Mellin-Barnes approach to hadronic vacuum polarization and $g_{\mu}-2$ - INSPIRE

DataBETA

Mellin-Barnes approach to hadronic vacuum polarization and $g_{\mu}-2$

Jérôme Charles
(
- Marseille, CPT
)
,
Eduardo de Rafael
(
- Marseille, CPT
)
,
David Greynat

Dec 6, 2017

23 pages

Published in:

Phys.Rev.D 97 (2018) 7, 076014

Published: May 1, 2018

e-Print:

1712.02202 [hep-ph]

DOI:

10.1103/PhysRevD.97.076014

View in:

reference search20 citations

Citations per year

Abstract: (APS)

It is shown that with a precise determination of a few derivatives of the hadronic vacuum polarization (HVP) self-energy function Π(Q2) at Q2=0, from lattice QCD (LQCD) or from a dedicated low-energy experiment, one can obtain an evaluation of the lowest order HVP contribution to the anomalous magnetic moment of the muon aμHVP with an accuracy comparable to the one reached using the e+e- annihilation cross section into hadrons. The technique of Mellin-Barnes approximants (MBa) that we propose is illustrated in detail with the example of the two loop vacuum polarization function in QED. We then apply it to the first few moments of the hadronic spectral function obtained from experiment and show that the resulting MBa evaluations of aμHVP converge very quickly to the full experimental determination.

Note:

37 pages, many figures. V2: Numerical results updated according to arXiv:1802.02995v1. V3: Published version with improvements suggested by the referee, conclusions unchanged

muon: magnetic moment
magnetic moment: anomaly
quantum electrodynamics: vacuum polarization
vacuum polarization: hadronic
vacuum polarization: correction
quantum electrodynamics: correction
correction: higher-order
higher-order: 2
quantum chromodynamics: lattice

References(41)

Figures(27)

[1]

Moment Analysis of Hadronic Vacuum Polarization - Proposal for a lattice QCD evaluation of $g_{\mu}-2$

Eduardo de Rafael
(
- Marseille, CPT
)

- Phys.Lett.B 736 (2014) 522-525
•
e-Print:
- 1406.4671
•
DOI:
- 10.1016/j.physletb.2014.08.003

[2]

Hadronic vacuum polarization in QCD and its evaluation in Euclidean spacetime

Eduardo de Rafael
(
- Marseille, CPT
)

- Phys.Rev.D 96 (2017) 1, 014510
•
e-Print:
- 1702.06783
•
DOI:
- 10.1103/PhysRevD.96.014510

[3]

Mellin-Barnes Approach to HVP and gμ - 2, invited talk at the First Workshop of the Muon g - 2 Theory Initiative 13795/

E. de Rafael

[4]

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

[5]

The Muon (g-2) Theory Value: Present and Future

Thomas Blum
(
- Connecticut U. and
- RIKEN BNL
)
,
Achim Denig
(
- Mainz U., Inst. Kernphys. and
- Mainz U.
)
,
Ivan Logashenko
(
- Novosibirsk, IYF
)
,
Eduardo de Rafael
(
- Marseille, CPT
)
,
B.Lee Roberts
(
- Boston U.
)

et al.

e-Print:
- 1311.2198

[6]

Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ)

- Eur.Phys.J.C 71 (2011) 1515,
- Eur.Phys.J.C 72 (2012) 1874 (erratum)
•
e-Print:
- 1010.4180
•
DOI:
- 10.1140/epjc/s10052-012-1874-8

[7]

$(g-2)_\mu$ and $\alpha(M^2_Z)$ re-evaluated using new precise data

Kaoru Hagiwara
(
- KEK, Tsukuba and
- Sokendai, Tsukuba
)
,
Ruofan Liao
(
- Liverpool U., Dept. Math.
)
,
Alan D. Martin
(
- Durham U. and
- Durham U., IPPP
)
,
Daisuke Nomura
(
- Tohoku U.
)
,
Thomas Teubner
(
- Liverpool U., Dept. Math.
)

- J.Phys.G 38 (2011) 085003
•
e-Print:
- 1105.3149
•
DOI:
- 10.1088/0954-3899/38/8/085003

[8]

Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon $g-2$ and ${\alpha (m_Z^2)}$ using newest hadronic cross-section data

Michel Davier
(
- Orsay, LAL
)
,
Andreas Hoecker
(
- CERN
)
,
Bogdan Malaescu
(
- Paris U., VI-VII
)
,
Zhiqing Zhang
(
- Orsay, LAL
)

- Eur.Phys.J.C 77 (2017) 12, 827
•
e-Print:
- 1706.09436
•
DOI:
- 10.1140/epjc/s10052-017-5161-6

[9]

Muon $g-2$ and $\alpha(M_Z^2)$ : a new data-based analysis

- Phys.Rev.D 97 (2018) 11, 114025
•
e-Print:
- 1802.02995
•
DOI:
- 10.1103/PhysRevD.97.114025

[10]

Towards a precise lattice determination of the leading hadronic contribution to $(g-2)_\mu$

Michele Della Morte
(
- Mainz U., Inst. Kernphys. and
- Helmholtz Inst., Mainz
)
,
Benjamin Jager
(
- Mainz U., Inst. Kernphys. and
- Helmholtz Inst., Mainz
)
,
Andreas Juttner
(
- CERN
)
,
Hartmut Wittig
(
- Mainz U., Inst. Kernphys. and
- Helmholtz Inst., Mainz
)

- JHEP 03 (2012) 055
•
e-Print:
- 1112.2894
•
DOI:
- 10.1007/JHEP03(2012)055

[11]

Strong-Isospin-Breaking Correction to the Muon Anomalous Magnetic Moment from Lattice QCD at the Physical Point

Collaborations

•

B. Chakraborty
(
- Jefferson Lab
)

et al.

