Muon-electron conversion in nuclei

Masafumi Koike (Saitama U)

2008.8.8 Muon WG Workshop@Izu

Kitano, Koike, and Okada, PRD 66, 096002 (2002)

1Introduction

Chart from

The Particle Adventure w

ebsite, http://particleadventure.org/

Flavors

!

"c!ei!1/2 s!ei!2/2 s13e"i"

!s!ei!1/2/"

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2 1/"

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"2 1/

"2

#

$

PDG 2008!

"0.97418 ± 0.00027 0.2255 ± 0.0019 (3.93 ± 0.36) · 10!3

0.230 ± 0.011 1.04 ± 0.06 (41.2 ± 1.1) · 10!3

(8.1 ± 0.6) · 10!3 (38.7 ± 2.3) · 10!3 0.77+0.18!0.24

#

$

Lepton Flavors

• No experimental indication of charged lepton flavor violation (LFV) so far

• Separately conserved in the interactions of the classical “Standard Model”

µ—

e—!µ !e

h!

!h!

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(

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)"

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0.22

)"

10!

4

Lept

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num

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(LF

),Le

pton

num

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Lept

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),Le

pton

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Lept

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),Le

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pton

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ber

(B)

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atin

gm

odes

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atin

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atio

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ing

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mon

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atio

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).B

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ns

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atio

n.

e!$

LF

<2.

7"

10!

6CL=

90%

888

µ!

$

LF

<1.

1"

10!

6CL=

90%

885

e!#0

LF

<3.

7"

10!

6CL=

90%

883

µ!

#0

LF

<4.

0"

10!

6CL=

90%

880

e!K

0 S

LF

<9.

1"

10!

7CL=

90%

819

µ!

K0 S

LF

<9.

5"

10!

7CL=

90%

815

e!%

LF

<8.

2"

10!

6CL=

90%

804

µ!%

LF

<9.

6"

10!

6CL=

90%

800

e!&0

LF

<2.

0"

10!

6CL=

90%

719

µ!

&0

LF

<6.

3"

10!

6CL=

90%

715

e!K$ (

892)

0LF

<5.

1"

10!

6CL=

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665

µ!

K$ (

892)

0LF

<7.

5"

10!

6CL=

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660

e!K$ (

892)

0LF

<7.

4"

10!

6CL=

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665

µ!

K$ (

892)

0LF

<7.

5"

10!

6CL=

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660

e!'

LF

<6.

9"

10!

6CL=

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596

µ!

'

LF

<7.

0"

10!

6CL=

90%

590

e!e+

e!LF

<2.

9"

10!

6CL=

90%

888

+!

LF

<1.

8"

10!

6CL=

90%

882

LF

<1.

5"

10!

6CL=

90%

882

17

"10!

6CL=

90%

885

!6

CL=

90%

885

. (Particle Data Group), Phys. Le

µ+modes are charge conjugates of the mo

µ!DECAY MODES

µ!DECAY MODES

µ!DECAY MODES

µ!DECAY MODES

Fraction (!

e !!e !µ

" 100%

e !!e !µ "

[d] (1.4±0.4) %

e !!e !µ e +

e !

[e] (3.4±0.4) #

Lepton Family number (LF ) violatin

Lepton Family number (LF ) violatin

Lepton Family number (LF ) violatin

Lepton Family number (LF ) violatin

e !!e !µ

LF[f ] < 1.2

%

e !"

LF

< 1.2

e !e +

e !

LF

< 1

e !2"

LF!!!!

LFV processes• A number of problems

motivate to extend the SM• Hierarchy problem:

Supersymmetry

• Quantization of electric charges: Grand Unified Theories

• Massive neutrinos: Models with

• Many extended models predict LFV processes

• Free of strong interactions, clean system

µ-e conversion

µ ! 3 e

! ! µ "

µ ! e !

etc.

