Measurement of multidifferential cross sections for dijet production in proton-proton collisions at s = 13 Te V

Abstract

A measurement of the dijet production cross section is reported based on proton-proton collision data collected in 2016 at $\sqrt{s}=13\mathrm{Te}V$ by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of up to 36.3 ${\mathrm{fb}}^{-1}$ . Jets are reconstructed with the anti- $k_{\text{T}}$ algorithm for distance parameters of $R=0.4$ and 0.8. Cross sections are measured double-differentially (2D) as a function of the largest absolute rapidity ${\left|y\right|}_{\max }$ of the two jets with the highest transverse momenta $p_{\text{T}}$ and their invariant mass $m_{1,2}$ , and triple-differentially (3D) as a function of the rapidity separation $y^{\ast }$ , the total boost $y_b$ , and either $m_{1,2}$ or the average $p_{\text{T}}$ of the two jets. The cross sections are unfolded to correct for detector effects and are compared with fixed-order calculations derived at next-to-next-to-leading order in perturbative quantum chromodynamics. The impact of the measurements on the parton distribution functions and the strong coupling constant at the mass of the $Z$ boson is investigated, yielding a value of ${\alpha }_{\text{S}}\left(m_Z\right)=0.1179\pm 0.0019$ .

Fig. 1

Illustration of the dijet rapidity phase space, highlighting the relationship between the variables used for the 2D and 3D measurements. The colored triangles are suggestive of the orientation of the two jets in the different phase space regions in the laboratory frame, assuming that the beam line runs horizontally

Fig. 2

Response matrix for the 2D measurement as a function of $m_{1,2}$ using jets with $R=0.8$. The entries represent the probability for a dijet event generated in the phase space region ($m_{1,2}^{\mathrm{gen}}$, ${|y|}_{\max }^{\mathrm{gen}}$) indicated on the x axis to be reconstructed in the phase space region ($m_{1,2}^{\mathrm{rec}}$, ${|y|}_{\max }^{\mathrm{rec}}$) indicated on the y axis. Response matrices for all other jet sizes and observables can be found in Appendix 1

Fig. 3

Breakdown of the experimental uncertainty for the 2D measurements as a function of $m_{1,2}$ using jets with $R=0.4$ (left) and 0.8 (right). The individual components and abbreviations are explained in Sect. 7. The abbreviation “Unf.” refers to the unfolding uncertainties. The shaded area represents the sum in quadrature of all statistical and systematic uncertainty components

Fig. 4

Breakdown of the experimental uncertainty for the 3D measurement as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ using jets with $R=0.4$. The individual components and abbreviations are explained in Sect. 7. The shaded area represents the sum in quadrature of all statistical and systematic uncertainty components. Similar plots for all other jet sizes and observables can be found in Appendix B

Fig. 5

Theoretical predictions for the 2D (upper) and 3D (lower) cross sections, as a function of $m_{1,2}$, illustrated here in the rapidity regions ${1.0<|y|}_{\max }<1.5$ and $y_{\mathrm{b}}<0.5$, $y^{\ast }<0.5$, together with the corresponding six-point scale uncertainty for ${\mu }_{\text{R}}={\mu }_{\text{F}}=m_{1,2}$ using the CT18 NNLO PDF set. In the upper panels, the curves and symbols are slightly shifted for better visibility. The lower panels show the ratio to the respective prediction at LO. The fluctuations in the NNLO predictions are due to the limited statistical precision of the calculation

Fig. 6

Nonperturbative correction factors obtained for jets with $R=0.4$ (upper) and 0.8 (lower) as a function of $m_{1,2}$, illustrated here in the rapidity region ($y_{\mathrm{b}}<0.5$, $y^{\ast }<0.5$). Individual correction factors are first derived from simulation using eight different MC configurations. The largest and smallest value obtained in each observable bin is then used to define the final correction factor and its associated uncertainty. The correction values are larger for jets with $R=0.8$, increasing to over 20% in the lowest $m_{1,2}$ bin

Fig. 7

Electroweak correction factors obtained for jets with $R=0.4$ (upper) and 0.8 (lower) as a function of $m_{1,2}$ in the five different ${|y|}_{\max }$ regions. The corrections depend strongly on the kinematic properties of the jets and are observed to be largest at central rapidities for $m_{1,2}>1\mathrm{Te}\mathrm{V}$

Fig. 8

Differential dijet cross sections, illustrated here for the 2D measurement as a function of $m_{1,2}$ using jets with $R=0.8$ (upper), and the 3D measurement as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ using jets with $R=0.4$ (lower). The markers and lines indicate the measured unfolded cross sections and the corresponding NNLO predictions, respectively. For better visibility, the values are scaled by a factor depending on the rapidity region, as indicated in the legend. Analogous plots for all other jet sizes and observables can be found in Appendix  B

Fig. 9

Comparison of the 2D dijet cross section as a function of $m_{1,2}$ to fixed-order theoretical calculations at NNLO, using jets with $R=0.4$ (left) and 0.8 (right). Shown are the ratios of the measured cross sections (markers) to the predictions obtained using the CT18 NNLO PDF set. The error bars and shaded yellow regions indicate the statistical and the total experimental uncertainties of the data, respectively, and the hatched teal band indicates the sum in quadrature of the PDF, NP, and scale uncertainties. Alternative theoretical predictions obtained using other global PDF sets are shown as colored lines. Similar plots for the individual rapidity regions can be found in Appendix B

