Design Status for SW (Electron Muon Ranger) Gianrossano Giannini, Pietro Chimenti,
Muon-electron conversion in nuclei - 大阪大学sato/0808muonwg/... · Muon-electron conversion in...
Transcript of Muon-electron conversion in nuclei - 大阪大学sato/0808muonwg/... · Muon-electron conversion in...
Muon-electron conversion in nuclei
Masafumi Koike (Saitama U)
2008.8.8 Muon WG Workshop@Izu
Kitano, Koike, and Okada, PRD 66, 096002 (2002)
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/"
2 c!ei!2/2/"
2 1/"
2s!ei!1/2/
"2 !c!ei!2/2/
"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!
!" !
h!!
#0" !
[g]
(
h!!
2#0" !
(1.
4±
0.5
)"
10
2h!
h+!
" !
(1.
20±
0.22
)"
10!
4
Lept
onFa
mily
num
ber
(LF
),Le
pton
num
ber
(L),
Lept
onFa
mily
num
ber
(LF
),Le
pton
num
ber
(L),
Lept
onFa
mily
num
ber
(LF
),Le
pton
num
ber
(L),
Lept
onFa
mily
num
ber
(LF
),Le
pton
num
ber
(L),
orBar
yon
num
ber
(B)
viol
atin
gm
odes
orBar
yon
num
ber
(B)
viol
atin
gm
odes
orBar
yon
num
ber
(B)
viol
atin
gm
odes
orBar
yon
num
ber
(B)
viol
atin
gm
odes
Lm
eans
lepto
nnum
ber
viol
atio
n(e
.g.
!!#
e+"!
"!
).Fol
low
ing
com
mon
usa
ge,LF
mea
ns
lepto
nfa
mily
viol
atio
nan
dnot
lepto
nnum
ber
viol
atio
n(e
.g.
!!#
e!"+
"!
).B
mea
ns
bar
yon
num
ber
viol
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=
90%
665
µ!
K$ (
892)
0LF
<7.
5"
10!
6CL=
90%
660
e!K$ (
892)
0LF
<7.
4"
10!
6CL=
90%
665
µ!
K$ (
892)
0LF
<7.
5"
10!
6CL=
90%
660
e!'
LF
<6.
9"
10!
6CL=
90%
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
News
News
News From the Field
For the News Media
Special Reports
Research Overviews
NSF-Wide Investments
Speeches & Lectures
Multimedia Gallery
NSF Current Newsletter
News Archive
News by Research Area
Arctic & Antarctic
Astronomy & Space
Biology
Chemistry & Materials
Computing
Earth & Environment
Education
Engineering
Mathematics
Nanoscience
People & Society
Physics
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 [email protected]
Opportunities, challenges and anticipation for PRISM/PRIME
http://www-kuno.phys.sci.osaka-u.ac.jp/~prism/ja/project-ov.html#prism
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
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$
+!
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