Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
Gilberto Colangelo, Franziska Hagelstein, Martin Hoferichter, Laetitia Laub, Peter Stoffer
Abstract
Abstract We reassess the impact of short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude on the anomalous magnetic moment of the muon, $$a_\mu =(g-2)_\mu /2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , by comparing different solutions that have recently appeared in the literature. In particular, we analyze the relevance of the exact axial anomaly and its impact on $$a_\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> and conclude that it remains rather limited. We show that all recently proposed solutions agree well within uncertainties on the numerical estimate of the impact of short-distance constraints on $$a_\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> , despite differences in the concrete implementation. We also take into account the recently calculated perturbative corrections to the massless quark loop to update our estimate and outline the path towards future improvements.