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This document summarizes recent results from the MEG experiment searching for the rare decay of muons into electrons and photons (μ→eγ). It describes the theoretical motivation for this process coming from models beyond the Standard Model. It then provides an overview of the MEG detector design, including the muon beam, drift chambers, timing counter, and liquid xenon calorimeter used to reconstruct the positron and photon. The document outlines the analysis framework and compares the independent UCI results to the published MEG collaboration results.

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January 29 2010 1/55 Some Recent Results from the MEG Experiment on µ → eγ: Benjamin Golden Joint Particle Seminar February 8, 2012 University of California, Irvine
Outline • Part I - The Theory of Lepton Flavor – Lepton Flavor Symmetries in the Standard Model – Lepton Flavor Symmetries and the Lack Thereof Beyond the Standard Model • Part II - The MEG Detector – Event Signatures – Hardware Design • Part III - Event Reconstruction – Photon Reconstruction – Positron Reconstruction • Part IV – A UCI Search for µ → eγ – Likelihood Framework – PDFs – Results – Comparison with (collaboration) published results
Part I The Theory of Lepton Flavor: A Window to the UV Completion of the Standard Model
The Standard Model Achromatic Sector: Leptons • SU(2)L x U(1)Y couples to leptons, there are no right-handed ν’s • Three generations are known to exist: f=e,µ,τ • Left-handed leptons: Right-handed leptons: • With massless neutrinos, the SM conserves lepton flavor for each generation classically – Result of 3 accidental global U(1) symmetries: – Gives 3 Noether charges: • Instantons spoil the classical conservation of Lf but exactly preserve – B – L (Sufficient to keep neutrinos massless even at non-perturbative level) – (Lτ – Le), (Lµ – Le) (Sufficient to exclude µeγ) • Neutrino masses must enter the SM Lagrangian in some unknown way – µeγ receives contributions from active neutrino loops – With experimental information on ∆mij 2 , these diagrams alone imply undetectably small rates for µeγ – Additional diagrams with new matter content would be needed to enhance Br(µeγ) to something detectable – An observation of µeγ would demonstrate the existence of new physics Lf f f l       = ν L Rff l )(R = ff f LeL -iq → ff f ReR -iq → fff N-NQ = µ± e ± γ W± νiUµi U* ei
~eµ~ CLFV in SUSY Models: A Little Help from the Sleptons • The SUSY flavor problem – µeγ can proceed in SUSY through diagrams that communicate slepton mixing to leptons – BR(µeγ)<10-11 requires a fine alignment between lepton and slepton mass matrices – Yet lepton masses come from Yukawa interaction, while slepton masses arise from SUSY breaking – Addressed by a number of proposed solutions, all with highly model dependent consequences for BR(µeγ), here focus on one example: Gravity mediation • Gravity Mediation – SUSY broken in a hidden sector, gravitational interactions generate diagonal squark and slepton mass matrices, all with the same universal scalar mass at MPlanck ~ 1018 GeV – Slepton mixing appears from RGE’s running from MPlanck to electroweak scale – An oft-cited, cliché of an example is SO(10) GUT – At MPlanck, theory is tied down by choice of m0 (scalar mass),M1/2 (gaugino mass), A0 (trilinear coupling) – Fix tan β, make assumptions about parameters in superpotential – Scan (m0,M1/2,A0)in a region that allows a squark mass below 2.5 TeV (LHC accessible) × µ e γ ~χ0 Large mixing in ν Yukawas Small mixing in ν Yukawas
CLFV’s Place in the Landscape of Gauge Hierarchy Problem Solutions: Generic • Non-SUSY solutions to hierarchy problem allow µeγ for other reasons • Dynamical EWSB (Technicolor) – Fermion condensate develops dynamically, plays the role of the Higgs – Requires non-universal gauge groups that induce LFV couplings of gauge boson to lepton mass eigenstates • Little Higgs – New vector bosons, fermions, scalars cancel 1-loop corrections to Higgs – LFV from gauge bosons and exotic scalar multiplets • Extra Dimensions – Planck mass is actually small (Gravity weak from loss of flux to extra dimensions) – RHN in bulk generate µeγ where KK states play similar role to sparticles • Some discerning power available: Linear correlation in BR(µeγ) & BR(µNeN) would favor MSSM over these
Part II The MEG Detector: At the Frontier of Low Energy Precision Measurement
Signal and Background • Accidentals are dominant background at rates high enough to reach 10-13 sensitivity Signal µ+ →e+ γ µµ++ γγee++ Radiative decay background µ+ →e+ νeνµ γ ν ν µµ++ee++ γγ Accidental background µ+ →e+ νeνµ + µ+ →e+ ννγ or e+ e- →γγ or e+ Z→e+ Zγ ν νµµ++ee++ γγ ΘΘeeγγ == 180°180° EEee ≈≈ EEγγ ≈≈ 52.852.8 MeVMeV TTee = T= Tγγ ΘΘeeγγ = any angle= any angle EEee, E, Eγγ << 52.852.8 MeVMeV TTee = T= Tγγ ΘΘeeγγ == randomrandom EEee, E, Eγγ << 52.852.8 MeVMeV TTee –T–Tγγ == randomrandom • For fixed MEG acceptance: Naccidental /Nμ ∝ Rate × ∆teγ × ∆Ee × (∆Eγ)2 × (∆Θeγ )2 Ee ~ flatEγ ~ rising linearly
1 History of µ→eγ Searches 10-2 10-4 10-16 10-6 10-8 10-10 10-14 10-12 1940 1950 1960 1970 1980 1990 2000 2010 MEGA BranchingFractionUpperLimit MEG goal MEG 2009+201 0 result
MEG Timeline: Past, Present, and Future • Data Taking – 1998: Original LOI (PSI-RR-99-05) – 2002: Proposal with a goal of 10-13 sensitivity – 2007: (Nov-Dec): Engineering run – 2008: (Sep-Dec): 1st physics run, some hardware problems – 2009: (Nov-Dec): 2nd physics run – 2010: (Aug-Dec): 3rd physics run – 2011: (July-Nov): 4th physics run – 2012: continue data taking • Physics Analysis for Br(µeγ) – 2008 Data Analysis: • 90% CL UL = 2.8 x 10-11 • Sensitivity = 1.3 x 10-11 – 2009 Data Analysis: • 90% CL UL = 9.6 x 10-12 [Collaboration result] • Sensitivity = 3.3 x 10-12 [Collaboration result] • Also the object of independent UCI analysis [Primary Content of this Talk] – 2009+2010 Data Analysis: • 90% CL UL = 2.4 x 10-12 • Sensitivity = 1.6 x 10-12
MEG Experiment Design • ~ 3x107 µ ＋ /s beam incident on a thin stopping target • Positron detection – Gradient B-field to sweep out e+ quickly and keep bending radius constant – Low mass drift chambers to measure energy, emission angles, & path to timing counter – Timing counter with scintillating plastic for precise time measurement • Photon detection – Energy, position, and time measured in a liquid xenon calorimeter – Fast response time, high light yield, high photocathode coverage
Paul Scherrer Institut (PSI) • The other accelerator lab in Switzerland • Highest power operating proton accelerator – 2.2 mA, 590 MeV kinetic energy, 1.3 MW beam power – Extremely reliable – Provides secondary pion, muon, neutron beams 590 MeV proton ring cyclotron MEG Office Apartment: 45 minute journey through forest
