin; Hoid, Bai-Long; Kubis, Bastian

doi:10.1007/jhep08(2019)137

Title: Three-pion contribution to hadronic vacuum polarization

Journal Article · Mon Aug 26 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep08(2019)137· OSTI ID:1609313

^[1]; Hoid, Bai-Long ^[2];

^[2]

Univ. of Washington, Seattle, WA (United States)
Univ. of Bonn (Germany)

We address the contribution of the 3π channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e⁺e^- → 3π amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon (g - 2)_μ, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances ω and Φ, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for (g - 2)_μ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying γ* → 3π amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various e⁺e^- → 3π data sets. Overall, we obtain a$$3π\atop{μ}$$|≤1.8 GeV = 46.2(6)(6) × 10^-10 as our best estimate for the total 3π contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the 2π channel below 1 GeV, this covers nearly 80% of the total HVP contribution, leading to a$$HVP\atop{μ}$$ = 692.3(3.3) × 10^-10 when the remainder is taken from the literature, and thus reaffirming the (g-2)_μ anomaly at the level of at least 3.4σ. As side products, we find for the vacuum-polarization-subtracted masses M_ω = 782.63(3)(1) MeV and M_Φ = 1019.20(2)(1) MeV, confirming the tension to the ω mass as extracted from the 2π channel.

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Research Organization:: Univ. of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-00ER41132

OSTI ID:: 1609313

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 8; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 266 works

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