The muon as a laboratory for studying charged lepton-flavour violation (cLFV) has proven to be one of the most sensitive areas to probe for "New Physics”, due to the muon's copious production rate and relatively long lifetime. The search at the intensity frontier with precision-type experiments is complementary to the search for new particles at the high-energy frontier of TeV colliders. Of the three "golden” muon channels: μ → eγ, μ → 3e and μ → e conversion, an overview of the status of the coincidence experiments MEG, together with the latest results, which constitute the most stringent limit to date on this decay and the recently initiated Mu3e experiment, will be give

Kettle, Peter-Raymond

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Hyperfine Interact (2013) 214:47–54DOI 10.1007/s10751-013-0789-6The “Golden” cLFV channels μ → eγand μ → eee — the high-intensity frontierPeter-Raymond KettlePublished online: 26 February 2013© Springer Science+Business Media Dordrecht 2013Abstract The muon as a laboratory for studying charged lepton-flavour violation(cLFV) has proven to be one of the most sensitive areas to probe for “New Physics”,due to the muon’s copious production rate and relatively long lifetime. The searchat the intensity frontier with precision-type experiments is complementary to thesearch for new particles at the high-energy frontier of TeV colliders. Of the three“golden” muon channels: μ → eγ , μ → 3e and μ → e conversion, an overview of thestatus of the coincidence experiments MEG, together with the latest results, whichconstitute the most stringent limit to date on this decay and the recently initiatedMu3e experiment, will be given.Keywords Muon decay · Lepton flavour violation · MEG · Mu3e1 IntroductionLepton-flavour violation (LFV) is a key area of investigation in the search for“New Physics” beyond the Standard Model (SM) and is seen as a complementaryapproach to the direct searches at the high-energy frontier of TeV-scale colliders.Since the original experimental confirmation of flavour mixing in the neutral leptonsector, in the form of neutrino oscillations [1–3] and with it, the consequence thatlepton flavour is a broken symmetry, the impetus in the charged lepton sector hasalso increased with next generation experiments such as MEG II (μ → eγ ), Mu3e(μ → 3e) both at PSI in Switzerland, COMET (μ → e) at J-PARC in Japan andMu2e (μ → e) at Fermilab in the US, all in the planning. Also, the next generationThe 5th International Symposium on Symmetries in Subatomic Physics (SSP 2012), Groningen,The Netherlands, 18–22 June 2012.P.-R. Kettle (B)Laboratory for Particle Physics, Paul Scherrer Institut PSI, 5232 Villigen PSI, Switzerlande-mail: peter-raymond.kettle@psi.ch48 P.-R. KettleTable 1 Current experimentallimits on LFV muon decaysChannel Experiment B-Limit (90 %C.L.) Ref.μ → eγ MEG ≤2.4·10−12 [4]μ → 3e SINDRUM ≤1.0·10−12 [5]μAu → eAu SINDRUM II ≤7·10−13 [6]B-factories SuperKEKB + Belle II in Japan and Super-B in Italy, which will addressthe cLFV tau decays.Despite the overwhelming success of the SM being one of the most tested theoriesof nature, there are however still recognized deficiencies, which have formed thegeneral opinion that it be seen rather as a low-energy manifestation of a morefundamental theory at higher energies, in which mixing or flavour changing can benaturally introduced by the extra degrees of freedom given by the additional particlesin the high-energy sector. In most such classes of models beyond the SM, a sizablefraction of the LFV parameter-space is predicted to be experimentally accessible toboth the current and next-generation experiments.2 The “Golden” muon channels and “New Physics”The muon is considered as one of the most sensitive probes for studying cLFV dueto its copious production rate and relatively long lifetime, nevertheless for the nextgeneration experiments stopping rates in excess of the world’s most intense muonbeams (Order 108 muons/s) at the Paul Scherrer Institut PSI are required. Theinclusion of finite but tiny neutrino masses into the SM gives predictions for cLFVmuon channels which are far beyond the experimental reach of O(10−54). Henceany signal seen by these experiments would be a clear and unambiguous sign of NewPhysics beyond the SM. Of the three so-called “Golden” Channels: μ → eγ , μ → eeeand μ → e conversion predicted to have branching ratios within the reach of eithernext-generation experiments or as in the case of μ → eγ , seen in many classes ofmodels to have the highest sensitivity to “New Physics”, to be within the reach ofthe currently running MEG experiment at PSI, the first two are coincidence-typeexperiments. They are best probed using continuous (DC) muon beams, owing to thelimiting combinatorial backgrounds, whereas in the μ → e conversion experimentswhere a single high-energy electron is sought, high-intensity pulsed beams can beused. The current most stringent