Extension of Geometric Scaling to Large $x$
M. N. Mondragón, J.G. Contreras · arXiv (Cornell University) · 2005
We perform a detailed analysis on the validity of geometric scaling in the total $\\gamma^*\\mathrm{p}$ cross section, $\\sigma_{\\gamma^*\\mathrm{p}}$. We propose to separate the small and large $x$ behavior writing $\\sigma_{\\gamma^*\\mathrm{p}}$ as a product of two functions $W$ and $S$ representing, respectively, the dynamical degrees of freedom dominant at small $x$ and a contribution only important at large $x$. Defining a reduced cross section $\\tilde{\\sigma}_{\\gamma^*\\mathrm{p}} \\equiv\\sigma_{\\gamma^*\\mathrm{p}}/S$, we observe geometric scaling for $\\tilde{\\sigma}_{\\gamma^*\\mathrm{p}}$ over nine orders of magnitude, up to the highest measured values of $x$ and $Q^2$.