Probing heavy neutrinos in the COMET experiment

We argue that the COMET experiment --- a dedicated experiment for the $\mu$-$e$ conversion search --- can be a powerful facility to search for heavy neutrinos in the mass range $1\,{\rm MeV} \lesssim M \lesssim 100\,{\rm MeV}$. The stopped muons captured by the target nuclei or decaying in orbit are efficiently produce heavy neutrinos via the active-sterile mixing. The produced heavy neutrinos then decay to electron-positron pair (plus an active neutrino), which events are clearly seen by the cylindrical drift chamber surrounding the target. The expected sensitivity is comparable to the PS191 bound when the COMET experiment achieves $\sim 10^{17}$ stopping muons in the target.


Introduction
Heavy neutrino is one of the most interesting new physics candidates. What makes this particle promising is the well-established fact that the neutrinos are massive. The most simple and natural way to account for the neutrino masses is introducing gaugesinglet fermions into the standard model. In such a theory, the left-handed neutrinos ν Lα (α = e, µ, τ ) are often mixed with the gauge-singlet fermions after the electroweak symmetry breaking, such that Here ν Lα denote the flavor eigenstates of the left-handed neutrinos, U αi is the Maki-Nakagawa-Sataka matrix, ν i stand for the mass eigenstates of the ordinary neutrinos (i = 1, 2, 3), ν H is the heavy neutrino, and Θ α (|Θ α | ≪ 1) is the active-sterile mixing which rules the strength of the gauge interactions for ν H * .
There is yet another motivation to consider the heavy neutrinos, namely, the baryon asymmetry of the universe. It is known that a (nearly) degenerate pair of heavy neutrinos in the mass range 1 MeV M 100 GeV can account for the baryon asymmetry of the universe through the oscillation taking place in the early universe [1,2,3,4,5,6,7].
Having these strong motivations, SHiP [19,20] and DUNE [21] are planning dedicated searches for heavy neutrinos. These experiments will explore hitherto unexplored ranges of parameters far beyond the current bounds, as flagships of hidden particle searches in the coming decades. Until physics run of these projects turn on, it would be desirable to have alternative searches with shorter-term ability. The heavy neutrinos are efficiently produced by muon and/or meson decay just like the ordinary neutrinos. Thus a relevant question is if we can employ some existing or forthcoming facilities in high intensity frontier.
In this paper, we focus on the COMET experiment [22] -a dedicated experiment for the µ-e conversion search -as an example of such an idea. The COMET experiment plans * The extension to the multi-generation case is trivially done by replacing Θ α ν H with j Θ αj ν Hj . In this paper, we shall consider one heavy neutrino just for simplicity.
to stop ∼ 10 16 (10 18 ) muons on the target in Phase-I (Phase-II) [22]. With these enormous numbers of muon, this experiment is potentially capable of discovering heavy neutrinos in unexplored parameter range beyond the strongest bound set by the PS191 [23,24]. The details are the followings.

Expected sensitivity
The COMET experiment searches the µ-e conversion process by looking for the single Suppose for simplicity that the heavy neutrino is in the mass range 1 MeV M 100 MeV and predominantly couples to muons, namely |Θ µ | 2 ≫ |Θ e,τ | 2 . In what follows, we focus on this parameter regime unless otherwise stated. Then the daughter ν µ produced by the above two processes is "replaced" with the heavy neutrino ν H at the rate |Θ µ | 2 .
Namely, when N stop Within this parameter range, the main decay mode of ν H is ν H → 3ν and the subdom- The latter subdominant mode is detectable if the electron pair hit the CDC with sufficient energies. A schematic view of the decay event is shown in Fig. 1. Since the energy of the parent heavy neutrino ν H is almost equal to the muon mass m µ = 105 MeV, typical energy of each electron is ∼ 35 MeV. † The third branch of importance (in the normal discussion) is the µ-e conversion, but this is of course negligible in the study of the heavy neutrinos. ‡ In this paper, we do not consider the effect of the heavy neutrino mass in the production rate, since our aim in this paper is estimating the ability of the COMET experiment in comparison with the PS191 bounds. The decay width of each process is given by The fraction for the latter detectable mode is 1/4 − sin 2 θ W + 2 sin 4 θ W = 0.13 § . Let us assume that the neutrinos are the Majorana particles. Then the lifetime of ν H is given by The number of events is estimated by   The dotted curve labeled "PS191" is the 90% CL limit placed by PS191 [23,24]. The dashed curve labeled "K + → µ + ν H " is the bound placed by the peak search in kaon decay [25]. The left panel shows the case where the timing acceptance A time is taken as 0.3. The right panel shows the case where A time = 0.8.
limits in each panel. The dotted curve labeled "PS191" is the 90% CL limit placed by PS191 [23,24]. The dashed curve labeled "K + → µ + ν H " is the bound set by the peak search in kaon decay [25]. Although the event estimation by Eq. (4) is applicable only for the Phase I whose goal is N stop µ = 1.3 × 10 16 , we also put the curve for N stop µ = 2.0 × 10 18 to get an idea how good the whole COMET project is, under the assumption that the Phase II setup can keep the same performance for the heavy neutrino search.

Discussions
We conclude from Fig. 2 that the heavy neutrino search with the COMET experiment is an idea with good potential. It is important to note, however, that the curves in Fig. 2 are drawn under the assumption that the heavy neutrinos exclusively contribute to the detections of e ± pair. A potential background is the e ± pair creation by gamma rays. According to Ref. [22], the radiative muon capture µ − + A → ν µ + A ′ + γ and the radiative pion capture π − + A → γ + A ′ are followed by γ → e − + e + . When these follow-up pair creations take place in the CDC volume, they mimic the heavy neutrino signal. More detailed and precise analysis may thus need a thorough understanding of the pair creation by gamma rays inside the CDC volume.
A possible way to reject these background is selecting the directions of the e ± momenta.
For the e ± creation by gamma rays coming from the inner region than the CDC volume, the momenta of e ± tend to be outgoing for the momentum conservation. On the other hand, the e ± from the heavy neutrino decay can be emitted to ingoing directions at significant rates. The typical γ factor of e ± in the ν H rest frame is γ e = M/3 me , whereas the gamma factor of ν H in the laboratory frame is γ ν H = mµ M . Hence, roughly speaking, if γ e > γ ν H , namely if M > 3m e m µ = 13 MeV, then e ± can head in the opposite directions from the heavy neutrino momentum. In such a mass regime distributions for the momentum direction may help to reject the background.
When we consider the full parameter space {Θ e , Θ µ , Θ τ , M}, the thing gets more complicated, owing to the fact the signal decay ν H → e − e + ν is conducted by both of the charged and the neutral currents. However, the electron component |Θ e | is much more severely constrained than the other two parameters [11,18]. The plots in Fig. 2 (with the replacement mentioned above) therefore cover all the cases of practical interests.