limits on these decays are summarized in Table 1.In order to unravel the complex nature of lepton mixing and neutrino massesand to distinguish between the different beyond the SM-predictions for cLFV,all of the “Golden Channels” need to be investigated, as they are all subject topossible different forms of mediation in the interaction. Concentrating here on thecoincidence channels μ → eγ and μ → eee, a comparison of the physics potential,based on an effective model [7] is shown in Fig. 1. Both the sensitivity to and mass-reach attainability for “New Physics” mediating mass scales  are compared in termsof the dimensionless parameter κ , which represents the relative strength of eitherthe photonic loop contributions, dipole couplings (κ  1) or the 4-fermion couplings(κ  1) of the interaction. Also shown are the projected branching ratio sensitivities,and exclusion zones from previous experiments (MEGA and SINDRUM).The “Golden” cLFV Muon Channels 49Fig. 1 Shows the sensitivityof the two “coincidenceexperiments” to the mass-scaleof “New Physics”  mediatingthose reactions (see text,figure taken from [7])For small values of κ (dominant dipole contribution) the MEG experimentis clearly seen to be more sensitive by order 1/αem(fine structure constant) andtherefore any next-generation μ → eee experiment must aim at a sensitivity betterthan 10−15 to be competitive over the whole range of κ . The current MEG-limitexcludes mass-scales below approximately 1,000 TeV for small κ .3 MEG experiment search for μ → eγThe MEG experiment, located at the π E5 channel of the 590 MeV, 1.3 MW protoncyclotron facility of the Paul Scherrer Institut PSI in Switzerland, has been searchingfor the LFV-decay μ → eγ since the end of 2008. The event signature from thestopped muon decay is a simple 2-body topology with a back-to-back photon andpositron in the final state, coincident in time with each acquiring half the muonrest mass (52.8 MeV). The experiment employs one of the world’s highest intensitysurface muon beams capable of more than 108 muons per sec. together with aliquid xenon (LXe) scintillation detector and gradient-field superconducting positronspectrometer, incorporating ultra-thin tracking detectors and ultra-fast scintillationtiming detectors to detect the photon and positron from the decay respectively, asshown in Fig. 2. A more detailed description is given in [8].The five observables to be extracted from the detector information are: photonenergy (Eγ ), positron energy (Ee), azimuthal (φeγ ) and polar (θeγ ) relative anglesand the relative time (teγ ) between the positron and the photon. The photon energy,position and timing are precisely determined through information received from50 P.-R. KettleFig. 2 Schematic of the MEG experiment, showing the beam elements: Wien-filter, collimatorsystem and BTS superconducting transport solenoid and central degrader system. Coupled to theseare the He-filled COBRA superconducting spectrometer, consisting of a gradient-field magnet andcentral target system. A set of radial drift chambers (DC) and two sets of fast scintillation counterarrays for timing and trigger purposes (TC) complete the positron tracking and detection side. The900 l C-shaped liquid xenon (LXe) photon detector is also shown and the downstream insertionsystem allowing the remote insertion of our Cockcroft-Walton beam pipe, for calibration purposesthe 846 photomultiplier tubes (PMTs) immersed in the 900 litre volume of theLXe detector. A depth-dependent energy resolution of 1.9 % (depth>2 cm) and2.4 % (depth<2 cm) respectively for signal photons of 52.8 MeV was measuredusing photons of 55 MeV from the pion charge-exchange reaction, while a positionalresolution of 5 mm over the front-face and 6 mm in the depth was measured. Onthe positron side, the energy resolution is extracted from the kinematic edge ofthe Michel decay (μ+ → e+νν¯), while the response function is described by a tripleGaussian function with a resolution (core fraction) of 310 keV (80 %) and 320 keV(79 %) respectively for the 2009 and 2010 data samples. The respective angular andvertex resolutions, determined by a double-turn reconstruction, treating each turnas a separate track and comparing their differences at a common point of closestapproach to the beam-axis, were found to be 6.7 (7.2) mrad in φ and 9.4 (11.0) mrad inθ respectively for 2009 (2010). The target vertex resolutions were 1.5 (2.0) mm alongthe beam-axis and 1.1 (1.1) mm vertically for 2009 (2010) data. The combining of boththe positron and photon positional and angular resolutions results in a final angularresolution on the relative angle of 13.1 (14.0) mrad in φeγ and 14.5 (17.1) mrad inθeγ respectively for the 2009 (2010) data samples. The relative timing resolution teγ ,determined from the simultaneously measured radiative decay muons in the Eγ side-band yields 146 (122) ps for the 2009 (2010) data.3.1 Combined analysis of 2009 and 