Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis - INSPIRE

DataBETA

Precise determination of the low-energy hadronic contribution to the muon $g-2$ from analyticity and unitarity: An improved analysis

May 1, 2016

13 pages

Published in:

Phys.Rev.D 93 (2016) 11, 116007

Published: Jun 28, 2016

e-Print:

1605.00202 [hep-ph]

DOI:

10.1103/PhysRevD.93.116007

View in:

ADS Abstract Service

reference search30 citations

Citations per year

Abstract: (APS)

The two-pion low-energy contribution to the anomalous magnetic moment of the muon, aμ≡(g-2)μ/2, expressed as an integral over the modulus squared of the pion electromagnetic form factor, brings a relatively large contribution to the theoretical error, since the low accuracy of experimental measurements in this region is amplified by the drastic increase of the integration kernel. We derive stringent constraints on the two-pion contribution by exploiting analyticity and unitarity of the pion electromagnetic form factor. To avoid the poor knowledge of the modulus of this function, we use instead its phase, known with high precision in the elastic region from Roy equations for pion-pion scattering via the Fermi-Watson theorem. Above the inelastic threshold we adopt a conservative integral condition on the modulus, determined from data and perturbative QCD. Additional high precision data on the modulus in the range 0.65–0.71 GeV, obtained from e+e- annihilation and τ-decay experiments, are used to improve the predictions on the modulus at lower energies by means of a parametrization-free analytic extrapolation. The results are optimal for a given input and do not depend on the unknown phase of the form factor above the inelastic threshold. The present work improves a previous analysis based on the same technique, including more experimental data and employing better statistical tools for their treatment. We obtain for the contribution to aμ from below 0.63 GeV the value (133.258±0.723)×10-10, which amounts to a reduction of the theoretical error by about 6×10-11.

Note:

13 pages, latex using revtex 4, 8 figures; revised version includes two additional references, improved discussions, figures touched up

11.55.Fv
13.40.Gp
25.80.Dj
muon: magnetic moment
magnetic moment: anomaly
pi: form factor
form factor: electromagnetic
form factor: analytic properties
electron positron: annihilation
tau: decay

References(65)

Figures(9)

[1]

The Muon anomalous magnetic moment: A Harbinger for 'new physics'

Andrzej Czarnecki
(
- Alberta U.
)
,
William J. Marciano
(
- Brookhaven
)

- Phys.Rev.D 64 (2001) 013014
•
e-Print:
- hep-ph/0102122
•
DOI:
- 10.1103/PhysRevD.64.013014

[2]

The theoretical prediction for the muon anomalous magnetic moment

M. Davier
(
- Orsay, LAL
)
,
W.J. Marciano
(
- Brookhaven
)

- Ann.Rev.Nucl.Part.Sci. 54 (2004) 115-140
•
DOI:
- 10.1146/annurev.nucl.54.070103.181204

[3]

Muon (g-2): Experiment and theory

James P. Miller
(
- Boston U.
)
,
Eduardo de Rafael
(
- Marseille, CPT
)
,
B.Lee Roberts
(
- Marseille, CPT
)

- Rept.Prog.Phys. 70 (2007) 795
•
e-Print:
- hep-ph/0703049
•
DOI:
- 10.1088/0034-4885/70/5/R03

[4]

The Muon g-2

Fred Jegerlehner
(
- Silesia U. and
- Humboldt U., Berlin
)
,
Andreas Nyffeler
(
- Harish-Chandra Res. Inst.
)

- Phys.Rept. 477 (2009) 1-110
•
e-Print:
- 0902.3360
•
DOI:
- 10.1016/j.physrep.2009.04.003

[5]

Muon (g-2): Experiment and Theory

James P. Miller
(
- Boston U.
)
,
Eduardo de Rafael
(
- Marseille, CPT
)
,
B. Lee Roberts
(
- Boston U.
)
,
Dominik Stöckinger
(
- Dresden, Tech. U.
)

- Ann.Rev.Nucl.Part.Sci. 62 (2012) 237-264
•
DOI:
- 10.1146/annurev-nucl-031312-120340

[6]

Review of Particle Physics

et al.