Muon Delivery to MEG: Beam & Target • Muon Beam – Produce pions in graphite target – Extract 29 MeV/c muons from π+ decay at rest (can be stopped in thin target) – Wien filter for µ/e separation – Beam transport solenoid for focusing – Mylar degrader to slow muons (~300 µm) – 3x107 µ/s, final spot size σx,y ~ 1 cm • Muon Stopping Target – 205 µm thick polyethylene – 20° slant from beam direction for more stopping power – Holes to check alignment using reconstructed e+ tracks 590 MeV proton beam target µ+ beam line µ+ /e+ separator beam transport solenoid MEG Detector Degrader µ+
COBRA Magnetic Field COnstant Bending RAdius Positrons swept out quickly z θ • R=Psin(θ)/QB • B-field must decrease with |z| to keep R constant and independent of θ (range: 0.5-1.3 T) • Allows precise selection window in R for high momentum tracks • R changes with |z| in such a way to make fewer turns in the DCH • Simplifies pattern recognition • Helps limit rate for stable chamber operation
The Drift Chamber • Measure e+ energy, extrapolate to target for angles and decay vertex • Extrapolate to TIC to correct impact time by flight time (to ~1 cm in path length) • 16 chambers radially aligned at 10.5° intervals • 2 planes of drift cells staggered by ½ cell; 18 wires each chamber • Acceptance matched to that of calorimeter • Radial position from drift time • Resistive wires for approximate Z by charge division, pattern etched on cathode pads to interpolate Z • Gas: He – Ethane mixture (50:50): (X0~650 m, vd saturates at ~4 cm/µs) • Goals: σR = 200 µm σZ = 300 µm σe+ energy = 180 keV • Total average path of one turn .002 X0
Timing Counter • Primary purpose: trigger & precise e+ time • Inner layer of 256 scintillating plastic fibers – Coupled to APD’s (tolerate B-field, Smaller->easier to align with small fibers) – Each end of COBRA at fixed Z – Used for z measurement and in the trigger • Outer layer of 15 scintillating plastic bars – Coupled to PMT’s – Each end of COBRA at fixed φ – Used for impact time and φ measurement • 29 cm < |z| < 109 cm • TIC surrounded by N2 because PMT’s have short life in Helium • Goal: σt = 40 ps
Liquid Xenon Calorimeter Liq. Xe H.V. Vacuum for thermal insulation Al Honeycomb window PMT Refrigerator Cooling pipe Signals fillerPlastic 1.5m Density 2.95 g/cm3 Boiling and melting points 165 K, 161 K Energy per scintillation photon 24 eV Radiation length 2.77 cm Decay time 4.2, 22, 45 ns Scintillation light wave length 175 nm Scintillation light absorption length > 100 cm Attenuation length (Rayleigh scattering) 30 cm Refractive index 1.56 • Relatively high light yield, uniform response • No self-absorption of scintillation light: attenuation only from impurities • 900 L liquid xenon (largest LXE volume) • 846 mesh phototubes on surfaces, in LXE • Thin magnet wall to reduce photon conversions • Goal is to measure photon properties: – Position: σRMS = 3.5 mm – Time: σRMS = 40 ps – Energy: σRMS = ~900 keV at 52.8 MeV
Dedicated Calibration Tools • Calorimeter – CEX reaction: π− +p (LH2 target)  π0 + n followed by π0  γγ (98.8%) • Select events with 83 MeV γ in NaI detector and a back-to-back γ in XEC (55 MeV) • Used to measure γ energy scale, resolution; γ time resolution, PMT time delays • Position resolution of γ from data with lead collimator in front of XEC entrance – Cockcroft-Walton proton accelerator (Li2B4O7 target) – LEDs mounted in XEC • Flash with different intensities • Calibrate PMT gains – QE measured by scintillation light from α sources mounted at known positions (241 Am) • Laser measurements of reference marks on drift chambers and target for primary alignment • Relative TIC-XEC timing from Dalitz data (π0  e+ e- γ ) Reaction Eγ [MeV] Uses p + Li → Be + γ 17.6 Monitor light yield p + B → C + γ + γ 4.4 + 11.6 Cross-time LXE and timing counter check α source wire LED LED
Part III Event Reconstruction: Getting Particle Kinematics from Waveforms I don’t know what I’m looking at.
Photon Reconstruction in the Calorimeter • Position (of 1st conversion) – Fit to pattern of light on inner face PMTs – Angles at target from e+ vertex and γ conversion position • Energy – First estimate from sum of all PMT signals weighted by local photocathode coverage – Apply corrections as function of position, determined from calibration photons (55 MeV, 17.6 MeV) • Large variation of photocathode coverage with position for shallow depth conversions • Same occurs near edges in transverse coordinate • Time – Weighted average of PMT leading edge times – Correct for flight time from vertex to conversion position
Positron Reconstruction in the Drift Chamber & Timing Counter • Drift Chamber – Hit Reconstruction • Identify cells with waveforms consistent with through-going charged particle • Hit time from leading edge of pulse • Z from charge division – Clustering: Group hits on a chamber, spatially consistent with charged particle – Tracking • Group clusters into tracks • Drift times using TIC time to get track time – Kalman Filter to fit track • Calculates positron energy • Extrapolation to target for angles and vertex • Extrapolation to TIC for path length • Provides event-by-event uncertainties in track parameters (energy uncertainty, …) • Timing Counter – Impact time at bar from waveform leading edges of PMTs – Correct for time of flight from vertex to bar
Part IV Current MEG Results & UCI Analysis on 2009 Data:
Summary of Published MEG Results (October 2011) |teγ|<0.28ns; cosΘeγ< -0.9996 51<Eγ<55 MeV; 52.3<Ee<55 MeV BR(best fit) LL 90% CL UL 90% CL 2009 3.2×10-12 0.17×10-12 9.6×10-12 2010 -0.99×10-13 -- 1.7×10-12 2009+2010 -0.15×10-13 -- 2.4×10-12 Expected UL (2009+2010) 1.6×10-12 2009 Data  2010 Data  (~2 x as much data as 2009) Contours: 1σ 1.64σ 2σ
• A rare decay search is very sensitive to the exact values of selection cuts • If it is known which events satisfy cuts during analysis, 2 extreme cases of bias: – Cut to eliminate individual events, yielding better upper limit than justified – Cut to retain individual events, producing a signal where none is present • Use “Hidden Signal Box” technique (<0.2% of data in blind box) – Signal-like events are hidden until selection cuts and likelihood function are determined • 48 E≤ γ 58 MeV≤ • | Teγ | 0.7 ns≤ – Sidebands adjacent to signal box (16% of data) • Can look at radiative decays for Eγ 48 MeV≤ • Can look at accidental photons in | Teγ | > 0.7 ns • Analysis Window – 48 E≤ γ 58 MeV≤ – | Teγ | 2.1 ns≤ • Effective constraint on accidentals by including sidebands in fit • Collaboration uses | Teγ | 0.7 ns, adds constraint on accidentals from sideband extrapolation≤ – |φeγ|, | θeγ | 50 mrad (angles btw. reversed e+ and≤ γ vectors) – 50 E≤ e 56 MeV≤ Blind Analysis Technique: Setting σexperimenter bias = 0 UCI Analysis Window BLIND BOX (Collaboration Analysis Window) Left Sideband Right Sideband Bottom Sideband
