CMS-PAS-TOP-24-012

CMS-PAS-TOP-24-012
Search for $CP$ violation in events with top quarks and Z bosons
CMS Collaboration
28 March 2025

Abstract: A search for the violation of the charge-parity ( $CP$ ) symmetry in the production of top quarks in association with Z bosons is presented, using events with three charged leptons and additional jets. For the first time in this final state, observables that are odd under the $CP$ transformation are employed. Also for the first time, physics-informed machine learning techniques are used to construct these observables. While standard model (SM) processes are predicted to be symmetrically distributed around zero on these observables, $CP$ -violating modifications of the SM would introduce asymmetries. Two $CP$ -odd operators $c_{\mathrm{tW}}^{\mathrm{I}}$ and $c_{\mathrm{tZ}}^{\mathrm{I}}$ in the SM effective field theory are considered that may modify the interactions between top quarks and electroweak bosons. The search is performed in a sample of proton-proton collision data collected by the CMS experiment at the CERN LHC in 2016-2018 at a center-of-mass energy of 13 TeV and in 2022 at 13.6 TeV, corresponding to a total integrated luminosity of 175 fb $^{-1}$ . The obtained results are consistent with the SM prediction within two standard deviations, and exclusion limits of $-$ 2.7 $< c_{\mathrm{tW}}^{\mathrm{I}} <$ 2.5 and $-$ 0.2 $< c_{\mathrm{tZ}}^{\mathrm{I}} <$ 2.0 are set at 95% confidence level.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Example Feynman diagrams for $\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ (left) and $\mathrm{t}\mathrm{Z}\mathrm{q}$ (right) production with vertices that can be modified by $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ ( $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ ) highlighted in red (blue) color.
png pdf	Figure 1-a: Example Feynman diagrams for $\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ (left) and $\mathrm{t}\mathrm{Z}\mathrm{q}$ (right) production with vertices that can be modified by $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ ( $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ ) highlighted in red (blue) color.
png pdf	Figure 1-b: Example Feynman diagrams for $\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ (left) and $\mathrm{t}\mathrm{Z}\mathrm{q}$ (right) production with vertices that can be modified by $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ ( $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ ) highlighted in red (blue) color.
png pdf	Figure 2: Left (right): Distribution of $g_{c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}}$ ( $g_{c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}}$ ) for events in the $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ -like ( $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like) category in $\mathrm{t}\mathrm{Z}\mathrm{q}$ ( $\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ ) events. The contributions from the SM, linear, and quadratic contributions when each Wilson coefficient is set to one are plotted separately. For better visibility the interference contribution in the $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like category has been scaled by 4.
png pdf	Figure 2-a: Left (right): Distribution of $g_{c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}}$ ( $g_{c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}}$ ) for events in the $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ -like ( $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like) category in $\mathrm{t}\mathrm{Z}\mathrm{q}$ ( $\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ ) events. The contributions from the SM, linear, and quadratic contributions when each Wilson coefficient is set to one are plotted separately. For better visibility the interference contribution in the $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like category has been scaled by 4.
png pdf	Figure 2-b: Left (right): Distribution of $g_{c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}}$ ( $g_{c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}}$ ) for events in the $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ -like ( $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like) category in $\mathrm{t}\mathrm{Z}\mathrm{q}$ ( $\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ ) events. The contributions from the SM, linear, and quadratic contributions when each Wilson coefficient is set to one are plotted separately. For better visibility the interference contribution in the $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like category has been scaled by 4.
png pdf	Figure 3: Left (right): Distribution of $g_{c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}}$ ( $g_{c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}}$ ) for events in the $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ -like ( $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like) category, compared to the prediction obtained when all fit parameters are set to their maximum likelihood value in the linear fit. The ratio panels show the ratio between data (black dots), the prediction of the linear (blue line), and quadratic (green line) fits, over the prefit value. The red, blue, and green bands show the prefit uncertainty and the postfit uncertainties of the linear and quadratic fits, respectively.
