Relativistic constituent quark model with infrared confinement

We refine the relativistic constituent quark model developed in our previous papers to include the confinement of quarks. It is done, first, by introducing the scale integration in the space of $\alpha$ parameters, and, second, by cutting this scale integration on the upper limit which corresponds to an infrared cutoff. In this manner one removes all possible thresholds present in the initial quark diagram. The cutoff parameter is taken to be the same for all physical processes. We adjust other model parameters by fitting the calculated quantities of the basic physical processes to available experimental data. As an application, we calculate the electromagnetic form factors of the pion and the transition form factors of the $\omega$ and $\eta$ Dalitz decays.

Figure 1

Diagram describing the meson mass operator.

Figure 2

Diagrams describing meson electromagnetic vertex function.

Figure 3

Diagrams describing $M^{\pm }\to W^{\pm }$ (upper panels) and $V\to \gamma$ (lower panels) transitions.

Figure 4

Diagrams describing $P\to \gamma \gamma$ and $V\to P\gamma$ transitions.

Figure 5

Form factor ${\pi }^{\pm }\to {\pi }^{\pm }{\gamma }^{*}$ as a function of the spacelike photon momentum $Q^2$. Data are taken from the JLAB $F_{\pi }$ Collaboration [19], DESY [18], and CERN NA7 Collaboration [20].

Figure 6

Form factor $\gamma {\gamma }^{*}\to {\pi }^0$ as a function of the spacelike photon momentum $Q^2$. Data are taken from CLEO [16].

Figure 7

Diagrams describing the Dalitz decays $P\to \gamma l^{+}{l}^{-}$ (upper panels) and $V\to P{l}^{+}{l}^{-}$ (lower panels).

Figure 8

The calculated form factors of the Dalitz decays $\omega \to {\pi }^0{l}^{+}{l}^{-}$, $\eta \to \gamma l^{+}{l}^{-}$, and ${\eta }^{\prime }\to \gamma l^{+}{l}^{-}$ as functions of the dilepton mass $M=\sqrt{q^2}$. Experimental data are taken from 29, 30 for $\omega \to {\pi }^0{\mu }^{+}{\mu }^{-}$ and $\eta \to \gamma {\mu }^{+}{\mu }^{-}$, from 31 for $\eta \to \gamma e^{+}{e}^{-}$, and from 29 for ${\eta }^{\prime }\to \gamma e^{+}{e}^{-}$ (the five uncorrected by background points are included). For comparison we plot the VMD curves.