Search for heavy neutral leptons using tau lepton decays at BaBaR

This article presents a model-independent search for an additional, mostly sterile, heavy neutral lepton (HNL), that is capable of mixing with the Standard Model $\tau$ neutrino with a mixing strength of $|U_{\tau 4}{|}^2$, corresponding to the absolute square of the extended Pontecorvo-Maki-Nakagawa-Sakata matrix element. Data from the BABAR experiment, with a total integrated luminosity of $424{\mathrm{fb}}^{-1}$, are analyzed using a kinematic approach that makes no assumptions on the model behind the origins of the HNL, its lifetime or decay modes. No significant signal is found. Upper limits on $|U_{\tau 4}{|}^2$ at the 95% confidence level, depend on the HNL mass hypothesis and vary from $2.31\times {10}^{-2}$ to $5.04\times {10}^{-6}$ (with all uncertainties considered), across the mass range $100<m_4<1300\mathrm{MeV}/c^2$; the more stringent limits being placed at higher masses.

Figure 1

1D projections of the (top) reconstructed invariant-mass and (bottom) reconstructed energy of the outgoing hadronic system from ${\tau }^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}+{\nu }_4$, as fractions of that of the $\tau$-lepton, for some of the HNL mass hypotheses studied. Samples are normalized for a nominal $2\times {10}^6$ reconstructed signal events to allow direct comparisons between the samples.

Figure 2

Example of reconstructed invariant-mass and energy ($m_h$, $E_h$) (as fraction of incoming $\tau$ mass and energy) of the outgoing hadronic system from ${\tau }^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}+{\nu }_4$ for HNL masses of 100, 500, 700, and $1000\mathrm{MeV}/c^2$. No selection criteria are applied other than particle identification. The simulated signal samples in these plots assume a nonsignal (tag) $\tau$ lepton decaying leptonically to an electron and SM neutrinos.

Figure 3

Electron tag: Reconstructed mass (left) and energy (right) of the outgoing hadronic system, as fractions of that of the incoming $\tau$ lepton, for the (top) positive $\tau$ signal channel and (bottom) negative $\tau$ signal channel. The “All other $\tau$” component contains all other $\tau$ decays which are not ${\tau }^{+(-)}\to {\pi }^{-(+)}{\pi }^{+(-)}{\pi }^{+(-)}+{\overline{\nu }}_{\tau }({\nu }_{\tau })$. The individual contributions are detailed in Tables 1 and 2. The lower figures show ratios of the total MC yield to data yield, in each bin. The error bars are statistical.

Figure 4

Muon tag: Reconstructed mass (left) and energy (right) of the outgoing hadronic system, as fractions of that of the incoming $\tau$ lepton, for the (top) positive $\tau$ signal channel and (bottom) negative $\tau$ signal channel. The “All other $\tau$” component contains all other $\tau$ decays which are not ${\tau }^{+(-)}\to {\pi }^{-(+)}{\pi }^{+(-)}{\pi }^{+(-)}+{\overline{\nu }}_{\tau }({\nu }_{\tau })$. The individual contributions are detailed in Tables 1 and 2.

Figure 5

Electron tag ($\mathrm{non}\text{−}\tau$): 2D templates showing reconstructed invariant mass and energy (as fraction of incoming $\tau$ mass and energy) for SM non-$\tau$ background processes, the ${\mu }^{+}{\mu }^{-}$ background is not shown since the yield is zero.

Figure 6

Muon tag ($\mathrm{non}\text{−}\tau$): 2D templates showing reconstructed invariant mass and energy (as fraction of incoming $\tau$ mass and energy) for SM non-$\tau$ background processes.

Figure 7

Electron tag: 2D Templates of reconstructed hadronic invariant mass and energy ($m_h$, $E_h$) (as fraction of incoming $\tau$ mass and energy) for data (top), SM $\tau$ MC template for ${\tau }^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}{\nu }_{\tau }$ (middle) and all other $\tau$ decays (bottom).

Figure 8

Muon tag: 2D Templates of reconstructed hadronic invariant mass and energy ($m_h$, $E_h$) (as fraction of incoming $\tau$ mass and energy) for data (top), SM $\tau$ MC template for ${\tau }^{-}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}{\nu }_{\tau }$ (middle) and all other $\tau$ decays (bottom).

Figure 9

Examples of reconstructed outgoing hadronic invariant mass and energy ($m_h$, $E_h$) (as fraction of incoming $\tau$ mass and energy) for HNL masses of $m_4=0\mathrm{MeV}/c^2$ (left column), $500\mathrm{MeV}/c^2$ (middle column), and $1000\mathrm{MeV}/c^2$ (right column) for three $m_{a_1}$ possibilities: $1190\mathrm{MeV}/c^2$ (top row), $1230\mathrm{MeV}/c^2$ (middle row), and $1270\mathrm{MeV}/c^2$ (bottom row). These samples are used to reweight the 2D template histograms and the shift in the derived value of $|U_{\tau 4}{|}^2$ is quoted as an uncertainty.

Figure 10

Upper limits at 95% CL on $|U_{\tau 4}{|}^2$. The magenta line represents the result when uncertainties are included. The magenta line is expected to be a very conservative upper limit. Limits from nomad [29], charm [20], and delphi [30] are also shown for reference. The recent ArgoNeuT result is also shown [31].