The charm-quark contribution to light-by-light scattering in the muon $$(g-2)$$ from lattice QCD
En-Hung Chao, Renwick J. Hudspith, Antoine Gérardin, Jeremy Green, Harvey B. Meyer
Abstract
Abstract We compute the hadronic light-by-light scattering contribution to the muon $$g-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical ( u , d , s ) quarks at the SU(3) $$_\mathrm{f}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow/> <mml:mi>f</mml:mi> </mml:msub> </mml:math> symmetric point with degenerate pion and kaon masses of around 415 MeV. It includes the connected charm contribution, as well as the leading disconnected Wick contraction, involving the correlation between a charm and a light-quark loop. Cutoff effects turn out to be sizeable, which leads us to use lighter-than-physical charm masses, to employ a broad range of lattice spacings reaching down to 0.039 fm and to perform a combined charm-mass and continuum extrapolation. We use the $$\eta _c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>η</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> meson to define the physical charm-mass point and obtain a final value of $$a_\mu ^\mathrm{HLbL,c}= (2.8\pm 0.5) \times 10^{-11}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mrow> <mml:mi>HLbL</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2.8</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , whose uncertainty is dominated by the systematics of the extrapolation. Our result is consistent with the estimate based on a simple charm-quark loop, whilst being free of any perturbative scheme dependence on the charm mass. The mixed charm–light disconnected contraction contributes a small negative amount to the final value.