The hadronic vacuum polarization contribution to $(g-2)_\mu$ from $2+1$ flavours of O($a$) improved Wilson quarks

Understand

We report on our ongoing project to determine the leading-order hadronic vacuum polarisation contribution to the muon $g-2$, using ensembles with $N_f=2+1$ flavours of O($a$) improved Wilson quarks generated by the CLS effort, with pion masses down to the physical value.

• We employ O($a$) improved versions of the local and conserved vector currents to compute the contributions of the light, strange and charm quarks to $(g-2)_\mu$, using the time-momentum representation.
• We perform a detailed investigation of the systematic effects arising from constraining the long-distance regime of the vector correlator.
• To this end we make use of auxiliary calculations in the iso-vector channel using distillation and the L\"uscher formalism.