Event Selection Criteria: Quality Control • Basic strategy – If we wouldn’t believe a signal event with some characteristic, we remove such events from the sample – Incorporate the dependence of resolutions on event properties into event-by- event probability density functions (PDFs) • Positron – Track quality (# of hits, chamber extent, χ2 of fit, etc…) – Remove events not consistent with a muon stopping in the target – Imposed some cuts not present in collaboration analysis • Photon – Cosmic ray veto based on conversion depth and ratio of inner/outer face γ’s – Preserve events with in-time pileup by removing energy in secondary shower centroid – Reject irrecoverable pile-up events
Maximum Likelihood Analysis • Fit for numbers of signal (NSig) and accidental (NAcc) events by maximizing an extended likelihood function – N= NSig +NRD + Nacc – NRD is fixed to expectation from bottom sideband extrapolation – Kinematic observables: Ee, Eγ, teγ, φeγ,θeγ – S is probability for a signal to result in the set of observables of a given event, similarly for R and A (S, R, & A are called PDFs) • Some differences with collaboration likelihood fit – Collaboration handles background differently ― NRD is floated rather than fixed ― Fit in 3 times smaller time region, 3 times fewer accidentals in the fit – Collaboration adds Gaussian constraints to likelihood function on NAcc and NRD ― Means of Gaussians from extrapolations ― Sigmas of Gaussians from statistical uncertainties of predictions • Normalization sample is a highly pre-scaled, simultaneous Michel e+ sample: – BR(µ→eγ)= NSig * (9.7 x 10-13 ± 10%) – 9.7 x 10-13 is also the branching ratio for which we expect to see 1 event in analysis window in a background-free experiment (single event sensitivity) ( ) ( ) ∏=       ++ − = obsobs N i AccRDSig obs N AccSig A N N R N N S N N N NN NNL 1! exp ,
• Fit accidental Ee (i.e. Michel) spectrum with model: theoretical*acceptance ⊗ resolution – Acceptance: error function plateauing at high energy – Resolution: sum of two Gaussians • Use event-by-event estimator of Ee uncertainty from Kalman track fitter (δEe), expect strong correlation with Ee resolution – Fit spectrum in nine bins of δEe – Interpolate between bins by deforming shape of PDF from one bin to next • Differences from collaboration analysis – Collaboration divides positrons into only 2 categories based on track fit χ2 , # of hits, etc… – A PDF for each category is prepared, no interpolation done between them PDFs: Accidental Positron Energy δEe<0.345 MeV 0.345≤δEe<0.365 MeVInterpolation of PDF shape Norm alized δE e
PDFs: Signal Positron Energy • Take signal Ee PDF from resolution component of fit to Michel spectrum (sum of 2 Gaussians) • Varies significantly with δEe as one would expect – Full RMS varies by 60% – Again interpolate PDF shape between bins • Average Ee resolution: σcore=310 keV, 83% in core, σtail=1.5 MeV • Differences from collaboration analysis – Collaboration uses only the 2 positron categories – PDF for each category, no interpolation done between them – Full RMS changes by just ~14%
PDFs: Signal Photon Energy • Eγ resolution from 55 MeV γ source (π0 γγ) – Gaussian high energy part (σEγ) – Exponential low energy tail from early conversions, shower escape through inner face • Response map prepared in 3D bins of conversion point – Spatial variations of performance (e.g., PMT saturation near edges) – Smooth each parameter with series of 2D linear interpolation surfaces • Resolution: 2.1% (1.1 MeV) for deep events (w>2 cm), ~3% when shallower • Differences from collaboration analysis – Same 3D response map is used – Collaboration does not smooth, arbitrarily similar events may get 40% different PDF widths σEγ
• Plot accidental Eγ distribution in time sidebands – Hard to model γ’s from different sources, resolution, acceptance, pileup – Use histogram itself as PDF shape – Try binning in each of 3 dimensional coordinates of 1st conversion • Distribution expected to change due to spatial variations of Eγresolution • Fit histogram of one bin to other bins of the same coordinate and check for bad χ2 • Only significant variation is with conversion depth (w) • Use four bins of conversion depth and interpolate PDF shape between • Differences from collaboration analysis – Collaboration analysis fits complicated model to distribution – Full three-dimensional binning in conversion position – No interpolation between bins PDFs: Accidental Photon Energy w<1.5 cm 1.5≤w<3.7cm 3.7≤w<7.2 cm w>7.2 cm
PDFs: Accidental and Signal Relative Time • Accidental time PDF from time sidebands – Expect flat distribution aside from any trigger effects – Distribution indeed consistent with flat line – Flat line used for the PDF – No event-by-event variation necessary • Signal time PDF from µ→eνeνµ γ in lower Eγ sideband – Fit Gaussian + accidental background floor – No significant variation with event properties – Use constant PDF – Resolution in teγ of 150 ps • Differences from collaboration analysis – Collaboration prepares different signal PDF for each positron category, width changes by only 2σ – Includes correlation of mean of teγ with Ee • Error in Ee changes path length of projection to timing counter • Taking signal MC result on faith of ~50 ps / MeV
PDFs: Accidental Relative Angles • Fit accidental φeγ and θeγ distributions in time sidebands to polynomials • Sensitive to trigger effects and acceptance edge effects • For fixed φeγ and θeγ, fixing the photon conversion location almost fixes the full orientation – Bin φeγ distribution in coordinate along inner face arc (v) – Bin θeγ distribution in coordinate along beam axis (u) • Interpolate PDF shape between bins • Differences with collaboration analysis – Same technique for binning in conversion coordinates – No interpolation of PDF shape between bins φ θ u<-12 cm -12 ≤u<-2.5 cm u>14.5 cm
• Simulate relative angle resolutions using component resolutions – Combine the effects of: • Resolution in e+ angle: from 2 turn tracks – Measure θe resolution in bins of δEe and interpolate between them – Measure φe resolution in bins of δEe and φe, only interpolate in φe • Vertex resolution at target: from measured correlations – Vertex position error is correlated with and dominated by angle error – Measure correlations with data and tracking algorithm • Photon position resolution: from lead collimator data + MC – Resolutions in each of 3 coordinates binned in relevant coordinates – Smooth parameters of resolution function with interpolation surfaces – Average relative angle resolutions (full RMS): θeγ~ 16.8 mrad, φeγ~15.1 mrad • Differences with collaboration analysis – Collaboration prepares 2 PDFs for positron angles: 2 categories, no interpolation – No smoothing of photon position resolutions in the conversion coordinates PDFs: Signal Relative Angles -100≤φe<400 mrad 500≤φe<950 mrad Fixed δEe < 0.258 MeV
