Lepton Flavor Violation

Nuclear Physics B (Proc. Suppl.) 143 (2005) 64–69 www.elsevierphysics.com

Lepton Flavor Violation — Experimental — M. Aokia a

School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan Lepton flavor violation (LFV) in the charged sector has been gaining great interests these days. Experimental researches looking for muon LFV such as MEG and MECO are in preparation, and aiming to discover the muon LFV signal within this decade. There is also another activity called PRISM/PRIME project underway, which aims to expand muon LFV research furthermore. The status of those experimental studies will be described. The idea of building Muon Factory and its relevance to the future of neutrino physics is also commented upon.

1. Introduction Lepton flavor invariance, which was built in the Standard Model (SM) a priori, does no longer hold since the neutrino oscillation was firmly established by unquestionable proofs obtained from a series of excellent experiments[1]. This fact generally implies the existence of LFV in charged sector due to the mixing of neutrino flavors in the intermediate state, but the strength of such a process is suppressed by GIM-like mechanism to a level of 10−60 [2]. This is far beyond the experimentally accessible sensitivity, thus LFV is practically still forbidden in the framework of neutrino-oscillation-extended SM. This is a very fortunate situation since the experimental observation of LFV immediately means something new; the physics beyond our current knowledge. Table 1 shows the present limits on some of LFV processes. Several different theoretical models gave a numerical predictions to the branching ratios of LFV processes[13–15], and those predictions are only a few orders of magnitudes less than the current experimental limits. One of such a model is that based on the combination of supersymmetric model (SUSY) with a see-saw mechanism by right-handed heavy neutrino[16]. Since the MSW large angle solution was confirmed by KamLAND result[17], it seems to be possible to cover the interesting mass range of the right-handed 0920-5632/$ – see front matter © 2005 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2005.01.089

Table 1 Experimental limits on the branching ratios for LFV processes.

Process µ− Ti → e− Ti µ− Au → e− Au µ+ → e+ γ µ+ → e+ e+ e− π 0 → µ− e+ KL0 → µe K + → π + µ+ e− KL0 → π 0 µ+ e− τ → eγ τ → µγ

Current limits < 6.1 × 10−13 < 5 × 10−13 < 1.2 × 10−11 < 1.0 × 10−12 < 3.4 × 10−9 < 4.7 × 10−12 < 2.1 × 10−10 < 3.1 × 10−9 < 2.7 × 10−6 < 1.1 × 10−6

Ref. [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

heavy neutrino by LFV experiments under preparation, µ → eγ (MEG[20]) and µ− −e− conversion (MECO[21]). The experimental studies of these processes are very important to understand the structure of neutrino sector. Another model based on SUSY Grand Unified Theory[18,19] also gave a prediction to the branching ratio of µ → eγ and µ− −e− conversion. In this model, relatively large top-quark mass results in rather larger radiative corrections to the slepton mass matrix, and the off-diagonal element of the slepton mass matrix became sizable. As a

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result, smuon-selectron mixing in the intermediate state of the processes might induce LFV, and the calculations show the branching ratio being only a few orders of magnitude below the current experimental limits. LFV would provide an information about the slepton mass matrix. From the experimental point of view, the experimental sensitivity of LFV processes are limited by the available number of parent particles. For example, tau-LFV experiment would be able to improve the sensitivity by 2-3 orders of magnitudes in near future at super B-factory[22] by means of increasing the accelerator luminosity. As for the muon-LFV (µ-LFV), there are several novel ideas of building new generation of muon beams with high intensity and high quality. This will provide us the improvement of more than several orders of magnitude in the sensitivity. The improvement is even higher than the increase of primary proton intensity. These µ-LFV experiments will be described here. 2. µ+ → e+ γ Experiments 2.1. Event Signature and Backgrounds The event signature of µ+ → e+ γ is monoenergetic e+ and gamma emitted back-to-back at once. The major source of background is an accidental coincidence of two independent muon decays, in which the gamma is from either radiative muon decay (µ+ → e+ νe ν µ γ) or annihilationin-flight of e+ or external bremsstrahlung of e+ . The fraction of accidental background events is expressed as: 2 BRbg ∝ Rµ × ∆Ee × ∆Eγ2 × ∆teγ × ∆θeγ ,

where Rµ is the instantaneous rate of the initial muon beam, ∆Ee and ∆Eγ are the positron and photon energy resolutions, respectively, ∆teγ is the timing resolution between positron and photon, and ∆θeγ is the angular resolution between positron and photon. It is very important to improve all of those factors evenly. 2.2. MEG Experiment at PSI MEG[20] aims a sensitivity below 10−13 for the + µ → e+ γ and currently under construction at PSI. The improvement over the previous experiment, MEGA at LANL[5], will be obtained by

