Leading hadronic contribution to (g−2)μ from lattice QCD with Nf

Abstract

The comparison of the theoretical and experimental determinations of the anomalous magnetic moment of the muon (g − 2) µ constitutes one of the strongest tests of the Standard Model at low energies. In this article, we compute the leading hadronic contribution to (g − 2) µ using lattice QCD simulations employing Wilson quarks. Gauge field ensembles at four different lattice spacings and several values of the pion mass down to its physical value are used. We apply the O(a) improvement programme with two discretizations of the vector current to better constrain the approach to the continuum limit. The electromagnetic current correlators are computed in the time-momentum representation. In addition, we perform auxiliary calculations of the pion form factor at timelike momenta in order to better constrain the tail of the isovector correlator and to correct its dominant finite-size effect. For the numerically dominant light-quark contribution, we have rescaled the lepton mass by the pion decay constant computed on each lattice ensemble. We perform a combined chiral and continuum extrapolation to the physical point, and our final result is a hvp µ = (720.0 ± 12.4 stat ± 9.9 syst ) · 10 −10 . It contains the contributions of quarkdisconnected diagrams, and the systematic error has been enlarged to account for the missing isospin-breaking effects.

Global fits of the SM parameters

“…and from α s . Equation (5.5) is in excellent agreement with the very recent result obtained from a lattice gauge theory simulation[41], a c µ (vacuum polarization; lattice) = (14.66 ± 0.45 stat. ± 0.06 syst.…”

“…It should also be remarked that Ref. [41] finds a rather large total hadronic vacuum polarization effect, so that if confirmed, there would cease to be a conflict between the measurement of a µ [42] and the SM, which currently amounts to more than 3 σ . But then there would be a new discrepancy between the dispersive and lattice approaches to vacuum polarization.…”

Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization

“…Our results for the matrix elements |A l/c | are listed in Table VI. There are sizable differences between |A l | and |A c |, likely due to cut-off effects, which are studied in [58,59]. This is a clear indication that an improved version of the currents (defined e.g.…”

“…One way to [58]. The difference in |A l | and |A c | is likely due to cut-off effects, which are studied in [58,59].…”

Opportunities for Lattice QCD in quark and lepton flavor physics

“…[10]. The referenced contributions are ETMC 2013 [186], HPQCD 2016 [187], Mainz 2017 [188], BMW 2017 [189], RBC/UKQCD 2018 [10], ETMC 2018 [190], SK 2019 [192], FNAL/HPQCD/MILC 2019 [191], Mainz 2019 [197], HLMNT 2011 [198], DHMZ 2012 [199], DHMZ 2017 [8], Jegerlehner 2017 [200], KNT 2018 [9], and "No new physics" [201]. The innermost error-bar corresponds to the statistical uncertainty.…”