Phenomenology of leading nucleon production in $ep$ collisions at HERA in the framework of fracture functions

In recent years, several experiments at the $e^{-}p$ collider HERA have collected high precision deep-inelastic scattering (DIS) data on the spectrum of leading nucleon carrying a large fraction of the proton’s energy. In this paper, we have analyzed recent experimental data on the production of forward protons and neutrons in DIS at HERA in the framework of a perturbative QCD. We propose a technique based on the fractures functions framework, and extract the nucleon fracture functions (FFs) ${\mathcal{M}}_2^{(n/p)}(x,Q^2;x_L)$ from global QCD analysis of DIS data measured by the ZEUS Collaboration at HERA. We have shown that an approach based on the fracture functions formalism allows us to phenomenologically parametrize the nucleon FFs. Considering both leading neutron as well as leading proton production data at HERA, we present the results for the separate parton distributions for all parton species, including valence quark densities, the antiquark densities, the strange sea distribution, and the gluon distribution functions. We proposed several parametrizations for the nucleon FFs and open the possibility of these asymmetries. The obtained optimum set of nucleon FFs is accompanied by Hessian uncertainty sets which allow one to propagate uncertainties to other observables interest. The extracted results for the $t$-integrated leading neutron $F_2^{\mathrm{LN}(3)}(x,Q^2;x_L)$ and leading proton $F_2^{\mathrm{LP}(3)}(x,Q^2;x_L)$ structure functions are in good agreement with all data analyzed, for a wide range of fractional momentum variable $x$ as well as the longitudinal momentum fraction $x_L$.

Figure 1

Nominal coverage of the ZEUS-02 [86] data sets used in our global QCD fits for one selected bin of $x_L=0.24$.

Figure 2

Nominal coverage of the ZEUS-06 [55] data sets used in our global QCD fits for two selected bins of $x_L=0.575$ and 0.89.

Figure 3

Typical kinematical coverage in the ($x$, ${\mathrm{Q}}^2$) plane for the ZEUS-09 data sets included in our global QCD fits for four selected bins of $x_L=0.495$, 0.820, 0.845, and 0.870.

Figure 4

Our results for the ${\mathcal{W}}_{u_v}(x_L)$ and ${\mathcal{W}}_{d_v}(x_L)$ as a function of $x_L$ at the input scale $Q_0^2=2{\mathrm{GeV}}^2$.

Figure 5

The nucleon FFs $x{\mathcal{M}}_i(x,Q^2;x_L)$ for all parton species resulting from our QCD analysis at the input scale, which is taken to be $Q_0^2=2{\mathrm{GeV}}^2$. The results have been presented for a fixed value of $x_L=0.5$.

Figure 6

The nucleon FFs $x{\mathcal{M}}_i(x,Q^2;x_L)$ for all parton species resulting from our QCD analysis at the input scale, which is taken to be $Q_0^2=2{\mathrm{GeV}}^2$. The results have been presented for a fixed value of $x_L=0.8$.

Figure 7

Our theory predictions for the structure function ratio $r^{\mathrm{LP}(3)}(x,Q^2;x_L)=\frac{F_2^{\mathrm{LP}(3)}(x,Q^2;x_L)}{F_2^p(x,Q^2)}$ and its uncertainties at 68% C.L. in comparison with the ZEUS-06 data [55].

Figure 8

The tagged-neutron structure function $F_2^{\mathrm{LN}(3)}$ as a function of $x$ for some selected values of ${\mathrm{Q}}^2$ at a fixed value of $x_L=0.31$. Our theory predictions have been compared with the ZEUS-02 leading neutron data [53].

Figure 9

The tagged-neutron structure function $F_2^{\mathrm{LN}(3)}$ as a function of $x$ for some selected values of $Q^2$ at fixed value of $x_L=0.61$. Our theory predictions have been compared with the ZEUS-02 leading neutron data [53].