Structure of heavy mesons in the light-front quark model

We investigate the structure of ground-state heavy mesons within the light-front quark model, utilizing wave functions derived from the single Gaussian ansatz (SGA) and the Gaussian expansion method (GEM). By performing a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>χ</a:mi><a:mn>2</a:mn></a:msup></a:math> fit to static properties such as mass spectra and decay constants, we determine the model parameters for each approach. We then compare the impacts of both methods on the light-front wave functions and structural observables. Our analysis reveals significant differences in the distribution amplitudes <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ϕ</c:mi><c:mrow><c:mn>2</c:mn><c:mo>;</c:mo><c:mi>M</c:mi></c:mrow></c:msub><c:mo stretchy="false">(</c:mo><c:mi>x</c:mi><c:mo stretchy="false">)</c:mo></c:math> near the end points, with GEM showing enhanced amplitudes and correct asymptotic behavior <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>ϕ</g:mi></g:mrow><g:mrow><g:mn>2</g:mn><g:mo>;</g:mo><g:mi>M</g:mi></g:mrow></g:msub><g:mo stretchy="false">(</g:mo><g:mi>x</g:mi><g:mo stretchy="false">→</g:mo><g:mn>1</g:mn><g:mo stretchy="false">)</g:mo><g:mo>∝</g:mo><g:mo stretchy="false">(</g:mo><g:mn>1</g:mn><g:mo>−</g:mo><g:mi>x</g:mi><g:mo stretchy="false">)</g:mo></g:mrow></g:math>, consistent with perturbative QCD. This end point behavior is linked to the short-range (high-momentum) wave function governed by color Coulomb interaction and relativistic kinematics. GEM accurately reproduces a power-law damping <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:msub><n:mrow><n:mi>ψ</n:mi></n:mrow><n:mrow><n:mn>0</n:mn></n:mrow></n:msub><n:mo stretchy="false">(</n:mo><n:mi>k</n:mi><n:mo stretchy="false">→</n:mo><n:mi>∞</n:mi><n:mo stretchy="false">)</n:mo><n:mo>∝</n:mo><n:mn>1</n:mn><n:mo>/</n:mo><n:msubsup><n:mrow><n:mi>k</n:mi></n:mrow><n:mrow><n:mo>⊥</n:mo></n:mrow><n:mrow><n:mn>2</n:mn></n:mrow></n:msubsup></n:mrow></n:math>, aligning with perturbative QCD predictions. Furthermore, the electromagnetic form factors of pseudoscalar mesons in the low-<s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>Q</s:mi><s:mn>2</s:mn></s:msup></s:math> region fall off faster with GEM than with SGA. Overall, while both methods adequately describe static properties, GEM provides a more accurate description of structural properties, being more sensitive to details and asymptotic behaviors.