Probing Physics beyond the Standard Model with the Mu3e Experiment

(1)

Probing Physics beyond the Standard Model with the Mu3e Experiment

Ann-Kathrin Perrevoort for the Mu3e Collaboration

NIKHEF, Amsterdam (formerly Physics Institute, Heidelberg)

Flavour and Dark Matter Karlsruhe September 26, 2018

(2)

Mu3e in a Nutshell

Target Inner pixel layers

Outer pixel layers Recurl pixel layers

Scintillator tiles μ Beam

• Search for cLFV inµ → eee

• ObserveO(10¹⁵)toO(10¹⁶)muons

• Precise tracking of e⁺/e⁻

• High geometric and momentum acceptance (p_T>10 MeV)

• Online reconstruction of all tracks

• Filtering ofµ → eee candidates

• Current limit:

BR<1.0⋅10⁻¹² at 90%CL (SINDRUM 1988)

What can Mu3e achieve?

• What else can we look for with so many muon decays?

A. Perrevoort (NIKHEF) BSM Physics with Mu3e Flavour and DM 2018 1 / 33

(3)

Outline

• µ → eee in eﬀective theories

• Dark photons inµ decays

• Lepton flavour violating two body decaysµ → e X

(4)

(5)

Signal and Background

Signal Background

Signalµ⁺ → e⁺e⁻e⁺ Combinatorial background

Internal conversion µ⁺ → e⁺e⁻e⁺νµνe

• Common vertex

• Coincident

• ∑Ee=m_µ

• ∑p⃗e=0

• No common vertex

• Not coincident

• ∑Ee≠m_µ

• ∑p⃗e≠0

• Common vertex

• Coincident

• ∑Ee<m_µ

• ∑p⃗e≠0

(6)

Sensitivity to µ → eee in Phase I

• Full Geant4-based detector simulation

• Generators of physics processes (SM and BSM)

• Track reconstruction and vertex fit

(7)

Sensitivity to µ → eee in Phase I

Reconstructed µ → eee events (signal and background)

• Long tracks only

• Cuts on ∆te_ie_j, χ²_vertex,dvertex-target,

∣∑p⃗e∣,meee

• Background-free with 2.6⋅10¹⁵ stopped µ

• Signal eﬃciency 17%

⇒ BR≥5.2⋅10⁻¹⁵ at 90%CL

[MeV]

meee

96 98 100 102 104 106 108 110

Events per 0.2 MeV

−4

10

−3

10

−2

10

−1

10 1 10

102 _-12

at 10

→ eee µ at 10-13

→ eee µ at 10-14

→ eee µ at 10-15

→ eee µ ν

ν

→ eee µ

muon stops 1015

⋅ 2.6

muons/s at 108

Mu3e Phase I

(8)

µ → eee in Eﬀective Theories

Use an EFT approach to model possible New Physics LEFT=∑

i

c_i Λ²O_i

• Kinematics diﬀer for each operator

→ diﬀerent sensitivities

→ characteristic decay distributions

• Complementarity of µ → eee, µ → eγ,µ → e conversion

(9)

Sensitivity to µ → eee using Eﬀective Theories

Phase space

Eﬃciency is 17% ⇒ BR≥5.2⋅10⁻¹⁵ at 90%CL

2]

2[MeV mee

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 103

×

Generated distribution

2]

2[MeV mee

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

0 100 200 300 400 500 600 700

After reconstruction and vertex fit

(10)

µ → eee in Eﬀective Theories

Dipole operatorem_µµ_Rσ^µνe_LF_µν

2]

2[MeV mee

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

1 10 102

103

2]

2[MeV mee

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

1 10 102

103

(11)

µ → eee in Eﬀective Theories

Vector 4-fermion operator (µ_Rγ^µe_R)(e_Lγ^µe_L) Eﬃciency is 19% ⇒ BR≥4.6⋅10⁻¹⁵ at 90%CL

2] [MeV

2ee

m

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

0 100 200 300 400 500 600 700 800 900

2] [MeV

2ee

m

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

0 50 100 150 200 250

(12)

µ → eee in Eﬀective Theories

µ/s Days of Data Taking at 108

0 50 100 150 200 250 300

Branching Fraction Limit at 90% CL

−15

10

−14

10

−13

10

−12

10

−11

10

Mu3e Phase I SINDRUM Phase space Dipole operator 4-fermion operator

(13)

(14)

