Prompt Leptonic Decay Signatures

• Prompt leptonic decay signatures are observable phenomena where high-pT charged leptons originate from a primary interaction vertex, serving as clear indicators of potential new physics.
• The methodology relies on precise lepton reconstruction, kinematic cuts, and background suppression techniques, as exemplified by recent ATLAS analyses.
• Experimental results set stringent constraints on heavy neutral lepton mixing parameters, thereby impacting Seesaw models and other theories beyond the Standard Model.

Prompt leptonic decay signatures are decisive observables in collider and neutrino phenomenology that probe physics at and beyond the Standard Model by exploiting final states with charged leptons (often electrons or muons) which originate directly from a prompt vertex rather than from secondary decays. These signatures—typically characterized by isolated lepton kinematics and distinct charge or flavor combinations—can result from new heavy particle production, lepton number or flavor violating dynamics, or the mixing of Standard Model and exotic neutral leptons. The promptness of the decay (i.e., the production of leptons within detector resolution of the interaction point) is critical for background suppression and for setting stringent constraints on new-physics scenarios.

1. Definition and Theoretical Motivation

Prompt leptonic decay signatures refer to final states containing high transverse momentum (pₜ) charged leptons produced within a few hundred microns of the primary interaction vertex. Such signatures predominantly arise from electroweak two- and three-body decays of heavy particles (e.g., $W \to \ell N$, where $N$ is a heavy neutral lepton (HNL) that decays promptly to leptons), and can also result from new-physics processes that violate lepton flavor or lepton number.

In Standard Model extensions featuring HNLs with masses below the electroweak scale, mixing with electron and muon neutrinos enables the decay chain $W \to \ell N$ followed by $N \to \ell' \nu$. If the HNL lifetime is sufficiently short (i.e., mixing angle $|U_\ell|^2$ is large), both prompt charged leptons emerge from the interaction point, yielding an unambiguous prompt leptonic signature (Collaboration, 28 Aug 2025).

Prompt signatures are leveraged to probe lepton number violating (LNV) processes—where, e.g., same-sign dileptons appear in the final state in violation of total lepton number conservation, as in Majorana neutrino scenarios (Collaboration, 28 Aug 2025). This property is also essential in searches for rare decay modes, new gauge bosons, and for elucidating the origins of neutrino masses and baryogenesis.

2. Experimental Methodologies and Event Selection

The prototypical search for prompt leptonic decay signatures involves several steps, exemplified by the ATLAS analysis at $\sqrt{s}=13$ TeV and $140\,\mathrm{fb}^{-1}$ (Collaboration, 28 Aug 2025):

• Lepton Reconstruction and Identification: Use of tracking, calorimetry, and muon spectrometry to select isolated electrons and muons with strict identification and isolation requirements. For instance, "signal" electrons must pass a "Medium" working point with $>90\%$ efficiency at high $pₜ$.
• Final-State Topologies: Events are required to have either (a) three charged leptons (e.g., $e^\pm e^\pm \mu^\mp$) or (b) two "signal" leptons plus an additional "baseline" lepton (to maximize efficiency, e.g., in $\mu^\pm \mu^\pm e^\mp$).
• Charge and Flavor Criteria: Selection of same-sign, opposite-flavor, or charge-exotic combinations to suppress dominant Standard Model (SM) backgrounds such as $WZ$, $ZZ$, and top-quark processes. For LNV signatures, same-sign lepton pairs are required, as expected from prompt Majorana HNL decays ($N\to\ell^{\pm}W^{\mp*}\to\ell^{\pm}\ell'^{\mp}\nu$).
• Kinematic Discriminants: Variables like the leading lepton $p_t$, the effective mass $$m_{\mathrm{eff}} = \sum p_T(\text{jets})+\sum p_T(\text{leptons})+E_T^{\mathrm{miss}}$$, and the transverse mass $m_T$ are employed for background reduction and signal enhancement.
• Background Estimation: Control and signal regions are defined to constrain backgrounds using data-driven estimates (for nonprompt and fake leptons by the matrix method) and Monte Carlo simulations (for SM multi-boson and top production). Systematic uncertainties from luminosity, scale/resolution, efficiency, and theoretical cross sections are incorporated into a profile-likelihood statistical fit.
• Statistical Analysis: A profile-likelihood fit in each signal region is performed to test for excesses and set exclusion limits on the mixing parameters.

This methodology ensures that promptness is enforced by reconstructing vertices compatible with the primary interaction, with additional cuts on lepton impact parameter and transverse displacement as needed.