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using a continuous muon beam, a novel liquidxenon scintillation detector and a magnetic spectrometer with a graded field. By using the continuous muon beam, instantaneous beam intensity will be reduced by an order of magnitudes while the total number of muons available at the same running time will be increased by factor 1.6. The liquid-xenon scintillation detector consists of 0.8 m3 of liquid xenon viewed by an array of 800 photo-multipliers from all the sides. There is no segmentation of the liquid-xenon tank so the single gamma event is recorded by many numbers of phototubes at once. This improves the timing resolution of photon detection down to 150 ps-FWHM; almost 10 times better than MEGA, and drastically reduce the accidental background fraction. The magnetic spectrometer utilizes a solenoid magnet with a graded magnetic field in which the magnetic field is arranged so that the e+ from the µ+ → e+ γ decay follows a trajectory with a constant radius regardless to the emission angle. This field configuration also helps to sweep e+ quickly out of the sensitive region of the detector. This experiment is currently under construction, and will start the data taking from 2006. The expected single event sensitivity after two years of running is 4 × 10−14 to µ+ → e+ γ. 3. µ− − e− Conversion When a negative charged muon is stopped in a material, it is trapped by an atom and forms a muonic atom. The muon quickly cascades down the energy levels of the muonic atom to 1s ground state. After that, the muon either takes a Michel decay in orbit or is captured by a nucleus or would take a process of coherent conversion to electron, µ− + (A, Z) → e− + (A, Z) . The last one is LFV process and thus the observation of this process indicates new physics. There are many different diagrams potentially contribute to the process. One is that connects virtual γ from µ+ → e+ γ to the nucleus. This is so-called photonic process, and the branching ratio is expressed in terms of the branching ratio

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M. Aoki / Nuclear Physics B (Proc. Suppl.) 143 (2005) 64–69

Figure 1. Schematic layout of the MECO detector

of µ+ → e+ γ,

428 BR(µ+ → e+ γ) , = − − B(A, Z) BR(µ N → e N )

where B(A,Z) is a parameter representing the rate dependence on the mass number and the atomic number. The value of B(A, Z) is typically 1 ∼ 2. Thus, µ+ → e+ γ is more sensitive to photonicLFV than µ− − e− conversion by almost two orders of magnitudes. On the other hand, µ+ → e+ γ process is not sensitive to nonphotonic-LFV, such as Higgs mediated contributions for examples, while µ− − e− conversion is sensitive to[23]. There is also another study that shows the atomic number dependence of the branching ratio in µ− − e− conversion process[24]. Once we discover the µ− −e− conversion, the measurement of the branching ratios with several different materials will provide us very important information about the interaction type of LFV process. 3.1. Event Signature and Backgrounds The event signature of coherent µ− −e− conversion in a muonic atom is a mono-energetic single electron emitted out of a target atom. The energy of electron is, Eµe = mµ − Bµ − Erec , where mµ is the muon mass, Bµ is the binding energy of the 1s muonic atom, and Erec is the nuclear recoil energy. Usually, the nuclear recoil energy is very small. Eµe is different for various nucleus since

Bµ is different between different nuclear charges. For examples, it is Eµe = 104.3 MeV for titanium and Eµe = 94.9 MeV for lead. In all cases, it is almost twice as large as the end point energy of normal Michel decay in vacuum. The potential source of the background is an electron from a muon decay in orbit since its energy spectrum extends to the signal region of µ− − e− conversion. However the spectrum falls off very steeply as the fifth power of Eµe − Ee toward its end point. An e+ energy resolution better than 1 MeV-FWHM would be enough. In addition, there is no accidental background at all. Thus, the search for this process has the large potential to improve the experimental sensitivity by using a high muon rate without suffering from accidental background, which would imply a serious limitation to µ+ → e+ γ.

3.2. MECO Experiment at BNL MECO[21] is a new experiment at BNL-AGS, searching for µ− +Al → e− +Al at a sensitivity below 10−16 , and currently under preparation. Figure 1 shows a schematic layout of the MECO detector. The improvement over the previous experiment, SINDRUM-II[4], will be obtained by the combination of a new-generation high-intensity muon beam line and a long-solenoid detector. The former consists of 1) pulsed proton beam for pulsed muon, 2) large-acceptance pion capture solenoid, 3) muon momentum selection by means of curved solenoid. Muon stopping rate will be about 1011 /s for negative charged muon, which is almost 1000 fold increase over the present world record. The long-solenoid detector allows tracking system located in distance from muon stopping target. That reduces the hit rate on the tracking system caused by the neutral particles coming from the muon stopping target. The experiment is under preparation, and mainly waiting for the budget approval for the magnet construction. The magnet construction may take three years, thus the data taking would start from 2008. The expected single event sensitivity is 2 × 10−17 , which provides almost one order of magnitude better sensitivity than MEG in the photonic LFV process.

