Color dipole picture at low-$x$ DIS: The mass range of active photon fluctuations

We investigate the mass range of the quark-antiquark fluctuations of the photon that are active in producing the total photoabsorption cross section in the color dipole picture, emphasizing the notions of color transparency and saturation. We consider the implications of measurements at future extensions of the available electron-proton-scattering energy.

Figure 1

The theoretical results for the photoabsorption cross section ${\sigma }_{{\gamma }^{*}p}(\eta (W^2,Q^2),\xi )$ in the CDP as a function of the low-$x$ scaling variable $\eta (W^2,Q^2)=(Q^2+m_0^2)/{\mathrm{\Lambda }}_{\mathrm{sat}}^2(W^2)$ for different values of the parameter $\xi$ that determines the (squared) mass range $M_{q\overline{q}}^2\le m_1^2(W^2)=\xi {\mathrm{\Lambda }}_{\mathrm{sat}}^2(W^2)$ of the ${\gamma }^{*}\to q\overline{q}$ fluctuations that are taken into account. The experimental results [5] for ${\sigma }_{{\gamma }^{*}p}(\eta (W^2,Q^2))$ lie on the full line corresponding to $\xi ={\xi }_0=130$; compare Refs. [1, 2].

Figure 2

The theoretical results for the photoabsorption cross section as a function of $\eta (W^2,Q^2)$ for different values of $W$. The dependence on $W$ is due to logarithmic $\eta$-scaling violations ${\sigma }^{(\infty )}(W^2)\sim \ln W^2$; compare case (ii) in Sec. IV. For $\xi$ the value $\xi ={\xi }_0=130$ is used, and the results for $W=275\mathrm{GeV}$ are identical to the results shown by the full line in Fig. 1. By definition, $\mu (W^2)\equiv m_0^2/{\mathrm{\Lambda }}_{\mathrm{sat}}^2(W^2)$.

Figure 3

The photoabsorption cross section as a function of the energy $W$ for different values of $Q^2$. Note that a fixed value of $Q^2$ is associated with a fixed mass range of $q\overline{q}$ dipole states, $M_{q\overline{q}}^2\le m_1^2$ as determined by (3.7). Compare also Table 2. Transition from color transparency to saturation at fixed $Q^2$ is a consequence of the two-gluon coupling of the $q\overline{q}$-dipole state.