PDFs: Signal Relative Angle Correlations • Signal φeγ PDF correlated with signal Ee PDF – Error in e+ momentum (path length) affects projection to target – Size and sign of effect depend on φe • Signal φeγ PDF correlated with signal θeγ PDF – Error in θe affects vertex z and x, and thus φe – Size depends on e+,γ angle resolutions • Correlations measured directly with data & tracking algorithm, collaboration relies on Target x y Correct Ee Error in Ee Target z x Correct θe Error in θe Example of simulated correlation for a certain event
PDFs: Radiative Decay • Relative time PDF is same as signal • Other variables (Ee, Eγ, φeγ,θeγ ) are correlated by RD BR from theory • Need to multiply by acceptances and convolve with response functions – Acceptance and response functions differ for each event – Strength of correlations differ for each event – Perform for each event, most computing intensive part of analysis • Differences with collaboration analysis – Collaboration folds φeγ,θeγ into opening angle resolution, convolve in (Ee, Eγ, Θeγ) – Ignores correlation between error in Ee and error in φeγ – Ignores correlation between error in θeγ and error in φeγ 1D Projections of RD PDF onto each kinematic observable for an example event
Confidence Level and Sensitivity • Need 90% confidence interval on NSig with nuissance parameter NAcc: • Feldman-Cousins technique using profile likelihood statistic – At some test point Ni Sig calculate L ratio for data: – Generate experiments of Ni Sig according to PDFs, for each compute: – Confidence level at test point is probability P(Ri data>Ri sim) over the simulations • Collaboration analysis has 2 nuissance parameters since is NRD floated • Blind estimates of sensitivity – Set NSig=0 andNRD,NAcc=expected number in analysis window – Simulate ensemble of experiments and plot distribution of 90% UL – Median value at 4.9 x 10-12 – Collaboration result of 3.3 x 10-12 – Fit and calculate 90% UL in time sidebands where no signal is expected: 3-5 x 10-12 ( )AccSig NNL , ),(/ max max Acc i Sig i data NNLLR = ),(/ max max j j Acc i Sig i sim NNLLR = Best fit NSig Test NSig Rdata Rsim
• Fit to analysis window – Best fit NSig =1.5 – NSig =0 falls in 90% CI – NSig =8.1 (90% CL UL) – BR(µeγ)< 7.9 x 10-12 (90% CL) – 28% of simulated UL’s at this level or greater for null experiment • Collaboration result – Best fit NSig =3.4 – NSig =0 just outside 90% CI – NSig =10.4 (90% CL UL) – BR(µeγ)< 9.6 x 10-12 (90% CL) – 3% of simulated UL’s at this level or greater for null experiment • Why the difference? – UCI selection cuts removed some events including 2nd ranked event in LSig/Ltotal End Result Signal PDF RD PDF Accidental PDF Total
Conclusion • An independent, UCI likelihood analysis was performed on 2009 data to search for µeγ • Results consistent with null hypothesis • BR(µeγ)< 7.9 x 10-12 (90% CL) improves collaboration result by 20% • Both results improve limit from MEGA of BR(µeγ)< 1.2 x 10-11 (90% CL) • Current most stringent published result is collaboration analysis of 2009+2010 data: BR(µeγ)< 2.4 x 10-12 (90% CL) • MEG will continue running toward the goal of reaching few x 10-13 sensitivity Large mixing in ν Yukawas Small mixing in ν Yukawas
Backup
Moving Forward from Previous Experience Exp./Lab Year σRMS Resolutions Stop rate [MHz] Duty cycle [%] BR (90% CL) Ee [%] Eγ [%] ∆teg[ps] ∆θeg[mrad] LANLLANL 19791979 3.73.7 3.43.4 810810 1616 2.42.4 6.46.4 1.7 x 101.7 x 10-10-10 Crystal BoxCrystal Box 19861986 3.43.4 3.43.4 765765 3737 0.40.4 6.96.9 4.9 x 104.9 x 10-11-11 MEGAMEGA 19991999 0.510.51 1.91.9 680680 77 250250 6.76.7 1.2 x 101.2 x 10-11-11 MEG prop. 20X X 0.38 1.7 64 8 30 100 2 x 10-13 • MEG uses continuous muon beam – Accidental background rate proportional to instantaneous beam rate – For same resolutions as MEG, MEGA would’ve faced 8 times the accidental background rate • MEG utilizes liquid xenon calorimeter – Good photon timing resolution (43 ps) and high detection efficiency (60%) – MEGA used Pb layer to convert photon to e+ e- pairs, then measured in drift chambers – Thin converter for good energy resolution limits the acceptance (~5%) – Time resolution ~ 600 ps
Systematic Uncertainties • Sources of systematic uncertainties – PDF shapes: means, widths, correlation magnitudes – Predicted number of radiative decays since it is fixed – Normalization • Inclusion in the analysis – In CL calculation: PDF shapes, true NSig, and true NRD fluctuated by estimated uncertainties – Get feel for effects by changing things and refitting for Nsig • Effects from systematic uncertainties: σ(NSig) ~ 0.6 • Largest sources from center of φeγ PDF and teγ resolution • Effects from statistical uncertainty of fit: σ(NSig) ~ 3

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UCISem

  • 1.
    January 29 20101/55 Some Recent Results from the MEG Experiment on µ → eγ: Benjamin Golden Joint Particle Seminar February 8, 2012 University of California, Irvine
  • 2.
    Outline • Part I- The Theory of Lepton Flavor – Lepton Flavor Symmetries in the Standard Model – Lepton Flavor Symmetries and the Lack Thereof Beyond the Standard Model • Part II - The MEG Detector – Event Signatures – Hardware Design • Part III - Event Reconstruction – Photon Reconstruction – Positron Reconstruction • Part IV – A UCI Search for µ → eγ – Likelihood Framework – PDFs – Results – Comparison with (collaboration) published results
  • 3.
    Part I The Theoryof Lepton Flavor: A Window to the UV Completion of the Standard Model
  • 4.
    The Standard ModelAchromatic Sector: Leptons • SU(2)L x U(1)Y couples to leptons, there are no right-handed ν’s • Three generations are known to exist: f=e,µ,τ • Left-handed leptons: Right-handed leptons: • With massless neutrinos, the SM conserves lepton flavor for each generation classically – Result of 3 accidental global U(1) symmetries: – Gives 3 Noether charges: • Instantons spoil the classical conservation of Lf but exactly preserve – B – L (Sufficient to keep neutrinos massless even at non-perturbative level) – (Lτ – Le), (Lµ – Le) (Sufficient to exclude µeγ) • Neutrino masses must enter the SM Lagrangian in some unknown way – µeγ receives contributions from active neutrino loops – With experimental information on ∆mij 2 , these diagrams alone imply undetectably small rates for µeγ – Additional diagrams with new matter content would be needed to enhance Br(µeγ) to something detectable – An observation of µeγ would demonstrate the existence of new physics Lf f f l       = ν L Rff l )(R = ff f LeL -iq → ff f ReR -iq → fff N-NQ = µ± e ± γ W± νiUµi U* ei
  • 5.
