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| CMS-EXO-24-011 ; CERN-EP-2026-057 | ||
| Measurement of dijet angular distributions and search for beyond the standard model physics in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 26 March 2026 | ||
| Submitted to Physics Letters B | ||
| Abstract: A measurement is presented of dijet angular distributions in proton-proton collisions at $ \sqrt{s} = $ 13 TeV, using data collected with the CMS detector at the CERN LHC and corresponding to an integrated luminosity of 138 fb$ ^{-1} $. For the first time, the dijet angular distributions, corrected for detector effects, are compared with the predictions of perturbative quantum chromodynamics at next-to-next-to-leading order, including next-to-leading-order electroweak corrections. While data are generally found to be in agreement with predictions, a small difference in shape of the normalized distributions is seen for dijet masses ranging from 2.4 to 4.8 TeV and above 6 TeV. The distributions are used to search for proposed signatures of quark compositeness, extra spatial dimensions, quantum black holes, dark-matter mediators, axion-like particles, and anomalous gluon couplings. The most stringent limits to date are set for most of these scenarios. Quark contact interactions are excluded at 95% confidence level (CL) up to a scale of 17 (37) TeV for destructive (constructive) interference in a benchmark scenario, valid to next-to-leading order in quantum chromodynamics, and in which only left-handed quarks participate. The coupling of axion-like particles to the gluon, $ c_{\text{g}}/f_{\text{a}} $, is constrained to be lower than 0.42$ \text{TeV}^{-1} $ at 95% CL. The anomalous triple-gluon coupling, $ C_{\text{G}}/\Lambda^2 $, in a standard model effective field theory is constrained to be lower than 0.0076$ \text{TeV}^{-2} $ at 95% CL. | ||
| Links: e-print arXiv:2603.25458 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-a:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-b:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-c:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-d:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-e:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-f:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 1-g:
Example diagrams of dijet production processes in QCD and BSM physics. Upper row: $ t $-channel quark-gluon scattering in QCD (left), quark-quark scattering via a BSM contact interaction (center left), quark pair production through an $ s $-channel BSM resonance (center right), and quark pair production through gravitons in models with extra spatial dimensions (right). Lower row: quark pair production through a quantum black hole (left), gluon pair production through an axion-like particle (center), and gluon pair production with a dimension-6 effective field theory anomalous gluon coupling operator (right). A description of the symbols in the diagrams is given in Section 5. |
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Figure 2:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins up to 4.8 TeV. The data distributions at the detector level (points) are compared to NNLO predictions, corrected for the detector response (black dotted lines). The vertical bars on the points represent statistical and experimental systematic uncertainties combined in quadrature. The horizontal bars show the bin widths. Theoretical uncertainties are indicated with the blue bands. The prediction from various BSM scenarios, with parameter values given in the legend, are shown by the different dot-dashed lines. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 2-a:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins up to 4.8 TeV. The data distributions at the detector level (points) are compared to NNLO predictions, corrected for the detector response (black dotted lines). The vertical bars on the points represent statistical and experimental systematic uncertainties combined in quadrature. The horizontal bars show the bin widths. Theoretical uncertainties are indicated with the blue bands. The prediction from various BSM scenarios, with parameter values given in the legend, are shown by the different dot-dashed lines. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 2-b:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins up to 4.8 TeV. The data distributions at the detector level (points) are compared to NNLO predictions, corrected for the detector response (black dotted lines). The vertical bars on the points represent statistical and experimental systematic uncertainties combined in quadrature. The horizontal bars show the bin widths. Theoretical uncertainties are indicated with the blue bands. The prediction from various BSM scenarios, with parameter values given in the legend, are shown by the different dot-dashed lines. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 2-c:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins up to 4.8 TeV. The data distributions at the detector level (points) are compared to NNLO predictions, corrected for the detector response (black dotted lines). The vertical bars on the points represent statistical and experimental systematic uncertainties combined in quadrature. The horizontal bars show the bin widths. Theoretical uncertainties are indicated with the blue bands. The prediction from various BSM scenarios, with parameter values given in the legend, are shown by the different dot-dashed lines. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 2-d:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins up to 4.8 TeV. The data distributions at the detector level (points) are compared to NNLO predictions, corrected for the detector response (black dotted lines). The vertical bars on the points represent statistical and experimental systematic uncertainties combined in quadrature. The horizontal bars show the bin widths. Theoretical uncertainties are indicated with the blue bands. The prediction from various BSM scenarios, with parameter values given in the legend, are shown by the different dot-dashed lines. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 3:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins above 4.8 TeV. Notations as in Fig. 2. |
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Figure 3-a:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins above 4.8 TeV. Notations as in Fig. 2. |
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Figure 3-b:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins above 4.8 TeV. Notations as in Fig. 2. |
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Figure 3-c:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins above 4.8 TeV. Notations as in Fig. 2. |
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Figure 3-d:
Normalized $ \chi_{\text{dijet}} $ distributions for the $ M_{\mathrm{jj}} $ bins above 4.8 TeV. Notations as in Fig. 2. |
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Figure 4:
The 95% CL upper limits on the universal quark coupling $ g_{\text{q}} $ as functions of a vector or axial-vector mediator mass, with $ g_{\text{DM}}= $ 1.0 and $ m_{\text{DM}}= $ 1 GeV. The observed (solid line) and expected (dashed line) limits and their 68% and 95% confidence intervals (shaded bands) are shown. A dashed horizontal line shows the coupling strength for a benchmark DM mediator with $ g_{\text{q}}= $ 1. Results are compared to the previous searches using dijet angular [23] (blue dotted line) and dijet mass [21] (red dotted line) distributions. The vertical scale on the right axis gives the corresponding values of $ \Gamma/m_{\text{med}} $. |
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Figure 5:
The 95% CL upper limits on the ALP gluon coupling (left) in linear EFT, $ c_\text{g} $, as functions of the characteristic energy scale, $ f_\text{a} $, assuming $ m_\text{a}= $ 1 MeV. Only $ \chi_{\text{dijet}} $ distributions with $ M_{\mathrm{jj}} < f_\text{a} $ are used to obtain the limits on $ c_\text{g} $. The 95% CL upper limits on the anomalous triple-gluon coupling (right), $ C_\text{G} $, in SMEFT as functions of the BSM physics energy scale, $ \Lambda $. Only $ \chi_{\text{dijet}} $ distributions with $ M_{\mathrm{jj}} < \Lambda $ are used to obtain the limits on $ C_\text{G} $. The observed limits (solid lines), expected limits (dashed lines), and their 68% and 95% confidence intervals (shaded bands) are shown. |
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Figure 5-a:
The 95% CL upper limits on the ALP gluon coupling (left) in linear EFT, $ c_\text{g} $, as functions of the characteristic energy scale, $ f_\text{a} $, assuming $ m_\text{a}= $ 1 MeV. Only $ \chi_{\text{dijet}} $ distributions with $ M_{\mathrm{jj}} < f_\text{a} $ are used to obtain the limits on $ c_\text{g} $. The 95% CL upper limits on the anomalous triple-gluon coupling (right), $ C_\text{G} $, in SMEFT as functions of the BSM physics energy scale, $ \Lambda $. Only $ \chi_{\text{dijet}} $ distributions with $ M_{\mathrm{jj}} < \Lambda $ are used to obtain the limits on $ C_\text{G} $. The observed limits (solid lines), expected limits (dashed lines), and their 68% and 95% confidence intervals (shaded bands) are shown. |
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Figure 5-b:
The 95% CL upper limits on the ALP gluon coupling (left) in linear EFT, $ c_\text{g} $, as functions of the characteristic energy scale, $ f_\text{a} $, assuming $ m_\text{a}= $ 1 MeV. Only $ \chi_{\text{dijet}} $ distributions with $ M_{\mathrm{jj}} < f_\text{a} $ are used to obtain the limits on $ c_\text{g} $. The 95% CL upper limits on the anomalous triple-gluon coupling (right), $ C_\text{G} $, in SMEFT as functions of the BSM physics energy scale, $ \Lambda $. Only $ \chi_{\text{dijet}} $ distributions with $ M_{\mathrm{jj}} < \Lambda $ are used to obtain the limits on $ C_\text{G} $. The observed limits (solid lines), expected limits (dashed lines), and their 68% and 95% confidence intervals (shaded bands) are shown. |
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Figure 6:
