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

Abstract

We show how the sum of a hard singularity, $F_{2H}(x,Q_0^2)\sim x^{-\lambda }$ and a soft Pomeron $F_{2P}(x,Q_0^2)\sim Const.$ for the singlet piece of the structure function $F_{2S}=F_{2H}+F_{2P}$ for $Q_0^2\sim afewGe{V}^2$, 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, $0\text{lsim}{Q}^2\le 8.5Ge{V}^2$, and ii) For large Q^2, $10\text{lsim}{Q}^2\le 1500Ge{V}^2$ if evolved with QCD. The x range is $6\times 10^{-6}\text{lsim}x\text{lsim}0.04$. 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.

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