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 <math><msup><mi>γ</mi><mo>*</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></math> transition form factor <math><msup><mi>G</mi><mrow><msup><mi>γ</mi><mo>*</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></mrow></msup><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> for a wide range of photon momentum transfer squared <math><msup><mi>Q</mi><mn>2</mn></msup></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 <math><msup><mi>G</mi><mrow><msup><mi>γ</mi><mo>*</mo></msup><msup><mi>π</mi><mn>0</mn></msup><mi>γ</mi></mrow></msup><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></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 <math><msup><mi>Q</mi><mn>2</mn></msup></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.

China

Pakistan

M. Atif Sultan

Jiayin Kang

Spain

Mexico

Adnan Bashir

Lei Chang

Neutral pion to two-photons transition form factor revisited

The pion scalar, vector, and tensor form factors are calculated within a symmetry-preserving contact interaction model (CI) of quantum chromodynamics (QCD), encompassed within a Dyson-Schwinger and Bethe-Salpeter equations approach. In addition to the traditional rainbow-ladder truncation, a modified interaction kernel for the Bethe-Salpeter equation is adopted. The implemented kernel preserves the vector and axial-vector Ward-Takahashi identities, while also providing additional freedom. Consequently, new tensor structures are generated in the corresponding interaction vertices, shifting the location of the mass poles appearing in the quark-photon and quark tensor vertex and yielding a notorious improvement in the final results. Despite the simplicity of the CI, the computed form factors and radii are compatible with recent lattice QCD simulations.

Xiaobin Wang

Zanbin Xing

Khépani Raya

Pion scalar, vector, and tensor form factors from a contact interaction