Strange and charm quark contributions to the muon anomalous magnetic moment in lattice QCD with twisted-mass fermions

We present a lattice calculation of the hadronic vacuum polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon in isospin symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>f</a:mi></a:msub><a:mo>=</a:mo><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:math> flavors of Wilson-clover twisted-mass quarks at five lattice spacings and at values of the quark mass parameters that are close and/or include the isospin symmetric QCD point of interest. After computing the small corrections necessary to precisely match this point, and carrying out an extrapolation to the continuum limit based on the data at lattice spacings <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>a</c:mi><c:mo>≃</c:mo><c:mn>0.049</c:mn></c:math>, 0.057, 0.068, 0.080 fm and spatial lattice sizes up to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>L</e:mi><e:mo>≃</e:mo><e:mn>7.6</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>fm</e:mi></e:math>, we obtain <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi>a</g:mi><g:mi>μ</g:mi><g:mrow><g:mi>HVP</g:mi></g:mrow></g:msubsup><g:mo stretchy="false">(</g:mo><g:mi>s</g:mi><g:mo stretchy="false">)</g:mo><g:mo>=</g:mo><g:mo stretchy="false">(</g:mo><g:mn>53.57</g:mn><g:mo>±</g:mo><g:mn>0.63</g:mn><g:mo stretchy="false">)</g:mo><g:mo>×</g:mo><g:msup><g:mn>10</g:mn><g:mrow><g:mo>−</g:mo><g:mn>10</g:mn></g:mrow></g:msup></g:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi>a</m:mi><m:mi>μ</m:mi><m:mrow><m:mi>HVP</m:mi></m:mrow></m:msubsup><m:mo stretchy="false">(</m:mo><m:mi>c</m:mi><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mo stretchy="false">(</m:mo><m:mn>14.56</m:mn><m:mo>±</m:mo><m:mn>0.13</m:mn><m:mo stretchy="false">)</m:mo><m:mo>×</m:mo><m:msup><m:mn>10</m:mn><m:mrow><m:mo>−</m:mo><m:mn>10</m:mn></m:mrow></m:msup></m:math>, for the quark-connected strange and charm contributions, respectively. Our findings agree well with the corresponding results by other lattice groups.