Structure functions and cross-sections

This interactive website evaluates the unpolarized inclusive structure functions, F₁ and F₂, as well as the inclusive virtual photon and electron scattering cross sections, σ and dσ/dWdQ², respectively, as functions of (x,Q²) or (W,Q²), where x is the Bjorken variable. The particular choice of variable set can be defined by the user by deciding whether to check the Show W grid instead of x box. The ranges of variables can be defined as well, by implementing the choices of values into the boxes for Q², in GeV² and x (or W in GeV). Here, First and Last stand for the minimal and maximal values, respectively, while the grid step size may be defined in "Step". To show only one single value, the user can simply assign the same number to First and Last. All the observables can be presented as functions of Q² or x (or W), by checking the respective icons in the column "Abscissa". The inclusive cross sections depend on the polarization parameter of the virtual photon, which determines the weight of the longitudinal part with respect to the transverse one. Therefore, if cross sections are to be computed, in order to evaluate the virtual photon polarization parameter the user is required to specify the incoming electron beam energy in GeV in the box E_beam. This is not necessary in the case of the structure function computations.

The inclusive electron scattering observables and their uncertainties are computed from the CLAS/world experimental data with the interpolation procedure described in [2]. By ticking the corresponding boxes, the user may choose whether the observables should be computed from CLAS data only [1] or from the combination of CLAS and world data [1,2]. The resonant contributions to the inclusive electron scattering observables have been evaluated in [3,4] with a Breit-Wigner ansatz for the coherent sum of resonances, by making use of the experimental results from CLAS on the γ_vpN electroexcitation amplitudes [5,6,7,8] and momentum dependent resonance hadronic decay widths [9]. For the computation of the resonant contributions, the box "Resonant contributions" should be checked. In addition, the difference between total and resonant contributions, as well as the ratio between resonant and total contributions can be displayed by checking "Difference" and "Ratio", respectively.

The statistical uncertainties of the electron scattering observables can be evaluated from the total number of events collected in (W,Q²) bins for the integrated luminosity defined by the user. To display this, the box "Calculate σ uncertainty from luminosity" should be checked and the integrated luminosity should be inserted in the box "L", in μb⁻¹, together with the choice of bin sizes, ΔW in GeV and ΔQ² in GeV².

Finally, the computed results can be presented in different formats by checking the appropriate boxes in the two bottom rows.

References

1. M. Osipenko et. al. A Kinematically Complete Measurement of the Proton Structure Function F₂ in the Resonance Region and Evaluation of Its Moments // Phys.Rev.D67:092001,2003 arXiv:hep-ph/0301204
2. A. A. Golubenko, V. V. Chesnokov, B. S. Ishkhanov, V. I. Mokeev Evaluation of the inclusive electron scattering observables in the resonance region from the experimental data Phys. Part. Nuclei 50, 587–592 (2019) arXiv:1902.02900
3. A. N. Hiller Blin, V. Mokeev, M. Albaladejo, C. Fernández-Ramírez, V. Mathieu, A. Pilloni, A. Szczepaniak, V. D. Burkert, V. V. Chesnokov, A. A. Golubenko, M. Vanderhaeghen Nucleon resonance contributions to unpolarized inclusive electron scattering // Phys.Rev.C100:035201,2019 arXiv:1904.08016
4. A.N. Hiller Blin, W. Melnitchouk, V. Mokeev, et al. Work in progress for submission to PRC
5. V.D. Burkert , Few Body Syst. 59, 57 (2018)
6. V.I. Mokeev , Few Body Syst. 59, 46 (2018) .
7. E.L. Isupov , https://userweb.jlab.org/~isupov/couplings/
8. V.I. Mokeev , https://userweb.jlab.org/~mokeev/resonance_electrocouplings/
9. I.G. Aznauryan , Phys. Rev. C 67, 015209 (2003) arXiv:nucl-th/0206033