2010 dataThe presented combined 2009+2010 results constitute a total of 1.8·1014 stoppedmuons and include improvements to several aspects: the relative detector alignment,magnetic field map, treating of positron variable correlations and improved likeli-hood tools and methods. The number of μ → eγ events as well as radiative muonThe “Golden” cLFV Muon Channels 51Branching ratio0 5 10 15 20-1210×Confidence level00.10.20.30.40.50.60.70.80.91200920102009 + 2010Fig. 3 Left Confidence intervals for the μ → eγ branching ratio B versus data sets analyzed, right fitresults—best estimates and cofindence intervals at 90 % C.L. of B(μ → eγ )decay (RMD) and background events in the 5-D central analysis region, definedby 48 ≤ Eγ ≤ 58 MeV, 50 ≤ Ee ≤ 56 MeV, |teγ | ≤ 0.7 ns, |θeγ | ≤ 50 mrad, |φeγ | ≤50 mrad, is determined from a maximum likelihood analysis. The probability densityfunctions (PDFs) used are predominantly based on measured response functionsfrom data. The use of side-band data in estimating the number of RMD andbackground events is valid since the expected background in the central analysisregion is also dominated by accidentals. Such issues as the photon resolution positiondependence or positron track-quality are taken into account on an event-by-eventbasis. The confidence intervals on the number of signal events is calculated by afrequentist method with profile likelihood-ratio ordering. Finally, the sensitivity ofthe experiment with a null signal hypothesis was determined by toy Monte-Carloexperiments to be 3.3·10−12 (2009), 2.2·10−12 (2010) and 1.6·10−12 (2009+2010),consistent with the branching ratio upper limit derived from the side-bands.The results of the likelihood fit to the central region, post optimization of theanalysis procedure, background study and unblinding are given in the table of Fig. 3,together with plots of the confidence intervals for the μ → eγ branching ratio B. Thefinal result of B(μ → eγ )≤ 2.4·10−12 at 90 % C.L. constitutes the most stringent limiton this decay to date and improves the previous limit by a factor of five.The 2011 run was also successfully completed doubling the total data statistics,with the analysis currently being pursued. The MEG experiment is expected tocontinue until the end of 2012 or early 2013 enabling one to explore the 10−13 B-region. R&D efforts are also underway for MEG II aiming at an order of magnitudeimprovement in the sensitivity reach.4 Mu3e experiment μ → eeeThe next-generation μ → eee search is in the planning; a Letter-of-Intent wassubmitted to the PSI PAC in 2012 and is to be followed by a proposal in 2013. Theambitious goal of reaching a sensitivity of 10−16 at 95 % C.L. [9] is to be soughtafter in a staged approach, with the initial stage I experiment, aiming at a sensitivityof 10−15, foreseen to be undertaken at PSI’s π E5 channel, while for the final goal,a muon beam rate in the GHz-range is required. The novel idea of using the SINQ52 P.-R. Kettlespallation neutron source target window as a source for a high-intensity surface muonbeam (HiMB) is currently under study at PSI and initial results look promising.The ultimate goal constitutes an improvement of four orders of magnitude over theprevious best limit attained by the SINDRUM experiment [5] and will allow modelsinvolving new particles, such as Supersymmetry, extended Higgs models with newscalar bosons or models with extra dimensions, to be tested with unprecedentedsensitivity as demonstrated in Fig. 1. Despite the lower sensitivity compared to theMEG experiment in the lower κ-range (c.f. Fig. 1) the search for the μ → eee decayis considered experimentally easier than that of μ → eγ , due to the reduction of thecombinatorial background by the presence of three particles required in the finalstate.4.1 Experimental signature, backgrounds and experimental considerationsThe decay signature for a positive muon is three charged particles in the final state,two positrons and an electron, showing opposite curvature in a magnetic field. Thesemust be coincident in time, be derived from the same vertex and the topology shouldbe co-planar. Furthermore, the vectorial sum of the momenta must vanish, while thetotal energy must sum to the muon mass and the individual energies should rangebetween 0 and 53 MeV.The main sources of background are two-fold, so-called physics background com-ing from radiative muon decay with either internal μ → eνν¯ee or external μ → eνν¯γconversion, its suppression depending strongly on the granularity and resolution ofthe detectors, or accidental background which scales with the square of the beamintensity. The radiative decays are the most serious form of background since theycan produce oppositely charged leptons from the same vertex, if conversion occursin the target or surrounding detector materials. The accidentals are combinatorialsfrom Michel or radiative decays with e.g. positrons undergoing Bhabha scatteringor