!R

SUSY with the MuonLFV diagram in SUSY-GUT

LFV diagram in Standard Model

mixing in massive neutrinos

! e

! e˜ ˜

B

mixing

! e

mixing

!µ !e

W

large top Yukawa coupling

" (m! / mW)4

# 10$26

LFV diagram in SUSY-GUT

LFV diagram in Standard Model

mixing in massive neutrinos

! e

! e˜ ˜

B

mixing

! e

mixing

!µ !e

W

large top Yukawa coupling

" (m! / mW)4

# 10$26

µ~µ

~

µ-LFV

µ-EDM g-2! µ-e conversion

! µ ! e !

md

ms

mb

!

"

# # #

$

%

& & &

m!e

m!µ

m! "

#

$

% % %

&

'

( ( (

m˜ d

m˜ s

m˜ b

!

"

# # #

$

%

& & &

m˜ e e

2 !m˜ e µ

2 !m˜ e "

2

!m˜ µ e

2

m˜ µ µ

2 !m˜ µ "

2

!m˜ " e

2 !m˜ " µ

2

m˜ " ˜ "

2

#

$

% % %

&

'

( ( (

"#$%&

'()*+,-.,(#*%/,+0 1'()*+,

1"#$%&,+%2$'-)$%*/3'(1 4546-)$%*/3'(1

(78-9:;(3$<1=->:;(3$<1

(78-,(#*%/,+-+13/''$*/+, (78-3?$%@(;-'()*+,-ABC

CPV

µ

LFV diagram in SUSY-GUT

LFV diagram in Standard Model

mixing in massive neutrinos

! e

! e˜ ˜

B

mixing

! e

mixing

!µ !e

W

large top Yukawa coupling

" (m! / mW)4

# 10$26

µ~µ

~

µ

M. Aoki, NuFACT03

“Golden Trio”

Experimental Limits

Current Planned

MEGA (1999) PSI J-PARC

SINDRUM II (1998) MECO PRIME

SINDRUM (1988)

Belle (2004) Belle

µ ! e!

µ-e conv.

! ! µ"

µ+! e

+e+e!

1.2 ! 10!11

6.1 ! 10!13

1.0 ! 10!12

10!14

10!15

10!8

2 ! 10!17*

Br(µ-e conv.) !!(µ-e conv.)

!(µ capture)*

3.1 ! 10!7

5! 10!19

08/08/07 21:50The MECO Experiment

ページ 1/2http://www.bnl.gov/rsvp/MECO.htm

RSVP home

About MECO

MECO @ UC Irvine

About KOPIO

Project participants

Science in the NationalInterest

Brookhaven home

The MECO Experiment

The physicists who designed MECO (Muon to Electron

COnversion) wish to observe an event so rare (1 in

10^17) that searching for it can be compared to trying to

find a single slightly different penny in 400 years of the

national budget! To perform this search, they plan to make

a beam of 100 billion muons per second, or 1,000 times

more intense than the best muon beam in the world, now

at the Paul Scherrer Institute in Switzerland.

The MECO experimental apparatus

What they are looking for is a muon that, instead of decaying by way of the

weak force into an electron and 2 neutrinos, converts “cleanly” into an electron.

The observation of muon-to-electron conversion would signal the existence of a

fifth unseen force in the Universe, and entire families of particles now only

predicted by theory. Just as the physics of Isaac Newton could predict the

behavior of matter in the everyday world, but failed at speeds near the speed of

light, the current Standard Model appears to break down when it tries to predict

the behavior of particles at extremely high energies. Theorists have been

working hard on new explanations, for example, Supersymmetry, which implies

the existence of a hidden universe of currently unknown particles underpinning

the matter we observe to date.

08/08/07 21:51nsf.gov - News - NSF Terminates Rare Symmetry Violating Processes (RSVP) Project - US National Science Foundation (NSF)

ページ 1/2http://www.nsf.gov/news/news_summ.jsp?cntn_id=104351&org=NSF&from=news

NSF Web Site

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Press Release 05-138

NSF Terminates Rare Symmetry Violating

Processes (RSVP) Project

August 11, 2005

The National Science Foundation today terminated a planned physics project called RareSymmetry Violating Processes (RSVP) originally slated to begin construction this year atBrookhaven National Laboratory on Long Island.

