Delta-to-N-gamma Coulomb Quadrupole Amplitude in PQCD

We present a leading-order pQCD calculation of the helicity-flip $\Delta\to N\gamma^*$matrixelement$G_0$(Coulombquadrupoleamplitude$C2$), taking into account the transverse momenta of the quarks and the contribution from the gluons. In the large $Q^2$ limit, its scaling behavior acquires a double-logarithmic correction ${\log }^2(Q^2\mathrm{/}{\mathrm{\Lambda }}^2)$ compared with the standard scaling analysis, due to the contribution from the orbital motion of the small-$x$ partons. Based on this and on the latest JLab experimental results of the $C2-M1$ ratio $R_{SM}$ at $Q^2$ = 3 $\sim$ 4 GeV${}^2$, we make a phenomenological prediction for the latter at higher values of $Q^2$.