Absorbing discretization effects with a massive renormalization scheme: The charm-quark mass

This is the authors' abstract. We don't add key points for this paper.

We present the first numerical implementation of the massive symmetric-momentum-subtraction (mSMOM) renormalization scheme and use it to calculate the charm-quark mass. Based on ensembles with three flavors of dynamical domain-wall fermions with lattice spacings in the range 0.11–0.08 fm, we demonstrate that the mass scale which defines the mSMOM scheme can be chosen such that the extrapolation has significantly smaller discretization effects than the SMOM scheme. Converting our results to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>MS</a:mi><a:mo stretchy="true">¯</a:mo></a:mover></a:math> scheme we obtain <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mover accent="true"><e:mi>m</e:mi><e:mo stretchy="false">¯</e:mo></e:mover><e:mi>c</e:mi></e:msub><e:mo stretchy="false">(</e:mo><e:mn>3</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi><e:mo stretchy="false">)</e:mo><e:mo>=</e:mo><e:mn>1.008</e:mn><e:mo stretchy="false">(</e:mo><e:mn>13</e:mn><e:mo stretchy="false">)</e:mo><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi></e:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mover accent="true"><m:mi>m</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>c</m:mi></m:msub><m:mo stretchy="false">(</m:mo><m:msub><m:mover accent="true"><m:mi>m</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>c</m:mi></m:msub><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>1.292</m:mn><m:mo stretchy="false">(</m:mo><m:mn>12</m:mn><m:mo stretchy="false">)</m:mo><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>GeV</m:mi></m:math>.