Techniques for mass peak reconstruction in Searches for Long-Lived Heavy Neutral Leptons Decaying to a Lepton and a \(ρ\) Meson

TL;DR

This work develops two analytic, kinematics-based strategies for reconstructing the mass of long-lived heavy neutral leptons in the semileptonic decay N→ℓρ with ρ→ππ0, where the π0 is not directly observed. By rotating to a frame aligned with the HNL flight direction and applying either a ρ-mass constraint or a W-mass constraint, the authors derive solvable relations for the missing π0 momentum and the HNL mass, including an adaptive treatment to handle kinematic ambiguities. Particle-level studies in SHiP-like fixed-target and LHC-like collider environments show that the ρ-mass constraint yields precise mass peaks (e.g., m_N ≈ 1.00 GeV with a narrow width for μρ, and a distinct m_N ≈ 1.28 GeV peak for μπ), while the W-mass constraint delivers competitive mass resolution for collider-produced HNLs, particularly when using the adaptive mass approach. The work highlights the complementary use of both methods to enhance sensitivity and discrimination between decay hypotheses, and it discusses extensions to τ-coupled HNLs, noting the need for detector-level validation and DV-resolution considerations.

Abstract

The precise reconstruction of the mass peak of long-lived heavy neutral leptons (HNLs) helps to improve the sensitivity for sterile neutrino searches in both fixed-target and collider environments (e.g., SHiP and the LHC). We present an analytical framework for reconstructing the HNL mass peak in the semileptonic HNL decay channel \(N\rightarrow lρ\) with \(ρ\toππ^0\), using only the lepton and the charged pion emerging from the decay vertex together with kinematic constraints and the known particle masses. Incorporating mass constraints from intermediate resonances (e.g., the \(ρ\) meson) or the parent particle (e.g., the \(W\) boson at the collider experiments), we propose two methods, suitable for experiments with displaced vertex tracking capabilities. The particle-level simulation's results demonstrate that the \(ρ\)-mass constraint method yields promising HNL mass resolution in both beam-dump and collider-based environments. The W-mass constraint method, limited to the HNLs produced via \(W\)-boson decays at the collider-based experiments, shows better HNL mass resolution than the \(ρ\)-mass constraint method.

Figures (10)

• Figure 1: Quark-level decay of an HNL: $N \rightarrow \ell^- + W^{*+} \rightarrow \ell^- + u\bar{d}$, where the $u\bar{d}$ hadronizes into either a $\pi^+$ (pseudoscalar) or a $\rho^+$ (vector meson), which eventually decays into a $\pi^+$ and $\pi^0$
• Figure 2: Longitudinal neutral–pion momentum $p_{\pi^{0}}^{\parallel}$. The filled (red) histogram shows the nominal (particle level), while the hatched (blue/green) histograms show the two kinematic solutions $q_{\min}^{\parallel}$ and $q_{\max}^{\parallel}$ obtained with the $\rho$-mass constraint method. The sample corresponds to $N\!\to\!\mu\rho$ with $m_{N,GeN}=1~\mathrm{GeV}$ and $c\tau=50~\mathrm{m}$, generated with EventCalc--SHiP in a SHiP-like configuration. The $q_{\min}^{\parallel}$ solution is softer and peaks at low momentum, whereas $q_{\max}^{\parallel}$ is broader and extends to higher momenta.
• Figure 3: Reconstructed HNL mass $m_{N}^{\rho,\text{min/max}}$ using the $\rho$-mass constraint method for $N\!\to\!\mu\rho$ and $N\!\to\!\mu\pi$ samples ($m_{N,Gen}=1~\mathrm{GeV}$, $c\tau=50~\mathrm{m}$), generated with EventCalc--SHiP in a SHiP-like configuration. For $N\!\to\!\mu\rho$, the two branches yield nearly identical spectra that peak at the true mass, while $N\!\to\!\mu\pi$ (with no $\rho$ present) produces a displaced, narrower peak at higher mass, allowing a clean separation of decay hypotheses.
• Figure 4: Longitudinal neutral pion momentum $p_{\pi^{0}}^{\parallel}$ for an LHC-like sample with $m_{N, Gen}=2~\mathrm{GeV}$, produced via $pp\!\to\! W^{\pm}\!+\!X \to \ell N\!+\!X$ and $N\!\to\!\ell\rho$. The filled histogram shows the nominal (particle level), while the hatched histograms correspond to the two kinematic solutions $q_{min/max}^{\parallel}$ obtained with the $\rho$-mass constraint method. The $q_{\min}^{\parallel}$ solution is softer and peaks at low momentum, whereas $q_{\max}^{\parallel}$ is broader and extends to higher momenta.
• Figure 5: Comparison of reconstructed HNL mass using the $\rho$-mass constraint method in an LHC-like sample ($pp\!\to\!W^{\pm}\!+\!X\to\ell N\!+\!X$, $N\!\to\!\ell\rho$). Overlaid distributions are shown for $m_{N, Gen}=2~\mathrm{GeV}$ and $3~\mathrm{GeV}$. For each mass hypothesis, the two branches $m_{N}^{\rho,\mathrm{min}}$ and $m_{N}^{\rho,\mathrm{max}}$ produce nearly identical spectra peaking at the true value.