Dark Photon Searches with Mu3e

Dark Photon A^′

• Vector portal:

A^′ as messenger to a dark sector

• Interaction with SM particles via kinetic mixing with the photon

L_A^′ =−^ϵ₂F_µν^′ F^µν−¹₄F_µν^′ F^′^µν+¹₂m_A′A^′_µA^′^µ

• A^′ with m_A′ <m_µ can be emitted in muon decays

(15)

Dark Photon Searches with Mu3e

Dark photons in muon decays

• µ → eννA^′

‘stable’ A^′ or decay to dark particles

• µ → eνν(A^′ → ee)

prompt decay of A^′ to e⁺e⁻

• µ → eννA^′ followed by A^′ → ee long-lived A^′

A' e

ν

e A'^* e μ

e ν

ν

A'^*

e e μ

e ν

ν

(16)

Invisible Dark Photons: µ → eννA

^′

• Only e⁺ can be detected

⇒ Deviation in thepe spectrum of SM µdecays

• Can be easily interpreted as detector misalignment

• Single-e⁺ events rejected in filter farm

A' e

ν

[MeV]

pe

0 10 20 30 40 50 60

dN/N per 1MeV

−3

10

−2

10

−1

10

1 Mass mA'

2 MeV 5 MeV 10 MeV 20 MeV 30 MeV 40 MeV 50 MeV 60 MeV 70 MeV 80 MeV 90 MeV 100 MeV

generated

[MeV]

rec

pe

0 10 20 30 40 50 60

dN/N per 1MeV

−3

10

−2

10

−1

10

1 Mass mA'

2 MeV 5 MeV 10 MeV 20 MeV 30 MeV 40 MeV 50 MeV 60 MeV 70 MeV 80 MeV 90 MeV 100 MeV

reconstructed

(17)

Invisible Dark Photons: µ → eννA

^′

• Only e⁺ can be detected

⇒ Deviation in thep_e spectrum of SM µdecays

• Can be easily interpreted as detector misalignment

• Single-e⁺ events rejected in filter farm

A' e

ν

Misalignment vertex layers shifted in z

[MeV/c]

rec p

0 10 20 30 40 50 60

0 5000 10000 15000 20000 25000 30000

Aligned Misaligned

Positron Momentum of Michel Decay

al )/nentries mis -p al (p

0 10 20 30 40 50 60

−0.2

−0.15

−0.1

−0.05 0 0.05 103−

× Relative Difference

Misalignment study by U. Hartenstein

(18)

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

• Observe three electrons from a common vertex

⇒ Same dataset as inµ → eee searches

• Search for resonance inmee

• Main background fromµ → eeeννand

combinations of Bhabha scattering events with Michel decays

e A'^* e μ

e ν

ν

(19)

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Signal

sharp peak in m_ee

[MeV]

mee

0 20 40 60 80 100 120

dN/N per 1 MeV

−3

10

−2

10

−1

10

1 both

All tracks: mee

= 20 MeV mA'

= 45 MeV mA'

= 70 MeV mA'

Background

combinatorial BG contributes a factor ∼800 less

[MeV]

mee

0 20 40 60 80 100 120

N per 1 MeV

1 10 102

103

104

105

106

107

108 both

All tracks: mee

Combined background Internal conversion Bhabha

(20)

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Two possible e⁺e⁻ combinations Both e⁺e⁻ pairs

[MeV]

mee

0 20 40 60 80 100 120

dN/N per 1 MeV

−3 10

−2 10

−1 10

1 both

All tracks: mee = 20 MeV mA'

= 45 MeV mA'

= 70 MeV mA'

Lowerm_ee pair for m_ee<45 MeV

[MeV]

mee

0 20 40 60 80 100 120

dN/N per 1 MeV

−3 10

−2 10

−1 10

1 low

= 45 MeV mA'

= 70 MeV mA'

Higherm_ee pair form_ee≥45 MeV

[MeV]

mee

0 20 40 60 80 100 120

dN/N per 1 MeV

−3 10

−2 10

−1 10

1 high

= 45 MeV mA'

= 70 MeV mA'

(21)

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Sensitivity in phase I assuming 2.6⋅10¹⁵ muon decays

[MeV]

mA'

0 10 20 30 40 50 60 70 80

−12

10

−11

10

−10

10

−9

10

−8

10

−7

10 Mu3e Phase I SIM: 2.6_×₁₀¹⁵_µ_stops

(22)

