Lepton Flavor Violation in Charged Lepton Decays 1
MEG detector 2
MEG Results arXiv:1606.05081 3
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Mu2e at Fermilab 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 E e ~105 MeV) Expected limits: 10 -16 5
Mu3e detector 6
Reduction of irreducible background 7
Mu3e Prospects 8
Limits on LFV 9
Limits on LFV in tau decays 10
Elektron and muon (g-2) 11
Hadronic cross section − → e e + Hadrons 12
Penning Trap: electron g-2 Storage of a single electron for several weeks! 134 kHz 6 T 13
Frequency measurments: f c and f a n=1 n=1 +hf c spontan. spontan. n=0 Coupled system: n c =1 detunes the axial frequency w/r to n c =0. Axial frequncy is used to indicate state. 14
Electron g-2 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 15
Experimental determination of muon g-2 Principle: • store polarized muons in a storage ring; eB ω = 2 revolution with cyclotron frequency ω c C 2 mc • measure spin precession around the eB ω = magnetic dipole field relative to the g eB ω = 2 S mc C 2 2 m direction of cyclotron motion ω = ω − ω a S C Precession: e 1 ω = − − − β × a B ( a ) E µ µ γ − a 2 m c 1 First measurements: µ CERN 70s Difference between Lamor Effect of electrical focussing = a 0 . 001 165 937 ( 12 ) and cyclotron frequency fields (relativistic effect). − µ = γ = 0 for 29.3 = a 0 . 001 165 911 ( 11 ) + µ ⇔ = p 3 . 094 GeV/c μ 16
(g-2) µ Experiment at BNL E=24GeV 1 µ / 10 9 protons on target 2 × 7.1 m 6x10 13 protons / 2.5 sec + + µ µ ν ν µ + + µ ν e e ν “V-A” structure of weak decay: e e Use high-energy e + from muon decay to measure the muon polarization Weak charged current couples to LH fermions (RH anti-fermions) 17
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Measure electron rate: [ ] − λ = t + ω + ϕ N ( t ) N e 1 A cos( t ) 0 a ω a = 24 detectors 229 023 . 59 ( 16 ) Hz π 2 (0.7ppm) ω = a a µ e ? B m c 19 µ
From ω a to a µ - How to measure the B field <B> is determined by measuring the proton nuclear magnetic resonance (NMR) frequency ω p in the magnetic field. ω ω ω ω ω / a a p a = a = a = a = + (1 ) e ω µ ω e µ µ µ µ 4 / B p p µ p µ m c m c g µ µ 2 2 µ µ p p µ Frequencies can be ⇓ measured very precisely ω ω / = a p a µ µ µ − ω ω / / µ p a p Measured via ground µ µ + / µ p =3.183 345 39(10) state hyperfine structure of muonium W. Liu et al., Phys. Rev. Lett. 82 , 711 (1999). 20
NMR trolley 375 fixed NMR probes around the ring 17 trolley NMR probes ω p /2 π = 61 791 400(11) Hz (0.2ppm) 21
B field determination The B field variation at the The B field averaged over center of the storage region. azimuth. <B> ≈ 1.45 T 22
Muon g-2 − = × 10 a 11 659 203 ( 8 ) 10 ( 0 . 7 ppm ) + µ − = × 10 a 11 659 214 ( 8 ) 10 ( 0 . 7 ppm ) − µ − = × 10 a 11 659 208 ( 6 ) 10 ( 0 . 5 ppm ) µ Potential new physics contributions? 23
New Fermilab muon g-2 experiment Repeat the measurement w/ better setup 24
3200 miles journey of the muon ring 25
Electron EDM Electron EDM is a result of Electron EDM violates CP and T. quantum loops containing CKM phases: only 4-loop diagrams do not cancel! 26
Principle of EDM measurement B E Spin precision in magnetic and electric field for magnetic and electrical dipole moment: 1 2 g d E ω = µ + B 2 L e B e 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. 27
Principle of EDM measurement 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 . 28
Electron EDM 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 d e 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.E eff = <d.E> is non zero in atoms/molecules, it is also much larger than achievable in laboratory. For ThO: E eff =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. 29
Thorium Oxide ThO Eeff= 84 GV/cm Without any field applied: M=0 M=-1 M=+1 Meta stable Degenerated states triplet state J=1 Ground state 30
With small external E-field E lab Polarization of the ThO and splitting of the engery levels. > 0 E eff N = -1 E lab H N = +1 < E 0 eff M = -1 M = 0 M = +1
Additional B-field shift the levels > E 0 eff + µ ⋅ B N = -1 − µ ⋅ E lab B B H + µ ⋅ B N = +1 − µ ⋅ B < E 0 eff M = -1 M = 0 M = +1
+ d ⋅ e E > 0 E eff eff + µ ⋅ B N = -1 − µ ⋅ E lab B − d ⋅ e E B eff H + µ ⋅ B + d ⋅ e E N = +1 − d ⋅ eff − µ ⋅ e E B eff < E 0 eff M = -1 M = 0 M = +1
C P = +1 P = -1 Preparation/Readout Lasers + d ⋅ e E > 0 E eff eff + µ ⋅ B N = -1 − µ ⋅ E lab B − d ⋅ e E B eff H + µ ⋅ B + d ⋅ e E N = +1 − d ⋅ eff − µ ⋅ e E B eff < E 0 eff M = -1 M = 0 M = +1
Measurement 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 35
Measurement Next, a pure superposition of Zeeman sublevels |X N > is prepared by pumping out the orthogonal superposition |Y N > using linearly polarized light resonant with the transition. 36
Measurement 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 d e . 37
Measurement 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,M J = 0> transition with rapidly switched orthogonal (ˆx and ˆy ) linear polarizations and detecting the C → X fluorescence from each polarization, the population is projected onto the |X N and |Y N > states. 38
Determination of the phase φ The probability of detecting the molecule in the state |X N > or |Y N > is: 2 2 P Y N = ψ = φ P X N = ψ = φ 2 2 sin cos y N f X N f with 39
Electron EDM ACME collaboration, 2014 Assuming E eff =84 GV/cm 40
Electron EDM 41
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