- Phys.Rev.Lett. 120 (2018) 15, 152001
•
e-Print:
- 1710.11212
•
DOI:
- 10.1103/PhysRevLett.120.152001

[12]

Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment

ETM

Collaboration

•

Florian Burger
(
- Humboldt U., Berlin
)

et al.

- JHEP 02 (2014) 099
•
e-Print:
- 1308.4327
•
DOI:
- 10.1007/JHEP02(2014)099

[13]

The hadronic vacuum polarization contribution to $a_{\mu}$ from full lattice QCD

et al.

- Phys.Rev.D 96 (2017) 3, 034516
•
e-Print:
- 1601.03071
•
DOI:
- 10.1103/PhysRevD.96.034516

[14]

Slope and curvature of the hadronic vacuum polarization at vanishing virtuality from lattice QCD

Sz. Borsanyi
(
- Wuppertal U.
)
,
Z. Fodor
(
)
,
T. Kawanai
(
- Julich, Forschungszentrum
)
,
S. Krieg
(
- Wuppertal U. and
- Julich, Forschungszentrum
)
,
L. Lellouch
(
- Marseille, CPT
)

et al.

- Phys.Rev.D 96 (2017) 7, 074507
•
e-Print:
- 1612.02364
•
DOI:
- 10.1103/PhysRevD.96.074507

[15]

Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles

Budapest-Marseille-Wuppertal

Collaboration

•

Sz. Borsanyi
(
- Bergische U., Wuppertal (main)
)

et al.

- Phys.Rev.Lett. 121 (2018) 2, 022002
•
e-Print:
- 1711.04980
•
DOI:
- 10.1103/PhysRevLett.121.022002

[16]

A lattice calculation of the hadronic vacuum polarization contribution to $(g-2)_\mu$

M. Della Morte
(
- Southern Denmark U., CP3-Origins
)
,
A. Francis
(
- York U., Canada
)
,
A. Gérardin
(
- U. Mainz, PRISMA and
- Mainz U., Inst. Kernphys.
)
,
V. Gülpers
(
- Southampton U.
)
,
G. Herdoíza
(
- Madrid, IFT
)

et al.

- EPJ Web Conf. 175 (2018) 06031
•
e-Print:
- 1710.10072
•
DOI:
- 10.1051/epjconf/201817506031

[17]

Strange and charm HVP contributions to the muon ( $g - 2)$ including QED corrections with twisted-mass fermions

D. Giusti
(
- INFN, Rome3 and
- Rome III U.
)
,
V. Lubicz
(
- INFN, Rome3 and
- Rome III U.
)
,
G. Martinelli
(
- INFN, Rome3 and
- Rome III U.
)
,
F. Sanfilippo
(
- INFN, Rome3
)
,
S. Simula
(
- INFN, Rome3
)

- JHEP 10 (2017) 157
•
e-Print:
- 1707.03019
•
DOI:
- 10.1007/JHEP10(2017)157

[18]

Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study

et al.

- JHEP 09 (2017) 153
•
e-Print:
- 1706.05293
•
DOI:
- 10.1007/JHEP09(2017)153

[19]

A precise determination of the HVP contribution to the muon anomalous magnetic moment from lattice QCD

RBC and
UKQCD

Collaborations

•

Christoph Lehner
(
- Brookhaven
)

for the collaborations.

- EPJ Web Conf. 175 (2018) 01024
•
e-Print:
- 1710.06874
•
DOI:
- 10.1051/epjconf/201817501024

[20]

Measuring the leading hadronic contribution to the muon g-2 via $\mu e$ scattering

MUonE

Collaboration

•

G. Abbiendi
(
- INFN, Bologna
)

et al.

- Eur.Phys.J.C 77 (2017) 3, 139
•
e-Print:
- 1609.08987
•
DOI:
- 10.1140/epjc/s10052-017-4633-z

[21]

B.E. Lautrup
,
A. Peterman
,
E. de Rafael

- Phys.Rept.C 3 (1972) 193

[22]

Hadronic contributions to the muon g-2 and low-energy QCD

Eduardo de Rafael
(
- Marseille, CPT
)

- Phys.Lett.B 322 (1994) 239-246
•
e-Print:
- hep-ph/9311316
•
DOI:
- 10.1016/0370-2693(94)91114-2

[23]

Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment

T. Blum
(
- RIKEN BNL
)

- Phys.Rev.Lett. 91 (2003) 052001
•
e-Print:
- hep-lat/0212018
•
DOI:
- 10.1103/PhysRevLett.91.052001

[24]

Finite-volume effects in the muon anomalous magnetic moment on the lattice

Christopher Aubin
(
- Fordham U.
)
,
Thomas Blum
(
- Connecticut U.
)
,
Peter Chau
(
- San Francisco State U.
)
,
Maarten Golterman
(
- San Francisco State U.
)
,
Santiago Peris
(
- Barcelona, IFAE and
- Barcelona, Autonoma U.
)

et al.

- Phys.Rev.D 93 (2016) 5, 054508
•
e-Print:
- 1512.07555
•
DOI:
- 10.1103/PhysRevD.93.054508

[25]

A BHLS model based moment analysis of muon g-2, and its use for lattice QCD evaluations of $a_\mu^{\rm had}$

M. Benayoun
(
- Paris U., VI-VII
)
,
P. David
(
- Diderot U., Paris and
- Paris U., VI-VII
)
,
L. DelBuono
(
- Paris U., VI-VII
)
,
F. Jegerlehner
(
- Humboldt U., Berlin and
- DESY, Zeuthen
)

e-Print:
- 1605.04474

1-25 of 41
1
2
25 / page