    ~eµ~ CLFV in SUSYModels: A Little Help from the Sleptons • The SUSY flavor problem – µeγ can proceed in SUSY through diagrams that communicate slepton mixing to leptons – BR(µeγ)<10-11 requires a fine alignment between lepton and slepton mass matrices – Yet lepton masses come from Yukawa interaction, while slepton masses arise from SUSY breaking – Addressed by a number of proposed solutions, all with highly model dependent consequences for BR(µeγ), here focus on one example: Gravity mediation • Gravity Mediation – SUSY broken in a hidden sector, gravitational interactions generate diagonal squark and slepton mass matrices, all with the same universal scalar mass at MPlanck ~ 1018 GeV – Slepton mixing appears from RGE’s running from MPlanck to electroweak scale – An oft-cited, cliché of an example is SO(10) GUT – At MPlanck, theory is tied down by choice of m0 (scalar mass),M1/2 (gaugino mass), A0 (trilinear coupling) – Fix tan β, make assumptions about parameters in superpotential – Scan (m0,M1/2,A0)in a region that allows a squark mass below 2.5 TeV (LHC accessible) × µ e γ ~χ0 Large mixing in ν Yukawas Small mixing in ν Yukawas
  • 6.
    CLFV’s Place inthe Landscape of Gauge Hierarchy Problem Solutions: Generic • Non-SUSY solutions to hierarchy problem allow µeγ for other reasons • Dynamical EWSB (Technicolor) – Fermion condensate develops dynamically, plays the role of the Higgs – Requires non-universal gauge groups that induce LFV couplings of gauge boson to lepton mass eigenstates • Little Higgs – New vector bosons, fermions, scalars cancel 1-loop corrections to Higgs – LFV from gauge bosons and exotic scalar multiplets • Extra Dimensions – Planck mass is actually small (Gravity weak from loss of flux to extra dimensions) – RHN in bulk generate µeγ where KK states play similar role to sparticles • Some discerning power available: Linear correlation in BR(µeγ) & BR(µNeN) would favor MSSM over these
  • 7.
    Part II The MEGDetector: At the Frontier of Low Energy Precision Measurement
  • 8.
    Signal and Background •Accidentals are dominant background at rates high enough to reach 10-13 sensitivity Signal µ+ →e+ γ µµ++ γγee++ Radiative decay background µ+ →e+ νeνµ γ ν ν µµ++ee++ γγ Accidental background µ+ →e+ νeνµ + µ+ →e+ ννγ or e+ e- →γγ or e+ Z→e+ Zγ ν νµµ++ee++ γγ ΘΘeeγγ == 180°180° EEee ≈≈ EEγγ ≈≈ 52.852.8 MeVMeV TTee = T= Tγγ ΘΘeeγγ = any angle= any angle EEee, E, Eγγ << 52.852.8 MeVMeV TTee = T= Tγγ ΘΘeeγγ == randomrandom EEee, E, Eγγ << 52.852.8 MeVMeV TTee –T–Tγγ == randomrandom • For fixed MEG acceptance: Naccidental /Nμ ∝ Rate × ∆teγ × ∆Ee × (∆Eγ)2 × (∆Θeγ )2 Ee ~ flatEγ ~ rising linearly
  • 9.
    1 History of µ→eγSearches 10-2 10-4 10-16 10-6 10-8 10-10 10-14 10-12 1940 1950 1960 1970 1980 1990 2000 2010 MEGA BranchingFractionUpperLimit MEG goal MEG 2009+201 0 result
  • 10.
    MEG Timeline: Past,Present, and Future • Data Taking – 1998: Original LOI (PSI-RR-99-05) – 2002: Proposal with a goal of 10-13 sensitivity – 2007: (Nov-Dec): Engineering run – 2008: (Sep-Dec): 1st physics run, some hardware problems – 2009: (Nov-Dec): 2nd physics run – 2010: (Aug-Dec): 3rd physics run – 2011: (July-Nov): 4th physics run – 2012: continue data taking • Physics Analysis for Br(µeγ) – 2008 Data Analysis: • 90% CL UL = 2.8 x 10-11 • Sensitivity = 1.3 x 10-11 – 2009 Data Analysis: • 90% CL UL = 9.6 x 10-12 [Collaboration result] • Sensitivity = 3.3 x 10-12 [Collaboration result] • Also the object of independent UCI analysis [Primary Content of this Talk] – 2009+2010 Data Analysis: • 90% CL UL = 2.4 x 10-12 • Sensitivity = 1.6 x 10-12
  • 11.
    MEG Experiment Design •~ 3x107 µ ＋ /s beam incident on a thin stopping target • Positron detection – Gradient B-field to sweep out e+ quickly and keep bending radius constant – Low mass drift chambers to measure energy, emission angles, & path to timing counter – Timing counter with scintillating plastic for precise time measurement • Photon detection – Energy, position, and time measured in a liquid xenon calorimeter – Fast response time, high light yield, high photocathode coverage
  • 12.
    Paul Scherrer Institut(PSI) • The other accelerator lab in Switzerland • Highest power operating proton accelerator – 2.2 mA, 590 MeV kinetic energy, 1.3 MW beam power – Extremely reliable – Provides secondary pion, muon, neutron beams 590 MeV proton ring cyclotron MEG Office Apartment: 45 minute journey through forest
  • 13.
    Muon Delivery toMEG: Beam & Target • Muon Beam – Produce pions in graphite target – Extract 29 MeV/c muons from π+ decay at rest (can be stopped in thin target) – Wien filter for µ/e separation – Beam transport solenoid for focusing – Mylar degrader to slow muons (~300 µm) – 3x107 µ/s, final spot size σx,y ~ 1 cm • Muon Stopping Target – 205 µm thick polyethylene – 20° slant from beam direction for more stopping power – Holes to check alignment using reconstructed e+ tracks 590 MeV proton beam target µ+ beam line µ+ /e+ separator beam transport solenoid MEG Detector Degrader µ+
  • 14.
    COBRA Magnetic Field COnstantBending RAdius Positrons swept out quickly z θ • R=Psin(θ)/QB • B-field must decrease with |z| to keep R constant and independent of θ (range: 0.5-1.3 T) • Allows precise selection window in R for high momentum tracks • R changes with |z| in such a way to make fewer turns in the DCH • Simplifies pattern recognition • Helps limit rate for stable chamber operation
  • 15.