- Chin.Phys.C 38 (2014) 090001
•
DOI:
- 10.1088/1674-1137/38/9/090001

[7]

A new approach to evaluate the leading hadronic corrections to the muon $g$ -2

C.M. Carloni Calame
(
- Pavia U.
)
,
M. Passera
(
- INFN, Padua
)
,
L. Trentadue
(
- Parma U. and
- INFN, Milan Bicocca
)
,
G. Venanzoni
(
- Frascati
)

- Phys.Lett.B 746 (2015) 325-329
•
e-Print:
- 1504.02228
•
DOI:
- 10.1016/j.physletb.2015.05.020

[8]

The new muon g-2 experiment at Fermilab

Muon g-2

Collaboration

•

G. Venanzoni
(
- Frascati
)

for the collaboration.

- Nucl.Phys.B Proc.Suppl. 225-227 (2012) 277-281
•
DOI:
- 10.1016/j.nuclphysbps.2012.02.058

[9]

Measurement of muon g-2 and EDM with an ultra-cold muon beam at J-PARC

J-PARC g-2

Collaboration

•

Tsutomu Mibe
(
- KEK, Tsukuba
)

for the collaboration.

- Nucl.Phys.B Proc.Suppl. 218 (2011) 242-246
•
DOI:
- 10.1016/j.nuclphysbps.2011.06.039

[10]

Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL

Muon g-2

Collaboration

•

G.W. Bennett
(
- Brookhaven
)

et al.

- Phys.Rev.D 73 (2006) 072003
•
e-Print:
- hep-ex/0602035
•
DOI:
- 10.1103/PhysRevD.73.072003

[11]

Hadronic contributions to the muon anomalous magnetic moment Workshop. $(g-2)_{\mu}$ : Quo vadis? Workshop. Mini proceedings

C. Aubin
(
- Fordham U.
)
,
Maurice Benayoun
(
- Paris U., VI-VII
)
,
Johan Bijnens
(
- Lund U., Dept. Theor. Phys.
)
,
Tom Blum
(
- Connecticut U.
)
(ed.)
,
Irenel Caprini
(
- Bucharest, IFIN-HH
)

et al.

e-Print:
- 1407.4021

[12]

High-statistics measurement of the pion form factor in the rho-meson energy range with the CMD-2 detector

CMD-2

Collaboration

•

R.R. Akhmetshin

et al.

- Phys.Lett.B 648 (2007) 28-38
•
e-Print:
- hep-ex/0610021
•
DOI:
- 10.1016/j.physletb.2007.01.073

[13]

Reanalysis of hadronic cross-section measurements at CMD-2

CMD-2

Collaboration

•

R.R. Akhmetshin

et al.

- Phys.Lett.B 578 (2004) 285-289
•
e-Print:
- hep-ex/0308008
•
DOI:
- 10.1016/j.physletb.2003.10.108

[14]

Measurement of the eþe- → πþπ- cross section with the CMD-2 detector in the 370-520-MeV energy range, Pis’

V.M. Aulchenko

- Zh.Eksp.Teor.Fiz. 84 (2006) 491

[15]

Update of the e+ e- ---> pi+ pi- cross-section measured by SND detector in the energy region 400-MeV < s**(1/2) < file1000-MeV

M.N. Achasov
(
- Novosibirsk, IYF and
- Novosibirsk State U.
)
,
K.I. Beloborodov
(
- Novosibirsk, IYF and
- Novosibirsk State U.
)
,
A.V. Berdyugin
(
- Novosibirsk, IYF and
- Novosibirsk State U.
)
,
A.G. Bogdanchikov
(
- Novosibirsk, IYF and
- Novosibirsk State U.
)
,
A.V. Bozhenok
(
- Novosibirsk, IYF and
- Novosibirsk State U.
)

et al.

- J.Exp.Theor.Phys. 103 (2006) 380-384,
- Zh.Eksp.Teor.Fiz. 130 (2006) 437-441
•
e-Print:
- hep-ex/0605013
•
DOI:
- 10.1134/S106377610609007X

[16]

Precise measurement of the e+ e- ---> pi+ pi- (gamma) cross section with the Initial State Radiation method at BABAR

BaBar

Collaboration

•

Bernard Aubert
(
- Annecy, LAPP
)

et al.