At the recommendation of NSF management, the National Science Board, NSF'spolicymaking body, voted to cancel the RSVP project while it was still in the design stage,due to large increases in both construction and operating costs. The project had beenbudgeted at about $145 million for construction between Fiscal Year (FY) 2005 and 2010.

The project's two experiments - intended to investigate the relationship between theelectron and its heavier cousin the muon, and to examine differences in the behavior ofmatter and antimatter - were to be conducted through added incremental use of anexisting Brookhaven particle accelerator called the Alternating Gradient Synchrotron(AGS), which currently serves as the source for a project called the Relativistic Heavy IonCollider. In recent months, the future budget and operating schedule of the RHIC facilityhave become uncertain. Since the plan for RSVP was to use the AGS in an incrementalmode, uncertainty in the future of the RHIC project translates into increased risk andpotential increased costs for RSVP. There were also cost increases in other elements ofthe project.

"Although the discovery potential of RSVP remains high," said Michael Turner, NSFAssistant Director for Mathematics and Physical Sciences, "continuing the RSVP project inthe present budgetary environment would lead to an unacceptable loss of researchopportunities in elementary particle physics and other areas of science. While this decisioneliminates a significant elementary particle physics project, NSF reaffirms its strongcommitment to work with our partners in the funding of elementary particle physics toensure that the United States can continue to operate at the frontiers of this field, inwhich the discovery opportunities are so rich."

NSF initially approved RSVP for inclusion in the agency's budget request in October 2000,and RSVP appeared in the President's FY 2005 budget as a new construction project. Inthe fall of 2004, a pre-baseline analysis revealed additional costs that could double thecost of construction and more than double the cost of operations.

NSF initiated a process to reach a decision about how to deal with that situation. Thisprocess included obtaining advice from the High Energy Physics Advisory Panel on thecurrent scientific value of RSVP, and conducting a rigorous baseline review of the projectby external experts. At the end of the evaluation, NSF management recommendedtermination.

In announcing its decision, the NSB noted the loss of the science opportunity.Brookhaven's Alternate Gradient Synchrotron is the highest-intensity high-energy protonsource in the world. The intensity of the proton beam delivered by the AGS would haveenabled NSF-funded university researchers to search for very rare events that couldreveal the effects of new elementary particles and forces far above the energy reach ofany current or future terrestrial particle accelerator.

Following today's action by the National Science Board, NSF will work with RSVP on anorderly phase-out of activities over the next few months.

-NSF-

Media ContactsCurtis Suplee, NSF (703) 292-8070 csuplee@nsf.gov

Opportunities, challenges and anticipation for PRISM/PRIME

http://www-kuno.phys.sci.osaka-u.ac.jp/~prism/ja/project-ov.html#prism

2Muon-electron conversion in nuclei

Muon-electron conversion in nuclei

µ!

e!

eµ

!0

!

N N

!

Muo

nic

atom

W. Molzon, NP02

Muonic atom

• Muonic atom: a muon in the 1S atomic orbital

• Small orbital radius

• Relativistic effect

Initial state

!K" = #1

2!V " =

(Z!)2mµ

2208

82Pb

####$ 18.9 MeV

a(µ)B =

1

Z!mµ

208

82Pb

!!!!" 3.1 fm

r = 1.2 fm ! A1/3

208

82Pb

""""# 7.2 fm

Monochromatic electron

• Nucleus is assumed to be in its ground state in final state

• Outgoing mono-chromatic electron

Final state

Ee = Eµ ! Ebind ! Erecoil

! Eµ " Ebind

! (90 – 105)MeV

Muon-electron conversion

• mu– beam stopped in a target material forming a muonic atom

• Cascades down to 1S state

• Converted electron emitted out off atom

Gold target of SINDRUM II

experiment (PSI)µ!

N ! e!

N

http://sindrum2.web.psi.ch/home/gold2000.html

Why conversion?• Rich information on

LFV processes

• Clean signal

* Simple signature

* Well separated from endpoint of mu decay spectrum

* No accidental coincidence, well understood backgrounds

e!µ

!

