Measurements of differential cross sections for associated production of a $W$ boson and jets in proton-proton collisions at $\sqrt{s}=8\mathrm{TeV}$

Differential cross sections for a $W$ boson produced in association with jets are measured in a data sample of proton-proton collisions at a center-of-mass energy of 8 TeV recorded with the CMS detector and corresponding to an integrated luminosity of $19.6{\mathrm{fb}}^{-1}$. The $W$ bosons are identified through their decay mode $W\to \mu \nu$. The cross sections are reported as functions of jet multiplicity, transverse momenta, and the scalar sum of jet transverse momenta ($H_{\mathrm{T}}$) for different jet multiplicities. Distributions of the angular correlations between the jets and the muon are examined, as well as the average number of jets as a function of $H_{\mathrm{T}}$ and as a function of angular variables. The measured differential cross sections are compared with tree-level and higher-order recent event generators, as well as next-to-leading-order and next-to-next-to-leading-order theoretical predictions. The agreement of the generators with the measurements builds confidence in their use for the simulation of $W+\text{jets}$ background processes in searches for new physics at the LHC.

Figure 1

Distribution of inclusive jet multiplicity, for reconstructed data (points) and simulated signal and backgrounds (histograms). The ratio of simulated and measured data events is shown below the distribution. The data points are shown with statistical error bars. The error band represents the total statistical and systematic uncertainty.

Figure 2

Systematic uncertainties in the measured cross section as a function of jet multiplicity, including uncertainties due to jet energy scale (JES), background normalization, $b$ tagging efficiency, finite number of simulated events used to construct the response matrix (MC stat), and other systematic uncertainties mentioned in Sec. 8. The largest contribution to the other uncertainties is the uncertainty on the integrated luminosity, which is 2.6%. Statistical uncertainty of the unfolded data and total uncertainty in the measured cross section are also shown.

Figure 3

Measured cross section versus exclusive (left) and inclusive (right) jet multiplicity, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions), for which we currently have predictions only up to $W+4$ jets. Black circular markers with the gray hatched band represent the unfolded data measurement and its total uncertainty. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 4

Cross sections differential in the transverse momenta of the four leading jets, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, BlackHat$+$sherpa, and NNLO inclusive one-jet production (indicated as ${\mathrm{N}}_{\text{jetti}}$ NNLO). The BlackHat$+$sherpa and NNLO predictions are corrected for hadronization and multiple-parton interaction effects. Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 5

Cross sections differential in $H_{\mathrm{T}}$ for inclusive jet multiplicities 1–4, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa2, BlackHat$+$sherpa, and NNLO inclusive one-jet production (indicated as ${\mathrm{N}}_{\text{jetti}}$ NNLO). The BlackHat$+$sherpa and NNLO predictions are corrected for hadronization and multiple-parton interaction effects. Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 6

Cross sections differential in dijet $p_{\mathrm{T}}$ (calculated from the two leading jets) for inclusive jet multiplicities 2–4, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 7

Cross sections differential in dijet invariant mass (calculated from the two leading jets) for inclusive jet multiplicities 2–4, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 8

Cross sections differential in the pseudorapidities of the four leading jets, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, BlackHat$+$sherpa, and NNLO inclusive one-jet production (indicated as ${\mathrm{N}}_{\text{jetti}}$ NNLO). The BlackHat$+$sherpa and NNLO predictions are corrected for hadronization and multiple-parton interaction effects. Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 9

Cross sections differential in $\mathrm{\Delta }y(j_1,j_2)$ for inclusive jet multiplicities 2–4, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 10

Cross sections differential in $\mathrm{\Delta }y(j_1,j_3)$ (left) and $\mathrm{\Delta }y(j_2,j_3)$ (right) for an inclusive jet multiplicity of 3, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 11

Cross sections differential in $\mathrm{\Delta }y(j_F,j_B)$ for inclusive jet multiplicities 2–4, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 12

Cross sections differential in $\mathrm{\Delta }\varphi (j_1,j_2)$ (left) and $\mathrm{\Delta }\varphi (j_F,j_B)$ (right) for an inclusive jet multiplicity of 2, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 13

Cross section differential in $\mathrm{\Delta }R(j_1,j_2)$ for an inclusive jet multiplicity of 2, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 14

Cross sections differential in $\mathrm{\Delta }\varphi (j_n,\mu )$ for inclusive jet multiplicities $n=1–4$, compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.

Figure 15

Average number of jets $⟨N_{\text{jets}}⟩$ as a function of $H_{\mathrm{T}}$ for inclusive jet multiplicities 1–2 (top row) and as a function of $\mathrm{\Delta }y(j_1,j_2)$ and $\mathrm{\Delta }y(j_F,j_B)$ for an inclusive jet multiplicity of 2 (bottom row), compared to the predictions of MadGraph, MadGraph5_amc@nlo, sherpa 2, and BlackHat$+$sherpa (corrected for hadronization and multiple-parton interactions). Black circular markers with the gray hatched band represent the unfolded data measurements and their total uncertainties. Overlaid are the predictions together with their uncertainties. The lower plots show the ratio of each prediction to the unfolded data.