Gluon distributions and fits using dipole cross sections

Abstract

I investigate the relationship between the gluon distribution obtained using a dipole model fit to low-x data on F 2 (x, Q 2 ) and standard gluons obtained from global fits with the collinear factorization theorem at fixed order. I stress the necessity to do fits of this type carefully, and in particular to include the contribution from heavy flavours to the inclusive structure function. I find that the dipole cross-section must be rather steeper than the gluon distribution, which at least partially explains why dipole model fits produce dipole cross-sections growing quite strongly at small x, while DGLAP based fits have valence-like, or even negative, small-x gluons as inputs. However, I also find that the gluon distributions obtained from the dipole fits are much too small to match onto the conventional DGLAP gluons at high Q 2 ∼ 50GeV 2 , where the two approaches should coincide. The main reason for this discrepancy is found to be the large approximations made in converting the dipole cross-sections into structure functions using formulae which are designed only for asymptotically small x. The shortcomings in this step affect the accuracy of the extracted dipole cross-sections in terms of size and shape, and hence also in terms of interpretation, at all scales.

Quantum chromodynamics at high energy and statistical physics

“…The integration contour C should go parallel with the imaginary axis in the complex γ -plane and cross the interval [0, γ 0 ]. Each partial wave of wave-number γ has a phase velocity v φ (γ ) = ω(γ ) γ , (124) whose expression is found by imposing that the exponential factor in the integrand of Eq. (123) …”

The Longitudinal Structure Function at HERA

“…The resummation prediction [8] and dipole model prediction [14] (very similar in [15]) have a different shape, and it is perhaps possible to distinguish the former at lower Q 2 . At Q 2 ≥ 10 GeV 2 the uncertainty on fixed order predictions is a few percent.…”

Universal Features of QCD Dynamics in Hadrons and Nuclei at High Energies

“…Both the IPsat model and the b-CGC model provide excellent fits to HERA data for x ≤ 0.01 [21,22]. An important caveat [23] to the success of the saturation models is that the saturation scale, at median impact parameters, extracted from these fits is ≤ 1 GeV 2 even at the lowest x values at HERA [21,24]. The saturation scale extracted from the fit in the IPsat model is shown in Fig.…”