µ e

!0

!0

N Nq qq

e!µ

!

eµ

!0

N N

µ-e

• Muon-induced

* muon decay in orbit

* Radiative muon capture

• Pion-induced

* Radiative pion capture

• Cosmic ray

• Electrons in the beam

Backgrounds

µ! + A

ZN !AZN + e!!e!µ

e+e!

undetected

µ! + A

ZN !A

Z!1N" + !µ"

e+e!

!! + A

ZN !A

Z!1N" + "

µ!

N!

!

N!

!

e!

e+

!µ

du

undetected

W

µ!

e!

W!e

!µ

N N

u

d

u

!e!

e+

undetected

N!

!

N!

d

!!

!

Kuno&Okada, RMP 73, 151 (2001)

• Muon-induced

* muon decay in orbit

* Radiative muon capture

• Pion-induced

* Radiative pion capture

• Cosmic ray

• Electrons in the beam

Backgrounds

µ! + A

ZN !AZN + e!!e!µ

e+e!

undetected

µ! + A

ZN !A

Z!1N" + !µ"

e+e!

!! + A

ZN !A

Z!1N" + "

Electron energy spectrum[SINDRUM II with Pb (1994)]

http://sindrum2.web.psi.ch/home/lead92.html

Benefits of muon storage ring

• Unprecedented purity of muon beam

* Reduced contamination of electrons and pions

* Shorter lifetime of muonic atom is allowed

* Variety of nuclei as a target material

* Systematic experiments leads to a new handle to the new physics?

Studies in the Past

Muon wave function

Electron wave function

Momentum transfer LFV interaction

Nucleon distribution in nuclei

Weinberg & Feinberg (1959) Constant Plane wave Dipole

Approximate formula

Shanker (1979) Dirac eq. Dirac eq. AllApproximate

formula

Czarnezki, Marciano &

Melnikov (1998)Dirac eq. Dirac eq.

Integrated over all q

Dipole + Vector

Experimental data (3 points)

Kosmas (2001)Schrödinger

eq.Plane wave Four-Fermi

Experimental data

Present work Dirac eq. Dirac eq.Integrated over

all qAll

Experimental data

q2

= !m2

µ

q2

= !m2

µ

q = mµ ! Ebind

3Muon-electron conversion in various

nuclei

Outline

m-e conversion amplitudes & rates

Proton & neutron distribution

Dirac Equations

Muon & electron wave functions

Overlap integrals

Effective LagrangianLint = !

4GF"

2(mµAR µ!µ!PLeFµ! + mµAL µ!µ!PReFµ! + h.c.)

!

GF"

2

!

q=u,d,s

"

#

gLS(q) ePRµ + gRS(q) ePLµ$

qq

+!

gLP(q) ePRµ + gRP(q) ePLµ"

q!5q

+!

gLA(q) e!µPLµ + gRA(q) e!µPRµ"

q!µ!5q

+!

gLV(q) e!µPLµ + gRV(q) e!µPRµ"

q!µq

+h.c.

!

+1

2

!

gLT(q) e!µ!PRµ + gRT(q) e!µ!PLµ"

q!µ!q

Photonic

Scalar

Pseudoscalar

Vector

Axial vector

Tensor

Conversion amplitude

!N|q!0q|N" =

!

"

#

"

$

2Z"(p) + (A # Z)"(n) (q = u)

Z"(p) + 2(A # Z)"(n) (q = d)

0 (q = s)

!N|q!iq|N" = 0 (i = 1, 2, 3)

[Kosmas et al. (2001)]

!N|qq|N" = ZG(q,p)S !(p) + (A # Z)G(q,n)

S !(n)

G(u,p)S = G

(d,n)S = 5.1 G

(d,p)S = G

(u,n)S = 4.3 G

(s,p)S = G

(s,n)S = 2.5

Coherent conversion amplitude

M =4GF!

2

!

d3x

"

mµA!

R !µ(e)!,E ""#PR!

(µ)1s + mµA!

L !µ(e)!,E ""#PL!

(µ)1s

#

"N|F"# |N#

+GF!