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Investigate currently uncovered parameter space (BR(A^′ → ee) =1)

[GeV]

mA'

−2

10 10⁻¹ 1 10

2ε

−8

10

−7

10

−6

10

−5

10

−4

10

(g-2)e

KLOE 2013 KLOE 2015

KLOE 2016 KLOE 2014 WASA

HADES PHENIX 2σ

µ± (g-2)

favored

E774

E141

APEX

A1 NA48/2

BABAR 2009

BABAR 2014

BESIII

Mu3e Phase I

Mu3e Phase II

Mu3e: Work in progress adapted from 1705.04265

Phase II: 5.5⋅10¹⁶ µ decays at 2⋅10⁹µ/s,

improvements to the detector not considered

(23)

Longlived A

^′

: µ → eννA

^′

with subsequent A

^′

→ ee

• Search for e⁺e⁻ pairs from displaced vertices + resonance

• Background from Bhabha scattering and photon conversion

• Decay lengths of several cm can be studied cτ =0.8 mm¹⁰_ϵ2⁻⁸10 MeV

mA′

[Echenard et al., JHEP 01 (2015), 113]

⇒ Extend reach to smallerϵ²

• Needs modifications of reconstruction and event filtering

• Currently under study

A'^*

e e μ

e ν

ν

(24)

(25)

LFV Two Body Decays: µ → e X

• Motivation: Familon

(Wilczek, PRL 49 (1982) 1549)

Spontaneous breaking of flavour symmetry

→ (Pseudo-)Goldstone boson

emitted in flavour-changing decays

• µ⁺ → e⁺X⁰

Neutral, light boson X not observed Monoenergetic positron

• Background:

µ⁺ → e⁺νµνe,µ⁺ → e⁺γ νµνe, µ⁺ → e⁺e⁻e⁺νµνe, Bhabha scattering, photon conversion, ...

10 20 30 40 50

0 0.2 0.4 0.6 0.8 1

Michel spectrum (leading order) μ→eX signal (mX=60MeV)

p_e [MeV]

entries/dpe [a.u.]

(26)

Previous Experiments Searching for µ → e X

Jodidio et al. at TRIUMF (Phys.Rev. D34, 1986)

• 1.8⋅10⁷ highly polarized muons

• Search for massless familon expected to be isotropic

• Look for excess in end-point of Michel spectrum at cosθ=−1

• BR<2.6⋅10⁻⁶ at 90%CL

[MeV]

Ee

10 20 30 40 50

[a.u.]e/dEeνµν+ e→+µΓd

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 _cos_θ_{= 1} θ = 0 cos

= -1 θ cos

Michel spectrum,θ=∠( ⃗P_µ,p⃗_e)

(27)

Previous Experiments Searching for µ → e X

TWIST at TRIUMF

(Bayes et al. Phys.Rev. D91, 2014)

• 5.8⋅10⁸ µdecays analyzed from highly polarizedµbeam

• Search for anisotropicµ → e X decays

∂Γ

∂cosθ∝1−APµcosθ

• Massive X (on average):

BRA=0 < 9⋅10⁻⁶ at 90%CL BR_A₌₊₁<10⋅10⁻⁶ at 90%CL BR_A₌₋₁< 6⋅10⁻⁶ at 90%CL

Collected Events

0 5000 10000 15000 20000 25000 30000 35000 40000

Momentum (MeV/c)

10 20 30 40 50

θ cos

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

Signal Momentum (MeV/c)

20 25 30 35 40 45 50

5 10 15 20

25 90% C.I., A = -1 ) 2 (in MeV/c 0 Mass of X

20 30 40 50 60 70 80

20 25 30 35 40 45 50

)6 10× Branching Ratio (

5 10 15 20

25 90% C.I., A = 0

20 25 30 35 40 45 50

0 5 10 15 20

25 90% C.I., A = +1 )6 10×Branching Ratio (

0 0

(28)

Searching for µ → e X with Mu3e

• High muon rate

⇒Cannot store all single-track events

• But: online reconstruction of all tracks as ‘short’ tracks

(i.e. no reconstruction of recurler)

→ Keep histogram of momenta for µ → e X searches

• No acceptance forp_T<10 MeV

• Calibration with Michel edge, use of Mott and Bhabha scattering under investigation

