Geometrical scaling of heavy-quark contributions in the low $x$ region

Abstract

We describe the determination of the heavy quarks structure functions $F_{2,L}^{\mathcal{Q}\bar{\mathcal{Q}}}$ with help of the scaling properties. We observe that the structure functions for inclusive charm and bottom production exhibits geometric scaling at low $x$. The geometrical scaling means that the heavy quark structure function is a function of only one dimensionless variable $\tau \equiv Q^2/Q_{sat}^2(x)$ including quark mass. These results are valid for any value of $\delta$, being $x^{-\delta }$ the behavior of the parton densities at low $x$. The determination of the heavy quark structure function is presented as a parameterization of the proton structure function $F_2(x,Q^2)$ and its derivative. Analytical expressions for $F_{2,L}^{\mathcal{Q}\bar{\mathcal{Q}}}$ in terms of the effective parameters of the parameterization of $F_2(x,Q^2)$ ,with respect to the BDH and ASW models, are presented. To study the heavy quark production processes, we use the collinear results in DAS approach. Numerical calculations and comparison with HERA data demonstrate that the suggested method provides reliable $F_2^{\mathcal{Q}\bar{\mathcal{Q}}}$, $R^{c\bar{c}}$ and ${\sigma }^{\mathcal{Q}\bar{\mathcal{Q}}}$ at low $x$ in a wide range of the low absolute four-momentum transfers squared ($4{\mathrm{GeV}}^2<Q^2<2000{\mathrm{GeV}}^2$). Also, in the HERA kinematic range, the ratio of $F_2^{c\bar{c}}/F_2^{b\bar{b}}$, $F_2^{c\bar{c}}/F_2^{BDHM}$ and $F_2^{b\bar{b}}/F_2^{BDHM}$ are obtained. Expanding the method to low and ultra low values of $x$ can be considered in the process analysis of the LHeC and FCC-eh colliders.

References in corpus (12)

• Implications of CTEQ global analysis for collider observables
• Mining for Gluon Saturation at Colliders
• The Longitudinal Heavy Quark Structure Function F_{L}^{Q\bar{Q}} in the Region Q^2 \gg m^2 at O(α_s^3)
• Charged Current Neutrino Cross Section and Tau Energy Loss at Ultra-High Energies
• Heavy-quark contributions to the ratio F_L/F_2 at low x
• Transverse momentum dependent parton densities in processes with heavy quark generations
• An Evaluation of The Proton Structure Functions $F_2$ and $F_L$ at Small $x$
• Heavy-flavor PDF evolution and variable-flavor number scheme uncertainties in deep-inelastic scattering
• The ratio of the beauty structure functions $R^b=F_L^b/F_2^b$ at low x
• Geometrical scaling in charm structure function ratios
• Importance of the heavy-quarks longitudinal structure function measurements at future circular collider energies
• Influence of gluon behavior on heavy-quark pair production

Cited by in corpus (1)

• Heavy quark structure functions from unifying the color dipole picture and double asymptotic scaling approaches