mistaken back-curl events. Finally, certain pion decays can potentially contributeas background such as π → eeeν or π → μνγ with subsequent photon conversion.However, these are considered negligible due to the high suppression factor ofthe beam line O(10−12). Therefore, in order to distinguish μ → eee decays frombackground processes efficiently at a level of 10−16, a combination of excellent energyand momentum resolutions for the detectors as well as a precise vertexing and TOF-measurements combined with kinematic constraints are required.4.2 Detector conceptIn order to achieve the sensitivity goal and suppress the main backgrounds excellentvertex and timing resolutions are required to cope with a stopping rate of more than109 particles s−1. Furthermore, a precise determination of the momenta is necessaryin order to apply the kinematic constraints. The reconstruction of candidate tracksis mainly limited by multiple scattering in the target and detector materials. Con-sequently a strict materials budget must be adhered to, requiring the detectors beoperated in a He-environment inside the solenoidal magnetic field of about 1–1.5 T(Fig. 4).The “Golden” cLFV Muon Channels 53Fig. 4 Schematic of the Mu3e detector concept, showing the central extended target and inner andouter-layer silicon pixel trackers together with a scintillating-fibre tracker. On both the upstream anddownstream sides fast scintillating tile “recurling stations” with outer Si-pixel layers are implementedDue to the high stopping rate and track multiplicity a high granularity Si-basedtracking detector solution has been chosen, so-called HV-MAPS, a high-voltageversion of “Monolithic Active Pixel Sensors”, with the great advantage that itenables implementation of the pixel readout circuit directly in the silicon layer[10], with the added possibility of “thinning-down” to a total thickness of between30–50 μm. A total of two double-layered central-barrel detectors are planned withadditional US/DS double-layered “recurling stations”. A total of 250 million pixelsfor a granularity of 80×80 μm. The “recurling stations” not only increase the detectoracceptance but also contribute significantly to the momentum resolution, due to thesuperior resolution of a 180◦ spectrometer concept.The scintillating-fibre hodoscope in the central region, consisting of five lay-ers of fibres totaling 4,000 channels, is readout using SiPMs at each end and5 GSs−1waveform digitizers. This provides a timing resolution of 1 ns for all par-ticles. For the ultimate timing resolution of recurling tracks, two scintillating-tilehodoscopes, each with 3,000 channels complement the “recurling stations” with atiming resolution of between 50–100 ps. This is expected to reduce the accidentalbackground by 2–3 orders of magnitude.The readout of the experiment is based on FPGA and GPU technology whichcontinuously (no trigger) outputs the fully digitized, zero-suppressed raw data atabout 150 GBs−1, while also implementing on-line track reconstruction.5 ConclusioncLFV searches have gained much impetus in recent years with next-generationexperiments planned for all the “Golden Channels” in the muon sector. Significantprogress is expected especially from the PSI experiments, with hopefully first signalevents seen after a search spanning more than sixty years.54 P.-R. KettleReferences1. Fukuda, Y., et al., Super-Kamiokande Collaboration: Evidence for oscillation of atmosphericneutrinos. Phys. Rev. Lett. 81, 1562–1567 (1998)2. Ahmad, Q.R., et al., SNO Collaboration: Measurement of the charged current interactionsproduced by B-8 solar neutrinos at the Sudbury Neutrino Observator. Phys. Rev. Lett. 87, 071301(2001)3. Eguchi, K., et al., KamLAND Collaboration: First results from KamLAND: Evidence for reactorantineutrino disappearanc. Phys. Rev. Lett. 90, 021802 (2003)4. Adam, J., et al., MEG: New limit on the lepton-flavour-violating decay mu → e gamma. Phys.Rev. Lett. 107, 171801 (2011)5. Bellgardt, U., et al., SINDRUM Collaboration: Search for the Decay μ+ → e+e+e−. Nucl. Phys.,B 299, 1 (1988)6. Bertl, W.H., et al., SINDRUM II: A Search for μ → e conversion in muonic gold. Eur. Phys. J.C47, 337–346 (2006)7. de Gouvea, A.: (Charged) Lepton Flavor Violation. Nucl. Phys., B Proc. Suppl. 188, 303–308(2009)8. Adam, J., et al., MEG Collaboration: A limit for the μ → eγ decay from the MEG experiment.Nucl. Phys., B 834, 1–12 (2010)9. Blondel, A., et al.: Letter of Intent to PSI. Available at http://www.psi.ch/mu3e/DocumentsEN/LOI_Mu3e_PSI.pdf (2011)10. Peric, I.: A novel monolithic pixalated particle detector implemented in high-voltage CMOStechnology. Nucl. Instrum. Methods A582, 876–885 (2007)

The "Golden” cLFV channels μ → eγ and μ → eee — the high-intensity frontier

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The "Golden” cLFV channels μ → eγ and μ → eee — the high-intensity frontier

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