Charged Lepton Flavor Violation Experiments
Jim MillerBoston UniversityLomonosov, August 21, 2021

g1) Introduction to cLFV Experiments and current status of some ofthe measurements
2) Dedicated, ongoing or developing, muon experiments
3) The outlook for the future

J. Miller - cLFV Experiments2L(e)  1

L(  )  1

L( )  1

L(e)  1

L(  )  1

L( )  1

• The sum of each lepton flavor is conserved!

Muon Decay:   e  g  e  e + Muon to electron conversion:   N  e  NJ. Miller - cLFV Experiments

3• Neutrinos oscillate! e.g.  e   • Lepton flavor is not conserved in this process• Lepton Flavor Violation has not been observed whencharged leptons are involved• It is not known what the mechanism are for Lepton
Flavor conservation or for it s violation• Necessary to study lepton conservation propertiesof charged leptons to help figure this out

J. Miller - cLFV Experiments4• Forbidden in pre-neutrino osc. SM

J. Miller - cLFV Experiments5• Forbidden in the SM• In -SM, possible but extremelysuppressed(rate ~ Dm4 / Mw4 < 10-50)

qqg
W

W


e

J. Miller - cLFV Experiments

Example:Muon to electron
conversion

e-6

• Forbidden in the SMSUSY• In -SM, extremely suppressedg(rate ~ Dm4 / Mw4 < 10-50)• However, many New Physics models are compatible
with rates observable at next generation cLFVexperiments
-->gNe-N

J. Miller - cLFV Experiments

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Process

Current Limit

Next Generation exp

D decays

BR< ~1E-9

  gBR < 6.8 E-8  BR < 3.2 E-8

  eee 8.2
10MMBR <P3.6E-8

KL  eBR < 4.7 E-12

K+  eBR < 1.3 E-11

B0  eBR < 1.0 E-9

B+  K+e

BR < 9.1 E-8

  e+g

BR < 4.2 E-13

6x10-14 (MEG 2)  e+e+e-

BR < 1.0 E-12

10-16 (Mu3e Phase 2-PSI)N  e-NRe < 7.0 E-13

Few x 10-17 (Mu2e, COMET)  e   e

PMM  8.2 E  11

N  e+N

R < 1.7 E-12

LHC

10-9 - 10-10 (Belle II)
11LHCb, Belle II

Mu2e0bb• Some of the most promising cLFV measurements use muonsJ. Miller - cLFV Experiments

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2018
https://scipost.org/SciPostPhysProc.1
J. Miller - cLFV Experiments

9Charged Lepton Flavor Violation: ATLAS-LHC
Current ATLAS limits on the branching fractions for the LFV decays of Z and Higgs
bosons, as obtained at 95% of CL, along with the corresponding dataset.

Process

Current limit

Z → eμZ → eτB < 7.5 × 10−7B < 5.8 × 10−5
B < 8.1 × 10−6
B < 1.3 × 10−5Dataset

HL-LHC prospects(3000 fb-1)

8 TeV, 20 fb−1
13 TeV, 36 fb−1
B ≪9.8 × 10−6 (LEP)
13 TeV 139 fb-1
Oct 2020, better than LEP!
Z → μτ
8 TeV, 20 fb−1 andB ≪1.2 × 10−5 (LEP)
13 TeV, 36 fb−1
B < 9.5 × 10−6
13 TeV 139 fb-1
Oct 2020, better than LEP!
H → eμB < 6.1 × 10−5
13 TeV, 139 fb−1
H → eτ
B < 0.47%
13 TeV, 36 fb−1
B<0.05%
H → μτ
B < 0.28%13 TeV, 36 fb−1
B <0.05%
The symbol “≪” are current LEP limits that will be improved upon at LHC.
T. Davodek, L. Fiorini, Frontiers in Physics, https://doi.org/10.3389/fphy.2020.00149(2020)

Recent result from LHCb, arxiv:2103.11769v1

Br ( B  K     )0.044

0.846
0.041Br ( B   K   e   e  )3.1 s.d. from the SM prediction of 1RK 

gNew Physics models generally predict Lepton Flavor
Violation if Universality is violated

J. Miller - cLFV Experiments

11Different SUSY andnon-SUSY BSM
models

Large effects
Visible, butsmall
No sizableeffectAltmannshofer et al.,
NPB 830, 17 (2010)

Different SUSY andnon-SUSY BSM
models

Large effects
Visible, butsmall
No sizableeffectAltmannshofer et al.,
NPB 830, 17 (2010)

•
•
•
•

Relatively easy to produce copious numbers of muons
Muons are relatively long-lived
Muons can be stopped in material and localized
Several experiments now under development arededicated to looking for cLFV with stopped muons   e g(MEG at PSI)   e  e e (Mu3e at PSI)  N  e  N (Mu2e at FNAL, COMET at J-PARC, DeeMe at J-PARC)

J. Miller - cLFV Experiments

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LoopsContact Terms

Supersymmetry

Heavy Neutrinos

Two Higgs Doublets

Compositeness

Leptoquarks

New Heavy Bosons /Anomalous Couplings

NeN sensitive to wide array of New Physics models

J. Miller - cLFV Experiments

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J. Miller - cLFV Experiments

16• Measure back-to-back monoenergetic positron and gamma• MEG set current best limit on eg branching ratio set by MEG at 4.2e-13 (90% CL)• Upgrade under way to improve to achieve 6e-14 limit• Challenges:– Need to suppress backgrounds• Radiative muon decay (RMD)   e  e  g• Accidental coincidences between e+ from    e  e  and a gamma from
RMD or positron annihilation in flight– Need best possible measurement of energies and of the angle between the222gamma and the positron N acc  R  DEg  Dpe  D eg  Dteg  T• MEG currently in engineering runs to commission new equipment–Major improvements in calorimeter energy and position resolutions, new thinner
drift chamber, improved timing counters, DAQ handles higher rates• Increase flux up to 3e7 continuous stopped muons/s compared to ~1e7 previously– May be the ultimate rate limit, limiting ultimate eg sensitivity
arXiv:1801.04688v1J. Miller - cLFV Experiments

17eg
MEG@PSI•••••

Stop + in a thin target using ‘surface’ muons (28 MeV/c, 7% FWHM)
Look for back-to-back 53 MeV electron and gamma
Measure electron momentum and direction in drift chamber in magnetic field
Measure positron time in timing counters
Measure energy, position, time of gamma in liquid xenon scintillating
calorimeter, UV-sensitive PMT’s
J. Miller - cLFV Experiments18• Current best experimental limit BR<1e-12 (SINDRUM 1988)• Phase 1 under construction now at PSI– goal SES 2e-15– Use same muon beamline at PSI as MEG (e5)• Currently the most powerful in the world• 1e8 stopped muons/s for 2.5e7 seconds to reach sensitivity goal
• Phase 2 goal BR<1e-16 (90% CL)– Use high Intensity Muon Beam (HiMB) at PSI planned for >2025?
• Main backgrounds
 Internal conversions    e  e  e   e (with very low energy neutrinos) Radiative muon decay followed by conversion in target,    e  (g  e  e  )  e
 Accidental coincidence between e  e  pair from Bhabha scattering of Michel positronfrom ordinary muon decay, and a Michel positron from another decay• Suppress with– better than 1 MeV FWHM resolution on energy of eee» Minimize multiple scattering Ultra-thin pixelated Si tracker» challenge is cooling with helium gass
– Better than few 100 ps time resolution on tracks- use thin timing scintillators– High resolution on vertex reconstruction

arXiv:2009.11690v2
J. Miller - cLFV Experiments

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J. Miller - cLFV Experiments

20• Stop negative muons in material• Muon rapidly (10-16s) cascades to 1S
state (Al binding ~460 keV, r~20 fm),
forming muonic atom
•Two things most likely happen:
1. muon is captured by the nucleus(61%): -NA,Z→NA,Z-1

