Doubly virtual $({\pi }^0,\eta ,{\eta }^{\text{'}})\to {\gamma }^{*}{\gamma }^{*}$ transition form factors in the light-front quark model

Journal Article · Fri Apr 19 00:00:00 EDT 2019 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.99.076012· OSTI ID:1507811

Choi, Ho-Meoyng; Ryu, Hui-Young; Ji, Chueng-Ryong

We report our investigation on the doubly virtual transition form factors (TFFs) $F_{\mathrm{P}{\gamma }^{*}}(Q_1^2,Q_2^2)$ for the $\mathrm{P}\to {\gamma }^{*}\left(q_1\right){\gamma }^{*}\left(q_2\right)(\mathrm{P}={\pi }^0,\eta ,{\eta }^{\text{'}})$ transitions using the light-front quark model (LFQM). Performing a LF calculation in the exactly solvable manifestly covariant Bethe-Salpeter (BS) model as the first illustration, we use the $q_1^{+}=0$ frame and find that both LF and manifestly covariant calculations produce exactly the same results for $F_{\mathrm{P}{\gamma }^{*}}(Q_1^2,Q_2^2)$. This confirms the absence of the LF zero mode in the doubly virtual TFFs. We then map this covariant BS model to the standard LFQM using the more phenomenologically accessible Gaussian wave function provided by the LFQM analysis of meson mass spectra. For the numerical analyses of $F_{\mathrm{P}{\gamma }^{*}}(Q_1^2,Q_2^2)$, we compare our LFQM results with the available experimental data and the perturbative QCD (pQCD) and vector meson dominance (VMD) model predictions. As $(Q_1^2,Q_2^2)\to \infty$, our LFQM result for doubly virtual TFF is consistent with the pQCD prediction, i.e., $F_{\mathrm{P}{\gamma }^{*}}(Q_1^2,Q_2^2)~1/(Q_1^2+Q_2^2)$, while it differs greatly from the result of the VMD model, which behaves as $F_{\mathrm{P}{\gamma }^{*}}^{\mathrm{VMD}}(Q_1^2,Q_2^2)~1/\left(Q_1^2{Q}_2^2\right)$. Our LFQM prediction for $F_{{\eta }^{\text{'}}{\gamma }^{*}}(Q_1^2,Q_2^2)$ shows an agreement with the very recent experimental data obtained from the BABAR Collaboration for the ranges of $2<(Q_1^2,Q_2^2)<60{\mathrm{GeV}}^2$.

• Research Organization: North Carolina State University, Raleigh, NC (United States)
• Sponsoring Organization: USDOE Office of Science (SC); National Research Foundation of Korea (NRF)
• Grant/Contract Number: FG02-03ER41260; NRF-2017R1D1A1B03033129; 2015R1A2A2A01004238
• OSTI ID: 1507811
• Alternate ID(s): OSTI ID: 1609458
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Vol. 99 Journal Issue: 7; ISSN 2470-0010
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

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