    The Drift Chamber •Measure e+ energy, extrapolate to target for angles and decay vertex • Extrapolate to TIC to correct impact time by flight time (to ~1 cm in path length) • 16 chambers radially aligned at 10.5° intervals • 2 planes of drift cells staggered by ½ cell; 18 wires each chamber • Acceptance matched to that of calorimeter • Radial position from drift time • Resistive wires for approximate Z by charge division, pattern etched on cathode pads to interpolate Z • Gas: He – Ethane mixture (50:50): (X0~650 m, vd saturates at ~4 cm/µs) • Goals: σR = 200 µm σZ = 300 µm σe+ energy = 180 keV • Total average path of one turn .002 X0
  • 16.
    Timing Counter • Primarypurpose: trigger & precise e+ time • Inner layer of 256 scintillating plastic fibers – Coupled to APD’s (tolerate B-field, Smaller->easier to align with small fibers) – Each end of COBRA at fixed Z – Used for z measurement and in the trigger • Outer layer of 15 scintillating plastic bars – Coupled to PMT’s – Each end of COBRA at fixed φ – Used for impact time and φ measurement • 29 cm < |z| < 109 cm • TIC surrounded by N2 because PMT’s have short life in Helium • Goal: σt = 40 ps
  • 17.
    Liquid Xenon Calorimeter Liq.Xe H.V. Vacuum for thermal insulation Al Honeycomb window PMT Refrigerator Cooling pipe Signals fillerPlastic 1.5m Density 2.95 g/cm3 Boiling and melting points 165 K, 161 K Energy per scintillation photon 24 eV Radiation length 2.77 cm Decay time 4.2, 22, 45 ns Scintillation light wave length 175 nm Scintillation light absorption length > 100 cm Attenuation length (Rayleigh scattering) 30 cm Refractive index 1.56 • Relatively high light yield, uniform response • No self-absorption of scintillation light: attenuation only from impurities • 900 L liquid xenon (largest LXE volume) • 846 mesh phototubes on surfaces, in LXE • Thin magnet wall to reduce photon conversions • Goal is to measure photon properties: – Position: σRMS = 3.5 mm – Time: σRMS = 40 ps – Energy: σRMS = ~900 keV at 52.8 MeV
  • 18.
    Dedicated Calibration Tools •Calorimeter – CEX reaction: π− +p (LH2 target)  π0 + n followed by π0  γγ (98.8%) • Select events with 83 MeV γ in NaI detector and a back-to-back γ in XEC (55 MeV) • Used to measure γ energy scale, resolution; γ time resolution, PMT time delays • Position resolution of γ from data with lead collimator in front of XEC entrance – Cockcroft-Walton proton accelerator (Li2B4O7 target) – LEDs mounted in XEC • Flash with different intensities • Calibrate PMT gains – QE measured by scintillation light from α sources mounted at known positions (241 Am) • Laser measurements of reference marks on drift chambers and target for primary alignment • Relative TIC-XEC timing from Dalitz data (π0  e+ e- γ ) Reaction Eγ [MeV] Uses p + Li → Be + γ 17.6 Monitor light yield p + B → C + γ + γ 4.4 + 11.6 Cross-time LXE and timing counter check α source wire LED LED
  • 19.
    Part III Event Reconstruction: GettingParticle Kinematics from Waveforms I don’t know what I’m looking at.
  • 20.
    Photon Reconstruction inthe Calorimeter • Position (of 1st conversion) – Fit to pattern of light on inner face PMTs – Angles at target from e+ vertex and γ conversion position • Energy – First estimate from sum of all PMT signals weighted by local photocathode coverage – Apply corrections as function of position, determined from calibration photons (55 MeV, 17.6 MeV) • Large variation of photocathode coverage with position for shallow depth conversions • Same occurs near edges in transverse coordinate • Time – Weighted average of PMT leading edge times – Correct for flight time from vertex to conversion position
  • 21.
    Positron Reconstruction inthe Drift Chamber & Timing Counter • Drift Chamber – Hit Reconstruction • Identify cells with waveforms consistent with through-going charged particle • Hit time from leading edge of pulse • Z from charge division – Clustering: Group hits on a chamber, spatially consistent with charged particle – Tracking • Group clusters into tracks • Drift times using TIC time to get track time – Kalman Filter to fit track • Calculates positron energy • Extrapolation to target for angles and vertex • Extrapolation to TIC for path length • Provides event-by-event uncertainties in track parameters (energy uncertainty, …) • Timing Counter – Impact time at bar from waveform leading edges of PMTs – Correct for time of flight from vertex to bar
  • 22.
    Part IV Current MEGResults & UCI Analysis on 2009 Data:
  • 23.
    Summary of PublishedMEG Results (October 2011) |teγ|<0.28ns; cosΘeγ< -0.9996 51<Eγ<55 MeV; 52.3<Ee<55 MeV BR(best fit) LL 90% CL UL 90% CL 2009 3.2×10-12 0.17×10-12 9.6×10-12 2010 -0.99×10-13 -- 1.7×10-12 2009+2010 -0.15×10-13 -- 2.4×10-12 Expected UL (2009+2010) 1.6×10-12 2009 Data  2010 Data  (~2 x as much data as 2009) Contours: 1σ 1.64σ 2σ
  • 24.
    • A raredecay search is very sensitive to the exact values of selection cuts • If it is known which events satisfy cuts during analysis, 2 extreme cases of bias: – Cut to eliminate individual events, yielding better upper limit than justified – Cut to retain individual events, producing a signal where none is present • Use “Hidden Signal Box” technique (<0.2% of data in blind box) – Signal-like events are hidden until selection cuts and likelihood function are determined • 48 E≤ γ 58 MeV≤ • | Teγ | 0.7 ns≤ – Sidebands adjacent to signal box (16% of data) • Can look at radiative decays for Eγ 48 MeV≤ • Can look at accidental photons in | Teγ | > 0.7 ns • Analysis Window – 48 E≤ γ 58 MeV≤ – | Teγ | 2.1 ns≤ • Effective constraint on accidentals by including sidebands in fit • Collaboration uses | Teγ | 0.7 ns, adds constraint on accidentals from sideband extrapolation≤ – |φeγ|, | θeγ | 50 mrad (angles btw. reversed e+ and≤ γ vectors) – 50 E≤ e 56 MeV≤ Blind Analysis Technique: Setting σexperimenter bias = 0 UCI Analysis Window BLIND BOX (Collaboration Analysis Window) Left Sideband Right Sideband Bottom Sideband
  • 25.
    Event Selection Criteria:Quality Control • Basic strategy – If we wouldn’t believe a signal event with some characteristic, we remove such events from the sample – Incorporate the dependence of resolutions on event properties into event-by- event probability density functions (PDFs) • Positron – Track quality (# of hits, chamber extent, χ2 of fit, etc…) – Remove events not consistent with a muon stopping in the target – Imposed some cuts not present in collaboration analysis • Photon – Cosmic ray veto based on conversion depth and ratio of inner/outer face γ’s – Preserve events with in-time pileup by removing energy in secondary shower centroid – Reject irrecoverable pile-up events
  • 26.
