Lepton Flavor Violation in Charged Lepton Decays 1 MEG detector 2 - - PowerPoint PPT Presentation

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Lepton Flavor Violation in Charged Lepton Decays

MEG detector

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MEG Results

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arXiv:1606.05081

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Mu2e at Fermilab

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Mu2e in a nutshell:

• Generate pulsed beam of low energy negative muons
• Stop the muons in material: 0.002 stopped muons per

8 GeV proton. muons settle in 1S state.

• Wait for prompt backgrounds to disappear
• Measure the electron spectrum
• Look for the monoenergetic conversion

electron (for Al Ee ~105 MeV) Expected limits: 10-16

Mu3e detector

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Reduction of irreducible background

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Mu3e Prospects

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Limits on LFV

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Limits on LFV in tau decays

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Elektron and muon (g-2)

Hadronic cross section

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e e Hadrons

+ − →

Penning Trap: electron g-2

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134 kHz Storage of a single electron for several weeks! 6 T

Frequency measurments: fc and fa

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Coupled system: nc=1 detunes the axial frequency w/r to nc =0. Axial frequncy is used to indicate state.

n=0 n=1

spontan. +hfc

n=1

spontan.

Electron g-2

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Using QED to calculate α - triumph of QED

Agrees well with the value from spectroscopy and recoil measurement but has a 20 times smaller error

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Experimental determination of muon g-2

m eB

C

2 2 = ω

Principle:

• store polarized muons in a storage ring;

revolution with cyclotron frequency ωc

• measure spin precession around the

magnetic dipole field relative to the direction of cyclotron motion

      × − − − − = E a B a c m e

a

    β γ ω

µ µ µ

) 1 1 (

2

Precession:

Difference between Lamor and cyclotron frequency Effect of electrical focussing fields (relativistic effect).

GeV/c 094 . 3 29.3 for = ⇔ = =

μ

p γ

First measurements: CERN 70s

) 11 ( 911 165 001 . ) 12 ( 937 165 001 . = =

+ −

µ µ

a a mc eB g

S

2 = ω

mc eB

C

2 2 = ω

a S C

ω ω ω = −

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+

µ

e

ν

µ

ν

+

e

+

µ

+

e

e

ν

µ

ν

“V-A” structure of weak decay:

Use high-energy e+ from muon decay to measure the muon polarization

(g-2)µ Experiment at BNL

2×7.1 m

E=24GeV 1 µ / 109 protons on target 6x1013 protons / 2.5 sec

Weak charged current couples to LH fermions (RH anti-fermions)

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[ ]

) cos( 1 ) ( ϕ ω

λ

+ + =

−

t A e N t N

a t

Measure electron rate:

Hz ) 16 ( 59 . 023 229 2 = π ωa

24 detectors

(0.7ppm)

B c m e a

a µ µ

ω =

?

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From ωa to aµ - How to measure the B field

<B> is determined by measuring the proton nuclear magnetic resonance (NMR) frequency ωp in the magnetic field.

/ (1 ) 4 / 2 2

a p a a a p p p p p

a a e e B m c m c g

µ µ µ µ µ µ µ

ω ω ω ω ω ω µ ω µ µ µ µ = = = = +   

p a p p a

a ω ω µ µ ω ω

µ µ

/ / / − = ⇓

µµ+/µp=3.183 345 39(10)

• W. Liu et al., Phys. Rev. Lett. 82, 711 (1999).

Frequencies can be measured very precisely

Measured via ground state hyperfine structure

• f muonium

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NMR trolley

17 trolley NMR probes

375 fixed NMR probes around the ring ωp /2π = 61 791 400(11) Hz (0.2ppm)

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B field determination

The B field variation at the center of the storage region. <B>≈1.45 T The B field averaged over azimuth.

Muon g-2

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) 7 . ( 10 ) 8 ( 214 659 11

10

ppm a

−

× =

−

µ

) 7 . ( 10 ) 8 ( 203 659 11

10

ppm a

−

× =

+

µ

) 5 . ( 10 ) 6 ( 208 659 11

10

ppm a

−

× =

µ

Potential new physics contributions?

