Search for heavy Majorana neutrinos in vector boson scattering with $\tau$-lepton final states with the ATLAS detector

Technical Summary: Search for Heavy Majorana Neutrinos in Vector Boson Scattering with $\tau$-Lepton Final States

Problem and Motivation
The observation of neutrino oscillations confirms that neutrinos possess non-zero masses, a phenomenon not explained by the Standard Model (SM). The type-I seesaw mechanism offers a natural explanation by postulating the existence of heavy Majorana neutrinos ($N$), which suppress light neutrino masses via the relation $m_\nu \propto v^2/m_N$. While neutrinoless double beta decay searches probe the Majorana nature of light neutrinos, heavy Majorana neutrinos can be probed at colliders through Lepton Number Violating (LNV) processes. Specifically, same-sign (SS) dilepton production via Vector Boson Scattering (VBS) is a sensitive channel for heavy Majorana neutrinos with masses ($m_N$) in the TeV range, where resonant $W$-boson production becomes kinematically inaccessible. Previous searches by ATLAS and CMS have focused on SS electron and muon final states ($e^\pm e^\pm$, $e^\pm \mu^\pm$, $\mu^\pm \mu^\pm$). This paper addresses the gap in the search for heavy Majorana neutrinos coupling to third-generation leptons ($\tau$) in the VBS topology, a channel previously unexplored at the LHC for this specific topology.

Methodology
The analysis utilizes proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the ATLAS detector, corresponding to an integrated luminosity of $140 \text{ fb}^{-1}$. The search targets the process $pp \to W^\pm W^\pm jj \to \ell^\pm \ell'^\pm jj$ mediated by a heavy Majorana neutrino, where the final state involves same-sign $\tau$-leptons.

• Signal Channels: The analysis considers three signal regions (SRs) based on the decay modes of the $\tau$-leptons:
  1. $\tau_{\text{lep}}\tau_{\text{had}}$: One $\tau$ decays leptonically ($e$ or $\mu$) and the other hadronically ($\tau_{\text{had-vis}}$). This is further split into $e\tau_{\text{had}}$ and $\mu\tau_{\text{had}}$ SRs.
  2. $\tau_{\text{had}}\tau_{\text{had}}$: Both $\tau$-leptons decay hadronically.
• Event Selection: Events are required to contain a same-sign pair of leptons (either a prompt lepton and a $\tau_{\text{had-vis}}$, or two $\tau_{\text{had-vis}}$ candidates) and at least two jets. To isolate the VBS topology, the two leading jets must satisfy $m_{jj} > 300$ GeV and $|\Delta\eta_{jj}| > 4$. Events containing $b$-jets are vetoed to suppress top-quark backgrounds.
• Object Reconstruction: Electrons and muons are reconstructed with tight identification and isolation criteria. Hadronic $\tau$ candidates ($\tau_{\text{had-vis}}$) are reconstructed using a recurrent neural-network (RNN) based identification algorithm to distinguish them from QCD jets.
• Background Estimation:
  • Jet $\to \tau_{\text{had}}$ fakes: The dominant background, estimated using a data-driven "fake factor" method derived from a control region enriched in $W$+jets events.
  • Lepton $\to \tau_{\text{had}}$ fakes: Estimated using Monte Carlo (MC) simulation corrected with data-driven factors from $Z \to ee$ events.
  • Prompt $\tau$ backgrounds: Processes like $VV$, $Z$+jets, and $t\bar{t}$ are estimated using MC simulation (Sherpa, Powheg+Pythia).
• Statistical Analysis: A binned profile likelihood fit is performed on the transverse momentum ($p_T$) distribution of the leading $\tau_{\text{had-vis}}$ in the signal regions. Systematic uncertainties (experimental and theoretical) are incorporated as nuisance parameters.

Key Contributions

1. First VBS Search with $\tau$-Leptons: This work presents the first search for heavy Majorana neutrinos in the VBS topology using same-sign $\tau$-lepton final states at the LHC.
2. Extended Mass Reach: The search probes heavy Majorana neutrino masses up to $m_N = 6.5$ TeV, significantly extending the reach of previous searches which were limited to lower masses or different topologies.
3. Two-Dimensional Constraints: Beyond setting limits on the mixing element $|V_{\tau N}|^2$, the analysis derives simultaneous constraints on the mixing planes $(|V_{eN}|^2, |V_{\tau N}|^2)$ and $(|V_{\mu N}|^2, |V_{\tau N}|^2)$, addressing scenarios where mixing with the first or second generation is non-negligible.

Results

• Observation: No significant deviation from the Standard Model background expectation was observed. The observed event yields in the $e\tau_{\text{had}}$, $\mu\tau_{\text{had}}$, and $\tau_{\text{had}}\tau_{\text{had}}$ SRs were 887, 579, and 270, respectively, consistent with the fitted background predictions.
• Exclusion Limits:
  • Upper limits at 95% confidence level (CL) on the squared mixing matrix element $|V_{\tau N}|^2$ were derived for $m_N$ between 92 GeV and 6.5 TeV.
  • The strongest exclusion was achieved at $m_N = 900$ GeV, with an observed (expected) limit of 0.30 (0.31).
  • For $m_N > 1.0$ TeV, these results set the most stringent limits on heavy Majorana neutrinos coupling to $\tau$-leptons.
  • The analysis establishes the first direct constraints for $m_N > 1.5$ TeV in this channel.
• Two-Dimensional Limits: Contours in the $(|V_{eN}|^2, |V_{\tau N}|^2)$ and $(|V_{\mu N}|^2, |V_{\tau N}|^2)$ planes were presented for $m_N = 1$ TeV and 5 TeV, excluding regions of parameter space where both mixing elements are large.

Significance
The paper claims that this search represents the highest mass scale explored at colliders for heavy Majorana neutrinos coupling specifically to third-generation leptons. By extending the exclusion limits to an unexplored mass range above 1.5 TeV and improving sensitivity for masses above 1.0 TeV, the results provide critical constraints on the parameter space of the type-I seesaw model involving third-generation mixing. The absence of a signal further tightens the bounds on the existence of heavy Majorana neutrinos in the VBS regime, complementing searches in resonant production and other lepton flavor channels.