charged lepton flavor violating process,seminar/pdf_2016_kouki/...yuichi uesaka collaborators t....
TRANSCRIPT
Yuichi Uesaka
Collaborators
T. Sato 1,
December 20, 2016 @ Particle Physics Theory Seminar, Osaka U.
Charged lepton flavor violating process,
๐โ๐โ โ ๐โ๐โ in a muonic atom
Y. Kuno 1, J. Sato 2, M. Yamanaka 3
1Osaka U., 2Saitama U., 3Kyoto Sangyo U.
YU, Y. Kuno, J. Sato, T. Sato & M. Yamanaka, Phys. Rev. D 93, 076006 (2016).
(Nuclear Theory, Osaka U.)
YU, Y. Kuno, J. Sato, T. Sato & M. Yamanaka, in preparation.
Contents
1. Introduction
2. Formulation
Charged Lepton Flavor Violation (CLFV)
Partial wave expansion
๏ผ. Summary
๐โ๐โ โ ๐โ๐โ in a muonic atom
๏ผ. Results
Decay rates (Branching ratios)
Model-discriminating power
Relativistic treatment for bound leptons
CLFV search using muons
1. Introduction
โข predicted in many theories beyond SM
Charged Lepton Flavor Violation (CLFV)
โข contribution of neutrino oscilation โ very small
Br ๐ โ ๐๐พ < 10โ54 cannot be observed by current technology
- A probe for new physics -
(does not contaminate the search for new physics)
e.g. SUSYโข forbidden in SM
If seen, that is an evidence of new physics !! (not ๐ osci.)
๐โ ๐โ ๐โ ๐๐ ๐๐ ๐๐ ๐+ ๐+ ๐+ ๐๐ ๐๐ ๐๐ others
+1 0 0 +1 0 0 -1 0 0 -1 0 0 0
0 +1 0 0 +1 0 0 -1 0 0 -1 0 0
0 0 +1 0 0 +1 0 0 -1 0 0 -1 0
๐ฟ๐
๐ฟ๐
๐ฟ๐
โข lepton flavor #, ๐ฟ๐, ๐ฟ๐ , ๐ฟ๐ ( Please distinguish them from lepton #, ๐ฟ = ๐ฟ๐ + ๐ฟ๐ + ๐ฟ๐. )
1. Introduction
lepton flavor violation in charged lepton sector = CLFV
CLFV search using muons
BR < 1.0 ร 10โ12 by SINDRUM
BR < 7 ร 10โ13 (๐โAu โ ๐โAu) by SINDRUM II
BR < 5.7 ร 10โ13 by MEG
Examples of CLFV processes using muons
a) ๐+ โ ๐+๐พ
b) ๐+ โ ๐+๐โ๐+
c) ๐โ๐ โ ๐โ๐
1. long lifetime and simple kinematics
BR ๏ผ Branching Ratio
Phys. Rev. Lett. 110, 201801 (2013).
Nucl. Phys. B 299, 1 (1988).
Eur. Phys. J. C 47, 337 (2006).
New experiments for โ๐โ โ ๐โ conversionโ are planned with higher sensitivity than previous ones.
Advantages of using muon for rare process
(COMET, DeeMe @ J-PARC, Mu2e @ Fermilab)
1. Introduction
(โก signal rate / total decay rate)
(โผ 108โ9 muons per a second)2. high intensity muon beam
๐โ๐โ โ ๐โ๐โ in a muonic atom
+๐๐
๐โ
๐โ
C
L
F
V
๐โ
๐โ
Features
โข 2 type CLFV interactions
โข atomic # ๐ : largeโ decay rate ฮ : large
M. Koike, Y. Kuno, J. Sato & M. Yamanaka,
Phys. Rev. Lett. 105,121601(2010)
๐ธ1
๐ธ2
๐โ
๐โ
๐โ
๐โ
๐โ
๐โ ๐โ
๐โ
๐พโ
ฮ โ ๐ โ 1 3
New CLFV search
using muonic atoms
๐๐๐๐ vertex
๐๐๐พ vertex
โข clear signal : two ๐โs (๐ธ1 + ๐ธ2 โ ๐๐ +๐๐ โ ๐ต๐ โ ๐ต๐)
R. Abramishili et al.,
COMET Phase-I Technical Design Report,
KEK Report 2015-1 (2015)
proposal in COMET
1. Introduction
(similar to ๐+ โ ๐+๐+๐โ)
(Rough) Estimation of decay rate
ฮ๐โ๐โโ๐โ๐โ = 2๐๐ฃrel ๐1๐๐ 0 2
๐ : cross section of ๐โ๐โ โ ๐โ๐โ
๏ผ wave function of 1๐ bound electron (non-rela)
๐1๐๐ ิฆ๐ฅ =
๐๐ ๐ โ 1 ๐ผ 3
๐exp โ๐๐ ๐ โ 1 ๐ผ ิฆ๐ฅ
Phys. Rev. Lett. 105,121601 (2010).
ฮ โ ๐ โ 1 3
๐ฃrel : relative velocity of ๐โ & ๐โ
ฮ = ๐๐ฃrelโซ d๐๐๐๐๐
(the same ๐ dependence in the both contact & photonic cases)
(sum of two 1๐ ๐โs)
1. Introduction
Suppose nuclear Coulomb potential is weak,
โfluxโ
(free particlesโ)
Branching ratio
Phys. Rev. Lett. 105,121601 (2010).
Br ๐โ๐โ โ ๐โ๐โ โก ว๐๐ฮ ๐โ๐โ โ ๐โ๐โ
ว๐๐ : lifetime of a muonic atom
How many muons decay, compared to created # ?
Constraint from previous CLFV experiments
2.2ฮผs for a muonic H (๐ = 1)
80ns for a muonic Pb (๐ = 82)
cf.
1. Introduction
increasing as atomic # ๐ is larger
Using muonic atom with large ๐is favored.
can product ๐ช 1018โ19 muonic atoms.
cf. Future experiment (COMET Phase-II)
To improve the previous estimation
ฮ๐โ๐โโ๐โ๐โ = 2๐๐ฃrel ๐1๐๐ 0 2 โ ๐ โ 1 3
Koike et al.
โข emitted ๐โ : plane wave
โข spacial extension of bound lepton
โข bound lepton : non-rela
( valid when nuclear Coulomb potential is sufficiently small)
In atoms with large ๐,
โ small orbital radius
โ relativistic (especially, ๐โ)
โ Coulomb distortion
not able to estimate differential decay rate
โ๐ dependenceโ doesnโt depend on CLFV int. always ฮ โ ๐ โ 1 3
More quantitive estimation is needed ! (important for large ๐)
approximations (๐๐ผ โช 1)
1. Introduction
Note
โซ wave length of emitted ๐โ
lepton wave function ๏ผ relativistic Coulomb
Improvement and expectation
this work
we can estimate energy & angular distribution of emitted ๐โ pair
โข Coulomb distortion of emitted ๐โ
โข finite orbit-size of bound leptons
โข relativistic effects for bound leptons
we may get different results, depending on CLFV interaction
influence for ฮ๐โ๐โโ๐โ๐โ
๏ผ
suppressed
enhanced
the improvement containsโฆ
other expectation
Totally, how CLFV decay rates are changed ?
1. Introduction
2. Formulation
โ๐ผ = โ๐๐๐๐ก๐๐๐ก + โ๐โ๐๐ก๐
+[โ. ๐. ]
๐
๐ ๐
๐
+[โ. ๐. ]
๐พโ
๐
๐
๐
๐
contact interaction
(short-range process)
photonic interaction
(long-range process)
Effective Lagrangian
2. Formulation
๐โ
๐โ
+๐๐๐1
๐2CLFV
๐โ๐โ โ ๐โ๐โ
initial state final state
bound ๐โ (๐๐บ) & bound ๐โ 2 scattering ๐โs (distorted wave)
ใปignore interaction among ๐โs
๐ธ1 + ๐ธ2 = ๐๐ +๐๐ โ ๐ต๐ โ ๐ต๐
ใปignore nuclear recoil energy
๐โ๐โ โ ๐โ๐โ process
๐โ
2. Formulation
Decay rate
ฮ = 2๐
๐
าง๐
๐ฟ(๐ธ๐ โ ๐ธ๐) ๐๐๐ 1 ๐1 ๐๐
๐ 2(๐2) ๐ป ๐๐๐ ๐ 1๐ ๐๐
๐ ๐(1๐ )2
get radial functions by solving Dirac eq. numerically
๐๐๐ (๐)
๐๐+1 + ๐
๐๐๐ ๐ โ ๐ธ +๐ + ๐๐ ๐ ๐๐ ๐ = 0
๐๐๐ (๐)
๐๐+1 โ ๐
๐๐๐ ๐ + ๐ธ โ๐ + ๐๐ ๐ ๐๐ ๐ = 0
๐ ๐ =๐๐ ๐ ๐๐
๐( ฦธ๐)
๐๐๐ ๐ ๐โ๐ ๐( ฦธ๐)
use partial wave expansion to express the distortion
๐๐๐ ๐ =
๐ ,๐,๐
4๐ ๐๐๐ (๐๐ , ๐, 1/2, ๐ |๐๐ , ๐)๐๐๐ ,๐โ ( ฦธ๐)๐โ๐๐ฟ๐ ๐๐
๐ ,๐
๐ : nuclear Coulomb potential
2. Formulation
ฮ ๐โ 1๐ ๐โ ๐ผ โ ๐โ๐โ
=1
2เถฑ๐๐
๐๐โ๐ต๐1๐โ๐ต๐
๐ผ
d๐ธ1เถฑโ1
1
d cos๐d2ฮ
d๐ธ1dcos๐
๐ ๐ธ1, ๐ 1, ๐ 2, ๐ฝ =
๐=1,โฏ,6
๐๐๐contact๐ ๐ธ1, ๐ 1, ๐ 2, ๐ฝ +
๐=๐ฟ,๐
๐๐๐photo๐
๐ธ1, ๐ 1, ๐ 2, ๐ฝ
d2ฮ
d๐ธ1dcos๐=
๐ 1,๐ 2,๐ 1โฒ ,๐ 2
โฒ ,๐ฝ,๐
๐ ๐ธ1, ๐ 1, ๐ 2, ๐ฝ ๐โ ๐ธ1, ๐ 1
โฒ , ๐ 2โฒ , ๐ฝ
ร ๐ค ๐ 1, ๐ 2, ๐ 1โฒ , ๐ 2
โฒ , ๐ฝ, ๐ ๐๐ cos๐
differential decay rate :
๐ธ1
๐ธ2
๐
Energy & angular distribution
2. Formulation
๐ธ1 : energy of an emitted electron
๐ : angle between two emitted electrons
๐๐ : Legendre polynomial
3. Results
Radial wave function (bound ๐โ)
๐ [fm]
[MeVโ1/2]
๐ = 82Pb case208
๐๐๐1๐ ๐ , ๐๐๐
1๐ ๐
(radius of 208Pb )
๐ต๐: 10.5 MeV
3. Results
๐๐๐1๐ ๐ : solid
๐๐๐1๐ ๐ : dotted
Radial wave function (bound ๐โ)
๐ [fm]
[MeV1/2]
Type ๐ต๐(MeV)
Rela 9.88 ร 10โ2
Non-rela 8.93 ร 10โ2
๐ = 81Pb case208
(considering ๐โ screening)
Relativity enhances the value near the origin.
๐๐1๐ ๐
3. Results
Radial wave function (scattering ๐โ)
๐ [fm]
[MeVโ3/2]๐๐๐ธ1/2
๐ =โ1 ๐
attracted by nuclear Coulomb potential
๐ = 82
๐ธ1/2 โ 48MeV
e.g. ๐ = โ1 partial wave
distorted wave
plane wave
Pb case208
โ enhanced value near the origin
โก local momentum increased effectively
3. Results
Contact process
๐โ
๐โ
๐โ
๐โ
overlap of bound ๐โ, bound ๐โ, and two scattering ๐โs
bound ๐โ
scattering ๐โ scattering ๐โ
bound ๐โ
๐ [fm]
transition rate UP!
bound ๐โ : non-rela โ rela
๐2๐๐1๐ ๐ ๐๐
1๐ ๐ ๐๐ธ1/2๐ =โ1 ๐ ๐๐ธ1/2
๐ =โ1 ๐
scat. ๐โ : plane โ distorted
wave functions move
to the center
3. Results
Upper limits of BR (contact process)
2.1 ร 1018 3.0 ร 1017
this work (1s)
needed # of muonic atoms (๐ = 82)
๐ต๐ (๐+ โ ๐+๐โ๐+) < 1.0 ร 10โ12
(SINDRUM, 1988)
atomic #, ๐
๐ต๐ ๐โ๐โ โ ๐โ๐โ < ๐ต๐๐๐ฅ
๐ฉ๐๐๐
๐1 เดฅ๐๐ฟ๐๐ เดฅ๐๐ฟ๐๐
this work
(1s+2s+โฆ)
Koike et al. (1s)
3. Results
YU, Y. Kuno, J. Sato, T. Sato & M. Yamanaka, Phys. Rev. D 93, 076006 (2016).
Photonic process
bound ๐โ bound ๐โ
scattering ๐โ scattering ๐โ
๐พโ
๐ [fm] ๐ [fm]
scat. ๐โ : plane โ distorted scat. ๐โ : plane โ distorted
๐2๐๐1๐ ๐ ๐๐ธ1/2
๐ =โ1 ๐ ๐0 ๐0๐ ๐2๐๐1๐ ๐ ๐๐ธ1/2
๐ =โ1 ๐ ๐0 ๐0๐
bound ๐โ : non-rela โ rela
๐โ
๐โ๐โ
๐โ
overlap integral downdistortion of scattering ๐โ
3. Results
๐ต๐ (๐+ โ ๐+๐พ) < 5.7 ร 10โ13
(MEG, 2013)
๐
๐ต๐ ๐โ๐โ โ ๐โ๐โ < ๐ต๐๐๐ฅ
๐ฉ๐๐๐
๐๐ฟ เดฅ๐๐ฟ๐๐๐๐๐ ๐น๐๐
Upper limits of BR (photonic process)
this work (1s)
Koike et al. (1s)
1.8 ร 1018 6.6 ร 1018
needed # of muonic atoms (๐ = 82)
3. Results
Phase shift effect of distortion
photonic process
bound ๐โ
bound ๐โ emitted ๐โ
emitted ๐โ
momentum transfers to bound leptons
bound ๐โ emitted ๐โ
bound ๐โ emitted ๐โ
contact process
make overlap integrals smaller
(makes a momentum of scattering ๐โ larger effectively)
no momentum mismatches
Totally (combined with the effect to enhance the value near the origin),
enhanced !! suppressedโฆ
3. Results
๐โ
๐โ
๐โ
๐โ
๐โ
๐โ ๐โ
๐โ
๐พโ
๐โ
๐โ
๐โ
๐โ
After finding CLFV, can the CLFV source be decided ?
โ๐ผ = ๐1 ๐๐ฟ๐๐ ๐๐ฟ๐๐ + โ. ๐.
โ๐ผ = ๐5 ๐๐ ๐พ๐๐๐ ๐๐ฟ๐พ๐๐๐ฟ + โ. ๐.
โ๐ผ = ๐๐ ๐๐ ๐๐๐๐๐ ๐น๐๐ + โ. ๐.
Model 2 : contact (opposite chirality)
Model 3 : photonic
๐๐ โ 0, ๐๐๐๐ ๐ = 0
Model 1 : contact (same chirality)
๐5 โ 0, ๐๐๐๐ ๐ = 0
๐1 โ 0, ๐๐๐๐ ๐ = 0
Here, only 3 very simple model will be considered.
Model-discriminating power
3. Results
Discriminating method 1
๐ dependence of ฮ/ฮ0
The ๐ dependences are different among interactions.
Compared to ๐ โ 1 3, that of contact process is larger,
while that of photonic process is smaller.
~ atomic # dependence of decay rates ~
3. Results
๐
๐ช ๐
๐ช๐ ๐ contact (same chirality)
contact (opposite chirality)
photonic
~ energy and angular distributions ~
Discriminating method 2
๐ = 82๐
๐ช
๐๐๐ช
๐๐๐๐๐๐จ๐ฌ๐ฝ[๐๐๐โ๐]
๐ธ1 : energy of an emitted electron
๐ : angle between two emitted electrons
๐๐จ๐ฌ๐
๐ธ1
๐ธ2
๐
๐๐[๐๐๐]
๐๐จ๐ฌ๐
๐๐[๐๐๐]
[๐๐๐โ๐]
photonic process
๐
๐ช
๐๐๐ช
๐๐๐๐๐๐จ๐ฌ๐ฝ
3. Results
contact processcontact process
4. Summary
contact process ๏ผdecay rate Enhanced (7 times in ๐ = 82)
๐โ๐โ โ ๐โ๐โ process in a muonic atom
Our finding
interesting candidate for CLFV search
โข Distortion of emitted electrons
โข Relativistic treatment of a bound electronare important in calculating decay rates.
energy and angular distributions of emitted electrons
How to identify interaction types, found by this analyses
atomic # dependence of the decay rate
photonic process๏ผdecay rate suppressed (1/4 times in ๐ = 82)
Conclusion
Distortion makes difference between 2 processes.
4. Summary
further analysis for experimental setup
Future work
estimation of background
calculation using various models beyond SM
moderate setting of experiment
โข main noise : Decay In Orbit (DIO)
โข What atom is favored ?
โข Is a better muon beam pulse or DC ?
interference among interactions
4. Summary