B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 1/46 Muon Physics at the Front-end of a Neutrino...

B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 1/46

Muon Physics at the Front-end of a Neutrino Factory

roberts @bu.edu

http://g2pc1.bu.edu/~roberts

“a particle of uncertain nature”

First published muon observation: Paul Kunze, Z. Phys. 83, 1 (1933)

Lee RobertsDepartment of Physics

Boston University


Outline

• Introduction to the muon• The Muon Trio:

– The Magnetic dipole moment: a

– The Electric Dipole Moment d

– Lepton Flavor Violation

• Other Muon Experiments• Summary and conclusions.

Some slides/figures have been borrowed from:

Klaus Jungmann, Dave Hertzog, Klaus Kirch

Jim Miller, Yasuhiro Okada and Andries van der Schaaf


Muon properties:• Born Polarized

• Decay is self-analyzing

High-energy e± carry muon spin information!


What has the muon done for us (besides being associated with the production of or ) ?

• The strength of the weak interaction– i.e. the Fermi constant GF (more properly G)

• The V - A nature of the weak interaction• Lepton flavor conservation in -decay

(thus far)• VEV of the Higgs field:

• Induced form-factors in nuclear -capture – complementary to -decay

• Constraints on new physics from a, – constrains many models of new physics


Theory of Magnetic and Electric Dipole

Moments

Proc. R. Soc. (London) A117, 610 (1928)


Magnetic and Electric Dipole Moments


The magnetic dipole moment directed along spin.

Dirac + Pauli moment

Dirac Theory: gs = 2

For leptons, radiative corrections dominate the

value of a ≃ 0.00116… Bottom line: Anomalous moment represents a sum rule over all physics, not just the known physics.


Modern Notation:

• Muon Magnetic Dipole Momoment a

• Muon EDM

chiral changing


The SM Value for the muon anomaly (10-

10)

# from Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795–881

10 (2)

11 659 178.3 (4.8)Eduardo de Rafael:Theory of the muon anomalousmagnetic momentP and T violation at low energies, Heidelberg, Jun - 2008

New BaBar e+e- → results expected in September


aμ is sensitive to a wide range of new physics

• e.g. SUSY (with large tanβ )

• many other things (extra dimensions, etc.)


C - cyclotron frequency

S - spin frequency

a - spin turns relative to the momentum

Spin Motion in a Magnetic Field

0


As spin precesses, the number of high E electrons oscillates with frequency a.

Count number of e- with Ethresh ≥ 1.8 GeV

Figure of merit: (MDM or EDM)


We count high-energy electrons as a function of time.


E821 achieved 0.5 ppm and the e+e- based theory is also at the 0.6 ppm level. Difference is 3.4

MdRR=Miller, de Rafael, Roberts, Rep. Prog. Phys. 70 (2007) 795

3.7


The Snowmass Points and Slopes give benchmarks to test observables with model predictions

Muon g-2 is a powerful discriminator ...no matter where the final value lands!

Model Version

Expt

Future?

Present


Complementary to LHC data: e.g.a provides the best measure of and tan

MSSM reference point SPS1a

With these SUSY parameters, LHC gets tan of 10.22 ± 9.1.

See: arXiv:0705.4617v1 [hep-ph]

> 0 by > 6

tan to < 20%

with improvements in theory and experiment things can improve to:


The search for a Muon Electric Dipole Moment


Purcell and Ramsey: EDM would violate ParityProposed to search for an EDM of the neutron

Phys. Rev. 78 (1950)

“raises directly the question of parity.”


Electric Dipole Moment: P T

If CPT is valid, an EDM would imply non-standard model CP.

Transformation Properties


The present EDM limits are orders of magnitude from the standard-model value

Particle Present EDM limit(e-cm)

SM value(e-cm)

n

199Hg

The discovery of a permanent EDM would change our picture of nature at least as profoundly as the discovery of neutrino mass has!


10-28Left -Right

MSSM ~

Multi Higgs

MSSM

~ 1

10-24

10-22

10-26

10-30

10-32

10-34

10-36

e EDM (e.cm)

E. Hinds’ e-EDM experiment

at Imperial College with YbF molecules

is startingto explore this region

Standard Model

de < 1.6 x 10-27 e.cm

Commins (2002)

Excluded region (Tl atomic beam)

with thanks to Ed Hinds

n

The SUSY CP problem!

