Heavy-quark contributions to the ratio FL/F2 at low values of the   Bjorken variable x
  We study the heavy-quark contributions to the proton structure functions $F_2^i(x,Q^2)$ and $F_L^i(x,Q^2)$, with $i=c,b$, for small values of Bjorken's $x$ variable and provide compact formulas for their ratios $R_i=F_L^i/F_2^i$ that are useful to extract $F_2^i(x,Q^2)$ from measurements of the doubly differential cross section of inclusive deep-inelastic scattering at DESY HERA. Our approach naturally explains why $R_i$ is approximately independent of $x$ and the details of the parton distribution functions in the low-$x$ regime. 
A.Yu. Illarionov, B.A. Kniehl, A.V. Kotikov