$<‘{\gamma }^{*}\overrightarrow{N}\Delta$ transition form factors: A new analysis of data on ${p(e,e}^{\prime }p){\pi }^0$ at $Q^2=2.8\mathrm{}$ and $4.0\hspace{0.5em}(\mathrm{GeV}{/c)}^2$

Recent JLab data of the differential cross section for the reaction ${p(e,e}^{\prime }p){\pi }^0$ in the invariant mass region of $1.1<W<\mathrm{}1.4\mathrm{}\hspace{0.5em}\mathrm{GeV}$ at four-momentum transfer squared $Q^2=2.8\mathrm{}$ and $4.0\hspace{0.5em}(\mathrm{GeV}{/c)}^2$ are analyzed with two models, both of which give an excellent description of most of the existing pion electroproduction data below $W<\mathrm{}1.5\mathrm{}\hspace{0.5em}\mathrm{GeV}.$ We find that at up to $Q^2=4.0\mathrm{}\hspace{0.5em}(\mathrm{GeV}{/c)}^2,$ the extracted helicity amplitudes $A_{3/2}$ and $A_{/2\mathrm{}}$ remain comparable with each other, implying that hadronic helicity is not conserved at this range of $Q^2.$ The ratios $E_{1+}{/M}_{1+}$ obtained show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and to become positive with increasing $Q^2.$ This is a possible indication of a very slow approach toward the pQCD region. Furthermore, we find that the bare helicity amplitude $A_{1/2}$ and $S_{1/2},$ but not $A_{3/2},$ starts exhibiting the scaling behavior at about $Q^2>~2.5(\mathrm{GeV}{/c)}^2.$