Lepton Flavor Violationin high-scale SUSYNP sensitivity by combined analysis Iwith right-handed neutrinos
Minoru NAGAI (Univ. of Tokyo → KEK)
collaborated with T. Moroi and T. T. Yanagida• Phys.Lett. B723 (2013) 107-112• arXiv:1305.7357 (to be published in PLB)

8 Dec, 201313年12月8日日曜日「ニュートリノフロンティア」研究会 ＠クロス・ウェーブ府中今日の話のまとめ（重い）SUSY model＋
重い右巻きニュートリノ
‖大きな Lepton Flavor Violation！？

13年12月8日日曜日

eutrinos oscillate ń Lepton family numbers are not conserved!

LFV in the SM with massive neutrinos•

an we observeLFVoscillations
in charged leptons decays?
Massive neutrinos
Neutrino
Dirac? Majorana (see-saw)?

mthe SM Lepton+ massive
neutrinos:
Flavoris not conserved
Br(µ2e )im i
Uµi Uei 2
MW< O(10 50 )< O(1 eV)

W2µǎi

Ǆ

e

Any LFV observations in the near future experiments
Cheng Li ’77, ’80; Petcov ‘77
uppression due to small neutrino masses
implies the existence of physics beyond the SM
massive neutrino + New Physics = Large LFV ?

In presence of NP at the TeV we can expect large effects!
13年12月8日日曜日

最小超対称標準模型(Minimal Supersymmetric Standard Model)
超対称性 (SUSY) ＝ ボゾンとフェルミオンの対称性
SquarkSleptonGluinoBino
Wino
Higgsino

電弱対称性の破れ

Neutralino
Chargino

Higgs２重項（２HDM）
Hdtan
13年12月8日日曜日

2+ Hu

2h, H, A, H+v2=
2= Hu / Hd

どうして超対称性模型？
ゲージ結合定数• 弦理論では超対称性は必須• 大統一理論への示唆• Hierarchy Problem (HP)

160

1SM

50
40

2

13020(mEW2とmSUSY2の微調整)

31MSSM10• 暗黒物質(DM)の候補が存在

510(neutralino, gravitino, ...)

15エネルギースケール• 軽いヒッグスを予言(Higgs の４点結合がゲージ結合定数で与えられる）

m2h = m2Z cos2 2 + 輻射補正項
tree• ミューオンの異常磁気能率を説明できる数少ない模型
yµ13年12月8日日曜日

mµtan
2mSUSYaSUSYµmµtanvloopµaµµLFV in SUSY models[Hisano et al ʼ95 ]˜kOrigin of ﬂavor-violationOﬀ-diagonal components ofslepton mass matrices(m2l̃ )ij

m2L̃ + m†e me
ae vd + me µ tanemi ¯l i FµL=2where

AL , A RBr(liBr(liµ24MIm2SUSYa†e vd + m†e µ tan
m2Ẽ + me m†em̃2l̃ ijli˜li(AL PL + AR PR )lj
MIm2SUSYlj )48 e=lj i ¯j )G2F

2 2tan|AL |2 + |AR |2•mass scale of SUSY particles•Size of ﬂavor-violation
13年12月8日日曜日(m2l̃ )ijli2MI

m4SUSY

AL , A R

tan2˜ljljlj

LFV in SUSY models
SUSY scalemuon g-2 -- O(100)GeV sleptons & EW gauginos

TeV-Scale

Hierarchy Problem -- ﬁne tuning btw m2W & m2SU SY
Dark Matter -- thermal or non-thermal production?
GUT -- only light gauginos? log-dependence

Size of ﬂavor violationOﬀ-diagonal components of slepton mass matrices

1. Arbitrary values (Anarchy)

too large LFV rates(SUSY ﬂavor problem)

2. No ﬂavour-mixing at tree-level(Universal)

Importance of radiativecorrections

13年12月8日日曜日

LFV in SUSY models with diagonal soft masses•• Non-zero oﬀ-diagonal elements
No LFV at tree-levelm2l̃

m20

1

11

Radiative Corrections

Ex) See-saw model

HL

H
Ry1
y =vuy13年12月8日日曜日

Ly1
Leff =(lL Hu )(lL Hu )MM̂N R

1 for MNẽLiy2 v2m =MSameorigin(y )kiRk(y )kj ẽ

LjH̃u(m̃2L )ijMX(y )ik (y )kj log
M k††m̂ UMNS[Casas, Ibarra ʼ01 ]1015 GeV

cf. SO(10) GUT: 16=6+3+3+2+1+1
qL dR uR lL eR R

LFV in SUSY models with RNs
200 GeV, MW̃ml̃

180 GeV[ Antusch, Arganda, Herrero, Teixeira ʼ06 ]-8

10-9BR (µ → e γ)

