Dispersion relation for hadronic light-by-light scattering: subleading contributions

A bstract In this work, we present an evaluation of subleading effects in the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. Using a recently derived optimized basis, we first study the matching of axial-vector contributions to short-distance constraints at the level of the scalar basis functions, finding that also the tails of the pseudoscalar poles and tensor mesons play a role. We then develop a matching strategy that allows for a combined evaluation of axial-vector and short-distance constraints, supplemented by an estimate of tensor-meson contributions based on simplified assumptions for their transition form factors. Uncertainties are primarily propagated from the axial-vector transition form factors and the variation of the matching scale, but we also consider estimates of the low-energy effect of hadronic states not explicitly included. In total, we obtain $$ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{subleading}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mtext>HLbL</mml:mtext> </mml:msubsup> </mml:mfenced> <mml:mtext>subleading</mml:mtext> </mml:msub> </mml:math> = 33 . 2(7 . 2) × 10 −11 , which in combination with previously evaluated contributions in the dispersive approach leads to $$ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{total}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mtext>HLbL</mml:mtext> </mml:msubsup> </mml:mfenced> <mml:mtext>total</mml:mtext> </mml:msub> </mml:math> = 101 . 9(7 . 9) × 10 −11 .