Hadronic light-by-light contribution to the muon anomaly from lattice QCD with infinite volume QED at physical pion mass
Thomas Blum, Norman H. Christ, Masashi Hayakawa, Taku Izubuchi, Luchang Jin, Chulwoo Jung, Christoph Lehner, Cheng Tu
Abstract
The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mi>g</a:mi> <a:mo>−</a:mo> <a:mn>2</a:mn> <a:mo stretchy="false">)</a:mo> <a:mrow> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:mrow> </a:math> , is computed in the infinite volume QED framework with lattice QCD. We report <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>a</e:mi> <e:mi>μ</e:mi> <e:mtext>HLbL</e:mtext> </e:msubsup> <e:mo>=</e:mo> <e:mn>12.47</e:mn> <e:mo stretchy="false">(</e:mo> <e:mn>1.15</e:mn> <e:mo stretchy="false">)</e:mo> <e:mo stretchy="false">(</e:mo> <e:mn>0.95</e:mn> <e:mo stretchy="false">)</e:mo> <e:mo>×</e:mo> <e:msup> <e:mn>10</e:mn> <e:mrow> <e:mo>−</e:mo> <e:mn>10</e:mn> </e:mrow> </e:msup> </e:math> where the first error is statistical and the second systematic. The result is mainly based on the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mn>2</k:mn> <k:mo>+</k:mo> <k:mn>1</k:mn> </k:mrow> </k:math> flavor Möbius domain wall fermion ensemble with inverse lattice spacing <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>a</m:mi> <m:mrow> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mo>=</m:mo> <m:mn>1.73</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>GeV</m:mi> </m:math> , lattice size <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>L</o:mi> <o:mo>=</o:mo> <o:mn>5.5</o:mn> <o:mtext> </o:mtext> <o:mtext> </o:mtext> <o:mi>fm</o:mi> </o:math> , and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>m</q:mi> <q:mi>π</q:mi> </q:msub> <q:mo>=</q:mo> <q:mn>139</q:mn> <q:mtext> </q:mtext> <q:mtext> </q:mtext> <q:mi>MeV</q:mi> </q:math> , generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations.