Three-pion contribution to hadronic vacuum polarization - INSPIRE

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Three-pion contribution to hadronic vacuum polarization

Martin Hoferichter
(
- Washington U., Seattle
)
,
Bai-Long Hoid
(
- Bonn U. and
- Bonn U., HISKP
)
,
Bastian Kubis
(
- Bonn U. and
- Bonn U., HISKP
)

Jul 2, 2019

24 pages

Published in:

JHEP 08 (2019) 137

Published: Aug 26, 2019

e-Print:

1907.01556 [hep-ph]

DOI:

10.1007/JHEP08(2019)137 (publication)

PDG:

{{\mathit \omega}{(782)}}

Report number:

INT-PUB-19-030

View in:

ADS Abstract Service

reference search456 citations

Citations per year

Abstract: (Springer)

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}_{\mu}^{3\pi }

|

_{≤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}_{\mu}^{\mathrm{HVP}}

= 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.

Note:

24 pages, 1 figure; Appendix B added; version published in JHEP

Chiral Lagrangians
Effective Field Theories
Nonperturbative Effects
Precision QED
vacuum polarization: hadronic
muon: magnetic moment
dispersion relation
quantum chromodynamics
analytic properties
low-energy theorem

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