New Fermilab muon g-2 experiment

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Repeat the measurement w/ better setup

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3200 miles journey of the muon ring

Electron EDM

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Electron EDM violates CP and T. Electron EDM is a result of quantum loops containing CKM phases: only 4-loop diagrams do not cancel!

Principle of EDM measurement

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Spin precision in magnetic and electric field for magnetic and electrical dipole moment:

1 2 2 E

L e B e

g d ω µ = + B 

While this method can be applied to measure the EDM of the neutron it cannot be applied for the electron: the E-field will accelerate the electron. Instead „heavy atoms and molecules that contain electrons with unpaired spin provide suitable environment for EDM measurement. B E

Principle of EDM measurement

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A bound electron with magnetic and electrical dipol moment inside a magnetic and electrical field experiences an energy shift. If it evolves in time, it aquires an additional phase φ.

Electron EDM

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But: A bound electron in an atom / molecule cannot experience a net electrical field - as there is no net accelertaion the net electrical field experienced by the electron should be zero! For heavy nuclei, electrons move at relativistic speed near heavy nucleous. Lorentz contraction causes de to spatially vary over the orbit. While the mean <E> is zero the mean <d.E> is not. Not only that the effective E-field defined as d.Eeff = <d.E> is non zero in atoms/molecules, it is also much larger than achievable in laboratory. For ThO: Eeff=84 GV/cm (scales with Z^3). Only unpaired electrons can create an EDM. And, since the relativistic contraction occurs only near the nucleous, the atoms/molecules must have unpaired electrons penetrating the core. Diatomic polarizable molecules are advantageous. The polarization using an moderate outside field (<100 V/cm ) leads to very strong effective E-field.

Thorium Oxide

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Ground state Meta stable triplet state J=1 Without any field applied: M=-1 M=+1 M=0 Degenerated states ThO Eeff= 84 GV/cm

M = -1 M = 0 M = +1

H

Elab

>

eff

E <

eff

E

N = +1 N = -1

With small external E-field Elab

Polarization of the ThO and splitting of the engery levels.

M = -1 M = 0 M = +1

H

Elab

>

eff

E <

eff

E

B ⋅ − µ

B ⋅ + µ

B ⋅ − µ

B ⋅ + µ

B

N = +1 N = -1

Additional B-field shift the levels

M = -1 M = 0 M = +1

H

Elab

>

eff

E <

eff

E

B ⋅ − µ

B ⋅ + µ

B ⋅ − µ

B ⋅ + µ

B

eff e E

d ⋅ +

eff e E

d ⋅ +

eff e E

d ⋅ −

eff e E

d ⋅ −

N = +1 N = -1

M = -1 M = 0 M = +1

H

Elab

>

eff

E <

eff

E

B ⋅ − µ

B ⋅ + µ

B ⋅ − µ

B ⋅ + µ

B

eff e E

d ⋅ +

eff e E

d ⋅ +

eff e E

d ⋅ −

eff e E

d ⋅ −

Preparation/Readout Lasers

C

P = +1 P = -1 N = +1 N = -1

Measurement

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At the entrance of the field region, the molecules are pumped from the |X> states to the |A> state, where they spontaneously decay to the |H>, equally populating the |J = 1,M = ±1> sublevels

Measurement

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Next, a pure superposition of Zeeman sublevels |XN> is prepared by pumping out the orthogonal superposition |YN> using linearly polarized light resonant with the transition.

Measurement

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Next, the molecule state precesses in the applied E and B fields for approximately 1.1 ms as the beam traverses the 22-cm-long interaction region. The relative phase accumulated between the Zeeman sublevels depends on the EDM de.

Measurement

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Near the exit of the field region, we read out the final state of the molecules: By exciting the |H, v = 0, J = 1> → |C, v = 0, J = 1,MJ = 0> transition with rapidly switched

• rthogonal (ˆx and ˆy ) linear polarizations and detecting the C → X fluorescence from

each polarization, the population is projected onto the |XN and |YN > states.

Determination of the phase φ

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The probability of detecting the molecule in the state |XN> or |YN> is:

2 2

cos

N X N f

P X ψ φ = =

2 2

sin

N y N f

P Y ψ φ = =

with

Electron EDM

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Assuming Eeff =84 GV/cm

ACME collaboration, 2014

Electron EDM

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