- Phys.Rev.Lett. 103 (2009) 231801
•
e-Print:
- 0908.3589
•
DOI:
- 10.1103/PhysRevLett.103.231801

[17]

Precise Measurement of the $e^+ e^- \to \pi^+\pi^- (\gamma)$ Cross Section with the Initial-State Radiation Method at BABAR

BaBar

Collaboration

•

J.P. Lees
(
- Annecy, LAPP
)

et al.

- Phys.Rev.D 86 (2012) 032013
•
e-Print:
- 1205.2228
•
DOI:
- 10.1103/PhysRevD.86.032013

[18]

Measurement of $\sigma(e^+ e^- \to \pi^+ \pi^- \gamma(\gamma)$ and the dipion contribution to the muon anomaly with the KLOE detector

KLOE

Collaboration

•

F. Ambrosino
(
- Naples U. and
- INFN, Naples
)

et al.

- Phys.Lett.B 670 (2009) 285-291
•
e-Print:
- 0809.3950
•
DOI:
- 10.1016/j.physletb.2008.10.060

[19]

Measurement of $\sigma(e^+ e^- \to \pi^+ \pi^-)$ from threshold to 0.85 GeV $^2$ using Initial State Radiation with the KLOE detector

KLOE

Collaboration

•

F. Ambrosino
(
- Naples U. and
- INFN, Naples
)

et al.

- Phys.Lett.B 700 (2011) 102-110
•
e-Print:
- 1006.5313
•
DOI:
- 10.1016/j.physletb.2011.04.055

[20]

Precision measurement of $\sigma(e^+e^-\rightarrow \pi^+\pi^-\gamma)/ \sigma(e^+e^-\rightarrow \mu^+\mu^-\gamma)$ and determination of the $\pi^+\pi^-$ contribution to the muon anomaly with the KLOE detector

KLOE

Collaboration

•

D. Babusci
(
- Frascati
)

et al.

- Phys.Lett.B 720 (2013) 336-343
•
e-Print:
- 1212.4524
•
DOI:
- 10.1016/j.physletb.2013.02.029

[21]

Measurement of the $e^+ e^− \to \pi^+ \pi^−$ cross section between 600 and 900 MeV using initial state radiation

BESIII

Collaboration

•

M. Ablikim
(
- Beijing, Inst. High Energy Phys.
)

et al.

- Phys.Lett.B 753 (2016) 629-638,
- Phys.Lett.B 812 (2021) 135982 (erratum)
•
e-Print:
- 1507.08188
•
DOI:
- 10.1016/j.physletb.2015.11.043

[22]

Hadronic structure in the decay tau- ---> pi- pi0 neutrino(tau)

CLEO

Collaboration

•

S. Anderson
(
- Minnesota U.
)

et al.

- Phys.Rev.D 61 (2000) 112002
•
e-Print:
- hep-ex/9910046
•
DOI:
- 10.1103/PhysRevD.61.112002

[23]

Branching ratios and spectral functions of tau decays: Final ALEPH measurements and physics implications

ALEPH

Collaboration

•

S. Schael
(
- Aachen, Tech. Hochsch.
)

et al.

- Phys.Rept. 421 (2005) 191-284
•
e-Print:
- hep-ex/0506072
•
DOI:
- 10.1016/j.physrep.2005.06.007

[24]

Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays

Michel Davier
(
- Orsay, LAL
)
,
Andreas Höcker
(
- CERN
)
,
Bogdan Malaescu
(
- Paris U., VI-VII
)
,
Chang-Zheng Yuan
(
- Beijing, Inst. High Energy Phys.
)
,
Zhiqing Zhang
(
- Orsay, LAL
)

- Eur.Phys.J.C 74 (2014) 3, 2803
•
e-Print:
- 1312.1501
•
DOI:
- 10.1140/epjc/s10052-014-2803-9

[25]

Measurement of the strong coupling constant alpha(s) and the vector and axial vector spectral functions in hadronic tau decays

OPAL

Collaboration

•

K. Ackerstaff

et al.

- Eur.Phys.J.C 7 (1999) 571-593
•
e-Print:
- hep-ex/9808019
•
DOI:
- 10.1007/s100529901061

1-25 of 65
1
2
3
25 / page