CMS-SMP-22-012

CMS-SMP-22-012 ; CERN-EP-2024-253
Search for rare decays of the Z and Higgs bosons to a $\mathrm{J}/\psi$ or $\psi(2\text{S})$ meson and a photon in proton-proton collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
22 November 2024
Phys. Lett. B 865 (2025) 139462
Abstract: A search is presented for rare decays of the Z and Higgs bosons to a photon and a $\mathrm{J}/\psi$ or a $\psi(2\text{S})$ meson, with the charmonium state subsequentially decaying to a pair of muons. The data set corresponds to an integrated luminosity of 123 fb $^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the LHC. No evidence for branching fractions of these rare decay channels larger than predicted in the standard model is observed. Upper limits at 95% confidence level are set: $\mathcal{B}(\mathrm{H}\to\mathrm{J}/\psi\gamma) <$ 2.6 $\times$ 10 $^{-4}$ , $\mathcal{B}(\mathrm{H}\to\psi(2\text{S})\gamma) <$ 9.9 $\times$ 10 $^{-4}$ , $\mathcal{B}(\mathrm{Z}\to\mathrm{J}/\psi\gamma) <$ 0.6 $\times$ 10 $^{-6}$ , and $\mathcal{B}(\mathrm{Z}\to\psi(2\text{S})\gamma) <$ 1.3 $\times$ 10 $^{-6}$ . The ratio of the Higgs boson coupling modifiers $\kappa_{\mathrm{c}}/\kappa_{\gamma}$ is constrained to be in the interval ( $-$ 157, $+$ 199) at 95% confidence level. Assuming $\kappa_{\gamma}=$ 1, this interval becomes ( $-$ 166, $+$ 208).
Links: e-print arXiv:2411.15000 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Leading-order Feynman diagrams of Z and Higgs boson rare decays to $\mathrm{J}/\psi$ or $\psi(2\text{S})$ , and a photon, through the direct (upper left) and indirect (upper right, lower left, and lower right) processes. These four diagrams are considered as the signal of this analysis.
png pdf	Figure 1-a: Leading-order Feynman diagrams of Z and Higgs boson rare decays to $\mathrm{J}/\psi$ or $\psi(2\text{S})$ , and a photon, through the direct (upper left) and indirect (upper right, lower left, and lower right) processes. These four diagrams are considered as the signal of this analysis.
png pdf	Figure 1-b: Leading-order Feynman diagrams of Z and Higgs boson rare decays to $\mathrm{J}/\psi$ or $\psi(2\text{S})$ , and a photon, through the direct (upper left) and indirect (upper right, lower left, and lower right) processes. These four diagrams are considered as the signal of this analysis.
png pdf	Figure 1-c: Leading-order Feynman diagrams of Z and Higgs boson rare decays to $\mathrm{J}/\psi$ or $\psi(2\text{S})$ , and a photon, through the direct (upper left) and indirect (upper right, lower left, and lower right) processes. These four diagrams are considered as the signal of this analysis.
png pdf	Figure 1-d: Leading-order Feynman diagrams of Z and Higgs boson rare decays to $\mathrm{J}/\psi$ or $\psi(2\text{S})$ , and a photon, through the direct (upper left) and indirect (upper right, lower left, and lower right) processes. These four diagrams are considered as the signal of this analysis.
png pdf	Figure 2: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-HP category. Upper right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-LP category. Lower left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ VBF category. Lower right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ HF category.
png pdf	Figure 2-a: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-HP category. Upper right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-LP category. Lower left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ VBF category. Lower right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ HF category.
png pdf	Figure 2-b: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-HP category. Upper right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-LP category. Lower left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ VBF category. Lower right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ HF category.
png pdf	Figure 2-c: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-HP category. Upper right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-LP category. Lower left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ VBF category. Lower right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ HF category.
png pdf	Figure 2-d: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-HP category. Upper right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ ggF-LP category. Lower left: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ VBF category. Lower right: $\mathrm{H}\to\mathrm{J}/\psi\gamma$ HF category.
png pdf	Figure 3: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ HP category. Upper right: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ LP category. Lower left: $\mathrm{H}\to\psi(2\text{S})\gamma$ category. Lower right: $\mathrm{Z}\to\psi(2\text{S})\gamma$ category.
png pdf	Figure 3-a: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ HP category. Upper right: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ LP category. Lower left: $\mathrm{H}\to\psi(2\text{S})\gamma$ category. Lower right: $\mathrm{Z}\to\psi(2\text{S})\gamma$ category.
png pdf	Figure 3-b: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ HP category. Upper right: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ LP category. Lower left: $\mathrm{H}\to\psi(2\text{S})\gamma$ category. Lower right: $\mathrm{Z}\to\psi(2\text{S})\gamma$ category.
png pdf	Figure 3-c: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ HP category. Upper right: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ LP category. Lower left: $\mathrm{H}\to\psi(2\text{S})\gamma$ category. Lower right: $\mathrm{Z}\to\psi(2\text{S})\gamma$ category.
png pdf	Figure 3-d: The upper panels show the background-only fit using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The resonant background contributions are added with the normalization fixed to the SM expectation. The vertical error bars on the data points show the statistical uncertainty. The bottom panels show the pulls for the fit result for the model with lowest $\chi^2$ . Upper left: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ HP category. Upper right: $\mathrm{Z}\to\mathrm{J}/\psi\gamma$ LP category. Lower left: $\mathrm{H}\to\psi(2\text{S})\gamma$ category. Lower right: $\mathrm{Z}\to\psi(2\text{S})\gamma$ category.
png pdf	Figure 4: The upper panel shows the results of the main background fit in the CR, using the power-law, exponential, and Bernstein polynomial functions with the optimal number of parameters determined with the F-test, and ranked according to the fit $\chi^2$ . The vertical error bars on the data points show the statistical uncertainty. The bottom panel shows the pulls for the fit result for the model with lowest $\chi^2$ .
png pdf	Figure 5: Observed and expected (with ${\pm}$ 1, ${\pm}$ 2 standard deviation bands) exclusion limits on the branching fraction of the $(\mathrm{H},\mathrm{Z}) \to \psi(n\text{S})\gamma$ decays.