Al27
Mg27*

Cause low energy background

2. muon decays in orbit(39%):
-NA,Z→e-eNA,Z
Muonic aluminum lifetime 864 ns
3. Rare, not seen: Muon to electron
conversion -NA,Z→e-NA,Z
Muon Capture• Stop muon in atom
• Muon rapidly (10-16s) cascades to 1S
state (binding ~460 keV, r~20 fm),
forming muonic atom
• Circles nucleus, lifetime ~864 ns• Two things most likely happen:
1. muon is captured by the nucleus:(61%) -NA,Z→NA,Z-1
2. muon decays in orbit (39%):
-NA,Z→e-eNA,Z
Muonic aluminum lifetime 864 ns
3. Rare, not seen: Muon to electron
conversion -NA,Z→e-NA,ZAl27
ee-Muon Decay-in-OrbitIn -N→e-N the muon interacts with nucleus
leaving it in ground state– Signature: delayed single isolated electron– Electron energy is rest mass of the muon Al27
minus the nucleus recoil + binding energy:
Ee = m – ENR - Eb ~ 104.97 MeV (Al)e-Decay of free muon,  =2200 ns:   e   e   Max Ee  53 MeVMuon bound in atomic orbit,  =864 ns:   Al  e   e    Al
Max Ee  104.96 MeV
Decay in orbit (DIO) backgroundIn -N→e-N the muon interacts with nucleus
leaving it in ground state– Signature: delayed single isolated electron– Electron energy is rest mass of the muon Al27
minus the nucleus recoil + binding energy:
Ee = m – ENR - Eb ~ 104.97 MeV (Al)e-Decay of free muon,  =2200 ns:   e   e   Max Ee  53 MeV
R =1e-15

eMuon boundin atomic orbit,  =864 ns:  Al  e  e    AlMax Ee  104.96 MeV
Decay in orbit (DIO) backgroundCurrent and future experimental status of -N→e-N
The ratio of production rate of a monoenergetic conversion
electron to the muon nuclear capture rate

• Current limit 7x10-13 (90% CL) on Au [SINDRUM II, EJP C 47( 2006)337]• COMET phase I (J-PARC), under construction, begins data 4taking 2024
• goal of expected sensitivity (SES)  3x10-15, on Al• Mu2e (FNAL), under construction• Run 1 (2025-2026) Al: (SES) 2.3e-16, 5.9e-16 (90% CL), 1.1e-15 (discovery) 1327 Al  e 1127 Na* SES 4.0 1016Also, DL=2
• Run 2 (2029- ) Al: (SES) 3x10-17 , 8x10-17 (90% CL), 2x10-16 (discovery)• COMET phase II , planned, goal of expected SES  3x10-17, on Al• Mu2e-II, under study, goal of expected SES  3x10-18, on Al• More distant future• COMET PRISM (COMET upgrade) develop muon storage ring ~10-18-10-19• High intensity muon facility and upgrade of Mu2e at FNAL, ~10-18

J. Miller - cLFV Experiments25

Mu2e (Fermilab)
Extinction
monitor

8 GeV, 8 kW

Stopping target
monitorRadiatively cooledtungsten

15mmstraw tubes
Ar-CO21348 CsI crystals
3.4x3.4x20 cm3
SiPM readout

Run 1 (2025-2026) SES 2.3e-16 x1000 improvement
Run 2 (starts 2029) SES 3e-17 x10000 improvement

J. Miller - cLFV Experiments

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COMET (J-PARC), Phase I and II(COherent Muon to Electron Transitions)
8 GeV protons
100 ns bunches,
1.17 s gap

Underconstruction

1 T detector
solenoidSES 3e-15x100

Future PlanSES 3e-17Alx10000

Phase II
• 15 m straw tubes, 5 mmdiameter; 150 keV resolution• 1920 LYSO crystals 2x2x12cm; 5% resolution at 105
MeV• Cosmic Ray Veto 10-4rejection

J. Miller - cLFV Experiments

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How can COMET and Mu2e make such a big leap insensitivity over previous experiments?
•Large increase in stopped muon rate
• Solenoidal beamline concept first proposed byDjilkabaev and Lobashev ~1990
https://aip.scitation.org/doi/pdf/10.1063/1.50918

A. Place production target in high-field solenoid
1. Captures low E pions in spirals, they decay tomuons which spiral down the beam line
B. Use negative gradient to ‘push’ spiraling muon
downstream , stop them in (Al) thin target• Toroidal sections cause vertical drift of spirals, dependingon sign and momentum, can use collimators to filter
undesirable particles and momenta

J. Miller - cLFV Experiments

28How can COMET and Mu2e conversion make such a
big leap in sensitivity over previous experiments?(2)•Use a pulsed muon beam, wait for prompt background tosubside before looking for the conversion electron. Most
previous experiments used a continuous muon beam,with background mixed in. See details in following talk by
S. DiFalco

