Fe b 20 20 Improved search for two body muon decay μ + → e + X

(The PIENU Collaboration) Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, CDMX 04510, México Physics Department, Osaka University, Toyonaka, Osaka, 560-0043, Japan Virginia Tech., Blacksburg, VA, 24061, USA SUPA School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom Department of Physics and Astronomy, University of British Columbia, Vancouver, B.C., V6T 1Z1, Canada TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., V6T 2A3, Canada Department of Engineering Physics, Tsinghua University, Beijing, 100084, China Physics Department, Arizona State University, Tempe, AZ 85287, USA Universidad Autónoma de Sinaloa, Culiacán, México PRISMA Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, Johann-Joachim-Becher-Weg 45, D 55128 Mainz, Germany University of Northern British Columbia, Prince George, B.C., V2N 4Z9, Canada KEK, 1-1 Oho, Tsukuba-shi, Ibaraki, Japan Brookhaven National Laboratory, Upton, NY, 11973-5000, USA (Dated: February 26, 2020)

When decay products from a massive boson X H are not detected due to, for example, a long lifetime, CLFV two body muon decay involving a massive boson µ + →e + X H can be sought by searching for extra peaks in the muon decay µ + →e + νν positron energy spectrum. The mass of the boson m XH can be reconstructed using the equation where m µ and m e are the masses of the muon and the positron, respectively, and E e is the total energy of the decay positron. Two-body muon decays µ + →e + X H were searched for by Derenzo et al. [18] using a magnetic spectrometer; experimental limits 1 on the branching ratio Γ(µ + →e + X H )/Γ(µ + →e + νν) < 2×10 −4 were set in the mass region from 98.1 to 103.5 MeV/c 2 . Exotic muon decays were also sought as a byproduct of the π + →e + ν branching ratio measurement [23] by Bryman and Clifford [19] using a NaI(Tℓ) calorimeter, resulting in upper limits on the branching ratio 3×10 −4 in the mass range from 39.3 to 93.4 MeV/c 2 . Muon decay in the mass region up to the kinetic limit was studied by Bilger et al. [20] using a germanium detector. The most sensitive experiment done so far by Bayes et al. [21] gave limits from 10 −5 to 10 −6 in the mass range from 3.2 to 86.6 MeV/c 2 . Figure 1 shows a summary of the present status of the search for µ + →e + X H decay with upper limits in the mass region from 45 to 105 MeV/c 2 . A massless boson X 0 was also searched for by Jodidio et al. [22],  [18][19][20][21], respectively. and the upper limit on the branching ratio was found to be Γ(µ + →e + X 0 )/Γ(µ + →e + νν) < 2.6×10 −6 .
The present work was carried out with data from the PIENU experiment principally designed to measure the branching ratio Γ[π + →e + ν(γ)]/Γ[π + →µ + ν(γ)] using pion decays at rest [24]. A 75 MeV/c π + beam from the TRIUMF M13 channel [25] was degraded by two thin plastic scintillator beam counters. Pion tracking was performed by two multiwire proportional chambers and two silicon strip detectors. The pion beam was stopped in an 8 mm thick plastic scintillator target. Positrons from π + →e + ν decays and µ + →e + νν decays following π + →µ + ν decays were measured by two thin plastic scintillators used as telescope counters and a calorimeter consisting of a 48 cm (dia.) × 48 cm (length) single crystal NaI(Tℓ) detector surrounded by pure CsI crystals [26]. A silicon strip detector and a multiwire proportional chamber were used to reconstruct tracks of decay positrons and define the acceptance. The energy resolution of the calorimeter was 2.2% (FWHM) for 70 MeV positrons. A total of 1.9×10 8 muon decays were used to search for the decay µ + →e + X H with lifetime τ X > 10 −9 s. The energy resolution is a factor of two improvement and the statistics are an order of magnitude larger than the previous TRIUMF experiment [19]. The present experiment is also sensitive to a higher mass region than that of Ref. [21].

II. ANALYSIS
The data in the PIENU experiment were taken in runs occurring from 2009 to 2012. Because the energy calibration system for the CsI crystals was not available before November 2010, the data were divided into two sets, before and after that date. Pions were identified using energy loss information in the beam counters. Any events with extra hits in the beam and telescope counters were rejected. To ensure the events were from muon decay, the late time region > 200 ns after the pion stop was selected. A solid angle cut of about 15% was used for the data set after November 2010. A tighter acceptance cut (corresponding to about 10% solid angle) was applied to the data taken before November 2010 to minimize electromagnetic shower leakage. Figure 2 shows the muon decay energy spectra for those two data sets obtained from the sum of energies observed in the calorimeter, telescope counters, and silicon strip detector (E sum , which is ∼1.5 MeV lower than the actual decay positron energy E e due to the energy loss in the target and inactive materials).
The two muon decay energy spectra were each fit to smooth 6th order polynomial functions in the energy region E sum = 6 to 43 MeV but excluding a region from -1.75 to +1.25 MeV around a possible signal peak where the search was to be performed. Then, for each m XH , the spectra were fit simultaneously to the polynomial functions with fixed fitting parameters obtained in the initial procedure plus a peak signal shape for the decay µ + →e + X H . To combine the two data sets, a common branching ratio was used as a free parameter in the fit. The validity of the fit procedure was confirmed using the simulated muon decay energy spectrum and the signal peak with the branching ratio 1.0×10 −4 at several energies. The polynomial function fit without any added signal shape resulted in The signal shapes were produced by a Monte Carlo (MC) simulation [27] that reproduced the peak of the decay π + →e + ν at 69.8 MeV. This procedure was repeated in the range E e = 10 to 42 MeV with 0.5 MeV steps.

III. RESULTS AND CONCLUSION
No extra peaks due to CLFV muon decay µ + →e + X H with a lifetime τ X > 10 −9 s were observed and upper lim-its on the branching ratio Γ(µ + →e + X H )/Γ(µ + →e + νν) from 10 −5 to 10 −4 were set for the mass region m XH = 47.8 to 95.1 MeV/c 2 as shown in Fig. 1. Statistics were the dominant source of uncertainty on the branching ratios. Systematic uncertainties and acceptance effects were approximately canceled by taking the ratio of the fit amplitude of signal events to the number of total muon decays. Improved and new limits in the mass region from 87.0 MeV/c 2 to 95.1 MeV/c 2 were set.