The strong CP problem!

199Hg


aμ (new physics) implications for d

Either dµ is of order 10–22 e cm, or the CP phase is strongly suppressed!


μ EDM may be enhancedabove mμ/me × e EDM

Magnitude increases withmagnitude of Yukawa couplings

and tan β

μ EDM greatly enhanced when heavy neutrinos non-degenerate

Model Calculations of EDM


Spin Frequencies: in B field with MDM & EDM

The EDM causes the spin to precess out of plane.

The motional E - field, β X B, is (~GV/m).

0


Number above (+) and below (-) the midplane will vary as:

Total frequency

Plane of the spin precession tipped by the angle

a


E821 looked for this vertical oscillation in 3 ways

• No significant oscillation was found

• The observed a is not from an EDM at the 2.2 level

• One can improve significantly at a neutrino factory, since an EDM limit of 10-23 e·cm needs NP 2 = 1016

*Coming soon to a preprint server near you

Bottom line: Muon EDM measurement needs the high intensity that could be available at a neutrino factory.

Also need modified technique!


Dedicated EDM Experiment

With a = 0, the EDM causes the spin to steadily precess out of the plane.

0

Use a radial E-field to turn off the a precession

“Frozen spin”


“Frozen spin” technique to measure EDM• Turn off the (g-2) precession with radial E• Up-Down detectors measure EDM asymmetry • Look for an up-down asymmetry building up with

time• Side detectors measure (g-2) precession

– To prove the spin is frozen

B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 30/46(by A. Streun)

PSI suggestion: Adelmann and Kirch hep-ex/0606034

A. Adelmann1, K. Kirch1, C.J.G. Onderwater2, T. Schietinger1, A. Streun1

1PSI, 2KVI


Muon EDM Limits: Present and Future

E821

E821: G. Bennett, et al., (Muon g-2 collaboration) to be submitted to PRD 2008

NuFact

Need:

NA 2 = 1016 for

d ≃ 10-23 e·cm

new (g-2)?


SUSY connection between MDM, EDM and the lepton flavor violating transition moment → e

→ e MDM, EDM~ ~

SUSY slepton mixing


Lepton Flavor Violation

2-body final state¹ + ! e+°¹ + ! e+e¡ e+

¹ ¡ + N ! e¡ + N(¹ +e¡ ) ! (¹ ¡ e+ )

+ e-→-e+

Bra

nchi

ng R

atio

Lim

it

10-1

10-3

10-5

10-7

10-9

10-11

10-13

1940 1950 1960 1970 1980 1990 2000

mono-energetic electron


Experimental bounds

Process Current Future

10-16 2e10-16 Comet

(Ti)

Under some assumptions the Lf = 1 rates are related


Presently active: → e (MEG @ PSI)

• First running is going on now– goal < 10-13


Muonic Atom: - bound in hydrogen-like atomic orbit

1s

2s2p

r

Lyman series

Balmer series

coherent process


e - conversion operators

have calculated the coherent -e conversion branching ratios in various nuclei for general LFV interactions to see:

(1) which nucleus is the most sensitive to mu-e conversion searches,

(2) whether one can distinguish various theoretical models by the Z dependence.

Relevant quark level interactions

Dipole

Scalar

Vector

R.Kitano, M.Koike and Y.Okada. 2002


The branching ratio is largestfor the atomic number of Z = 30 – 60.

For light nuclei, Z dependencessimilar for different operators

Sizable difference of Z dependences for dipole, scalar and vector interactions (relativistic effect of ).

-e conversion rate normalized to Al

dipole scalar vector

providing another way to discriminate different models

Kitano, Koike, Okada

Bottom line: If you can observe muon-electron conversion, a study of the Z dependence might help sort out which operators contribute.


The First -N e-N Experiment Steinberger and Wolf

• After the discovery of the muon it was realized it could decay into an electron and a photon, or convert to an electron in the field of a nucleus.