2

!

q=u,d,s

"

d3x

#

$

gLS(q) !µ(e)!,E PR!

(µ)1s + gRS(q) !

µ(e)!,E PL!

(µ)1s

%

"N|qq|N#

+

!

gLV(q) !µ(e)!,E

""PL!(µ)1s + gRV(q) !

µ(e)!,E

""PR!(µ)1s

"

!N|q""q|N"

#

!

|N! = Ground state"

Wave functions

Dirac equation

Wave function

0

0.05

– 0.05

0.1

0.15

0.2

0.25

0.3

0 20 40 60 80 100

u1u2

r / [mm-1]

Muo

n w

ave

func

tion

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 20 40 60 80 100

u1u2

r / [mm-1]

Elec

tron

wav

e fu

nctio

n

!(r) =

!

g(r)"µ!(#,$)

if(r)"µ

!!(#,$)

"

=1

r

!

u1(r)"µ!(#,$)

iu2(r)"µ

!!(#,$)

"

V (r) = !e

!!

r

E(r")dr" E(r) =

Ze

r2

!r

0!(p)(r!)r!2dr!

! ! "(L · ! + 1)(! = !1 for 1S state)

d

dr

!

u1

u2

"

=

#

$

!

!

rE ! V + mi

!(E ! V ! mi)!

r

%

&

!

u1

u2

"

Initial 1S state: Muon Final state: Electron

Ee = mµ ! Ebinding

Prot

on

Conversion rate

D =4!

2mµ

!

!

0

drr2"

" E(r)#"

ge(r)fµ(r) + fe(r)gµ(r)#

S(p) =1

2!

2

!

!

0drr2Z!(p)(r)

"

ge(r)gµ(r) " fe(r)fµ(r))

Neu

tron S(n) =

1

2!

2

!

!

0drr2(A " Z)!(n)(r)

"

ge(r)gµ(r) " fe(r)fµ(r)#

V (p) =1

2!

2

!

!

0drr2Z!(p)(r)

"

ge(r)gµ(r) + fe(r)fµ(r)#

V (n) =1

2!

2

!

!

0drr2(A " Z)!(n)(r)

"

ge(r)gµ(r) + fe(r)fµ(r)#

!conv = |M |2 g(p)LS,RS =

!

q

G(q,p)S gLS,RS(q)

g(n)LS,RS =

!

q

G(q,n)S gLS,RS(q)

g(p)LV,RV = 2gLV,RV(u) + gLV,RV(d)

g(n)LV,RV = gLV,RV(u) + 2gLV,RV(d)

Conversion rate

Overlap integrals

Dipole

Scalar-Proton

Scalar-Neutron

Vector-Proton

Vector-Neutron

= 2G2F

!

!

!

A!

RD + g(p)LS S(p)

+ g(p)LV V (p)

+ g(n)LS S(n)

+ g(n)LV V (n)

!

!

!

2

+2G2F

!

!

!

A!

LD + g(p)RSS(p)

+ g(p)RVV (p)

+ g(n)RSS(n)

+ g(n)RVV (n)

!

!

!

2

Overlap integrals

Atomic number

Assumption: !(n)(r) = !(p)(r)

0.20

0.15

0.10

0.05

0.001009080706050403020100

Dipole Scalar-Proton Vector-Proton Scalar-Neutron Vector-Neutron

Over

lap

inte

gra

ls/[m

5/2

µ]

[Nuclear data from C. W. De Jager et al. At. Data Nucl. Data Tables 36, 495 (1987); G. Fricke et al., ibid. 60, 177 (1995)]

AuTaErSb

Neutron distribution• Proton distribution is well determined through scattering

experiments

• Neutron distribution is only poorly known

• Assumption of

* Expected from isospin invariance from nuclei with the same number of neutrons and protons

* Good approximation for light nuclei

* Experimental data on neutron distribution only available for limited number of nuclei

* Gives insight to the tendency of the Z-dependence of the conversion amplitudes and rates

!(n)(r) = !