Normalized $ \chi_{\text{dijet}} $ distributions from data (points) corrected for detector effects for four different ranges of $ M_{\mathrm{jj}} $. The inner vertical bars on the points correspond to the systematic uncertainties in the data, and the outer ones to the total uncertainties. The horizontal bars give the bin widths. Theoretical NNLO QCD + NLO EW predictions are shown for central scale choices $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ (black dotted line) and $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = \langle p_{\mathrm{T}} \rangle $ (blue dashed line), both using the NNPDF3.1 PDF set. Prediction using the alternative CT14 PDF set (purple long-dashed-dotted line), and the NLO predictions from a previous CMS publication [22] (red short-dashed-dotted lines) are also plotted. Theoretical uncertainties with the central scale $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ and using NNPDF3.1 are indicated with the gray bands. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 6-a:
Normalized $ \chi_{\text{dijet}} $ distributions from data (points) corrected for detector effects for four different ranges of $ M_{\mathrm{jj}} $. The inner vertical bars on the points correspond to the systematic uncertainties in the data, and the outer ones to the total uncertainties. The horizontal bars give the bin widths. Theoretical NNLO QCD + NLO EW predictions are shown for central scale choices $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ (black dotted line) and $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = \langle p_{\mathrm{T}} \rangle $ (blue dashed line), both using the NNPDF3.1 PDF set. Prediction using the alternative CT14 PDF set (purple long-dashed-dotted line), and the NLO predictions from a previous CMS publication [22] (red short-dashed-dotted lines) are also plotted. Theoretical uncertainties with the central scale $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ and using NNPDF3.1 are indicated with the gray bands. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
png pdf |
Figure 6-b:
Normalized $ \chi_{\text{dijet}} $ distributions from data (points) corrected for detector effects for four different ranges of $ M_{\mathrm{jj}} $. The inner vertical bars on the points correspond to the systematic uncertainties in the data, and the outer ones to the total uncertainties. The horizontal bars give the bin widths. Theoretical NNLO QCD + NLO EW predictions are shown for central scale choices $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ (black dotted line) and $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = \langle p_{\mathrm{T}} \rangle $ (blue dashed line), both using the NNPDF3.1 PDF set. Prediction using the alternative CT14 PDF set (purple long-dashed-dotted line), and the NLO predictions from a previous CMS publication [22] (red short-dashed-dotted lines) are also plotted. Theoretical uncertainties with the central scale $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ and using NNPDF3.1 are indicated with the gray bands. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
png pdf |
Figure 6-c:
Normalized $ \chi_{\text{dijet}} $ distributions from data (points) corrected for detector effects for four different ranges of $ M_{\mathrm{jj}} $. The inner vertical bars on the points correspond to the systematic uncertainties in the data, and the outer ones to the total uncertainties. The horizontal bars give the bin widths. Theoretical NNLO QCD + NLO EW predictions are shown for central scale choices $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ (black dotted line) and $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = \langle p_{\mathrm{T}} \rangle $ (blue dashed line), both using the NNPDF3.1 PDF set. Prediction using the alternative CT14 PDF set (purple long-dashed-dotted line), and the NLO predictions from a previous CMS publication [22] (red short-dashed-dotted lines) are also plotted. Theoretical uncertainties with the central scale $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ and using NNPDF3.1 are indicated with the gray bands. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
png pdf |
Figure 6-d:
Normalized $ \chi_{\text{dijet}} $ distributions from data (points) corrected for detector effects for four different ranges of $ M_{\mathrm{jj}} $. The inner vertical bars on the points correspond to the systematic uncertainties in the data, and the outer ones to the total uncertainties. The horizontal bars give the bin widths. Theoretical NNLO QCD + NLO EW predictions are shown for central scale choices $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ (black dotted line) and $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = \langle p_{\mathrm{T}} \rangle $ (blue dashed line), both using the NNPDF3.1 PDF set. Prediction using the alternative CT14 PDF set (purple long-dashed-dotted line), and the NLO predictions from a previous CMS publication [22] (red short-dashed-dotted lines) are also plotted. Theoretical uncertainties with the central scale $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ and using NNPDF3.1 are indicated with the gray bands. The lower plots display the ratio of the data to the NNLO QCD + NLO EW predictions. |
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Figure 7:
