Neutral pion to two-photons transition form factor revisited

Based upon a combined formalism of Schwinger-Dyson and Bethe-Salpeter equations in quantum chromodynamics (QCD), we propose a QCD-kindred algebraic model for the dressed quark propagator, for the Bethe-Salpeter amplitude of the pion and the electromagnetic quark-photon interaction vertex. We then compute the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>γ</a:mi><a:mo>*</a:mo></a:msup><a:msup><a:mi>π</a:mi><a:mn>0</a:mn></a:msup><a:mi>γ</a:mi></a:math> transition form factor <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>G</c:mi><c:mrow><c:msup><c:mi>γ</c:mi><c:mo>*</c:mo></c:msup><c:msup><c:mi>π</c:mi><c:mn>0</c:mn></c:msup><c:mi>γ</c:mi></c:mrow></c:msup><c:mo stretchy="false">(</c:mo><c:msup><c:mi>Q</c:mi><c:mn>2</c:mn></c:msup><c:mo stretchy="false">)</c:mo></c:math> for a wide range of photon momentum transfer squared <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>Q</g:mi><g:mn>2</g:mn></g:msup></g:math>. The quark propagator is expanded out in its perturbative functional form but with dynamically generated dressed quark mass. It has complex conjugate pole singularities in the complex-momentum plane, which is motivated by the solution of the quark gap equation with rainbow-ladder truncation of the infinite set of Schwinger-Dyson equations. This complex pole singularity structure of the quark propagator can be associated with a signal of confinement, which prevents quarks from becoming stable asymptotic states. The Bethe-Salpeter amplitude is expressed without a spectral density function, which encapsulates its low- and large-momentum behavior. The QCD evolution of the distribution amplitude is also incorporated into our model through the direct implementation of Efremov-Radyushkin-Brodsky-Lepage evolution equations. We include the effects of the quark anomalous magnetic moment in the description of the quark-photon vertex, whose infrared enhancement is known to dictate hadronic properties. Once the QCD-kindred model is constructed, we calculate the form factor <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>G</i:mi><i:mrow><i:msup><i:mi>γ</i:mi><i:mo>*</i:mo></i:msup><i:msup><i:mi>π</i:mi><i:mn>0</i:mn></i:msup><i:mi>γ</i:mi></i:mrow></i:msup><i:mo stretchy="false">(</i:mo><i:msup><i:mi>Q</i:mi><i:mn>2</i:mn></i:msup><i:mo stretchy="false">)</i:mo></i:math> and find it consistent with direct QCD-based studies, as well as most available experimental data. It slightly exceeds the conformal limit for large <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>Q</m:mi><m:mn>2</m:mn></m:msup></m:math>, which might be attributed to the scaling violations in QCD. The associated interaction radius and neutral pion decay width turn out to be compatible with experimental data. Published by the American Physical Society 2024