Constraints from the CHARM experiment on heavy neutral leptons with tau mixing

We reanalyze the results of the searches for Heavy Neutral Leptons (HNLs) by the CHARM experiment. We study HNL decay channel $N\to e^{+}{e}^{-}\nu /{\mu }^{+}{\mu }^{-}\nu$ and show that, in addition to the constraints on the HNL’s mixings with ${\nu }_e$ or ${\nu }_{\mu }$, the same data also implies limits on the HNLs that mix only with ${\nu }_{\tau }$ and have masses in the range $290\mathrm{MeV}<m_N\lesssim 1.6\mathrm{GeV}$: the region in the parameter space that was considered in the literature as a target for HNLs searches.

Figure 1

Diagrams of leptonic decays of an HNL that mixes purely with ${\nu }_{\alpha }$ via the charged (a) and the neutral current (b).

Figure 2

The parameter space of HNLs with the pure $e$ (the top panel) and $\tau$ (the bottom panel) mixing. The current bounds are from CHARM [19, 20], NA62 [21], T2K [22], Belle [23, 24], DELPHI [25], NOMAD [26], ArgoNeuT [27]; see also [11] for a review and the references therein. For the pure $\tau$ mixing, we do not show the constraints imposed by the T2K experiment (unlike how it is done in [11]), since they are reported for nonzero couplings $U_{e/\mu }$ which dominate the production (The T2K experiment [22] is based on a search for decays of HNLs produced from kaons $K\to l_{\alpha }N$. Such decays can occur only through the $e/\mu$ mixings due to the small mass of kaon $m_K=493\mathrm{MeV}$.). Constraints from the CHARM experiment are taken from the literature, while our reanalysis for them is shown in Fig. 6. The light gray domain corresponds to couplings that are either excluded by BBN [12, 14] or too small to provide active neutrino masses. For the pure $\tau$ mixing, we also show sensitivities of the next generation Intensity frontier experiments (see text for details). In cyan, we show HNL parameter space that may be probed by neutrino observatories: the solid line shows the sensitivity of IceCube to the “double bang” signature from [28], while the dashed line corresponds to the sensitivity of KM3NeT to decays of HNLs produced in the atmosphere; see text and Appendix pp2 for details.

Figure 3

The layout of the CHARM facility, adopted from [19].

Figure 4

Diagrams of HNL production in leptonic and semileptonic decays of $D$ mesons: $D_s$, $D^0$, $D^{\pm }$ [diagrams (a), (b)], and $\tau$ lepton, which is produced in decays of $D_s$ meson only [diagrams (c), (d)].

Figure 5

The HNL mass dependence of the ratio of the numbers of produced HNLs with pure $\tau$ and $e$ mixing $N_{\mathrm{prod}}^{(\tau )}/N_{\mathrm{prod}}^{(e)}$; see Eq. (4), assuming the same values of the mixing angles $U_e^2=U_{\tau }^2$ for the two models. The solid line corresponds to $N_{\mathrm{prod}}^{(e)}$ calculated keeping the production from all $D$ mesons $D^{+}$, $D^0$, $D_s$, while the dashed line corresponds to the estimate of $N_{\mathrm{prod}}^{(e)}\equiv N_{\mathrm{prod}}^{\mathrm{CHARM}}$ calculated without the contribution of $D_s$, as has been done in the analysis [19] by the CHARM collaboration (see text for details). The kinks at $m_N=m_{D_s}-m_{\tau }\approx 200\mathrm{MeV}$ an $m_N\approx m_{\tau }-m_{\rho }\approx 1\mathrm{GeV}$ correspond to kinematic thresholds of the production channels $D_s\to N+\tau$, $\tau \to N+\rho$, correspondingly.

Figure 6

Parameter space of a single Majorana HNL that mixes with ${\nu }_{\tau }$. The excluded region is a combined reach of the DELPHI [25] and CHARM experiments (our result), which is also highlighted by the short dashed black line. Bounds from BBN are reproduced from [12, 14]. The sensitivity of future experiments is also shown (see text around Fig. 2 for details). The top panel covers the HNL mass region $m_N=0.1–35\mathrm{GeV}$, while the bottom panel is a zoom in of the mass domain $m_N=\mathcal{O}(1\mathrm{GeV})$.

Figure 7

The left panel: fraction of HNLs that point towards the detector (blue line) and fraction of HNLs whose decay products point towards the detector (red line). The middle and right panels: comparison of our estimates of the constraint from the CHARM experiment on the pure $e$ (the middle panel) and $\tau$ mixing (the right panel), with bounds reported in [19, 20]. We show two estimates: the red line corresponds to the rescale of the bound on the $e$ mixing from [19] (see Sec. 4 for details), while the blue line is our independent estimate based on Eq. (a1).

Figure 8

The integrand of Eq. (b3).