Isospin-violating vacuum polarization in the muon (g − 2) with SU(3) flavour symmetry from lattice QCD

A bstract We compute the isospin-violating part $$ {a}_{\mu}^{\textrm{HVP},38} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mrow> <mml:mi>HVP</mml:mi> <mml:mo>,</mml:mo> <mml:mn>38</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> of the hadronic-vacuum-polarization (HVP) contribution to the muon ( g − 2) in lattice QCD at the SU(3) f -symmetric point where M π = M K ≃ 416 MeV. All diagrams involving internal photons are evaluated in coordinate space, employing a Pauli-Villars-regulated photon propagator with a cutoff scale Λ well below the lattice cutoff. The counterterm ( m u – m d ), whose Λ dependence is consistent with the expected logarithmic behaviour, is calibrated using the experimental kaon mass splitting as input. The bare electromagnetic contribution at fixed Λ is compared to a phenomenological estimate based on the kaon-loop and pseudoscalar-pole contributions to the forward light-by-light amplitude. An extension of these calculations to physical pion and kaon masses appears promising.