Nucleon axial and pseudoscalar form factors using twisted-mass fermion ensembles at the physical point
Constantia Alexandrou, Simone Bacchio, Martha Constantinou, Jacob Finkenrath, R. Frezzotti, Bartosz Kostrzewa, Giannis Koutsou, Gregoris Spanoudes, Carsten Urbach
Abstract
We compute the nucleon axial and pseudoscalar form factors using three <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> twisted-mass fermion ensembles with all quark masses tuned to approximately their physical values. The values of the lattice spacings of these three physical point ensembles are 0.080, 0.068, and 0.057 fm and spatial sizes 5.1, 5.44, and 5.47 fm, respectively, yielding <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>m</c:mi><c:mi>π</c:mi></c:msub><c:mi>L</c:mi><c:mo>></c:mo><c:mn>3.6</c:mn></c:math>. Convergence to the ground-state matrix elements is assessed using multistate fits. We study the momentum dependence of the three form factors and check the partially conserved axial-vector current (PCAC) hypothesis and the pion pole dominance (PPD). We show that in the continuum limit, the PCAC and PPD relations are satisfied. We also show that the Goldberger-Treimann relation is approximately fulfilled and determine the Goldberger-Treiman discrepancy. Our final results are <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>g</e:mi><e:mi>A</e:mi></e:msub><e:mo>=</e:mo><e:mn>1.245</e:mn><e:mo stretchy="false">(</e:mo><e:mn>28</e:mn><e:mo stretchy="false">)</e:mo><e:mo stretchy="false">(</e:mo><e:mn>14</e:mn><e:mo stretchy="false">)</e:mo></e:math> for the nucleon axial charge, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mo stretchy="false">⟨</k:mo><k:msubsup><k:mi>r</k:mi><k:mi>A</k:mi><k:mn>2</k:mn></k:msubsup><k:mo stretchy="false">⟩</k:mo><k:mo>=</k:mo><k:mn>0.339</k:mn><k:mo stretchy="false">(</k:mo><k:mn>48</k:mn><k:mo stretchy="false">)</k:mo><k:mo stretchy="false">(</k:mo><k:mn>06</k:mn><k:mo stretchy="false">)</k:mo><k:msup><k:mtext>fm</k:mtext><k:mn>2</k:mn></k:msup></k:math> for the axial radius, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>g</s:mi><s:mrow><s:mi>π</s:mi><s:mi>N</s:mi><s:mi>N</s:mi></s:mrow></s:msub><s:mo>≡</s:mo><s:munder><s:mo>lim</s:mo><s:mrow><s:msup><s:mi>Q</s:mi><s:mn>2</s:mn></s:msup><s:mo stretchy="false">→</s:mo><s:mo>−</s:mo><s:msubsup><s:mi>m</s:mi><s:mi>π</s:mi><s:mn>2</s:mn></s:msubsup></s:mrow></s:munder><s:msub><s:mi>G</s:mi><s:mrow><s:mi>π</s:mi><s:mi>N</s:mi><s:mi>N</s:mi></s:mrow></s:msub><s:mo stretchy="false">(</s:mo><s:msup><s:mi>Q</s:mi><s:mn>2</s:mn></s:msup><s:mo stretchy="false">)</s:mo><s:mo>=</s:mo><s:mn>13.25</s:mn><s:mo stretchy="false">(</s:mo><s:mn>67</s:mn><s:mo stretchy="false">)</s:mo><s:mo stretchy="false">(</s:mo><s:mn>69</s:mn><s:mo stretchy="false">)</s:mo></s:math> for the pion-nucleon coupling constant, and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>G</bb:mi><bb:mi>P</bb:mi></bb:msub><bb:mo stretchy="false">(</bb:mo><bb:mn>0.88</bb:mn><bb:msubsup><bb:mi>m</bb:mi><bb:mi>μ</bb:mi><bb:mn>2</bb:mn></bb:msubsup><bb:mo stretchy="false">)</bb:mo><bb:mo>≡</bb:mo><bb:msubsup><bb:mi>g</bb:mi><bb:mi>P</bb:mi><bb:mo>*</bb:mo></bb:msubsup><bb:mo>=</bb:mo><bb:mn>8.99</bb:mn><bb:mo stretchy="false">(</bb:mo><bb:mn>39</bb:mn><bb:mo stretchy="false">)</bb:mo><bb:mo stretchy="false">(</bb:mo><bb:mn>49</bb:mn><bb:mo stretchy="false">)</bb:mo></bb:math> for the induced pseudoscalar form factor at the muon capture point. Published by the American Physical Society 2024