    Maximum Likelihood Analysis •Fit for numbers of signal (NSig) and accidental (NAcc) events by maximizing an extended likelihood function – N= NSig +NRD + Nacc – NRD is fixed to expectation from bottom sideband extrapolation – Kinematic observables: Ee, Eγ, teγ, φeγ,θeγ – S is probability for a signal to result in the set of observables of a given event, similarly for R and A (S, R, & A are called PDFs) • Some differences with collaboration likelihood fit – Collaboration handles background differently ― NRD is floated rather than fixed ― Fit in 3 times smaller time region, 3 times fewer accidentals in the fit – Collaboration adds Gaussian constraints to likelihood function on NAcc and NRD ― Means of Gaussians from extrapolations ― Sigmas of Gaussians from statistical uncertainties of predictions • Normalization sample is a highly pre-scaled, simultaneous Michel e+ sample: – BR(µ→eγ)= NSig * (9.7 x 10-13 ± 10%) – 9.7 x 10-13 is also the branching ratio for which we expect to see 1 event in analysis window in a background-free experiment (single event sensitivity) ( ) ( ) ∏=       ++ − = obsobs N i AccRDSig obs N AccSig A N N R N N S N N N NN NNL 1! exp ,
  • 27.
    • Fit accidentalEe (i.e. Michel) spectrum with model: theoretical*acceptance ⊗ resolution – Acceptance: error function plateauing at high energy – Resolution: sum of two Gaussians • Use event-by-event estimator of Ee uncertainty from Kalman track fitter (δEe), expect strong correlation with Ee resolution – Fit spectrum in nine bins of δEe – Interpolate between bins by deforming shape of PDF from one bin to next • Differences from collaboration analysis – Collaboration divides positrons into only 2 categories based on track fit χ2 , # of hits, etc… – A PDF for each category is prepared, no interpolation done between them PDFs: Accidental Positron Energy δEe<0.345 MeV 0.345≤δEe<0.365 MeVInterpolation of PDF shape Norm alized δE e
  • 28.
    PDFs: Signal PositronEnergy • Take signal Ee PDF from resolution component of fit to Michel spectrum (sum of 2 Gaussians) • Varies significantly with δEe as one would expect – Full RMS varies by 60% – Again interpolate PDF shape between bins • Average Ee resolution: σcore=310 keV, 83% in core, σtail=1.5 MeV • Differences from collaboration analysis – Collaboration uses only the 2 positron categories – PDF for each category, no interpolation done between them – Full RMS changes by just ~14%
  • 29.
    PDFs: Signal PhotonEnergy • Eγ resolution from 55 MeV γ source (π0 γγ) – Gaussian high energy part (σEγ) – Exponential low energy tail from early conversions, shower escape through inner face • Response map prepared in 3D bins of conversion point – Spatial variations of performance (e.g., PMT saturation near edges) – Smooth each parameter with series of 2D linear interpolation surfaces • Resolution: 2.1% (1.1 MeV) for deep events (w>2 cm), ~3% when shallower • Differences from collaboration analysis – Same 3D response map is used – Collaboration does not smooth, arbitrarily similar events may get 40% different PDF widths σEγ
  • 30.
    • Plot accidentalEγ distribution in time sidebands – Hard to model γ’s from different sources, resolution, acceptance, pileup – Use histogram itself as PDF shape – Try binning in each of 3 dimensional coordinates of 1st conversion • Distribution expected to change due to spatial variations of Eγresolution • Fit histogram of one bin to other bins of the same coordinate and check for bad χ2 • Only significant variation is with conversion depth (w) • Use four bins of conversion depth and interpolate PDF shape between • Differences from collaboration analysis – Collaboration analysis fits complicated model to distribution – Full three-dimensional binning in conversion position – No interpolation between bins PDFs: Accidental Photon Energy w<1.5 cm 1.5≤w<3.7cm 3.7≤w<7.2 cm w>7.2 cm
  • 31.
    PDFs: Accidental andSignal Relative Time • Accidental time PDF from time sidebands – Expect flat distribution aside from any trigger effects – Distribution indeed consistent with flat line – Flat line used for the PDF – No event-by-event variation necessary • Signal time PDF from µ→eνeνµ γ in lower Eγ sideband – Fit Gaussian + accidental background floor – No significant variation with event properties – Use constant PDF – Resolution in teγ of 150 ps • Differences from collaboration analysis – Collaboration prepares different signal PDF for each positron category, width changes by only 2σ – Includes correlation of mean of teγ with Ee • Error in Ee changes path length of projection to timing counter • Taking signal MC result on faith of ~50 ps / MeV
  • 32.
    PDFs: Accidental RelativeAngles • Fit accidental φeγ and θeγ distributions in time sidebands to polynomials • Sensitive to trigger effects and acceptance edge effects • For fixed φeγ and θeγ, fixing the photon conversion location almost fixes the full orientation – Bin φeγ distribution in coordinate along inner face arc (v) – Bin θeγ distribution in coordinate along beam axis (u) • Interpolate PDF shape between bins • Differences with collaboration analysis – Same technique for binning in conversion coordinates – No interpolation of PDF shape between bins φ θ u<-12 cm -12 ≤u<-2.5 cm u>14.5 cm
  • 33.
    • Simulate relativeangle resolutions using component resolutions – Combine the effects of: • Resolution in e+ angle: from 2 turn tracks – Measure θe resolution in bins of δEe and interpolate between them – Measure φe resolution in bins of δEe and φe, only interpolate in φe • Vertex resolution at target: from measured correlations – Vertex position error is correlated with and dominated by angle error – Measure correlations with data and tracking algorithm • Photon position resolution: from lead collimator data + MC – Resolutions in each of 3 coordinates binned in relevant coordinates – Smooth parameters of resolution function with interpolation surfaces – Average relative angle resolutions (full RMS): θeγ~ 16.8 mrad, φeγ~15.1 mrad • Differences with collaboration analysis – Collaboration prepares 2 PDFs for positron angles: 2 categories, no interpolation – No smoothing of photon position resolutions in the conversion coordinates PDFs: Signal Relative Angles -100≤φe<400 mrad 500≤φe<950 mrad Fixed δEe < 0.258 MeV
  • 34.
    PDFs: Signal RelativeAngle Correlations • Signal φeγ PDF correlated with signal Ee PDF – Error in e+ momentum (path length) affects projection to target – Size and sign of effect depend on φe • Signal φeγ PDF correlated with signal θeγ PDF – Error in θe affects vertex z and x, and thus φe – Size depends on e+,γ angle resolutions • Correlations measured directly with data & tracking algorithm, collaboration relies on Target x y Correct Ee Error in Ee Target z x Correct θe Error in θe Example of simulated correlation for a certain event
  • 35.
    PDFs: Radiative Decay •Relative time PDF is same as signal • Other variables (Ee, Eγ, φeγ,θeγ ) are correlated by RD BR from theory • Need to multiply by acceptances and convolve with response functions – Acceptance and response functions differ for each event – Strength of correlations differ for each event – Perform for each event, most computing intensive part of analysis • Differences with collaboration analysis – Collaboration folds φeγ,θeγ into opening angle resolution, convolve in (Ee, Eγ, Θeγ) – Ignores correlation between error in Ee and error in φeγ – Ignores correlation between error in θeγ and error in φeγ 1D Projections of RD PDF onto each kinematic observable for an example event
  • 36.
