Measurements of the pp$\to$ZZ production cross section and the Z$\to 4\ell$ branching fraction, and constraints on anomalous triple gauge couplings at $\sqrt{s} =$ 13 TeV

TL;DR

This CMS study measures ZZ production and Z→4ℓ decays at √s = 13 TeV using 35.9 fb^-1, reporting fiducial and total cross sections that agree with SM predictions, and providing unfolded differential distributions to probe kinematic properties of ZZ events. It also constrains anomalous ZZZ and ZZγ triple gauge couplings via the four-lepton mass spectrum, obtaining the most stringent limits to date without invoking form factors. The results reinforce the SM description of electroweak gauge interactions and offer high-precision benchmarks for NNLO/NLO QCD calculations, while delivering robust cross-checks of lepton reconstruction, background estimation, and unfolding methodologies in a high-luminosity LHC environment.

Abstract

Four-lepton production in proton-proton collisions, $\mathrm{pp}\to (\mathrm{Z}/ γ^*)(\mathrm{Z}/γ^*) \to 4\ell$, where $\ell = \mathrm{e}$ or $μ$, is studied at a center-of-mass energy of 13 TeV with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The ZZ production cross section, $σ(\mathrm{pp} \to \mathrm{Z}\mathrm{Z}) = 17.2 \pm 0.5\text{ (stat) }\pm 0.7\text{ (syst) }\pm 0.4(\mathrm{theo}) \pm 0.4\text{ (lumi)}$ pb, measured using events with two opposite-sign, same-flavor lepton pairs produced in the mass region $60 < m_{\ell^+\ell^-} < $120 GeV, is consistent with standard model predictions. Differential cross sections are measured and are well described by the theoretical predictions. The Z boson branching fraction to four leptons is measured to be $\mathcal{B}(\mathrm{Z}\to 4\ell) = 4.8 \pm 0.2\text{ (stat) }\pm 0.2\text{ (syst) } \pm 0.1\text{ (theo) }\pm 0.1\text{ (lumi) }\times 10^{-6}$ for events with a four-lepton invariant mass in the range 80 $ < m_{4\ell} < $ 100 GeV and a dilepton mass $m_{\ell\ell} > $4 GeV for all opposite-sign, same-flavor lepton pairs. The results agree with standard model predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZ$γ$ couplings at 95% confidence level: $-0.0012 < f_4^\mathrm{Z} < 0.0010$, $-0.0010 < f_5^\mathrm{Z} < 0.0013$, $-0.0012 < f_4^γ < 0.0013$, $-0.0012 < f_5^γ < 0.0013$.

Figures (12)

• Figure 1: Distributions of (upper) the four-lepton invariant mass $m_{4\ell\xspace}$ and (lower) the dilepton invariant mass of all $Z/\gamma^\ast$ bosons in selected four-lepton events. Both selected dilepton candidates are included in each event. In the $m_{4\ell\xspace}$ distribution, bin contents are normalized to a bin width of 25$\,\text{Ge\spaceV}$; horizontal bars on the data points show the range of the corresponding bin. Points represent the data, while filled histograms represent the SM prediction and background estimate. Vertical bars on the data points show their statistical uncertainty. Shaded grey regions around the predicted yield represent combined statistical, systematic, theoretical, and integrated luminosity uncertainties.
• Figure 2: (Top): the distribution of the reconstructed mass of $Z_1$, the dilepton candidate closer to the nominal $Z$ boson mass. Points represent the data, while filled histograms represent the SM prediction and background estimate. Vertical bars on the data points show their statistical uncertainty. Shaded grey regions around the predicted yield represent combined statistical, systematic, theoretical, and integrated luminosity uncertainties. (Bottom): the reconstructed $m_{Z_2}$ plotted against the reconstructed $m_{Z_1}$ in data events, with distinctive markers for each final state. For readability, only every fourth event is plotted.
• Figure 3: (Top): the distribution of the reconstructed four-lepton mass $m_{4\ell\xspace}$ for events selected with $80 < m_{4\ell\xspace} < 100\,\text{Ge\spaceV}\xspace$. Points represent the data, while filled histograms represent the SM prediction and background estimate. Vertical bars on the data points show their statistical uncertainty. Shaded grey regions around the predicted yield represent combined statistical, systematic, theoretical, and integrated luminosity uncertainties. (Bottom): the reconstructed $m_{Z_2}$ plotted against the reconstructed $m_{Z_1}$ for all data events selected with $m_{4\ell\xspace}$ between 80 and 100$\,\text{Ge\spaceV}$, with distinctive markers for each final state.
• Figure 4: Distributions of (upper) the four-lepton invariant mass $m_{ZZ\xspace}$ and (lower) dilepton candidate mass for four-lepton events selected with both $Z$ bosons on-shell. Points represent the data, while filled histograms represent the SM prediction and background estimate. Vertical bars on the data points show their statistical uncertainty. Shaded grey regions around the predicted yield represent combined statistical, systematic, theoretical, and integrated luminosity uncertainties. In the $m_{ZZ\xspace}$ distribution, bin contents are normalized to the bin widths, using a unit bin size of 50$\,\text{Ge\spaceV}$; horizontal bars on the data points show the range of the corresponding bin.
• Figure 5: The total ZZ cross section as a function of the proton-proton center-of-mass energy. Results from the CMS and ATLAS experiments are compared to predictions from matrix at NNLO in QCD, and mcfm at NLO in QCD. The mcfm prediction also includes gluon-gluon initiated production at LO in QCD. Both predictions use NNPDF3.0 PDF sets and fixed scales $\mu_\mathrm{F} = \mu_\mathrm{R} = m_Z$. Details of the calculations and uncertainties are given in the text. The ATLAS measurements were performed with a $Z$ boson mass window of 66--116$\,\text{Ge\spaceV}$, and are corrected for the resulting 1.6% difference. Measurements at the same center-of-mass energy are shifted slightly along the horizontal axis for clarity.