Importance of a Measurement of F_L(x,Q^2) at HERA

TL;DR

The paper addresses how a direct measurement of the longitudinal structure function F_L(x,Q^2) at HERA could illuminate the proton’s gluon content at small x and test the applicability of perturbative QCD for structure functions. It analyzes several theoretical scenarios, including double resummation, dipole models, and NNLO fixed-order calculations, and assesses how FL measurements—especially at low Q^2—could distinguish between them and improve global fits. The results indicate that FL is a powerful discriminator among competing approaches and essential for reliably determining the gluon distribution, potentially revealing the need for resummations or higher-twist effects. This work underlines the value of a low-energy HERA run to obtain FL data and its significance for predicting hadron collider phenomenology, such as at the LHC.

Abstract

I investigate what a direct measurement of the longitudinal structure function F_L(x,Q^2) could teach us about the structure of the proton and the best way in which to use perturbative QCD for structure functions. I assume HERA running at a lowered beam energy for approximately 4-5 months and examine how well the measurement could distinguish between different theoretical approaches. I conclude that such a measurement would provide useful information on how to calculate structure functions and parton distributions at small x.

Figures (7)

• Figure 1: The NLO consistency check of $F_L(x,Q^2)$ for the H1 fit.
• Figure 2: The NLO consistency check of $F_L(x,Q^2)$ for the H1 fit (left). The consistency check of $F_L(x,Q^2)$ for the NLO and NNLO MRST fits (right).
• Figure 3: The gluon extracted from the global fit at LO, NLO and NNLO (left). $F_L(x,Q^2)$ predicted from the global fit at LO, NLO and NNLO (right).
• Figure 4: Evolution of various predictions for $F_L(x,Q^2)$ at $x=0.0001$ (left) and $x=0.001$ (right).
• Figure 5: $F_L(x,Q^2)$ predicted from the global fit at LO, NLO and NNLO, from a fit which performs a double resummation of leading $\ln(1/x)$ and $\beta_0$ terms, and from a dipole model type fit (left). Comparison of data to various predictions. Also show are points at $Q^2=2{\rm GeV}^2$ that might have been measured at HERA III and for the two highest $x$ values might be at eRHIC (right).