→ 25 MeV≤mX≤95 MeV can be

investigated ⁰ ²⁰ ⁴⁰ ⁶⁰ ⁸⁰ mX[MeV]¹⁰⁰

[MeV]ep

0 10 20 30 40

50 Michel edge

Geometric acceptance Calibrate with Michel edge Find other

means of calibration

Inaccessible

(29)

Searching for µ → e X with Mu3e

Data selection

• χ² of track fit

• zof track propagated to target region

• Inclination angleλ01

(30)

Searching for µ → e X with Mu3e

Background

p [MeV]

0 20 40 60 80 100

Events per 100keV

0 0.2 0.4 0.6 0.8 1 1.2

106

×

BG: SM decays

Signal m_X=60 MeV

p [MeV]

0 20 40 60 80 100

Events per 100keV

0 0.2 0.4 0.6 0.8 1

103

×

=60MeV Signal: mX

(31)

Searching for µ → e X with Mu3e

[MeV]

mX

0 10 20 30 40 50 60 70 80 90

Branching Fraction at 90% CL

−9

10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10 Mu3e Phase I SIM: 2.6_×₁₀¹⁵_µ_stops

TWIST 2014

Mu3e online reco. (ext.calib.) Mu3e online reco. (sim. calib.)

Mu3e: Work in progress

TWIST results by courtesy of R. Bayes

(32)

Searching for µ → e X with Mu3e

Anisotropicµ → e X decays:

dΓ

dcosθ∝1+hPcosθ

Background

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 106

×

p [MeV]

0 10 20 30 40 50 60

)θcos(

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

h=0, mX =60 MeV

0 100 200 300 400 500 600 700

p [MeV]

0 10 20 30 40 50 60

)θcos(

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

h=+1, mX=60 MeV

0 0.2 0.4 0.6 0.8 1

103

×

p [MeV]

0 10 20 30 40 50 60

)θcos(

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

h=-1, mX=60 MeV

0 0.2 0.4 0.6 0.8 1

103

×

p [MeV]

0 10 20 30 40 50 60

)θcos(

−1

−0.8

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

(33)

Searching for µ → e X with Mu3e

[MeV]

mX

0 10 20 30 40 50 60 70 80 90

0 5 10 15 20 25 30 35 40 45 50

−9

×10

Short tracks h= 0 h=+1 h=-1

(34)

LFV Two Body Decays: µ → e X

Further channels involving familons

• µ → e X, X → ee:

it’s aµ → eee search

• µ → eeeee:

suﬀers from low acceptance at lowpT

can run at lower B field

(35)

Summary

• µ → eee in eﬀective theories

▸ Operators show characteristic decay distributions

▸ Sensitivity of some 10⁻¹⁵ in phase I

• Dark photons inµ decays

▸ Search formee resonances

▸ Investigate currently uncovered parameter space

• Lepton flavour violating two body decaysµ → e X

▸ Bump search on e⁺ momentum spectrum from online reconstruction

▸ More than 2 orders of magnitude more sensitive than previous searches

(36)

(37)

Appendix

µ → eee in Eﬀective Theories

Vector 4-fermion operator (µ_Rγ^µe_R)(e_Rγ^µe_R) Scalar 4-fermion operator(µReL)(eReL)

2] [MeV

2ee

m

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

0 0.2 0.4 0.6 0.8 1 1.2

103

×

2] [MeV

2ee

m

0 2 4 6 8 10 12×10³

]2[MeV

2 ee

m

0 2 4 6 8 10 12

103

×

0 50 100 150 200 250 300 350

(38)

Appendix

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Two possible e⁺e⁻ combinations (background) Both e⁺e⁻ pairs

[MeV]

mee

0 20 40 60 80 100 120

N per 1 MeV

1 10 102 103 104 105 106 107

108 both

All tracks: mee Combined background Internal conversion Bhabha

Lowerm_ee pair for m_ee<45 MeV

[MeV]

mee

0 20 40 60 80 100 120

N per 1 MeV

1 10 102 103 104 105 106 107

108 low

Higherm_ee pair form_ee≥45 MeV

[MeV]

mee

0 20 40 60 80 100 120

N per 1 MeV

1 10 102 103 104 105 106 107

108 high

(39)

Appendix

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Acceptance low for low p_T electrons, i. e. at low and highm_ee

[MeV]

mA'

0 10 20 30 40 50 60 70 80

genA'/NrecN

0 0.05 0.1 0.15 0.2 0.25

(40)

Appendix

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Comparison with external study Phase I: 1⋅10¹⁵ muons Echenard et al.,