M. Aoki / Nuclear Physics B (Proc. Suppl.) 143 (2005) 64–69

3.3. PRISM/PRIME Experiment PRISM[25] stands for Phase Rotation Intense Slow Muon source, and PRIME[26] stands for PRISM Muon Electron conversion experiment. PRISM aims to produce high intensity (1012 of µ± per second) muons with low momentum (68 MeV/c) and narrow energy spread (±0.5 − 1.0 MeV) and high purity. PRIME utilizes this high quality muon beam to search for µ− − e− conversion in a muonic atom. The goal is to improve the sensitivity down to a level of 10−18 which is an order of magnitude better than MECO goal. At such a level of sensitivity, the electron momentum resolution has to be less than 350 keV (FWHM) in order to suppress a background signal coming from the muon decay in orbit. The momentum resolution of electron is dominated by the uncertainty of the energy loss in the muon stopping target. Reducing the total thickness of the target is thus important. Once the target thickness is reduced, momentum range of muon beam in which muons are able to stop in the target will be narrowed down. One has to increase the number of muon in the momentum range so that the total muon yield does not decrease. PRISM provides the means of squeezing the muon beam in the momentum width of 1-2 MeV/c without sacrificing the total muon yield. PRISM consists of the following component: 1) high intensity pulsed proton beam, 2) large acceptance pion capture by using high solenoid field, 3) pion decay section, and 4) phase rotation section. Figure 2 shows a schematic layout of the PRISM beam line. Note that 1-3) (PRISM front end) are similar to the beam line component for MECO experiment. To be exact, there are many technical differences between PRISM front end and MECO beam line, thus it is impossible to simply use the MECO beam line as the PRISM front end. Nevertheless, it would not be totally wrong if I said that PRISM is a sort of MECO upgrade. The 4th component, phase rotation section, is a truely unique portion of PRISM. It is basically a Fixed Field Alternating Gradient (FFAG) synchrotron, in which synchrotron oscillation will take place for the muon beam bunch in the ring. During a quarter cycle of the synchrotron oscillation, the time spread and the energy spread of

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Figure 2. Schematic layout of the PRISM beam line.

the muon beam bunch are going to exchange into another. If the injected muon beam has narrow time spread, the output beam from PRISM will have narrow energy spread. Although the budget for building the whole PRISM system is not yet approved, the R&D of the FFAG phase rotator is underway[27]. 4. Muon Factory As was mentioned in the introduction, LFV would provide us an information about the offdiagonal element of the slepton mass matrix. It is also known that the on-diagonal element of the slepton mass matrix could be studied by using muon; muon electric dipole moment (EDM) and muon g-2. Thus, these µ-LFV and µ-EDM and muon g-2 are so called the golden muon trio for the study of slepton mass matrix[28]. It is really important to persuade the muon-trio physics at the same time.

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another phase rotation ring, PRISM-II. PRISMII would be an extended application of PRISM technology. In order to maximize the physics output from the high-intensity high-quality muon beam, the plan of constructing a facility called Muon Factory was proposed at the J-PARC[30]. The Muon Factory consists of PRISM/PRIME experiment, µ-EDM experiment with PRISM-II and muon g2[32]. Figure 3 shows a layout of Muon Factory at J-PARC. It will also provide us a facility for the development of muon beam manipulation technology such as phase rotation and ionization cooling. The evolution of these technologies will eventually leads us to the realization of neutrino factory[33]. Figure 3. PARC.

Layout of the Muon Factory at J-

There is also another discussion based on leptogenesis. It requires very light neutrino masses due to see-saw mechanism[29], and the range of light neutrino masses suggested by neutrino oscillation experiments strongly favors this mechanism. Leptogenesis is also quite attractive idea since it can explain the matter-antimatter asymmetry of the universe. However, it is very hard to test the leptogenesis since the right-handed neutrino will be too heavy to directly observe. One possibility is to seek side effects induced by the see-saw mechanism. As was mentioned in the introduction, heavy right-handed neutrino may cause LFV, thus searching for LFV is interesting also from that point of view. Another consequences of leptogenesis are CP violation in LFV and EDM since leptogenesis requires CP violation in lepton sector. It means that µ-EDM and µ-LFV are quite interesting together. There is an idea of µ-EDM experiment at a sensitivity of 10−24 level for J-PARC[31]. In order to perform the experiment, it is essential to realize high-intensity high-brightness muon beam at momentum region of several hundred MeV/c. It would be possible to use the phase rotation technique again. However, the momentum region is rather higher than PRISM, one has to build yet

5. Summary It is very important to study LFV processes since several well motivated models predict experimentally observable signal only a few orders of magnitudes below the current experimental limits. Several experiments searching for muon LFV are in preparation, and would be able to show positive signal within this decade. There is also a project that utilizes accelerator technology to manipulate the property of secondary muon beam, and aims to produce the high-intensity high-brightness muon beam. This technology will be indispensable for advancing the µ-LFV physics further more, and for the realization of µ-EDM experiment. REFERENCES 1. V. Barger, D. Marfatia and K. Whisnant, Int. Jour. Mod. Phys. E 12 569 (2003). 2. A. de Gouvˆea, in NEUTRINO FACTORIES AND SUPERBEAMS, 5th International Workshop on Neutrino Factories and Superbeams, NuFact03, edited by A. Para (American Institute of Physics, Melville, New York), p. 275 (2004). 3. P. Wintz, in Proceedings of the First International Symposium on Lepton and Baryon Number Violation, edited by H.V. KlapdorKleingrothaus and I.V. Krivosheina (Insti-

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