Double-parton scattering contribution to production of jet pairs with large rapidity separation at the LHC

For the first time in the literature, we discuss the production of a four-jet final state in proton-proton collisions at the LHC through the mechanism of double-parton scattering (DPS), in the context of jets with large rapidity separation. This is the region where searches for a Balitsky-Fadin-Kuraev-Lipatov (BFKL) signal are planned and/or being performed. The DPS contributions are calculated within the so-called factorized ansatz, and each step of DPS is calculated in the leading order (LO) collinear approximation. The LO pQCD calculations are shown to give a reasonably good description of recent CMS and ATLAS data on inclusive jet production; therefore, this formalism can be used to estimate the DPS effects. We demonstrate that the relative contribution (with respect to single parton scattering dijets and to the BFKL Mueller-Navelet jets) of DPS is growing at large rapidity distance between jets. This is consistent with our experience from previous studies of DPS effects in the case of open and hidden charm production. The calculated differential cross sections, as a function of rapidity distance between the jets that are the most remote in rapidity, are compared with recent results of leading logarithm and next-to-leading logarithm BFKL calculations for the Mueller-Navelet jet production at $\sqrt{s}=7\mathrm{TeV}$. The DPS contribution to widely rapidity separated jet production is carefully studied for the present energy $\sqrt{s}=7\mathrm{TeV}$, and also at the nominal LHC energy $\sqrt{s}=14\mathrm{TeV}$ and in different ranges of jet transverse momenta. The differential cross section as a function of dijet transverse momenta as well as two-dimensional ($p_T(y_{\min })\times p_T(y_{\max })$)-plane correlations for DPS mechanism are also presented. Some ideas as to how the DPS effects could be studied in the case of four-jet production are suggested.

Figure 1

A diagrammatic representation of the Mueller-Navelet jet production (left diagram) and of the double-parton scattering mechanism (right diagram).

Figure 2

Transverse momentum distribution of jets for different regions of the jet rapidity (left panel) and corresponding rapidity distribution of jets with different cuts in $p_t$, as specified in the right panel. The theoretical calculations were performed with the MSTW08 set of parton distributions [53]. The data points were obtained by the ATLAS Collaboration [32].

Figure 3

The same as in the previous figure but now together with the CMS experimental data [33]. In addition, we show decomposition into different partonic components, as explained in the figure caption.

Figure 4

Distribution in rapidity distance between jets ($35\mathrm{GeV}<p_t<60\mathrm{GeV}$) with maximal (the most positive) and minimal (the most negative) rapidities. The collinear pQCD result is shown by the short-dashed line and the DPS result by the solid line. The calculation has been performed for $\sqrt{s}=7\mathrm{TeV}$ (left panel) and $\sqrt{s}=14\mathrm{TeV}$ (right panel). For comparison we show also results for the classical BFKL Mueller-Navelet jets in leading-logarithm and next-to-leading-order-logarithm approaches from Ref. [15].

Figure 5

The same as in the previous figure, but now for a somewhat smaller lower cut on minijet transverse momentum.

Figure 6

The double-differential distribution in transverse momenta of jet with minimal [$p_T(y_{\min })$] and maximal [$p_T(y_{\max })$] rapidities. In the left panel we show the result for the full range of rapidities, and in the right panel we show the result only for large-rapidity separations of jets, as defined previously.

Figure 7

Distribution in transverse momentum imbalance (vector sum of transverse momenta of jets) between the jets with “minimal” and “maximal” rapidities.