# Extracting the longitudinal structure function FL(x,Q2) at small x from a Froissart-bounded parametrization of F2(x,Q2)

## TL;DR

This paper introduces a method to extract the longitudinal structure function FL(x,Q2) at small x using a Froissart-bounded parametrization of F2(x,Q2), ensuring compliance with boundary conditions and validated against HERA data.

## Contribution

A novel analytical approach to derive FL(x,Q2) from F2(x,Q2) that respects Froissart bounds and applies to ultra-low x and high Q2 regimes.

## Key findings

- Method yields reliable FL(x,Q2) at low x and various Q2 values.
- Analytical expressions explicitly relate FL to F2 parameters.
- Results agree with ZEUS and H1 data, supporting the approach's validity.

## Abstract

We present a method to extract, in the leading and next-to-leading order approximations, the longitudinal deep-inelastic scattering structure function FL(x,Q2) from the experimental data by relying on a Froissart-bounded parametrization of the transversal structure function F2(x,Q2) and, partially, on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations. Particular attention is paid on kinematics of low and ultra low values of the Bjorken variable x. Analytical expressions for FL(x,Q2) in terms of the effective parameters of the parametrization of F2(x,Q2) are presented explicitly. We argue that the obtained structure functions FL(x,Q2) within both, the leading and next-to-leading order approximations, manifestly obey the Froissart boundary conditions. Numerical calculations and comparison with available data from ZEUS and H1-Collaborations at HERA demonstrate that the suggested method provides reliable structure functions FL(x,Q2) at low x in a wide range of the momentum transfer (1 GeV2 < Q2 < 3000 GeV2) and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos.