Eta Prime Gluonic Contribution to the Nucleon Self-Energy in an Effective Theory

We estimate a possible <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal"/><msup><mrow><mi>η</mi></mrow><mrow><mi mathvariant="normal">′</mi></mrow></msup></math> gluonic contribution to the self-energy of a nucleon in an effective theory. The couplings of the topological charge density to nucleons give rise to OZI violating <math id="M2" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal"/><msup><mrow><mi>η</mi></mrow><mrow><mi mathvariant="normal">′</mi></mrow></msup></math> -nucleon interactions. The one-loop self-energy of nucleon arising due to these interactions is studied using a heavy baryon chiral perturbation theory. The divergences have been removed using appropriate form factors. The nontrivial structure of the QCD vacuum has also been taken into account. The numerical results are sensitive to the choice of the regulator to a nonnegligible extent. We get the total contribution to the nucleon mass coming from its interaction with the topological charge density <math id="M3" xmlns="http://www.w3.org/1998/Math/MathML"><mi>δ</mi><msub><mrow><mi>m</mi></mrow><mrow><mtext>tot</mtext></mrow></msub><mo>≅</mo><mo>-</mo><mo stretchy="false">(</mo><mn>2.5</mn><mtext>–</mtext><mn>7.5</mn><mo stretchy="false">)</mo></math> % of the nucleon mass