Studies of inclusive four-jet production with two $b$-tagged jets in proton-proton collisions at 7 TeV

Measurements are presented of the cross section for the production of at least four jets, of which at least two originate from $b$ quarks, in proton-proton collisions. Data collected with the CMS detector at the LHC at a center-of-mass energy of 7 TeV are used, corresponding to an integrated luminosity of $3{\mathrm{pb}}^{-1}$. The cross section is measured as a function of the jet transverse momentum for $p_{\mathrm{T}}>20\mathrm{GeV}$, and of the jet pseudorapidity for $|\eta |<2.4$ ($b$ jets), 4.7 (untagged jets). The correlations in azimuthal angle and $p_{\mathrm{T}}$ between the jets are also studied. The inclusive cross section is measured to be $\sigma (pp\to 2b+2j+X)=69\pm 3(\mathrm{stat})\pm 24(\mathrm{syst})\mathrm{nb}$. The $\eta$ and $p_{\mathrm{T}}$ distributions of the four jets and the correlations between them are well reproduced by event generators that combine perturbative QCD calculations at next-to-leading-order accuracy with contributions from parton showers and multiparton interactions.

Figure 1

Uncorrected transverse momentum (left) and pseudorapidity (right) distributions of data and simulations (pythia 6 and herwig++) for the leading $b$-tagged (top) and leading untagged (bottom) jets. Only statistical uncertainties are shown.

Figure 2

Response matrices obtained with the pythia 6 tune $\mathrm{Z}{2}^{*}$ simulation for the transverse momentum (left) and pseudorapidity (right) of the leading $b$-tagged (top) and leading untagged (bottom) jets.

Figure 3

Differential cross sections unfolded to the particle level as a function of the jet transverse momenta $p_{\mathrm{T}}$ (left) and pseudorapidity $\eta$ (right) compared to predictions of powheg+pythia 8 tune CUETS1. Scale factors of $10^8$, $10^6$, and $10^2$ are applied (for clarity) to the measurement of the leading, subleading, and third jet, respectively. The error bars on the data represent the total uncertainties, i.e., statistical and systematic added quadratically. The band represents the theoretical uncertainty due to the choice of the scales and PDFs.

Figure 4

Ratios of the absolute cross section predictions of powheg, MadGraph, pythia 6 (P6), pythia 8 (P8), and herwig++ over data (unfolded to the particle level) as a function of the jet transverse momenta $p_{\mathrm{T}}$ for each jet. The error bars on the data represent the total uncertainties, i.e., statistical and systematic added quadratically. Data are shown with markers at unity. The band represents the theoretical uncertainty due to the choice of the scales and PDFs (shown only around the powheg ratio for clarity, but affecting all predictions in the same way).

Figure 5

Ratios of the absolute cross section predictions of powheg, MadGraph, pythia 6 (P6), pythia 8 (P8), and herwig++ over data (unfolded to the particle level) as a function of the jet pseudorapidity $\eta$ for each jet. The error bars on the data represent the total uncertainties, i.e., statistical and systematic added quadratically. Data are shown with markers at unity. The band represents the theoretical uncertainty due to the choice of the scales and PDFs (shown only around the powheg ratio for clarity, but affecting all predictions in the same way).

Figure 6

Normalized cross sections unfolded to the particle level as a function of $\mathrm{\Delta }{\varphi }^{\text{light}}$, compared to predictions of powheg, MadGraph, pythia 8 (P8), and herwig++ (left), and of the powheg+pythia 8 tune CUETS1 without MPI (right). The lower panels show the ratios of the MC predictions over the data. The error bars on the data represent the total uncertainties, i.e., statistical and systematic added quadratically. Data are shown with markers at unity. The band represents the theoretical uncertainty due to the choice of the scales and PDFs (shown only around the powheg line for clarity, but affecting all predictions in the same way).

Figure 7

Normalized cross sections unfolded to the particle level as a function of ${\mathrm{\Delta }}_{\text{light}}^{\mathrm{rel}}{p}_{\mathrm{T}}$, compared to predictions of powheg, MadGraph, pythia 8 (P8), and herwig++ (left), and of the powheg+pythia 8 tune CUETS1 without MPI (right). The lower panels show the ratios of the MC predictions over the data. The error bars on the data represent the total uncertainties, i.e., statistical and systematic added quadratically. Data are shown with markers at unity. The band represents the theoretical uncertainty due to the choice of the scales and PDFs (shown only around the powheg line for clarity, but affecting all predictions in the same way).

Figure 8

Normalized cross sections unfolded to the particle level as a function of $\mathrm{\Delta }\mathrm{S}$, compared to predictions of powheg, MadGraph, pythia 8 (P8), and herwig++ (left), and of the powheg+pythia 8 tune CUETS1 without MPI (right). The lower panels show the ratios of the MC predictions over the data. The error bars on the data represent the total uncertainties, i.e., statistical and systematic added quadratically. Data are shown with markers at unity. The band represents the theoretical uncertainty due to the choice of the scales and PDFs (shown only around the powheg line for clarity, but affecting all predictions in the same way).