Abstract
We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, \( a_{\mu}^{\mathrm{hvp}} \), arising from quark-connected Feynman graphs. It is based on ensembles featuring N f = 2 + 1 + 1 dynamical twisted mass fermions generated by the European Twisted Mass Collaboration (ETMC). Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass. We employ three lattice spacings to examine lattice artefacts and several different volumes to check for finite-size effects. Incorporating the complete first two generations of quarks allows for a direct comparison with phenomenological determinations of \( a_{\mu}^{\mathrm{hvp}} \). Our final result including an estimate of the systematic uncertainty \( a_{\mu}^{\mathrm{hvp}} \) = 6.74(21)(18) · 10−8 shows a good overall agreement with these computations.
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References
Muon G-2 collaboration, G. Bennett et al., Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL, Phys. Rev. D 73 (2006) 072003.
B.L. Roberts, Status of the Fermilab Muon (g − 2) Experiment, Chin. Phys. C 34 (2010) 741.
F. Jegerlehner and A. Nyffeler, The Muon g-2, Phys. Rept. 477 (2009) 1.
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 [INSPIRE].
D.B. Renner, X. Feng, K. Jansen and M. Petschlies, Nonperturbative QCD corrections to electroweak observables, PoS(LATTICE 2011)022 [INSPIRE].
S. Bodenstein, C. Dominguez and K. Schilcher, Hadronic contribution to the muon g-2: A Theoretical determination, Phys. Rev. D 85 (2012) 014029 [INSPIRE].
J. Prades, E. de Rafael and A. Vainshtein, Hadronic Light-by-Light Scattering Contribution to the Muon Anomalous Magnetic Moment,.
ETM collaboration, R. Baron et al., Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks, JHEP 06 (2010) 111 [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 [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 [INSPIRE].
E. de Rafael, Hadronic contributions to the muon g-2 and low-energy QCD, Phys. Lett. B 322 (1994) 239 [INSPIRE].
T. Blum, Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 91 (2003) 052001 [INSPIRE].
Y. Iwasaki, Renormalization Group Analysis of Lattice Theories and Improved Lattice Action: Two-Dimensional Nonlinear O(N) σ-model, Nucl. Phys. B 258 (1985) 141.
R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. 1. O(a) improvement, JHEP 08 (2004) 007 [INSPIRE].
R. Frezzotti and G. Rossi, Twisted mass lattice QCD with mass nondegenerate quarks, Nucl. Phys. Proc. Suppl. 128 (2004) 193 [INSPIRE].
ETM collaboration, R. Baron et al., Light hadrons from N f = 2 + 1 + 1 dynamical twisted mass fermions, PoS(LATTICE 2010)123 [INSPIRE].
K. Osterwalder and E. Seiler, Gauge Field Theories on the Lattice, Annals Phys. 110 (1978) 440.
R. Frezzotti and G. Rossi, Chirally improving Wilson fermions. II. Four-quark operators, JHEP 10 (2004) 070 [INSPIRE].
K. Cichy, E. Garcia-Ramos, K. Jansen and A. Shindler, Computation of the chiral condensate using N f = 2 and N f = 2 + 1 + 1 dynamical flavors of twisted mass fermions, PoS(LATTICE 2013)128 [INSPIRE].
K. Cichy, E. Garcia-Ramos, K. Jansen and A. Shindler, Topological susceptibility from twisted mass fermions using spectral projectors, PoS(LATTICE 2013)129.
F. Burger et al., in preparation.
X. Feng, K. Jansen and D.B. Renner, Resonance Parameters of the rho-Meson from Lattice QCD, Phys. Rev. D 83 (2011) 094505 [INSPIRE].
ETM collaboration, K. Jansen, C. McNeile, C. Michael and C. Urbach, Meson masses and decay constants from unquenched lattice QCD, Phys. Rev. D 80 (2009) 054510.
M. Della Morte, B. Jager, A. Juttner and H. Wittig, Towards a precise lattice determination of the leading hadronic contribution to (g − 2) μ , JHEP 03 (2012) 055.
P. Boyle, L. Del Debbio, E. Kerrane and J. Zanotti, Lattice Determination of the Hadronic Contribution to the Muon g − 2 using Dynamical Domain Wall Fermions, Phys. Rev. D 85 (2012) 074504 [INSPIRE].
F. Jegerlehner, Muon g − 2 update, Nucl. Phys. Proc. Suppl. 181-182 (2008) 26.
T. Goecke, C.S. Fischer and R. Williams, Leading-order calculation of hadronic contributions to the muon g − 2 using the Dyson-Schwinger approach, Phys. Lett. B 704 (2011) 211.
M. Della Morte and A. Juttner, Quark disconnected diagrams in chiral perturbation theory, JHEP 11 (2010) 154 [INSPIRE].
A. Francis, B. Jaeger, H.B. Meyer and H. Wittig, A new representation of the Adler function for lattice QCD, Phys. Rev. D 88 (2013) 054502 [INSPIRE].
S. Groote and A. Pivovarov, Low-energy gluon contributions to the vacuum polarization of heavy quarks, JETP Lett. 75 (2002) 221 [INSPIRE].
M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, Reevaluation of the Hadronic Contributions to the Muon g − 2 and to α(M Z ), Eur. Phys. J. C 71 (2011) 1515 [Erratum ibid. C 72 (2012) 1874].
F. Jegerlehner and R. Szafron, ρ 0 − γ mixing in the neutral channel pion form factor \( F_{\pi}^e \) and its role in comparing e + e − with τ spectral functions, Eur. Phys. J. C 71 (2011) 1632.
K. Hagiwara, R. Liao, A.D. Martin, D. Nomura and T. Teubner, (g − 2) μ and α(\( M_Z^2 \) ) re-evaluated using new precise data, J. Phys. G 38 (2011) 085003.
M. Benayoun, P. David, L. DelBuono and F. Jegerlehner, An Update of the HLS Estimate of the Muon g − 2, Eur. Phys. J. C 73 (2013) 2453 [INSPIRE].
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The ETM collaboration., Burger, F., Feng, X. et al. Four-flavour leading-order hadronic contribution to the muon anomalous magnetic moment. J. High Energ. Phys. 2014, 99 (2014). https://doi.org/10.1007/JHEP02(2014)099
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DOI: https://doi.org/10.1007/JHEP02(2014)099