(p)(r)

Overlap Integrals (2)0.20

0.15

0.10

0.05

0.001009080706050403020100

Dipole Scalar-Proton Vector-Proton Scalar-Neutron Vector-Neutron

0.20

0.15

0.10

0.05

0.001009080706050403020100

Dipole Scalar-Proton Vector-Proton Scalar-Neutron Vector-Neutron

Atomic number

Over

lap

inte

gra

ls/[m

5/2

µ]

from hadronic atom spectroscopy!(p,n)(r)

[Nuclear data from C. Gracia-Recio et al. Nucl. Phys. A547, 473 (1992)]

Overlap Integrals (2)

Atomic number

0.20

0.15

0.10

0.05

0.001009080706050403020100

Scalar-Neutron Vector-Neutron

0.20

0.15

0.10

0.05

0.001009080706050403020100

Scalar-Neutron Vector-Neutron

[Nuclear data from C. Gracia-Recio et al. Nucl. Phys. A547, 473 (1992)]

Over

lap

inte

gra

ls/[m

5/2

µ]

from hadronic atom spectroscopy!(p,n)(r)

Hadronic atom spectroscopy

• A hadron (e.g. pion, antiproton) trapped in an atomic orbital, goes down to lower energy state emitting X-rays

• Annihilates through strong interaction between nucleus at n = 3, 4, or higher ––– far from the nucleus

• Two observed quantities: Energy shift and decay width

• Functional form of nucleon distribution is assumed; often Fermi function

• Nucleon distribution inside the nucleus is extrapolated from outside according to the assumed function

!(r) =!0

1 + exp

!

r ! c

z

"

• More direct observation of nucleus interior

• Nucleon distribution is often expressed in terms of Fourier-Bessel series

Scattering experiments

!(r) = "!

! (r ! R)"

#

n

j0

$n#r

R

%

Overlap integrals (3)0.20

0.15

0.10

0.05

0.001009080706050403020100

Dipole Scalar-Proton Vector-Proton Scalar-Neutron Vector-Neutron

from proton scattering experiments!(p,n)(r)

0.20

0.15

0.10

0.05

0.001009080706050403020100

Dipole Scalar-Proton Vector-Proton Scalar-Neutron Vector-Neutron

Atomic number

Over

lap

inte

gra

ls/[m

5/2

µ]

[Nuclear data from L. Ray et al. Phys. Rev. C 19, 1855 (1979), G. Pauletta et al. Phys. Lett. 106B, 470 (1981)]

Neutron distribution

• Assumption of

* Light nuclei: Good approximation by isospin symmetry

* Heavy nuclei: Muonic atom orbital is inside the nuclei, while extra neutrons are at the periphery

!(n)(r) = !

(p)(r)

Branching ratio

Br(µN ! eN) "!(µN ! eN)

!(µN ! !µN!)

Br(µN ! eN;Z)

Br(µN ! eN;13Al)

Branching Ratio

We plot the relative value to Aluminum

Branching Ratios

Atomic number

Br(

µN

!eN

;Z)

Br(

µN

!eN

;Z=

13)

Assumption: !(n)(r) = !(p)(r)

2.5

2.0

1.5

1.0

0.5

0.01009080706050403020100

Dipole Scalar Vector

Se

Cu

PbAl

Ti

Sr

Au

Ta

Er

Sb

Branching Ratio (2)2.5

2.0

1.5

1.0

0.5

0.01009080706050403020100

Dipole Scalar Vector

2.5

2.0

1.5

1.0

0.5

0.01009080706050403020100

Dipole Scalar Vector

from proton scattering experiments!(p,n)(r)

Atomic number

Br(

µN

!eN

;Z)

Br(

µN

!eN

;Z=

13)

Summary• LFV provides a valuable handle toward the physics

beyond the Standard Model.

• LFV conversion search is a clean and informative experiment.

• Pure muon beams enable conversion search for various nuclei.

• Nuclei with Z ~ (30 – 60) give large conversion amplitude and rate.

• Measurements of conversion rate for various nuclei are useful to distinguish the theoretical models.

µ-e

µ-e

µ-e