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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25562_Article_IEq1.gif" Format="GIF" Height="26" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mfenced close="|"> <msubsup> <mi>a</mi> <mi>μ</mi> <mtext>HLbL</mtext> </msubsup> </mfenced> <mtext>subleading</mtext> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{subleading}} $</EquationSource> </InlineEquation> = 33.2(7.2) × 10−11, which in combination with previously evaluated contributions in the dispersive approach leads to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25562_Article_IEq2.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mfenced close="|"> <msubsup> <mi>a</mi> <mi>μ</mi> <mtext>HLbL</mtext> </msubsup> </mfenced> <mtext>total</mtext> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{total}} $</EquationSource> </InlineEquation> = 101.9(7.9) × 10−11.

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

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2025年2月19日

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Martin Hoferichter,
Peter Stoffer,
Maximilian Zillinger

摘要

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 ${(a_{μ}^{HLbL}|}_{subleading}$ $ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{subleading}} $ = 33.2(7.2) × 10⁻¹¹, which in combination with previously evaluated contributions in the dispersive approach leads to ${(a_{μ}^{HLbL}|}_{total}$ $ {\left.{a}_{\mu}^{\textrm{HLbL}}\right|}_{\textrm{total}} $ = 101.9(7.9) × 10⁻¹¹.