J. Miller - cLFV Experiments

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Experimental advantage of muon to electron conversion
experiments compared to eg and eee
3. Pro: The conversion electron energy is well above the energies of theelectrons from muon decays, while the electrons, positrons, gammas fromto eg and eee or eee are in the same energy range as e .
As a result accidentals are not nearly as big a problem, which is thelimiting factor for future improvements in eg. Hole down the middleof detectors avoids almost all low energy decay electrons.
4. Con: Muon capture leads to a lot of neutrons that cause low energy
background for the detectors, and some protons that deposit a lot ofenergy in the straw tubes. Both are manageable.
8 GeV
Extinction
monitor

Stopping target
monitorJ. Miller - cLFV Experiments30

Mu2e-II at PIP-II
1.
2.
3.

Goal: another order of magnitude improvement in sensitivity overMu2e starting in next decade.
100 kW pulsed 800 MeV beam extracted on demand with desired
time structure
Upgrades needed beyond Mu2e are being studied and a Snowmass
whitepaper is being prepared
For Booster

Beam energy

800

MeV

Average current

2mA

Pulse length

0.55

ms

Repetition rate

20

HzFor Mu2e-II
Approximately CW, 162.5 MHzbunches configurable
PowerJ. Miller - cLFV Experiments>100 kW31

Summary•

Lepton Flavor Conservation of charged leptons and violation byneutrinos are central features in the SM , however the underlying
mechanism is not understood.

•Tests of charged lepton flavor violation are occurring across theboard in collider experiments- LHC, B factories, muon sources…

•Hint of LFV implied from LHCb B decay : tension with SM universality•

Dedicated new high-sensitivity experiments in the muon sector may
have highest sensitivity (depends on New Physics model), with massscales in the hundreds or thousands of TeV.

•Much improved experimental information expected in next few years
with improvements continuing into the next decade.

J. Miller - cLFV Experiments

32EndJ. Miller - cLFV Experiments33

Mu2e Signal and Backgrounds

Expected backgrounds
for livetime corresponding to 3.6x1020 POT

5s discovery

J. Miller - cLFV Experiments

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Charged Lepton Flavor Violation
Process Upper limit at 90% CL
on branching fraction
Upper bound on ceµ 2 + ceµ 2 1 TeV 2
1µ−Au → e−Au
π0 → e±µ∓D0 → e±µ∓KL → e±µ∓JHEP07 (2019) 022

5Λnp

7 × 10−139.1 × 10−6
3.6 × 10−1055
1.3 × 10−80.050
4.7 × 10−12
5.0 × 10−6-SM predicts tiny cLFV
• LFV is forbidden in the pre neutrino-oscillation SM– And we do not know why• Neutrinos oscillate and therefore violate lepton flavor conservation– But we do not know how (what’s the mechanism?)• But LFV involving charged leptons (cLFV) has never been observed• Given that the (near) conservation of Lepton Flavor is one of the central
features of the SM, but we don’t know why or how, it has long been asubject of intense experimental investigation• Even in the -SM, cLFV is extremely suppressed(rate ~ Dm4 / Mw4 < 10-50)• However, many New Physics models predict rates observable at next
generation cLFV experiments

+−3+B(π → µ νe) < 8.0 × 10 ,+−5+B(D → e ν) < 8.3 × 10 ,±∓0B(π → e µ ) < 3.6 × 100±∓−10,−8B(D → e µ ) < 1.3 × 10 ,+−6++ + −−6++ + −−6+B(D → e ν) < 8.8 × 10 ,B(D → π e µ ) < 2.9 × 10 ,JHEP07 (2019) 022

B(D → K e µ ) < 1.2 × 10 ,J. Miller - cLFV Experiments

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10000••1000•

Example of two types of effective LFVLagrangian terms, one that is sensitive toloops the other to contact interactions,relative importance dialed by parameter k
Mass scales L of Mu2e (muon to electronconversion) and MEG (eg) extend to1000’s of TeV
Mu2e I sensitive to both, MEG to only firstterm, both important to sort out type of
any LFV observed

J. Miller - cLFV Experiments

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