Reevaluation of the hadronic contributions to the muon g−2 and to \(\alpha (M^{2}_{Z})\)
M. Davier
1
A. Hoecker
0
B. Malaescu
1
2
Z. Zhang
1
0
CERN, 1211,
Geneva 23, Switzerland
1
Laboratoire de l'Acclrateur Linaire
, IN2P3/CNRS,
Universit Paris-Sud 11
, Orsay,
France
2
Now at CERN, 1211,
Geneva 23, Switzerland
We reevaluate the hadronic contributions to the muon magnetic anomaly, and to the running of the electromagnetic coupling constant at the Z-boson mass. We include new + cross-section data from KLOE, all available multi-hadron data from BABAR, a reestimation of missing low-energy contributions using results on cross sections and process dynamics from BABAR, a reevaluation of all experimental contributions using the software package HVPTools together with a reanalysis of inter-experiment and inter-channel correlations, and a reevaluation of the continuum contributions from perturbative QCD at four loops. These improvements lead to a decrease in the hadronic contributions with respect to earlier evaluations. For the muon g 2 we find lowest-order hadronic contributions of (692.3 4.2) 1010 and (701.5 4.7) 1010 for the e+ebased and -based analyses, respectively, and full Standard Model predictions that differ by 3.6 and 2.4 from the experimental value. For the e+e-based five-quark hadronic contribution to (MZ2 ) we find h(5a)d(MZ2 ) = (274.9 1.0) 104. The reduced electromagnetic coupling strength at MZ leads to an increase by 12 GeV in the central value of the Higgs boson mass obtained by the standard Gfitter fit to electroweak precision data.
1 Introduction
The Standard Model (SM) predictions of the anomalous
magnetic moment of the muon, a, and of the running
electromagnetic coupling constant, (s), are limited in
precision by contributions from virtual hadronic vacuum
polarisation. The dominant hadronic terms can be calculated with
a combination of experimental cross section data, involving
e+e annihilation to hadrons, and perturbative QCD. These
are used to evaluate an energy-squared dispersion integral,
ranging from the 0 threshold to infinity. The integration
kernels occurring in the dispersion relations emphasise low
photon virtualities, owing to the 1/s descend of the cross
section, and, in case of a, to an additional 1/s suppression.
In the latter case, about 73% of the lowest order hadronic
contribution is provided by the + ( ) final state,1 while
this channel amounts to only 13% of the hadronic
contribution to (s) at s = MZ2 .
In this paper, we reevaluate the lowest-order hadronic
contribution, ahad,LO, to the muon magnetic anomaly, and
the hadronic contribution, had(MZ2 ), to the running
(MZ2 ) at the Z-boson mass. We include new +
crosssection data from KLOE [1] and all the available
multihadron data from BABAR [29]. We also perform a
reestimation of missing low-energy contributions using results
on cross sections and process dynamics from BABAR. We
reevaluate all the experimental contributions using the
software package HVPTools [10], including a comprehensive
reanalysis of inter-experiment and inter-channel
correlations. Furthermore, we recompute the continuum
contributions using perturbative QCD at four loops [11]. These
improvements taken together lead to a decrease of the hadronic
contributions with respect to our earlier evaluation [10], and
thus to an accentuation of the discrepancy between the SM
prediction of a and the experimental result [12]. The
reduced electromagnetic coupling strength at MZ leads to
an increase in the most probable value for the Higgs
boson mass returned by the electroweak fit, thus relaxing the
tension with the exclusion results from the direct Higgs
searches.
1Throughout this paper, final state photon radiation is implied for all
hadronic final states.
Fig. 1 Cross section of e+e + versus centre-of-mass energy
for different energy ranges. Shown are data from TOF [17], OLYA
[18, 19], CMD [18], CMD2 [2023], SND [24], DM1 [25], DM2 [26],
KLOE [1, 13], and BABAR [2]. The error bars show statistical and
systematic errors added in quadrature. The light shaded (green) band
indicates the HVPTools average within 1 errors
2 New input data
The KLOE Collaboration has published new + cross
section data with + invariant mass-squared between 0.1
and 0.85 GeV2 [1]. The radiative photon in this analysis is
required to be detected in the electromagnetic calorimeter,
which reduces the selected data sample to events with large
photon scattering angle (polar angle between 50 and 130),
and photon energies above 20 MeV. The new data are found
to be in agreement with, but less precise than, previously
published data using small angle photon scattering [13]
(superseding earlier KLOE data [14]). They hence exhibit the
known discrepancy, on the resonance peak and above,
with other + data, in particular those from BABAR,
Fig. 2 Comparison between individual e+e + cross section measurements from BABAR [2], KLOE 08 [13], KLOE 10 [1],
CMD2 03 [20], CMD2 06 [2123], SND [24], and the HVPTools average. The error bars show statistical and systematic (...truncated)