• Without lepton flavor conservation, the expected branching fraction for e+ is about 10-5

• Steinberger and Wolf

-N e-N, (1955) Re

< 2 10-4

Absorbs e- from -

decay

Conversion e- reach this

counter

9”

( , ) ( , )

( , )

A Z e A ZR

A Z X


Two New Proposals for to e Conversion Experiments

• 2e at Fermilab – based on MECO / MELC proposals

• COMET at J-PARC

-to be upgraded to PRISM/PRIME

SINDRUM II @PSI

Data and simulation

decay in orbit (simulated) signal

prompts suppressed


The 2e Apparatus proposed for Fermilab

Straw Tracker

Crystal Calorimeter

Muon Stopping Target

Superconducting Production Solenoid

(5.0 T – 2.5 T)Superconducting

Detector Solenoid (2.0 T – 1.0 T)

Superconducting Transport Solenoid

(2.5 T – 2.1 T)

Collimators

p beam

Phase 1: 90% C.L. limit of Re< 6 x 10-17

Phase 2: 90% C.L. limit of Re ≲ 10-18ProtonTarget

TargetShielding(Copper)

Pions

MuonsTarget

Shielding(Tungsten)

Protons enter here

B=5T

B=2.5T


COMET Proposal @ J-PARC e conversion 90% CL Re < 10-16

curved detector to reduce low E DIO background


Re < 10-18

Bottom line: FFAG reduces p of the muon beam by phase rotation:

narrow t → narrow p ⇒ thinner stopping target

better e- resolution and eliminates the pions which can cause ZN ( background!


Flavor oscillations well established in quark sector

PredictedM-M

Conversion1957-

NamedSystem

“Muonium” ?L. Willmann, et al., PRL 82, 49 (1999)

Muonium to Anti-muonium Conversion


L. Willmann, et al., PRL 82, 49 (1999) (done @PSI)

90% CL:


Future Efforts at Existing Facilities• (g-2)

– FNAL ?– J-PARC ?

• MEG– running now!

• 2e– proposal being prepared for Fermilab

• COMET/ PRISM/PRIME– proposed to J-PARC, future under discussionBottom line: The ultimate sensitivity for e

conversion could be reached at the front end of a neutrino factory. The discovery of LFV would also significantly change our view of the world.


Summary

• Muon physics has provided much information in the development of the standard model, including a hint of new physics in a.

• The electric dipole moment could be measured to a competitive level (to e-) at a neutrino factory.

• Muon flavor violation can be pursued to the ultimate sensitivity, or studied systematically at a neutrino factory.

• The observation of either of these SM “forbidden” effects would be incredibly important in reshaping our view of nature.


Extra Projections


Comparison of three processes

If the photon penguin process dominates, there are simple relations among these branching ratios.

This is true in many, but not all SUSY modes.


PSI suggestion:

B = 1 T

p = 125 MeV/c

= 0.77, = 1.57

P ≈ 0.9

E = 0.64 MV/m

R = 0.35 m

In 1 year of running @ PSI

A. Adelmann1, K. Kirch1, C.J.G. Onderwater2, T. Schietinger1, A. Streun1

hep-ex/0606034


Comparison of three muon processes in various new physics models

SUSY GUT/Seesaw

B(→e ) >> B(→3e) ~ B(N→eN) Various asymmetries in polarized decays.

SUSY with large tan

→e conversion can be enhanced. Z-dependence in →e conversion BR.

Triplet Higgs for neutrino

B(→3e) > or ~ B(→e) ~B(N→eN)

RL model B(→3e) >> B(→eg) ~B(N→eN)Asymmetry in →3e

RPV SUSY Various patterns of branching ratios and asymmetries

want to measure all three LFV processes to disentangle the models

B. Lee Roberts, NuFact2008 4 July 2008 - p. 52/46

e Conversion is sensitive to a wide range of new physics

CΛ = 3000 TeV

-4HH μμμeg =10 ×g

Compositeness

Second Higgs doublet

2Z

-17

M = 3000 TeV/c

B(Z μe) <10

Heavy Z’, Anomalous Z coupling

Predictions at 10-15

Supersymmetry

2* -13μN eNU U = 8×10

Heavy Neutrinos

L

2μd ed

M =

3000 λ λ TeV/c

Leptoquarks

After W. Marciano


→ e branching ratio (typical example)

SU(5) and SO(10) SUSY GUT

SUSY seesaw model

The branching ratio can be largein particular for SO(10) SUSY GUT model.

J.Hisano and D.Nomura,2000

K.Okumura

SO(10)

SU(5)

Right-handed neutrino mass

Right-handed selectron mass

MEGA

MEG tan = 3

tan = 10

tan =

30

B. Lee Roberts, NuFact2008 – 4 July 2008 - p. 1/46 Muon Physics at the Front-end of a Neutrino...

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