Nucleon charges and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>σ</mml:mi> </mml:math> -terms in lattice QCD
Constantia Alexandrou, Simone Bacchio, Jacob Finkenrath, C. Iona, Giannis Koutsou, Yan Li, Gregoris Spanoudes
Abstract
We determine the nucleon axial, scalar, and tensor charges and the nucleon <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>σ</a:mi> </a:math> -terms using twisted mass fermions. We employ three ensembles with approximately equal physical volume of about 5.5 fm, three values of the lattice spacing, approximately 0.06, 0.07, and 0.08 fm, and with the mass of the degenerate up and down, strange and charm quarks tuned to approximately their physical values. We compute both isovector and isoscalar charges and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>σ</c:mi> </c:math> -terms and their flavor decomposition including the disconnected contributions. We use the Akaike information criterion to evaluate systematic errors due to excited states and the continuum extrapolation. For the nucleon isovector axial charge we find <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>g</e:mi> <e:mi>A</e:mi> <e:mrow> <e:mi>u</e:mi> <e:mo>−</e:mo> <e:mi>d</e:mi> </e:mrow> </e:msubsup> <e:mo>=</e:mo> <e:mn>1.250</e:mn> <e:mo stretchy="false">(</e:mo> <e:mn>24</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> , in agreement with the experimental value. Moreover, we extract the nucleon <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>σ</i:mi> </i:math> -terms and find for the light quark content <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>σ</k:mi> <k:mrow> <k:mi>π</k:mi> <k:mi>N</k:mi> </k:mrow> </k:msub> <k:mo>=</k:mo> <k:mn>41.9</k:mn> <k:mo stretchy="false">(</k:mo> <k:mn>8.1</k:mn> <k:mo stretchy="false">)</k:mo> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:mi>MeV</k:mi> </k:math> and for the strange <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>σ</o:mi> <o:mi>s</o:mi> </o:msub> <o:mo>=</o:mo> <o:mn>30</o:mn> <o:mo stretchy="false">(</o:mo> <o:mn>17</o:mn> <o:mo stretchy="false">)</o:mo> <o:mtext> </o:mtext> <o:mtext> </o:mtext> <o:mi>MeV</o:mi> </o:math> .