Abstract
We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $a_\mathrm{\mu}^{\rm hvp}$, 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 $a_\mathrm{\mu}^{\rm hvp}$. Our final result including an estimate of the systematic uncertainty $$a_{\mathrm{\mu}}^{\rm hvp} = 6.74(21)(18) \cdot 10^{-8}$$ shows a good overall agreement with these computations.
Highlights
We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, ahμvp, arising from quark-connected Feynman graphs
The value at the physical point obtained by the linear fit can be compared to the value obtained with only two dynamical quark flavours from our earlier lattice QCD analysis [4]
We can use a constant extrapolation to zero lattice spacing giving ahμv,upd = 5.72(13) · 10−8 which is compatible with the result quoted in eq (4.1)
Summary
The key quantity for the determination of the leading-order hadronic contribution to the muon g − 2 is the hadronic vacuum polarisation tensor Πeμmν (Q) with Euclidean momentum Q. It can be obtained from the correlator of two electromagnetic vector currents. Takahashi identities require the vacuum polarisation tensor to be transverse, i.e. Πeμmν (Q) = (QμQν − Q2δμν )Πem(Q2). Πem(Q2) is the hadronic vacuum polarisation function, for which the label “em” will be left out in the following to ease notation. Appears in the expression for the leading hadronic contribution to the anomalous magnetic moment of the muon in Euclidean space-time [11, 12]. The main task of the lattice calculation is the determination of ΠR(Q2) from the vector current correlator
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
