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

Abstract

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 $2<(Q_1^2,Q_2^2)<60{\mathrm{GeV}}^2$.

Authors:

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

Publication Date:

2019-04-19

Research Org.:

North Carolina State University, Raleigh, NC (United States)

Sponsoring Org.:

USDOE Office of Science (SC); National Research Foundation of Korea (NRF)

OSTI Identifier:

1507811

Alternate Identifier(s):

OSTI ID: 1609458

Grant/Contract Number:  

FG02-03ER41260; NRF-2017R1D1A1B03033129; 2015R1A2A2A01004238

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 99 Journal Issue: 7; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics