Nufact18 Virginia Tech Distinguishing muon LFV effective couplings using in a muonic atom YUesaka Y Kuno J S T Sato amp M Yamanaka Phys Rev D 93 076006 2016 ID: 808681
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Slide1
Joe Sato (Saitama University)
Nufact18
@ Virginia Tech
Distinguishing muon LFV effective couplings using in a muonic atom
Y.Uesaka, Y. Kuno, JS, T. Sato & M. Yamanaka, Phys. Rev. D 93, 076006 (2016).
Y.Uesaka, Y. Kuno, JS, T. Sato & M. Yamanaka, Phys. Rev. D 97, 015017 (2018).
M. Koike, Y. Kuno, JS, & M. Yamanaka, Phys. Rev. Lett. 105, 121601 (2010).
Y
. Kuno,
J
S
,
T.
Sato,
Y.Uesaka
& M. Yamanaka,
in preparation
Slide2Contents
1.
Introduction
2. Transition probability of
Charged Lepton Flavor Violation (CLFV)CLFV
searches using muonDistortion of scattering electrons & Relativity of bound leptons４
. Summary
in a muonic atom
３
. Distinguishment of CLFV interaction
Asymmetry of emitted electrons by polarizing muon
Atomic # dependence of decay rates
Energy-angular distribution of emitted electrons
Effective CLFV interactions
Difference between contact & photonic processes
Slide3Contents
1.
Introduction
2. Transition probability of
Charged Lepton Flavor Violation (CLFV)CLFV searches using muon
Distortion of scattering electrons & Relativity of bound leptons４. Summary
in a muonic atom
３
. Distinguishment of CLFV interaction
Asymmetry of emitted electrons by polarizing muon
Atomic # dependence of decay rates
Energy-angular distribution of emitted electrons
Effective CLFV interactions
Difference between contact & photonic processes
Slide4enhanced
in many theories beyond SM
Charged Lepton Flavor Violation (CLFV)
contribution of neutrino mixing → very small
cannot be observed by current technology
-
A probe for new physics -e.g. SUSY
forbidden
in SM
Searches for CLFV can access
high energy physics
with little SM backgrounds.
l
epton flavor violation for charged lepton
CLFV
cf. current experimental
upper limit
Slide5L. Calibbi & G. Signorelli, arXiv:1709.00294 [hep-ph].
CLFV searches in muon rare decay
1. high intensity
2. long lifetimeAdvantages of muon
current bounds
-
conversion
CLFV search using
-atom
exploring
interaction
New experiments for “
conversion” are planned with higher sensitivity than previous ones.
(COMET, DeeMe @ J-PARC, Mu2e @ Fermilab)
Slide6in a muonic atom
CLFV
F
eatures
2 CLFV mechanisms
atomic #
:
large
decay rate
:
large
M. Koike, Y. Kuno
, J. Sato, & M. Yamanaka,
Phys. Rev. Lett.
105
, 121601 (2010).
New CLFV
search
using muonic atoms
contact (
vertex )
photonic (
vertex )
clear signal :
R
.
Abramishvili
et al
.,
COMET Phase-I Technical Design
Report
(2016).
proposal in
COMET
(similar to
)
Slide7Comparison to other muonic CLFV
1.
2.
3.
✓
-
-
✓
✓
-
-
conv.
✓
-
✓
✓
✓
-
✓
-
-
✓
✓
-
✓
-
✓
✓
✓
-
1.
2
.
3
.
Typical effective CLFV interactions
Slide8Comparison
to
in a muonic atom
difference 1
:
signal
2
s
1
&
2
s
difference 2
:
interference among CLFV couplings
Slide9(Rough) Estimation of decay rate
: cross section of
：
wave function
of
bound electron
(non-relativistic)
Phys. Rev. Lett.
105
,121601 (2010).
: relative velocity of
&
(the same
dependence in
the both contact
& photonic
cases)
(sum of two
s)
Suppose nuclear Coulomb potential is weak,
“flux”
(free particles’)
Slide10Branching ratio of CLFV decay
Phys. Rev. Lett.
105,121601
(2010).
:
lifetime of a muonic atom
How many muonic atoms decay with CLFV,
compared to created #
?
BR with CLFV coupling fixed on allowed maximum
for a muonic H (
)
for a muonic Pb
(
)
cf.
due to existence prob.
of bound
at the origin
BR
increases
with atomic #
.
Using muonic atoms with
large
is favored
to search for
.
e.g.
for Pb
if
contact process is dominant
Slide11To improve calculation for decay rate
previous formula of CLFV decay rate by
Koike
et al.
emitted
s are expected to be back-to-back with equal energies
More quantitative estimation
is needed !
(important for large
)
Note
emitted
: plane wave
spatial extension of bound lepton
bound lepton
: non-relativistic
←
small orbital radius
←
relativistic
(especially,
)
←
Coulomb
distortion
used approximations
(
)
wave length of emitted
In atoms with large
,
“
dependence” comes from only
Slide12Contents
1.
Introduction
2. Transition probability of
Charged Lepton Flavor Violation (CLFV)
CLFV searches using muon
Distortion of scattering electrons & Relativity of bound leptons４. Summary
in a muonic atom
３
. Distinguishment of CLFV interaction
Asymmetry of emitted electrons by polarizing muon
Atomic # dependence of decay rates
Energy-angular distribution of emitted electrons
Effective CLFV interactions
Difference between contact & photonic processes
Slide13contact
interaction
photonic interaction
Effective Lagrangian for
constrained by
constrained by
Slide14contact
interaction
photonic interaction
Effective Lagrangian for
constrained by
constrained by
Slide15Our formulation for decay rate
get radial functions by solving “
Dirac eq. with
” numerically
use partial wave expansion to express the distortion
:
nuclear
Coulomb potential
: index of angular momentum
Slide16Contact process
overlap of bound
, bound
, and
two scattering
s
bound
scattering
scattering
bound
[fm]
transition rate
increases!
bound
:
non-relativistic
relativistic
scat.
:
plane
distorted
wave functions shift
to the center
Slide17Upper limits of BR (contact process)
this work (1s)
(
SINDRUM,
1988)
atomic #,
this work
(1s+2s+…)
Koike
et al.
(1s)
inverse of
(
)
Slide18Photonic process
bound
bound
scattering
scattering
[fm]
[fm]
scat.
:
plane
distorted
bound
:
non-relativistic
relativistic
overlap integral
decreases
distortion
of scattering
scat.
:
plane
distorted
Slide19(MEG, 2016)
Upper limits of BR (photonic process)
this work (1s)
Koike
et al.
(1s)
inverse of
(
)
this work
(1s+2s+…)
Slide20Effect of distortion
photonic process
bound
bound
emitted
emitted
momentum transfers to bound leptons
bound
emitted
bound
emitted
contact process
make overlap integrals smaller
Totally (combined with the effect to enhance the value near the origin),
enhanced !!
suppressed…
scat.
:
distorted wave
(Assuming momentum conservation at each vertex)
Slide21Contents
1.
Introduction
2. Transition probability of
Charged Lepton Flavor Violation (CLFV)
CLFV
searches using muonDistortion of scattering electrons &
Relativity of bound leptons
４
. Summary
in a muonic atom
３
. Distinguishment of CLFV interaction
Asymmetry of emitted electrons by polarizing muon
Atomic # dependence of decay rates
Energy-angular distribution of emitted electrons
Effective CLFV interactions
Difference between contact & photonic processes
Slide22dependence of
The
dependences
are different among interactions
.
That of contact process is strongly increasing,
while that of photonic process is moderately increasing
.
Distinguishing method 1
~ atomic #
dependence of decay rates ~
contact
photonic
Slide23~
energy and angular distributions ~
Distinguishing
method 2
: energy of an emitted electron
: angle between two emitted electrons
photonic
contact
The distributions
are (a little) different among interactions
.
Slide24Model distinguishing power
method
1. -dep. of decay rates
method 2. energy-angular distributionWe can distinguish “contact” or “photonic”.Can we distinguish “left” or “right” ?
e.g.
&
Slide25is expected
(
)
is expected
Measurement of angular distribution asymmetry
Y. Okada, K. Okumura & Y. Shimizu
,
Phys. Rev. D
61
, 094001 (2000).
cf
:
,
with polarized muon
Determination of dominant interaction !?
Y. Kuno
&
Y. Okada, Phys. Rev.
Lett.
77
,
434
(1996).
~
electron asymmetry from
polarized muon ~
Distinguishing
method 3
In preparation
Slide26Example 1
:
Final state is determined by 4 parameters, say,
(
)
:
:
:
2 are fixed for examples
Slide27
Slide28Example 2
:
Slide29
Slide30・
In all cases there is asymmetry
Useful to determine the parity violation of effective couplings
・ Shape of Assymetry can determine the interaction !?・ Relativistic treatment is important・Distortion is very importantEspecially for photonic interaction・
type In non-relativistic limit , exactly 0
Even if relativistic , if nuclear is point like the asymmetry is 0∵ asymmetry
・
type
In any case , non-zero
Slide31Contents
1.
Introduction
2. Transition probability of
Charged Lepton Flavor Violation (CLFV)
CLFV
searches using muonDistortion of scattering electrons &
Relativity of bound leptons
４
. Summary
in a muonic atom
３
. Distinguishment of CLFV interaction
Asymmetry of emitted electrons by polarizing muon
Atomic # dependence of decay rates
Energy-angular distribution of emitted electrons
Effective CLFV interactions
Difference between contact & photonic processes
Slide32contact process
：decay rate
Enhanced (7 times
in )
process in a muonic atom
Our finding
interesting candidate for CLFV searchDistortion of emitted electronsRelativistic treatment of a bound electron
are important in calculating decay rates.
energy and angular distributions of emitted electrons
H
ow to discriminate interactions, found by this analyses
atomic # dependence of the decay rate
photonic process
：
decay rate
suppressed
(1/4 times
in
)
Summary
D
istortion makes difference between 2 processes.
asymmetry of electron emission by polarized muon
Slide33backup
Slide34Coulomb prevents the contact process?
Use the
simple Hamiltonian (a muon & an electron in nuclear potential)
Assume that the form of the wave function is
find the parameter set to minimize the energy
We can safely neglect
the additional factor
.
Slide35Radial wave function (bound
)
[fm]
[
]
Type
(MeV)
Relativistic
Non-relativistic
Type
Relativistic
Non-relativistic
case
(considering
screening)
Relativity enhances the value near the origin.
Slide36Radial wave function
(scattering
)
[fm]
[
]
shifted by nuclear Coulomb potential
MeV
e.g.
partial wave
distorted wave
plane wave
case
①
enhanced
value near the origin
②
local momentum increased
effectively
Slide37Radial wave function (bound
)
[fm] [
]
case
(radius of
Pb
)
MeV
: solid
: dotted
It is important to consider finite nuclear charge radius.
Backup
Slide38Effect of finite size of muon wave
contact
(
-
)
contact (-
)
photonic
(
-
)
bound lepton
:
nonrelativistic
scattering
:
plane wave
(
: the rate in the previous approx.
)
Momentum fluctuation of bound muon
overlap integral
small
Slide39differential decay rate
:
contact
photonic
: energy of an emitted electron
: angle between two emitted electrons
: Legendre polynomial
Decay rate
Backup
Slide40angular distribution (
)
pair has same chirality
:
angle between two emitted
electrons
contact
(same chirality)
contact
(opposite chirality)
pair cannot emit same momentum
Discriminating
method 2
(due to Pauli principle)
Backup
Slide41Contribution from all bound
s
1S2S2P
3S3P
3D4STotal
1S
2S
2P
3S
3P
3D
4S
Total
1S
2S
2P
3S
3P
3D
4S
Total
1S
2S
2P
3S
3P
3D
4S
Total
contact
photonic
normalize the contribution of
to
it is sufficient to consider about
electrons for both cases
Backup
Slide42非対称度の測定
例
:
終
状態
の
kinematics
を決めるパラメータは
4
つ
(
)
:
の角度
:
:
2
つを固定して図を作成
Slide43
Slide44