png pdf	Figure 3-a: Left (right): Distribution of $g_{c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}}$ ( $g_{c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}}$ ) for events in the $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ -like ( $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like) category, compared to the prediction obtained when all fit parameters are set to their maximum likelihood value in the linear fit. The ratio panels show the ratio between data (black dots), the prediction of the linear (blue line), and quadratic (green line) fits, over the prefit value. The red, blue, and green bands show the prefit uncertainty and the postfit uncertainties of the linear and quadratic fits, respectively.
png pdf	Figure 3-b: Left (right): Distribution of $g_{c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}}$ ( $g_{c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}}$ ) for events in the $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ -like ( $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ -like) category, compared to the prediction obtained when all fit parameters are set to their maximum likelihood value in the linear fit. The ratio panels show the ratio between data (black dots), the prediction of the linear (blue line), and quadratic (green line) fits, over the prefit value. The red, blue, and green bands show the prefit uncertainty and the postfit uncertainties of the linear and quadratic fits, respectively.
png pdf	Figure 4: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ (upper row) and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ (lower row), separately for cases in which the other coefficient is set to zero (black solid line) or profiled (red dashed line). Plots in the left (right) column represent the linear (quadratic) fit. Gray lines represent the quantiles of the test statistics.
png pdf	Figure 4-a: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ (upper row) and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ (lower row), separately for cases in which the other coefficient is set to zero (black solid line) or profiled (red dashed line). Plots in the left (right) column represent the linear (quadratic) fit. Gray lines represent the quantiles of the test statistics.
png pdf	Figure 4-b: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ (upper row) and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ (lower row), separately for cases in which the other coefficient is set to zero (black solid line) or profiled (red dashed line). Plots in the left (right) column represent the linear (quadratic) fit. Gray lines represent the quantiles of the test statistics.
png pdf	Figure 4-c: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ (upper row) and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ (lower row), separately for cases in which the other coefficient is set to zero (black solid line) or profiled (red dashed line). Plots in the left (right) column represent the linear (quadratic) fit. Gray lines represent the quantiles of the test statistics.
png pdf	Figure 4-d: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ (upper row) and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ (lower row), separately for cases in which the other coefficient is set to zero (black solid line) or profiled (red dashed line). Plots in the left (right) column represent the linear (quadratic) fit. Gray lines represent the quantiles of the test statistics.
png pdf	Figure 5: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ , including linear contributions only (left) and both linear and quadratic contributions (right).
png pdf	Figure 5-a: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ , including linear contributions only (left) and both linear and quadratic contributions (right).
png pdf	Figure 5-b: Likelihood scans as a function of $c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ and $c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ , including linear contributions only (left) and both linear and quadratic contributions (right).

Tables
png pdf	Table 1: Input variables used for the $CP$ -equivariant neural networks, with the $CP$ -transformed value given in the second row.

Summary

We have presented a search for additional sources of the charge-parity (

$CP$ ) symmetry violation in the associated production of top quarks and a Z boson, in particular, on

$\mathrm{t}\overline{\mathrm{t}}\mathrm{Z}$ and

$\mathrm{t}\mathrm{Z}\mathrm{q}$ production in final states with three leptons. The measurement uses, for the first time in this topology,

$CP$ -odd observables which we have constructed using physics-informed machine learning techniques. These observables are predicted by the SM to be symmetrically distributed while asymmetries could arise from

$CP$ violating effects. The results are generally consistent with the SM prediction, and allow us to set limits on the

$c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}}$ and

$c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}}$ operators of

$-$ 2.7

$< c_{\mathrm{t}\mathrm{W}}^{\mathrm{I}} <$ 2.5 and

$-$ 0.2

$< c_{\mathrm{t}\mathrm{Z}}^{\mathrm{I}} <$ 2.0 at 95% confidence level.

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