High Energy Photon Deep Inelastic Scattering at Small and Large Q^2 with Soft Plus Hard Pomeron

We show how the sum of a hard singularity, $F_{2H}(x,Q^2_0)\sim x^{-\lambda}$ and a soft Pomeron $F_{2P}(x,Q^2_0)\sim Const.$ for the singlet piece of the structure function $F_{2S}=F_{2H}+F_{2P}$ for $Q_0^2\sim a few GeV^2$, plus a saturating expression for the strong coupling, $\tilde{\alpha}_s(Q^2)=4\pi/\beta_0 log[(Q^2+\Lambda^2)/\Lambda^2]$ give an excellent description of experiment i) For small Q^2, $0\lsim Q^2\leq 8.5 GeV^2$, and ii) For large Q^2, $10\lsim Q^2\leq 1 500 GeV^2$ if evolved with QCD. The x range is $6\times10^{-6}\lsim x \lsim 0.04$. The description for low Q^2 implies self-consistent values for the parameters in the exponents of x both for singlet and nonsinglet. One has to have $\alpha_{\rho}(0)=0.48$ and $\lambda=0.470 [\alpha_P(0)=1.470]$, in uncanny agreement with other determinations of these parameters, and in particular the results of the large Q^2 fits. The fit to data is so good that we may look for signals of a ``triple Pomeron" vertex, for which some evidence is found.