Tables
png pdf	Table 1: The SM predictions of the branching fractions of the Higgs and Z boson decays to $\psi(n\text{S})\gamma$ used in this analysis, and measured branching fractions for the $\psi(n\text{S})\to\mu\mu$ decays.
png pdf	Table 2: Summary of the selections of the eight signal regions (SRs) and the control region (CR). The SR1 category require a $m_{\mu\mu}$ value compatible with the $\mathrm{J}/\psi$ mass hypothesis, and is further slotted depending on the value of the LD variable (Z-HP, Z-LP), the Higgs boson production mode (ggF, VBF, HF), and the value of the $\cos\theta^*$ variable (ggF-HP, ggF-LP). The SR2 category requires a $m_{\mu\mu}$ value compatible with the $\psi(2\text{S})$ mass hypothesis and is not further categorized. The CR category is made orthogonal to the SRs by vetoing $m_{\mu\mu}$ values compatible with the $\psi(n\text{S})$ mass hypotheses.
png pdf	Table 3: Sources and types of systematic uncertainties described in Section 6. Normalization (norm.) uncertainties yield a variation in the number of events equal to the reported value. Other uncertainties also vary the shape of the mean and the width of the resonant background and signal $m_{\mu\mu\gamma}$ distributions by the indicated amount. Uncertainties in the same line are treated as correlated.
png pdf	Table 4: Observed (expected) upper limits at 95% CL on the normalized values with respect to the SM expectation, denoted as the signal strength parameter $\mu$ , of the product of the cross section $\sigma$ and the branching fraction $\mathcal{B}$ of the $(\mathrm{H},\mathrm{Z}) \to \psi(n\text{S})\gamma$ decays, and the branching fraction, assuming a SM Z and H boson cross section. The results are compared with previous ones [22,24].

Summary

A search for rare decays of the Z and H bosons to a photon and a

$\psi(n\text{S})$ meson decaying to a pair of muons is presented. The data were collected by the CMS experiment in proton-proton collisions at

$\sqrt{s}=$ 13 TeV during 2016--2018 and correspond to an integrated luminosity of 123 fb

$^{-1}$ . No statistically significant excess has been observed over the standard model expectations. Upper limits at 95% confidence level are set on the branching fractions: 0.6

$\times$ 10

$^{-6}$ and 1.3

$\times$ 10

$^{-6}$ for the

$\mathrm{Z}\to\mathrm{J}/\psi\gamma$ and

$\mathrm{Z}\to\psi(2\text{S})\gamma$ decays, respectively, and 2.6

$\times$ 10

$^{-4}$ and 9.9

$\times$ 10

$^{-4}$ for the

$\mathrm{H}\to\mathrm{J}/\psi\gamma$ and

$\mathrm{H}\to\psi(2\text{S})\gamma$ decays, respectively. The limit for

$\mathrm{H}\to\mathrm{J}/\psi\gamma$ translates to an interval constraint on the

$\kappa_{\mathrm{c}}/\kappa_{\gamma}$ ratio of the Higgs boson coupling modifiers of

$(-157,\, +199)$ . If the standard model value of

$\kappa_{\gamma}=$ 1 is assumed, the observed interval becomes

$(-166,\, +208)$ .

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