Gravitational form factors of the nucleon in the Skyrme model based on scale-invariant chiral perturbation theory

We investigate the role of the QCD scale anomaly in the gravitational form factors of the nucleon—particularly the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:mo stretchy="false">(</a:mo><a:mi>t</a:mi><a:mo stretchy="false">)</a:mo></a:math> form factor—as well as the associated stress distribution and internal forces, using a Skyrme model based on the scale-invariant chiral perturbation theory. A distinctive feature of this model is the inclusion of both the pion and the scalar meson, which respectively capture the effects of the current quark mass and gluonic quantum contributions to the scale anomaly. By varying the mass of the scalar meson, we evaluate the sensitivity of the gluonic scale anomaly to the nucleon properties. We find that the gluonic scale anomaly plays a crucial role in satisfying the stability conditions of the nucleon and provides an internal confining force. Moreover, we also evaluate the momentum-transfer dependence of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mo stretchy="false">(</e:mo><e:mi>t</e:mi><e:mo stretchy="false">)</e:mo></e:math>, which closely reproduces the lattice QCD results. With an appropriate choice of the anomalous dimension associated with the quark mass, its forward-limit value (i.e., the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>D</i:mi></i:math>-term) also matches the lattice data well.