Fig. 10

Comparison of the 3D dijet cross section for jets with $R=0.4$ (left) and 0.8 (right) as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ to fixed-order theoretical calculations at NNLO, shown here for three out of the total of 15 rapidity regions. The data points and predictions for alternative PDFs are analogous to those in Fig. 9. In addition, the separate contributions to the theory uncertainty due to the CT18 PDFs, NP corrections, and six-point scale variations are shown explicitly. Similar plots for all rapidity regions and observables can be found in Appendix  B

Fig. 11

Parton distributions obtained in a fit to HERA DIS data together with the CMS 2D or 3D dijet measurements. The top panels show the PDFs of the up and down valence quarks (upper row), of the gluon (lower left), and of the total sea quarks (lower right) as a function of the fractional parton momentum x at a factorization scale equal to the top quark mass. The middle (lower) panels show the relative uncertainty contributions obtained for the 2D (3D) fit, as well as the ratios of the fitted central values

Fig. 12

Parton distributions obtained in a fit to HERA DIS data together with the CMS dijet data, compared to a fit to HERA DIS data alone. Shown are the PDFs of the up and down valence quarks (upper row), of the gluon (lower left), and of the total sea quarks (lower right) as a function of the fractional parton momentum x at a factorization scale equal to the top quark mass. The bands indicate the fit uncertainty and are shown in the lower panels as a relative uncertainty with respect to the corresponding central values. The lines in the lower panels show the ratios between the fitted central values

Fig. 13

Response matrices for the 2D measurements as a function of ${|y|}_{\max }$ and $m_{1,2}$ for jets with $R=0.4$. The details correspond to those of Fig. 2

Fig. 14

Partial response matrices for the 3D measurements as a function of $m_{1,2}$ using jets with $R=0.4$ (upper) and 0.8 (lower), shown here for the five rapidity regions with $y_{\mathrm{b}}<0.5$. The details correspond to those of Fig. 2

Fig. 15

Partial response matrices for the 3D measurements as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ using jets with $R=0.4$ (upper) and 0.8 (lower), shown here for the five rapidity regions with $y_{\mathrm{b}}<0.5$. The details correspond to those of Fig. 2

Fig. 16

Overview of the 2D dijet cross section as a function of $m_{1,2}$ in all 5 ${|y|}_{\max }$ regions, using jets with $R=0.4$. The details correspond to those of Fig. 8

Fig. 17

Overview of the 3D dijet cross section as a function of $m_{1,2}$ in all 15 $(y^{\ast },y_{\mathrm{b}})$ regions, using jets with $R=0.4$ (left) and 0.8 (right). The details correspond to those of Fig. 8

Fig. 18

Overview of the 3D dijet cross section as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ in all 15 $(y^{\ast },y_{\mathrm{b}})$ regions, using jets with $R=0.8$. The details correspond to those of Fig. 8

Fig. 19

Breakdown of the experimental uncertainty for the 3D measurements as a function of $m_{1,2}$ using jets with $R=0.4$ (left) and 0.8 (right), in six out of 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 4

Fig. 20

(continuation of Fig. 19) Breakdown of the experimental uncertainty for the 3D measurements as a function of $m_{1,2}$ using jets with $R=0.4$ (left) and 0.8 (right), in the remaining nine out of 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 4

Fig. 21

Breakdown of the experimental uncertainty for the 3D measurements as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ using jets with $R=0.8$, in six out of 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 4

Fig. 22

(continuation of Fig. 21) Breakdown of the experimental uncertainty for the 3D measurements as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ using jets with $R=0.8$, in the remaining nine out of 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 4

Fig. 23

Comparison of the 2D dijet cross section for jets with $R=0.4$ (left) and 0.8 (right) as a function of $m_{1,2}$ to fixed-order theoretical calculations at NNLO, shown here for three inner ${|y|}_{\max }$ regions. The details correspond to those of Fig. 9

Fig. 24

(continuation of Fig. 23) Comparison of the 2D dijet cross section for jets with $R=0.4$ (left) and 0.8 (right) as a function of $m_{1,2}$ to fixed-order theoretical calculations at NNLO, shown here for two outermost ${|y|}_{\max }$ regions. The details correspond to those of Fig. 9

Fig. 25

Comparison of the 3D dijet cross section as a function of $m_{1,2}$ to fixed-order theoretical calculations at NNLO, using jets with $R=0.4$ (left) and 0.8 (right), in six out of the total 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 10

Fig. 26

(continuation of Fig. 25) Comparison of the 3D dijet cross section as a function of $m_{1,2}$ to fixed-order theoretical calculations at NNLO, using jets with $R=0.4$ (left) and 0.8 (right), in the remaining nine out of 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 10

Fig. 27

Comparison of the 3D dijet cross section as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ to fixed-order theoretical calculations at NNLO, using jets with $R=0.4$ (left) and 0.8 (right), in six out of the total 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 10

Fig. 28

(continuation of Fig. 27) Comparison of the 3D dijet cross section as a function of ${⟨p_{\text{T}}⟩}_{1,2}$ to fixed-order theoretical calculations at NNLO, using jets with $R=0.4$ (left) and 0.8 (right), in the remaining nine out of 15 $(y^{\ast },y_{\mathrm{b}})$ bins. The details correspond to those of Fig. 10