1010-10

10-111y =vu

SPS 1a1011mN1 = 10 GeV, mN2 = 10 GeV-5mν1 = 10 eV0 ≤ |θ1| ≤ π/4M̂R R†m̂ UMNSLarge Brfor larger MN

0 ≤ |θ2| ≤ π/4
θ3 = 010-121410-1310-14mN3 = 1013mN3 = 101210-15

θ13 = 1°
θ13 = 3°
θ13 = 5°
θ13 = 10°

GeV12mN3= 10GeV
mN3= 10GeV-141010-13-121010-1110-10GeV

10-910-810-7BR (τ → µ γ)

relation
between B(µ → e γ) and B(τ → µ γ) as a function of mN3 , for SPS 1a. The areas
13年12月8日日曜日

LHC7+8
m1/2 [GeV]1000

MSUGRA/CMSSM: tan(`) = 30, A = -2m0, µ > 0

Status: SUSY 2013

0¾oLSP

90095% CL limits.m SUSY
theory not included.
V)h (122 Ge

800

ATLAS Preliminary

Expected

0-lepton, 2-6 jets

0 L dt = 20.1 - 20.7 fb , s = 8 TeV

Observed
Expected

ATLAS-CONF-2013-047-1

Observed
Expected
Observed
Expected

700

600

GeV)

eV)

h (126h (124 G

Observed
Expected
Observed
Expected
Observed

0-lepton, 7-10 jets
arXiv: 1308.1841

Mg̃ > 1.4 TeV

0-1 lepton, 3 b-jets
ATLAS-CONF-2013-061

1-lepton + jets + METATLAS-CONF-2013-062

1-2 taus + jets + METATLAS-CONF-2013-026

2-SS-leptons, 0 - * 3 b-jets
ATLAS-CONF-2013-007~g (1400 GeV)

masses of coloredparticles are highly
constrained~g (1000 GeV)~q (2000 GeV)

400300)

0

1000

2000

3000

4000

5000

6000

m0 [GeV]

universal scalar mass @ GUT scale

13年12月8日日曜日

In a SUSY modelmq̃ > 1.8 TeV500~q (1600 GeV

universal gaugino mass @ GUT scale• Poor News : Non-observation of NP particles

Note, LFV is probably
induced by non-coloredparticles, which might
escape from LHC searchEvents /Sig+Bkg Fit (mH=126.5 GeV)

3000

Bkg (4th order polynomial)

2500

LHC7+82000
1500
1000

s=7 TeV, 0 Ldt=4.8fb-1
s=8 TeV, 0 Ldt=5.9fb-1• Great News : Discovery of Higgs boson
Y weights / 2 GeV Events - Bkg

500

200
1000-100-200(a)

HAa aSM(b)
Data S/B Weighted

100Sig+Bkg Fit (mH=126.5 GeV)
Bkg (4th order polynomial)

80

ATLAS 2011 - 2012

mH = 126.0 GeV

W,Z H A bb

s = 7 TeV: 0 Ldt = 4.7 fb-1

H A oo60

s = 7 TeV: 0 Ldt = 4.6-4.7 fb-1(*)

H A WW A li li
s = 7 TeV: 0 Ldt = 4.7 fb-1

40-1

s = 8 TeV: 0 Ldt = 5.8 fb

H A aa20Y weights - Bkg(c)840-4(d)-8100110mh
13年12月8日日曜日-1

s = 7 TeV: 0 Ldt = 4.8 fb-1

s = 8 TeV: 0 Ldt = 5.9 fb(*)

