Abstract
The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, α QED, and the weak mixing angle, θ W , are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. Jegerlehner, Electroweak effective couplings for future precision experiments, Nuovo Cim. C 034S1 (2011) 31 [arXiv:1107.4683] [INSPIRE].
J. Hewett et al., Fundamental Physics at the Intensity Frontier, arXiv:1205.2671.
K. Hagiwara, R. Liao, A.D. Martin, D. Nomura and T. Teubner, (g − 2) μ and α(M 2 Z ) re-evaluated using new precise data, J. Phys. G 38 (2011) 085003 [arXiv:1105.3149] [INSPIRE].
F. Jegerlehner, The Running fine structure constant alpha(E) via the Adler function, Nucl. Phys. Proc. Suppl. 181-182 (2008) 135 [arXiv:0807.4206] [INSPIRE].
D.B. Renner, X. Feng, K. Jansen and M. Petschlies, Nonperturbative QCD corrections to electroweak observables, PoS(LATTICE 2011)022 [arXiv:1206.3113] [INSPIRE].
X. Feng, G. Hotzel, K. Jansen, M. Petschlies and D.B. Renner, Leading-order hadronic contributions to a μ and α QED from N f = 2 + 1 + 1 twisted mass fermions, PoS(LATTICE 2012)174 [arXiv:1211.0828] [INSPIRE].
A. Francis, G. Herdoíza, H. Horch, B. Jäger, H.B. Meyer and H. Wittig, Study of the Couplings of QED and QCD from the Adler Function, PoS(LATTICE2014)163 [arXiv:1412.6934] [INSPIRE].
R. Baron et al., Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks, JHEP 06 (2010) 111 [arXiv:1004.5284] [INSPIRE].
European Twisted Mass collaboration, R. Baron et al., Computing K and D meson masses with N f = 2 + 1 + 1 twisted mass lattice QCD, Comput. Phys. Commun. 182 (2011) 299 [arXiv:1005.2042] [INSPIRE].
F. Jegerlehner, Hadronic Contributions to Electroweak Parameter Shifts: A Detailed Analysis, Z. Phys. C 32 (1986) 195 [INSPIRE].
C.S. Wood et al., Measurement of parity nonconservation and an anapole moment in cesium, Science 275 (1997) 1759 [INSPIRE].
SLAC E158 collaboration, P.L. Anthony et al., Precision measurement of the weak mixing angle in Moller scattering, Phys. Rev. Lett. 95 (2005) 081601 [hep-ex/0504049] [INSPIRE].
PVDIS collaboration, D. Wang et al., Measurement of parity violation in electron-quark scattering, Nature 506 (2014) 67 [INSPIRE].
Qweak collaboration, D.S. Armstrong, First result from Q weak , EPJ Web Conf. 73 (2014) 07008 [INSPIRE].
MOLLER collaboration, J. Benesch et al., The MOLLER Experiment: An Ultra-Precise Measurement of the Weak Mixing Angle Using Møller Scattering, arXiv:1411.4088 [INSPIRE].
SoLID collaboration, J.P. Chen, H. Gao, T.K. Hemmick, Z.E. Meziani and P.A. Souder, A White Paper on SoLID (Solenoidal Large Intensity Device), arXiv:1409.7741 [INSPIRE].
D. Becker, K. Gerz, S. Baunack, K. Kumar and F. Maas, P2 — The weak charge of the proton, PoS(Bormio 2013)024 [INSPIRE].
K.S. Kumar, S. Mantry, W.J. Marciano and P.A. Souder, Low Energy Measurements of the Weak Mixing Angle, Ann. Rev. Nucl. Part. Sci. 63 (2013) 237 [arXiv:1302.6263] [INSPIRE].
T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant, Phys. Rev. Lett. 109 (2012) 111807 [arXiv:1205.5368] [INSPIRE].
F. Jegerlehner and A. Nyffeler, The Muon g-2, Phys. Rept. 477 (2009) 1 [arXiv:0902.3360] [INSPIRE].
ETM collaboration, R. Baron et al., Light hadrons from N f = 2 + 1 + 1 dynamical twisted mass fermions, PoS(LATTICE 2010)123 [arXiv:1101.0518] [INSPIRE].
ETM collaboration, F. Burger, X. Feng, G. Hotzel, K. Jansen, M. Petschlies and D.B. Renner, Four-Flavour Leading-Order Hadronic Contribution To The Muon Anomalous Magnetic Moment, JHEP 02 (2014) 099 [arXiv:1308.4327] [INSPIRE].
F. Burger, G. Hotzel, K. Jansen and M. Petschlies, Leading-order hadronic contributions to the electron and tau anomalous magnetic moments, arXiv:1501.05110 [INSPIRE].
A. Abdel-Rehim et al., A first look at maximally twisted mass lattice QCD calculations at the physical point, PoS(LATTICE 2013)264 [arXiv:1311.4522] [INSPIRE].
A. Abdel-Rehim et al., Progress in Simulations with Twisted Mass Fermions at the Physical Point, PoS(LATTICE2014)119 [arXiv:1411.6842] [INSPIRE].
ETM collaboration, A. Abdel-Rehim et al., Simulating QCD at the Physical Point with N f = 2 Wilson Twisted Mass Fermions at Maximal Twist, arXiv:1507.05068 [INSPIRE].
G. Ecker, J. Gasser, A. Pich and E. de Rafael, The Role of Resonances in Chiral Perturbation Theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].
C. Aubin and T. Blum, Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks, Phys. Rev. D 75 (2007) 114502 [hep-lat/0608011] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
X. Feng, K. Jansen, M. Petschlies and D.B. Renner, Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling, Phys. Rev. Lett. 107 (2011) 081802 [arXiv:1103.4818] [INSPIRE].
C. Aubin, T. Blum, M. Golterman and S. Peris, Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice, Phys. Rev. D 86 (2012) 054509 [arXiv:1205.3695] [INSPIRE].
F. Burger, G. Hotzel, K. Jansen and M. Petschlies, The hadronic vacuum polarization and automatic \( \mathcal{O}(a) \) improvement for twisted mass fermions, JHEP 03 (2015) 073 [arXiv:1412.0546] [INSPIRE].
F. Jegerlehner, alphaQED, http://www-com.physik.hu-berlin.de/~fjeger/software.html (2012).
F. Jegerelehner, private communication.
X. Feng, S. Hashimoto, G. Hotzel, K. Jansen, M. Petschlies and D.B. Renner, Computing the hadronic vacuum polarization function by analytic continuation, Phys. Rev. D 88 (2013) 034505 [arXiv:1305.5878] [INSPIRE].
A. Francis, B. Jäger, H.B. Meyer and H. Wittig, A new representation of the Adler function for lattice QCD, Phys. Rev. D 88 (2013) 054502 [arXiv:1306.2532] [INSPIRE].
G.M. de Divitiis, R. Petronzio and N. Tantalo, On the extraction of zero momentum form factors on the lattice, Phys. Lett. B 718 (2013) 589 [arXiv:1208.5914] [INSPIRE].
F. Jegerlehner, Vector Boson Parameters: Scheme Dependence and Theoretical Uncertainties, Z. Phys. C 32 (1986) 425 [Erratum ibid. C 38 (1988) 519] [INSPIRE].
V.A. Dzuba, J.C. Berengut, V.V. Flambaum and B. Roberts, Revisiting parity non-conservation in cesium, Phys. Rev. Lett. 109 (2012) 203003 [arXiv:1207.5864] [INSPIRE].
J. Erler and M.J. Ramsey-Musolf, The Weak mixing angle at low energies, Phys. Rev. D 72 (2005) 073003 [hep-ph/0409169] [INSPIRE].
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
W.J. Marciano, Spin and precision electroweak physics, Spin structure in high energy processes. Proceedings of 21st SLAC Summer Institute on Particle Physics, Stanford U.S.A. (1993), pg. 35.
F. Jegerlehner, Renormalizing the standard model, Conf. Proc. C900603 (1990) 476 [INSPIRE].
W. Wetzel, The Hadronic Contribution to the W and Z Mass, Z. Phys. C 11 (1981) 117 [INSPIRE].
W.J. Marciano and A. Sirlin, On Some General Properties of the O(α) Corrections to Parity Violation in Atoms, Phys. Rev. D 29 (1984) 75 [Erratum ibid. D 31 (1985) 213] [INSPIRE].
A. Francis, G. von Hippel, H.B. Meyer and F. Jegerlehner, Vector correlator and scale determination in lattice QCD, PoS(LATTICE 2013)320 [arXiv:1312.0035] [INSPIRE].
ALEPH, CDF, D0, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, Tevatron Electroweak Working Group and SLD Electroweak and Heavy Flavour Group collaborations, Precision Electroweak Measurements and Constraints on the Standard Model, arXiv:1012.2367 [INSPIRE].
D. Wang et al., Measurement of Parity-Violating Asymmetry in Electron-Deuteron Inelastic Scattering, Phys. Rev. C 91 (2015) 045506 [arXiv:1411.3200] [INSPIRE].
T. Blum, T. Izubuchi and E. Shintani, New class of variance-reduction techniques using lattice symmetries, Phys. Rev. D 88 (2013) 094503 [arXiv:1208.4349] [INSPIRE].
Y. Saad, Tchebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems, Math. Comp. 42 (1984) 567.
H. Neff, N. Eicker, T. Lippert, J.W. Negele and K. Schilling, On the low fermionic eigenmode dominance in QCD on the lattice, Phys. Rev. D 64 (2001) 114509 [hep-lat/0106016] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1505.03283
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Burger, F., Jansen, K., Petschlies, M. et al. Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD. J. High Energ. Phys. 2015, 215 (2015). https://doi.org/10.1007/JHEP11(2015)215
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)215