Abstract
We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wavefunctions of heavy quarkonia are obtained from the Basis Light-Front Quantization (BLFQ) approach in a holographic basis. We study the transition form factor with both the traditional "good current" $J^+$ and the transverse current $\vec J_\perp$ (in particular, $J^R=J^x+i J^y$). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections ($m_j=0,\pm 1$). We use the $m_j=0$ state of the vector meson to obtain the transition form factor, since this procedure employs the dominant spin components of the light-front wavefunctions and is more robust in practical calculations. While the $m_j=\pm 1$ states are also examined, transition form factors depend on subdominant components of the light-front wavefunctions and are less robust. Transitions between states below the open-flavor thresholds are computed, including those for excited states. Comparisons are made with the experimental measurements as well as with Lattice QCD and quark model results. In addition, we apply the transverse current to calculate the decay constant of vector mesons where we obtain consistent results using either $m_j=0$ or $m_j=1$ light-front wavefunctions. This consistency provides evidence for features of rotational symmetry within the model.
Highlights
Radiative transitions offer insights into the internal structure of quark-antiquark bound states through electromagnetic probes
We calculated the transition form factors for heavy quarkonia obtained in the Basis Light-Front Quantization (BLFQ) approach
The majority of the predictions from the BLFQ approach is in reasonable agreement with experimental data and other model calculations when the mj 1⁄4 0 state of the vector meson and the transverse current JR 1⁄4 Jx þ iJy are employed
Summary
Radiative transitions offer insights into the internal structure of quark-antiquark bound states through electromagnetic probes. We derive the formulas for radiative transitions between 0−þ and 1−− mesons on the light front, using both the traditional “good current” Jþ 1⁄4 J0 þ Jz and the transverse current J⃗ ⊥ 1⁄4 ðJx; JyÞ. Though, in principle, these two choices should be equivalent due to Lorentz covariance, adoption of certain approximations in the model may lead to violation of the Lorentz symmetry that would be evident through inequivalent results. As we will see later, the transverse current allows us to extract the transition form factor through the mj 1⁄4 0 state of the vector meson, which is not accessible with Jþ.
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