JHEP 01 (2015), 113

(MeV) mee

0 20 40 60 80 100

Entries / 0.2 (MeV)

10-1 1 10 102 103 104 105 106 107

108 µ⁺→ e⁺e^-e⁺νµνe

-) +e

→ e γ( νe νµ e+

→ µ+ Accidental bkg

Mu3e simulation

[MeV]

mee

0 20 40 60 80 100

N per 0.2 MeV

−1

10 1 10 102

103

104

105

106

107

108 All tracks

High mee Low mee

Background Background

Internal conversion Internal conversion

Bhabha Bhabha

(41)

Appendix

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Comparison with external study Phase II: 5.5⋅10¹⁶ muons Echenard et al.,

JHEP 01 (2015), 113

(MeV) mee

0 20 40 60 80 100

Entries / 0.2 (MeV)

103 104 105 106 107 108 109

νe νµ e+ e- e+

→ µ+

-) +e

→ e γ( νe νµ e+

→ µ+ Accidental bkg

Mu3e simulation

[MeV]

mee

0 20 40 60 80 100

N per 0.2 MeV

103

104

105

106

107

108

109 All tracks

High mee Low mee

Background Background

Internal conversion Internal conversion

Bhabha Bhabha

(42)

Appendix

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Comparison with external study Echenard et al.,

JHEP 01 (2015), 113

[MeV]

mA’

0 10 20 30 40 50 60 70 80

efficiency

0 0.05 0.1 0.15 0.2 0.25 0.3

Mu3e simulation

[MeV]

mA'

0 10 20 30 40 50 60 70 80

genA'/NrecN

0 0.05 0.1 0.15 0.2 0.25

(43)

Appendix

Promptly Decaying Dark Photons: µ → eνν ( A

^′

→ ee )

Comparison with external study

10^-3 10^-² 10^-¹ 1

10^-11 10^-10 10^-⁹ 10^-⁸ 10^-⁷ 10^-⁶ 10^-⁵ 10^-⁴

mA'[GeV]

ϵ2 APEXTest

APEX

U70 E141

E774 aμ, 5σ

aμ,±2σfavored

ae DarkLight

BaBar A1

WASAHADES

Orsay/E137/CHARM

KLOE

HPS

PHENIX

Mu3e phase I Mu3e

phase II

NA48/2

SHiP Mu3e phase II

(this thesis) Mu3e phase I (this thesis)

adapted from Echenard et al., JHEP 01 (2015), 113

(44)

Appendix

Short Tracks: 4 Hits

(45)

Appendix

Short Tracks

[rad]

λ

−1.5 −1 −0.5 0 0.5 1 1.5

p [MeV]

0 10 20 30 40 50 60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eﬃciency.

[MeV/c]

pmc

0 10 20 30 40 50

[MeV/c]pσ

0 0.5 1 1.5 2 2.5 3

Momentum resolution.

(46)

Appendix

Long Tracks: 6 Hits

(47)

Appendix

Long Tracks: 8 Hits

(48)

Appendix

Long Tracks

[rad]

λ

−1.5 −1 −0.5 0 0.5 1 1.5

p [MeV]

0 10 20 30 40 50 60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Eﬃciency.

[MeV/c]

pmc

0 10 20 30 40 50

[MeV/c]pσ

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Momentum resolution.

(49)

Appendix

Searching for µ → e X with Mu3e

Background

p [MeV]

0 20 40 60 80 100

Events per 100keV

0 0.2 0.4 0.6 0.8 1

106

×

BG: SM decays

Signal m_X=60 MeV

p [MeV]

0 20 40 60 80 100

Events per 100keV

0 1 2 3 4 5 6 7

103

×

=60MeV Signal: mX

(50)

Appendix

Searching for µ → e X with Mu3e

[MeV]

mX

0 10 20 30 40 50 60 70 80 90

Branching Fraction at 90% CL

−9

10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10 Mu3e Phase I SIM: 2.6_×₁₀¹⁵_µ_stops TWIST 2014

Short tracks (ext.calib.) Short tracks (sim.calib.) Long tracks (ext.calib.) Long tracks (sim.calib.)

(51)

Appendix

Upgrades to Mu3e

Potential Mu3eGamma upgrade

• Search forµ → eγ

• Additional photon converter and tracking detectors

• Increase B field: from 1 T to 2 T

• Can also investigate µ → e Xγ and dark photons from displaced vertices