Contribution of neutral pseudoscalar mesons to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>a</mml:mi><mml:mi>μ</mml:mi><mml:mtext>HLbL</mml:mtext></mml:msubsup></mml:math> within a Schwinger-Dyson equations approach to QCD

Abstract

A continuum approach to quantum chromodynamics (QCD), based upon Schwinger-Dyson (SD) and Bethe-Salpeter (BS) equations, is employed to provide a tightly constrained prediction for the ${\ensuremath{\gamma}}^{*}{\ensuremath{\gamma}}^{*}\ensuremath{\rightarrow}{{\ensuremath{\pi}}^{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}},{\ensuremath{\eta}}_{c},{\ensuremath{\eta}}_{b}}$ transition form factors (TFFs) and their corresponding pole contribution to the hadronic light-by-light (HLbL) piece of the anomalous magnetic moment of the muon (${a}_{\ensuremath{\mu}}$). This work relies on a practical and well-tested quark-photon vertex Ansatz approach to evaluate the TFFs for arbitrary spacelike photon virtualities, in the impulse approximation. The numerical results are parametrized meticulously, ensuring a reliable evaluation of the HLbL contributions to ${a}_{\ensuremath{\mu}}$. We obtain ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{0}\ensuremath{-}\text{pole}}=\phantom{\rule{0ex}{0ex}}(6.14\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, ${a}_{\ensuremath{\mu}}^{\ensuremath{\eta}\ensuremath{-}\text{pole}}=(1.47\ifmmode\pm\else\textpm\fi{}0.19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, ${a}_{\ensuremath{\mu}}^{{\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{-}\text{pole}}=(1.36\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, yielding a total value of ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{0}+\ensuremath{\eta}+{\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{-}\text{pole}}=(8.97\ifmmode\pm\else\textpm\fi{}0.48)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, compatible with contemporary determinations. Notably, we find that ${a}_{\ensuremath{\mu}}^{{\ensuremath{\eta}}_{c}+{\ensuremath{\eta}}_{b}\ensuremath{-}\text{pole}}\ensuremath{\approx}{a}_{\ensuremath{\mu}}^{{\ensuremath{\eta}}_{c}\ensuremath{-}\text{pole}}=(0.09\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, which might not be negligible once the percent precision in the computation of the light pseudoscalars is reached.

Topics & Concepts