3. Interpretation of Results and Limits

The latest ATLAS search (Collaboration, 28 Aug 2025) sets leading constraints on prompt HNL decays in $W$ boson events. The main findings are:

• Mass and Mixing Constraints: For HNL masses $m_N$ in the range $8-65$ GeV, mixing with electron- and muon-type neutrinos is limited as:
  • $|U_{e}|^2 > 8\times10^{-5}$ excluded (full mass range),
  • $|U_{\mu}|^2 > 5.0 \times 10^{-5}$ excluded (full mass range).
• Best Sensitivity: In the mass window $15$–$30$ GeV,
  • $|U_{e}|^2 < 1.1\times 10^{-5}$,
  • $|U_{\mu}|^2 < 5 \times 10^{-6}$.
• No Excess Observed: No significant deviation from SM backgrounds was observed—the data agree with background expectations within $1.7\,\sigma$.

These results translate into stringent constraints on low-scale Seesaw models, restrict models with large mixing, and effectively limit regions relevant for HNL baryogenesis and neutrino mass explanations.

4. Signal Region Optimization and Discriminant Variables

Different final-state channels and kinematic regions are optimized by constructing multiple signal regions (SRs) targeting mass-dependent event topology:

• Three-Lepton Signal Regions: SRs are designed for distinct flavor combinations (e.g., $e^\pm e^\pm \mu^\mp$, $\mu^\pm \mu^\pm e^\mp$) and further separated by discriminants such as $m_{\mathrm{eff}}$, the reconstructed $W$ boson mass from leptons and missing energy, and angular separations.
• Two-Lepton Plus Baseline SRs: For slightly reduced quality requirements, the inclusion of an extra baseline lepton increases efficiency for lower-mass HNLs.
• Background Vetoes: SRs feature specialized vetoes to suppress SM contributions, for example, tight limits on $m_{\mathrm{eff}}$ to reject high-multiplicity backgrounds, or cuts on the reconstructed $W$ mass to reject $WZ$ and $ZZ$ events.

The statistical procedure selects, at each HNL mass hypothesis, those regions (or their combinations) yielding optimal sensitivity.

5. Comparison With Previous Approaches and Complementary Channels

Earlier searches for prompt prompt leptonic decay signatures (Collaboration, 2019) in ATLAS with partial datasets and using both prompt and displaced signatures showed that prompt searches are particularly powerful for HNLs with lifetimes short enough to decay near the interaction point (i.e., larger mixing angles), whereas displaced vertex strategies probe smaller mixing angles and longer-lived HNLs. Prompt strategies maintain high efficiency across $m_N \gtrsim 8$ GeV for $|U_\ell|^2 \gtrsim 10^{-5}$, while displaced searches extend the sensitivity to $|U_\ell|^2 \sim 10^{-6}$ for $m_N$ down to $4.5$ GeV. The complementary use of prompt and displaced signatures thus covers a wide swath of HNL lifetime–mixing parameter space (Collaboration, 2019).

Prompt lepton strategies are also vital for constraining other exotic scenarios, such as nonstandard $Z'$ bosons with off-diagonal lepton couplings—which can produce prompt, charged lepton pairs with nonstandard flavor and charge correlations and characteristic energy spectra (Hernández-López et al., 2013).

6. Implications for New Physics and Future Directions

The null result for prompt leptonic decay signatures in $W$ boson decays excludes significant parameter space relevant to minimal Seesaw models and variants addressing dark matter or baryon asymmetry via HNLs. The limits substantially improve over previous analyses, with increased data and optimized event selection. These constraints set a benchmark for ongoing and future LHC experiments, as well as for the design of next-generation searches.

Future directions include:

• Combining Prompt and Displaced Analyses: A statistical combination across prompt and displaced strategies can expand sensitivity across the full HNL decay-length spectrum.
• Multi-Flavor Mixing: Analyses could be extended to probe scenarios where HNLs mix simultaneously with multiple flavors, potentially affecting both the production and decay patterns.
• New Final States: Moving beyond trilepton and same-sign signatures, channels involving jets plus leptons, tau signatures, or hadronically decaying $W$ bosons might further increase sensitivity, especially at higher HNL masses.
• Higher Luminosity: The expected increase in integrated luminosity (HL-LHC era) will further reduce the statistical uncertainties, allowing the probing of even smaller mixing angles.

These comprehensive approaches ensure that prompt leptonic decay signatures remain foundational in probing neutrino mass generation mechanisms, LNV, and BSM physics at current and future colliders.

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Table: Summary of ATLAS Limits on HNL Mixing Parameters (Collaboration, 28 Aug 2025)

Mass Range (GeV)	Limit on $|U_e|^2$	Limit on $|U_\mu|^2$
8–65	$> 8 \times 10^{-5}$	$> 5 \times 10^{-5}$
15–30	$< 1.1 \times 10^{-5}$	$< 5 \times 10^{-6}$

This table succinctly organizes the key numerical exclusion limits for HNL production in $W$ decays, as determined from the prompt leptonic signature analysis.