$\rho$ meson form factors in a confining Nambu–Jona-Lasinio model

Elastic electromagnetic form factors for the ${\rho }^{+}$ meson are calculated in a Nambu–Jona-Lasinio model which incorporates quark confinement through the use of the proper-time regularization scheme. A comparison is made with recent lattice QCD results and previous quark model calculations for static quantities and the Sachs form factors. The results are qualitatively in good agreement with the lattice QCD calculations, with the exception of the quadrupole moment and corresponding form factor, which may be related to a lack of spherical symmetry on the lattice.

Figure 1

NJL gap equation in the Hartree-Fock approximation, where the thin line represents the elementary quark propagator, $S_0^{-1}\left(k\right)=/k-m+i\varepsilon$, and the shaded circle represents the four-fermion interaction.

Figure 2

Bethe-Salpeter equation for antiquark-quark (meson) correlations in the NJL model using the random phase approximation.

Figure 3

Feynman diagrams representing the electromagnetic current for a meson in our NJL model.

Figure 4

Inhomogeneous BSE whose solution gives the quark-photon vertex, represented as the large shaded oval. The small circle depicts the pointlike quark-photon driving term of Eq. (19), whereas the shaded circles with the double line represents the vector meson $t$ matrices.

Figure 5

Pion cloud contribution to the quark-photon vertex. The quark-photon interaction in the first two diagrams, represented by the shaded ovals, is given by the solution of the inhomogeneous BSE. The last diagram also includes the pion form factor determined without the pion cloud on the associated dressed quarks.

Figure 6

NJL model results for the $\rho \text{-meson}$ mass vs $m_{\pi }^2$. Comparison is made with lattice results from Ref. [25].

Figure 7

Squared charge radius $\langle r_C^2\rangle$ for the ${\rho }^{+}$ meson computed using the three levels of sophistication for the quark-photon vertex: pointlike (PL), using the inhomogeneous BSE (BSE), and including the pion cloud (BSE + pion cloud). Comparison is made with lattice results from Ref. [25].

Figure 8

${\rho }^{+}$ magnetic moment (${\mu }_{\rho }$) in units of nuclear magnetons vs $m_{\pi }^2$. The curves have the same conventions as Fig. 7.

Figure 9

${\rho }^{+}$ quadrupole moment (${\mathcal{Q}}_{\rho }$) vs $m_{\pi }^2$. The curves have the same conventions as Fig. 7.

Figure 10

${\rho }^{+}$ Sachs form factors as functions of $m_{\pi }^2$ at $Q^2=0.16 {\text{GeV}}^2$. The curves have the same conventions as Fig. 7.

Figure 11

${\rho }^{+}$ Sachs form factors for $m_{\pi }^2=0.49 {\text{GeV}}^2$. Comparison is made with lattice results from Ref. [26] and the curves have the same conventions as Fig. 7.