Abstract
We present a calculation of the weak mixing angle in the \( \overline{\mathrm{MS}} \) renormalization scheme which is relevant for experiments performed at very low energies or momentum transfers. We include higher orders in the perturbative QCD expansion, as well as updated phenomenological and theoretical input, and obtain the result \( { \sin}^2{\widehat{\theta}}_W(0)=0.23868(5)(2) \) for the reference values \( {\widehat{\alpha}}_s\left({M}_Z\right)=0.1182 \) and \( {\widehat{m}}_c\left({\widehat{m}}_c\right)=1.272\ \mathrm{GeV} \). The first quoted error is from the current Standard Model evaluation of the mixing angle at the Z boson mass scale. The second error represents the theoretical and parametric uncertainties induced by the evolution to the Thomson limit and is discussed in detail.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Czarnecki and W.J. Marciano, Polarized Moller scattering asymmetries, Int. J. Mod. Phys. A 15 (2000) 2365 [hep-ph/0003049] [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].
Qweak collaboration, D. Androic et al., First determination of the weak charge of the proton, Phys. Rev. Lett. 111 (2013) 141803 [arXiv:1307.5275] [INSPIRE].
D. Becker et al., The P2 experiment — a future high-precision measurement of the electroweak mixing angle at low momentum transfer, arXiv:1802.04759 [INSPIRE].
MOLLER collaboration, J. Benesch et al., The MOLLER experiment: an ultra-precise measurement of the weak mixing angle using Møller scattering, Jefferson Lab document JLAB-PHY-14-1986, U.S.A., (2014) [arXiv:1411.4088] [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].
P.A. Souder, Parity violation in deep inelastic scattering with the SoLID Spectrometer at JLab, Int. J. Mod. Phys. Conf. Ser. 40 (2016) 1660077 [INSPIRE].
NuTeV collaboration, G.P. Zeller et al., A precise determination of electroweak parameters in neutrino nucleon scattering, Phys. Rev. Lett. 88 (2002) 091802 [Erratum ibid. 90 (2003) 239902] [hep-ex/0110059] [INSPIRE].
B.C. Canas, E.A. Garces, O.G. Miranda, M. Tortola and J.W.F. Valle, The weak mixing angle from low energy neutrino measurements: a global update, Phys. Lett. B 761 (2016) 450 [arXiv:1608.02671] [INSPIRE].
C.S. Wood et al., Measurement of parity nonconservation and an anapole moment in cesium, Science 275 (1997) 1759 [INSPIRE].
L. Willmann et al., Trapped radioactive isotopes for fundamental symmetry investigations. The TRI μ P facility, Hyperfine Interact. 211 (2012) 39.
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].
J. Erler and S. Su, The weak neutral current, Prog. Part. Nucl. Phys. 71 (2013) 119 [arXiv:1303.5522] [INSPIRE].
J. Erler, C.J. Horowitz, S. Mantry and P.A. Souder, Weak polarized electron scattering, Ann. Rev. Nucl. Part. Sci. 64 (2014) 269 [arXiv:1401.6199] [INSPIRE].
M. Davier, A. Höcker, B. Malaescu and Z. Zhang, Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g − 2 and α(m 2 Z ) using newest hadronic cross-section data, Eur. Phys. J. C 77 (2017) 827 [arXiv:1706.09436] [INSPIRE].
F. Jegerlehner and R. Szafron, ρ 0 -γ mixing in the neutral channel pion form factor F e π and its role in comparing e + e − with τ spectral functions, Eur. Phys. J. C 71 (2011) 1632 [arXiv:1101.2872] [INSPIRE].
RBC/UKQCD collaboration, T. Blum et al., Lattice calculation of the leading strange quark-connected contribution to the muon g − 2, JHEP 04 (2016) 063 [Erratum ibid. 05 (2017) 034] [arXiv:1602.01767] [INSPIRE].
HPQCD collaboration, B. Chakraborty et al., Strange and charm quark contributions to the anomalous magnetic moment of the muon, Phys. Rev. D 89 (2014) 114501 [arXiv:1403.1778] [INSPIRE].
S. Okubo, φ meson and unitary symmetry model, Phys. Lett. 5 (1963) 165 [INSPIRE].
G. Zweig, An SU(3) model for strong interaction symmetry and its breaking II, CERN-TH-412, CERN, Geneva Switzerland, (1964).
J. Iizuka, Systematics and phenomenology of meson family, Prog. Theor. Phys. Suppl. 37 (1966)21 [INSPIRE].
RBC/UKQCD collaboration, T. Blum et al., Calculation of the hadronic vacuum polarization disconnected contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 116 (2016) 232002 [arXiv:1512.09054] [INSPIRE].
J. Erler, Calculation of the QED coupling α(M Z) in the modified minimal subtraction scheme, Phys. Rev. D 59 (1999) 054008 [hep-ph/9803453] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin, J.H. Kühn and J. Rittinger, Vector correlator in massless QCD at order O(α 4 s ) and the QED β-function at five loop, JHEP 07 (2012) 017 [arXiv:1206.1284] [INSPIRE].
T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The four loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].
M. Czakon, The four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].
L.J. Hall, Grand unification of effective gauge theories, Nucl. Phys. B 178 (1981) 75 [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Decoupling relations to O(α 3 s ) and their connection to low-energy theorems, Nucl. Phys. B 510 (1998) 61 [hep-ph/9708255] [INSPIRE].
K.G. Chetyrkin, J.H. Kühn and C. Sturm, Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD, Eur. Phys. J. C 48 (2006) 107 [hep-ph/0604234] [INSPIRE].
B.A. Kniehl and A.V. Kotikov, Heavy-quark QCD vacuum polarisation function: analytical results at four loops, Phys. Lett. B 642 (2006) 68 [hep-ph/0607201] [INSPIRE].
R. Alemany, M. Davier and A. Höcker, Improved determination of the hadronic contribution to the muon (g − 2) and to α(M 2 Z ) using new data from hadronic τ decays, Eur. Phys. J. C 2 (1998) 123 [hep-ph/9703220] [INSPIRE].
S. Eidelman, F. Jegerlehner, A.L. Kataev and O. Veretin, Testing nonperturbative strong interaction effects via the Adler function, Phys. Lett. B 454 (1999) 369 [hep-ph/9812521] [INSPIRE].
J. Erler and R. Ferro-Hernández, Calculation of the QED coupling α(M 2 Z ) in the \( \overline{\mathrm{MS}} \) scheme: an update, in preparation.
Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
J. Erler and M.-X. Luo, Hadronic loop corrections to the muon anomalous magnetic moment, Phys. Rev. Lett. 87 (2001) 071804 [hep-ph/0101010] [INSPIRE].
J. Erler, P. Masjuan and H. Spiesberger, Charm quark mass with calibrated uncertainty, Eur. Phys. J. C 77 (2017) 99 [arXiv:1610.08531] [INSPIRE].
F. Jegerlehner, Variations on photon vacuum polarization, arXiv:1711.06089 [INSPIRE].
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].
D. Bernecker and H.B. Meyer, Vector correlators in lattice QCD: methods and applications, Eur. Phys. J. A 47 (2011) 148 [arXiv:1107.4388] [INSPIRE].
A. Keshavarzi, D. Nomura and T. Teubner, The muon g − 2 and α(M 2 Z ): a new data-based analysis, arXiv:1802.02995 [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: 1712.09146
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Erler, J., Ferro-Hernández, R. Weak mixing angle in the Thomson limit. J. High Energ. Phys. 2018, 196 (2018). https://doi.org/10.1007/JHEP03(2018)196
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)196