Double parton scattering: Impact of nonperturbative parton correlations

We apply the phenomenological Reggeon field theory framework to investigate the relative importance of perturbative and nonperturbative multiparton correlations for the treatment of double parton scattering in proton-proton collisions. We obtain a significant correction to the so-called effective cross section for double parton scattering due to nonperturbative parton splitting. When combined with the corresponding perturbative contribution, this results in a rather weak energy and transverse momentum dependence of the effective cross section, in agreement with experimental observations at the Tevatron and the Large Hadron Collider. In addition, we observe that color fluctuations have a sizable impact on the calculated rate of double parton scattering and on the relative importance of the perturbative parton splitting mechanism.

Figure 1

Schematic view for the general RFT diagram for inclusive jet production in $pp$ collisions: the projectile and target triangles consist of fanlike enhanced Pomeron graphs; $V_J(p_J)$ is the parton $J$ emission vertex from a cut Pomeron. The cut plane is shown by the vertical dotted-dashed line.

Figure 2

Examples of enhanced Pomeron graphs of lowest orders, contributing to the structure of the projectile and target triangles in Fig. 1; Pomerons are shown by thick lines and multi-Pomeron vertices by filled circles.

Figure 3

Schematic view of RFT diagrams for double parton scattering: contribution of two independent parton cascades (a), projectile parton splitting (b), and double parton splitting (c).

Figure 4

Energy dependence of the effective cross section for the production of two dijets in double parton scattering. Left: for jet transverse momenta $p_{\mathrm{t}}^{\mathrm{jet}}>5\mathrm{GeV}/\mathrm{c}$ and $p_{\mathrm{t}}^{\mathrm{jet}}>50\mathrm{GeV}/\mathrm{c}$ (as indicated in the plots), integrated over the phase space. Right: for fixed $p_{\mathrm{t}}^{\mathrm{jet}}=5$ and $50\mathrm{GeV}/\mathrm{c}$ and ${\eta }^{\mathrm{jet}}=0$. Solid lines are both the (2v2) and (2v1) contributions to DPS taken into account; dashed lines are only the (2v2) contribution considered.

Figure 5

Effective cross section for the production of two dijets of $p_{\mathrm{t}}^{\mathrm{jet}}>p_{\mathrm{t}}^{\mathrm{cut}}$, integrated over the phase space, in double parton scattering at $\sqrt{s}=1.8\mathrm{TeV}$ (left) and $\sqrt{s}=13\mathrm{TeV}$ (right) as a function of $p_{\mathrm{t}}^{\mathrm{cut}}$: solid—all the DPS contributions taken into account, dashed—only the (2v2) contribution considered, dotted-dashed—including both the (2v2) and ${(2\mathrm{v}1)}_{\mathrm{s}}$ contributions.

Figure 6

Energy dependence for $p_{\mathrm{t}}^{\mathrm{cut}}=50\mathrm{GeV}/\mathrm{c}$ (left) and $p_{\mathrm{t}}^{\mathrm{cut}}$ dependence for $\sqrt{s}=13\mathrm{TeV}$ (right) of the ratio of the (2v1) to (2v2) contributions to the DPS cross section for double dijet ($p_{\mathrm{t}}^{\mathrm{jet}}>p_{\mathrm{t}}^{\mathrm{cut}}$) production (solid) and partial contributions to this ratio from hard (dashed) and soft (dotted-dashed) parton splitting mechanisms.

Figure 7

Energy dependence for $p_{\mathrm{t}}^{\mathrm{jet}}=50\mathrm{GeV}/\mathrm{c}$ (left) and $p_{\mathrm{t}}^{\mathrm{jet}}$ dependence for $\sqrt{s}=13\mathrm{TeV}$ (right) of the ratio of the (2v1) to (2v2) contributions to the DPS production of two dijets of fixed $p_{\mathrm{t}}^{\mathrm{jet}}$ for ${\eta }^{\mathrm{jet}}=0$ (solid lines). Partial contributions to this ratio from hard and soft parton splitting mechanisms are shown by dashed and dotted-dashed lines, respectively.

Figure 8

Energy dependence of the ratio $R_{{(2\mathrm{v}1)}_{\mathrm{h}}}$ of the ${(2\mathrm{v}1)}_{\mathrm{h}}$ to (2v2) contributions to the DPS production of two dijets of $p_{\mathrm{t}}^{\mathrm{jet}}>50\mathrm{GeV}/\mathrm{c}$ (solid line) and the ratios $R_{{(2\mathrm{v}1)}_{\mathrm{h}}}^{(ii)}$ for the combinations of large ($i=1$) and small ($i=2$) size parton Fock states—dashed and dotted-dashed lines, respectively.

Figure 9

Energy dependence of the ratios $2{\sigma }_{(ij)}^{4\text{jet}(2\mathrm{v}2)}/{({\sigma }_{pp}^{2\mathrm{jet}})}^2$ (solid lines) and $2{\sigma }_{(ij)}^{{4\text{jet}(2\mathrm{v}1)}_{\mathrm{h}}}/{({\sigma }_{pp}^{2\mathrm{jet}})}^2$ (dashed lines) for DPS production of two dijets of $p_{\mathrm{t}}^{\mathrm{jet}}>50\mathrm{GeV}/\mathrm{c}$ for different combinations of parton Fock states $(ij)$, as indicated in the figure.