Light front wave functions and diffractive electroproduction of vector mesons

We determine the leading Fock-state light front wave functions (LF-LFWFs) of the $\rho$ and $J/\psi$ mesons, for the first time from the Dyson-Schwinger and Bethe-Salpeter equations approach. A unique advantage of this method is that it renders a direct extraction of LF-LFWFs in presence of a number of higher Fock-states. Modulated by the current quark mass and driven by the dynamical chiral symmetry breaking, we find the $\rho$ and $J/\psi$ LF-LFWFs different in profile, i.e., the former are broadly distributed in $x$ (the longitudinal light-cone momentum fraction of meson carried by quark) while the latter are narrow. Moreover, the $\rho$ LF-LFWFs contribute less than 50% to the total Fock-state normalization, suggesting considerable higher Fock-states in $\rho$. We then use these LF-LFWFs to study the diffractive $\rho$ and $J/\psi$ electroproduction within the dipole picture. The calculated cross section shows general agreement with HERA data, except for growing discrepancy in $\rho$ production at low photon virtuality.

Figure 1

The LF-LFWF ${\psi }_{(1)}^0(x,{\mathit{k}}_T^2)$ of $\rho$ (left plot) and $J/\psi$ (right plot) respectively. See Eq. (2) for definition of ${\psi }_{(1)}^0(x,{\mathit{k}}_T^2)$.

Figure 2

Upper panel: diffractive $J/\psi$ electroproduction cross section obtained using bCGC model and DS-BSEs LF-LFWFs (solid curves). The dashed curves are 1.1 times the solid curves. The data is taken from H1 [67] (filled markers) and ZEUS [68] (empty markers). Note the selected ZEUS data is at $Q^2=3.1{\mathrm{GeV}}^2$ and $6.8{\mathrm{GeV}}^2$. Lower panel: results for $\rho$ (solid curves). The dashed curves are 1.3 times solid curves. The data is taken from H1 [69] (filled markers) and ZEUS [70] (empty markers). Deviation grows when $Q^2$ gets lower than $10{\mathrm{GeV}}^2$.

Figure 3

Longitudinal to transverse cross section ratio of $J/\psi$ and $\rho$ production at $W=90\mathrm{GeV}$. Upper panel: $J/\psi$ data taken from H1 [67] (filled markers) and ZEUS [68] (empty markers). Lower panel: $\rho$ data taken from H1 [69, 74] and ZEUS [70]. The low $Q^2$ region is shaded to indicate where the calculation gets less applicable. Different quark mass parameters are examined in the bCGC dipole model.