On the scaling properties of the total $\gamma^*\mathrm{p}$ cross section

M.N. Mondragon, J.G. Contreras

Abstract


We perform a detailed analysis on the scaling properties of the total $\gamma^*\mathrm{p}$ cross section, $\sigma_{\gamma^*\mathrm{p}}$. We write the cross section as a product of two functions $W$ and $V$ representing, respectively, the dynamical degrees of freedom and the contribution from the valence partons. Analyzing data from HERA and fixed target experiments, we find that $V$ is independent of $Q^2$ and concentrated at large $x$, while $W$ carries all the information on the $Q^2$ evolution of $\gamma^*\mathrm{p}$. We define the reduced cross section $\tilde{\sigma}_{\gamma^*\mathrm{p}} \equiv W=\sigma_{\gamma^*\mathrm{p}}/V$, and show that it is very close to a generalized homogeneous function. This property gives rise to geometric scaling for $\tilde{\sigma}_{\gamma^*\mathrm{p}}$ and it also explains the known geometric scaling of $\sigma_{\gamma^*\mathrm{p}}$ at low $x$. As a consequence of our {\em Ansatz}, we also obtain a compact parameterization of $\sigma_{\gamma^*\mathrm{p}}$ describing all data above $Q^2=1$~GeV$^2$.

Keywords


Deep Inelastic Scattering; Geometric Scaling

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REVISTA MEXICANA DE FÍSICA, year 67, issue 2, March-April 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf, e-mail: rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, March 1st., 2021.

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