On the Rise of the Proton Structure Function F_2 Towards Low x

TL;DR

A measurement of the derivative (∀ ln F2/∂ ln x)Q2 ≡ −λ(x, Q) of the proton structure functionF2 is presented in the lowx domain of deeply inelastic positron–proton scattering.

Abstract

A measurement of the derivative (d ln F_2 / d lnx)_(Q^2)= -lambda(x,Q^2) of the proton structure function F_2 is presented in the low x domain of deeply inelastic positron-proton scattering. For 5*10^(-5)<=x<=0.01 and Q^2>=1.5 GeV^2, lambda(x,Q^2) is found to be independent of x and to increase linearly with ln(Q^2).

Figures (3)

• Figure 1: Measurement of the function $\lambda(x,Q^2)\:$: the inner error bars represent the statistical uncertainty; the full error bars include the systematic uncertainty added in quadrature; the solid curves represent the NLO QCD fit to the H1 cross section data described in paper; the dashed curves represent the extrapolation of the QCD fit below $Q^2 = 3.5$ GeV$^2$.
• Figure 2: Measurement of the function $\lambda(x,Q^2)\:$: the inner error bars represent the statistical uncertainty; the full error bars include the systematic uncertainty added in quadrature; the solid curves represent the NLO QCD fit to the H1 cross section data described in paper; the minimum $Q^2$ value of the data included in this fit is $Q^2 = 3.5$ GeV$^2$.
• Figure 3: Determination of the coefficients $c(Q^2)$ (upper plot) and of the exponents $\lambda(Q^2)\:$ (lower plot) from fits of the form $F_2(x,Q^2) = c(Q^2) x^{-\lambda(Q^2) }$ to the H1 structure function data paper for $x \leq 0.01$; the inner error bars illustrate the statistical uncertainties, the full error bars represent the statistical and systematic uncertainties added in quadrature. The straight lines represent the mean coefficient $c$ (upper plot) and a fit of the form $a \ln [Q^2/\Lambda^2]$ (lower plot), respectively, using data for $Q^2 \geq 3.5$ GeV$^2$.