Normalized $ \chi_{\text{dijet}} $ distributions corrected for detector effects for three different ranges of $ M_{\mathrm{jj}} $. Notations as in Fig. 6. |
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Figure 7-a:
Normalized $ \chi_{\text{dijet}} $ distributions corrected for detector effects for three different ranges of $ M_{\mathrm{jj}} $. Notations as in Fig. 6. |
png pdf |
Figure 7-b:
Normalized $ \chi_{\text{dijet}} $ distributions corrected for detector effects for three different ranges of $ M_{\mathrm{jj}} $. Notations as in Fig. 6. |
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Figure 7-c:
Normalized $ \chi_{\text{dijet}} $ distributions corrected for detector effects for three different ranges of $ M_{\mathrm{jj}} $. Notations as in Fig. 6. |
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Figure 8:
The correlation matrix of the maximum likelihood estimators of the signal strength modifiers. The matrix is obtained after the fit to data. The bin numbers correspond to 11 times the index (starting at 0) of the $ M_{\mathrm{jj}} $ bin (3.0, 3.6, 4.2, 4.8, 5.4, 6.0, 7.0) GeV plus the index (starting at 0) of the $ \chi_{\text{dijet}} $ bin (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14). |
| Tables | |
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Table 1:
Observed number of events, $ N_{\text{dijet}} $, after selection in each $ M_{\text{jj}} $ bin. |
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Table 2:
Summary of the leading theoretical uncertainties in the normalized $ \chi_{\text{dijet}} $ distributions. The full analysis takes into account correlations between $ \chi_{\text{dijet}} $ bins; however, this table shows the contributions in the lowest $ \chi_{\text{dijet}} $ bin for two representative $ M_{\text{jj}} $ bins. This illustrates the magnitude of the contributions for these $ M_{\text{jj}} $ bins. |
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Table 3:
The different combinations of $ (\eta_{\text{LL}}, \eta_{\text{RR}}, \eta_{\text{RL}}) $ used in the search for CIs between quarks and the corresponding mass scale name. |
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Table 4:
Leading experimental uncertainties in the normalized $ \chi_{\text{dijet}} $ distributions. The uncertainties in the lowest $ \chi_{\text{dijet}} $ bin for two $ M_{\text{jj}} $ bins are shown as representative examples. |
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Table 5:
Observed and expected exclusion limits at 95% CL for various BSM models. The $ \pm $ 1 standard deviation values for the expected limits are quoted, as shown in the last column. |
| Summary |
| Normalized dijet angular distributions have been measured with the CMS detector over a wide range of dijet invariant masses, using proton-proton collisions at the LHC, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. For the first time, the dijet angular distributions corrected for detector effects have been compared with predictions of perturbative quantum chromodynamics at next-to-next-to-leading order. Predictions assuming two different choices for the factorization and renormalization scales, $ \mu_{\mathrm{F}} = \mu_{\mathrm{R}} = M_{\mathrm{jj}} $ or $ \langle p_{\mathrm{T}} \rangle $, are found to differ by more than the six variations of scales commonly used to quantify the uncertainty in the predictions. While data are generally found to be in agreement with the standard model predictions, a small difference in the shape of the normalized distributions is seen for dijet masses below 4.8 TeV and above 6.0 TeV. The distributions are used to set lower limits on beyond the standard model theories, including quark contact interaction models with next-to-leading-order quantum chromodynamic corrections, extra dimension models, quantum black hole production, dark-matter mediators, axion-like particles, and standard model effective field theory. The most stringent lower limits to date are set on the scale of graviton exchange. In the Giudice--Rattazzi--Wells convention, virtual graviton exchange is excluded up to a scale of 13.4 TeV at 95% confidence level (CL). The production of quantum black holes is excluded for masses below 8.5 and 6.3 TeV at 95% CL, depending on the scenario. Limits for different contact interaction models are obtained. In the benchmark scenario, valid to next-to-leading order in quantum chromodynamics and in which only left-handed quarks participate, quark contact interactions are excluded to a scale of 17 (37) TeV at 95% CL for destructive (constructive) interference. Mediators in a simplified model of interactions between quarks and dark matter with masses between 4 and 6.2 TeV are excluded at 95% CL for vector and axial-vector mediators. The ratio of the gluon operator coefficient $ c_{\text{g}} $ to the characteristic high-energy scale $ f_{\text{a}} $, $ c_{\text{g}}/f_{\text{a}} $, is determined to have a 95% CL upper limit of 0.42 $ \text{TeV}^{-1} $. The anomalous triple-gluon coupling, $ C_{\text{G}}/\Lambda^2 $, in a standard model effective field theory is constrained to be lower than 0.0076 $ \text{TeV}^{-2} $ at 95% CL. |
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