    Confidence Level andSensitivity • Need 90% confidence interval on NSig with nuissance parameter NAcc: • Feldman-Cousins technique using profile likelihood statistic – At some test point Ni Sig calculate L ratio for data: – Generate experiments of Ni Sig according to PDFs, for each compute: – Confidence level at test point is probability P(Ri data>Ri sim) over the simulations • Collaboration analysis has 2 nuissance parameters since is NRD floated • Blind estimates of sensitivity – Set NSig=0 andNRD,NAcc=expected number in analysis window – Simulate ensemble of experiments and plot distribution of 90% UL – Median value at 4.9 x 10-12 – Collaboration result of 3.3 x 10-12 – Fit and calculate 90% UL in time sidebands where no signal is expected: 3-5 x 10-12 ( )AccSig NNL , ),(/ max max Acc i Sig i data NNLLR = ),(/ max max j j Acc i Sig i sim NNLLR = Best fit NSig Test NSig Rdata Rsim
  • 37.
    • Fit toanalysis window – Best fit NSig =1.5 – NSig =0 falls in 90% CI – NSig =8.1 (90% CL UL) – BR(µeγ)< 7.9 x 10-12 (90% CL) – 28% of simulated UL’s at this level or greater for null experiment • Collaboration result – Best fit NSig =3.4 – NSig =0 just outside 90% CI – NSig =10.4 (90% CL UL) – BR(µeγ)< 9.6 x 10-12 (90% CL) – 3% of simulated UL’s at this level or greater for null experiment • Why the difference? – UCI selection cuts removed some events including 2nd ranked event in LSig/Ltotal End Result Signal PDF RD PDF Accidental PDF Total
  • 38.
    Conclusion • An independent,UCI likelihood analysis was performed on 2009 data to search for µeγ • Results consistent with null hypothesis • BR(µeγ)< 7.9 x 10-12 (90% CL) improves collaboration result by 20% • Both results improve limit from MEGA of BR(µeγ)< 1.2 x 10-11 (90% CL) • Current most stringent published result is collaboration analysis of 2009+2010 data: BR(µeγ)< 2.4 x 10-12 (90% CL) • MEG will continue running toward the goal of reaching few x 10-13 sensitivity Large mixing in ν Yukawas Small mixing in ν Yukawas
  • 39.
  • 40.
    Moving Forward fromPrevious Experience Exp./Lab Year σRMS Resolutions Stop rate [MHz] Duty cycle [%] BR (90% CL) Ee [%] Eγ [%] ∆teg[ps] ∆θeg[mrad] LANLLANL 19791979 3.73.7 3.43.4 810810 1616 2.42.4 6.46.4 1.7 x 101.7 x 10-10-10 Crystal BoxCrystal Box 19861986 3.43.4 3.43.4 765765 3737 0.40.4 6.96.9 4.9 x 104.9 x 10-11-11 MEGAMEGA 19991999 0.510.51 1.91.9 680680 77 250250 6.76.7 1.2 x 101.2 x 10-11-11 MEG prop. 20X X 0.38 1.7 64 8 30 100 2 x 10-13 • MEG uses continuous muon beam – Accidental background rate proportional to instantaneous beam rate – For same resolutions as MEG, MEGA would’ve faced 8 times the accidental background rate • MEG utilizes liquid xenon calorimeter – Good photon timing resolution (43 ps) and high detection efficiency (60%) – MEGA used Pb layer to convert photon to e+ e- pairs, then measured in drift chambers – Thin converter for good energy resolution limits the acceptance (~5%) – Time resolution ~ 600 ps
  • 41.
    Systematic Uncertainties • Sourcesof systematic uncertainties – PDF shapes: means, widths, correlation magnitudes – Predicted number of radiative decays since it is fixed – Normalization • Inclusion in the analysis – In CL calculation: PDF shapes, true NSig, and true NRD fluctuated by estimated uncertainties – Get feel for effects by changing things and refitting for Nsig • Effects from systematic uncertainties: σ(NSig) ~ 0.6 • Largest sources from center of φeγ PDF and teγ resolution • Effects from statistical uncertainty of fit: σ(NSig) ~ 3

Editor's Notes

  • #5 |m322 | ≈ 2.5 x 10-3 eV2 from SuperK atmospheric neutrino data m212 ≈ 7 x 10-5 eV2 from KamLAND + SNO + other solar neutrino data
  • #6 trilinear scalar soft-breaking terms like Hl_{L}l_{R} are proportional to Yukawas by A_{0}
  • #9 Select in a spherical cap, then solid angle subtend goes as 1-cos(dTheta), prop to dTheta^2 in lowest order expansion
  • #13 Neutron source: protons strike lead ejecting neutrons which are slowed in heavy water
  • #14 At rest pions decaying in target are trapped unless they are near the surface Wien filter separates e from mu by 7.5 sigma of beam profile Reason for e contamination: low energy e’s from decay of trapped muons, pair production from photons coming out of pi0 decay (factor 10 more than muon content) Want to reduce scattering of e+ in target and additional photon production from AIF What dictates target angle: match beam stopping distribution to get stops at center
  • #15 We can place DC at large R to avoid saturation with uninteresting and harmful low energy positrons. Since |p_{z}| and |p_{T}| are constant, if it has to cross more distance in x-y from bigger circles, it will take longer to make a turn.
  • #16 C=.03 cm/ps, so 1 cm = 33 ps Thin carbon frame, r=20-30 cm, 40-80 cm in Z 80 keV energy loss average Saturates for low E field (1.5 kV/cm) in inner half of cell
  • #17 160 degrees acceptance in phi
  • #18 Ionizing radiation from showers excites or ioinizes Xe, which then emits VUV scintillation light. (Compare to NaI response time ~ 100’s of ns) VUV absorbed in water vapor and oxygen. R_{inner}=68 cm R_{outer}=106 cm Absorption (attenuation) length is distance over which 63 % of particles are absorbed Require impurities at &amp;lt; 100 ppb
  • #19 NaI detector: NaI crystals for energy measurement Lead plate for pair production and scintillators to measure time (72 ps resolution) LED: &amp;lt;Q&amp;gt; at PMT is Gain*&amp;lt;N_{pe}&amp;gt;, sigma_{Q}=Gain*sqrt(&amp;lt;N_{pe}&amp;gt;) So sigma^{2}_{Q}=Gain*&amp;lt;Q&amp;gt;+noise uncert^2
  • #26 Cosmic ray: cuts 56% of cosmics, 99% signal efficiency (signal converts near inner face and illuminates lots of inner face PMTS so cut events with small inner/outer ratio) Pile-up: probability ~7% (Irrecoverable events: fail to find multiple peaks in inner face light distribution)
  • #27 Poisson probability to obtain Nobs if the expected number is N
  • #41 Duty cycle= bunch width/total period