H A ZZ A 4l-1

s = 7 TeV: 0 Ldt = 4.8 fb-1
s = 8 TeV: 0 Ldt = 5.8 fb

Combined
120

130

140

126GeV

150160ma a [GeV]s = 7 TeV: 0 Ldt = 4.6 - 4.8 fb-1

s = 8 TeV: 0 Ldt = 5.8 - 5.9 fb-1µ = 1.4 ± 0.3-101
Signal strength (µ)•Multi-channel•Consistent with SMwe expect that mh = 125 GeV intersects this quartic in
up to four places, leading to up to four preferred values
5for Xt /MS . Finally, we see that for fixed Xt /MS , theHiggs mass only increases logarithmically with MS itself.
0So weexpect
a mildMS fromh = 125
datinga 125
GeVlower
Higgsboundin theonMSSM
withmsmallA-terms-4-2024GeV.
requires scalar masses in the range of 5 to 10 TeV.
Now
demonstrate
generalwith
de- SuXt êMS
A let’svariationon this these“heavystop” points
scenariois Split
tailedcalculations[40,using
FeynHiggs.
in fig.
arepersymmetry41],
in which Shown
gauginosand1 higgsinos
contoursof constant
Higgs Mmassin the tan , X /MS
FIG. 1. Contour plot of mh in the tan vs. Xt /MS plane.
have masses
well belowofS and influence the trunning
2 set at mQ2 = mU = 2 TeV, 2and the result isThe stops
wereplane,mQcase,= m= 2 TeV(wheremandm4Uby theU running
QmodifiedMAt3mAt. Inforthis
thebelow
MisS
t
2
22
S
only weakly dependent
on the stop
mass up to ⇠ 5 TeV. The
are light
the softmasses
left-handed
1
mh of themcospreferred
2 +scalarlog+
superpartners,
andthemassscale
Zthird-generation
2
22 The band
2The2
solid curveis mh = 125
GeV with mt =12M
173.2 GeV.
4v
mM
quark
andright-handed
up-typequark
scalarfields).
t
S to mh =123-127SGeV. Finally,for a 125 GeV Higgs
be even larger [42–44].
around the curve corresponds
2 can2shaded(126band correspondstom=123
127
GeV,and(91h GeV)GeV)
the dashed lines correspond to varying mt from 172-174.
the dashed lines indicate the same range of Higgs masses[ Draper, Meade, Reece, Shih ʼ11 ]but with mt = 172 174 GeV. (The central value in all
135
3.0
our plots will
always be mh = 125 GeV at mt = 173.2
GeV.) From all this, we conclude that to be able to get
130 we must havemh ⇡ 125 GeV,
2.5

Implication of Higgs mass on SUSY models“Higgs mass = 126 GeV”

& 3.5

(2)

So this is an 120
absolute lower bound on tan just from theHiggs mass measurement. We also find that the Higgs
mass basically
115ceases to depend on tan for tan beyond⇠ 20. So for the rest of the paper we will take tan = 30
for simplicity.
110
Fixing tan , the Higgs mass is then a function of Xt
and MS . Shown in fig. 2 are contours of constant mh vsMS and Xt . 105
We see that for large MS , we want
1Xt
⇡ 3,MS510 20
1.7, M
1.5,@TeVDor 3.5
S2m50

100(3)

O(10 TeV)

2.0
MS @TeVDtanmh @GeVD

125

constraints on SUSY parameters

1.5
1.0
0.5
0.0-6-4-20
2Xt @TeVD

46large A term

6. Higgs
mass
as a functionof Mand
WeFIG.
also seethat thesmallest
the A-terms
the X
SUSYS , witht = 0. Thegreen
is the beoutput
FIG. 2. Contours of constant mh in the MS vs. Xt plane,scale
can bandabsolutely
are t̃of FeynHiggs together with its associated uncertainty. The blue line represents 1-loop renorwith tan = 30 and mQ = mU . The solid/dashed lines andgray bands are as in fig. 1.
malization
inMtheStandard Model (4)matched13年12月8日日曜日|Xt | &group1000 evolution
GeV,S & 500 GeV.

LFV in High-scale SUSY models
126 GeV Higgs boson + Null result of SUSY search
SUSY scaleO(10-100)TeV sfermions?OK for 2) OKmuon g-2, HP, DM, GUT

1) gaugino mass ~ sfermion mass

(gravity-med.)2) gaugino mass << sfermion mass(anomaly-med.)Size of ﬂavor violationOﬀ-diagonal components of slepton mass matrices
1. Arbitrary values (Anarchy)

The simplest and themost natural case.

2. No ﬂavour-mixing at tree-level (Universal)
The strongest constraint
comes from Kaon-mixing
13年12月8日日曜日

Kaon mixing parameter|ij | = 0.1[Moroi, MN (2013)]

maximal phasesRg̃

Excluded (2-σ)

d¯LKd¯R

12dR

12dLg̃

sL
12Im[ 12dR dL ]m2SUSYSuppressed If
the phases arecancelledsymmetry?
13年12月8日日曜日

SO(10) relation and C-invariancem2d˜ ,ij = md2˜ ,ijLRC-inv. : dLcdRd¯L sR

12dRSUSYis suppressedKsRd¯R

12dRg̃
12dLd¯L

12dLsLg̃

g̃

12dLIm[12dL ] = 012dRg̃

sL d¯RsL d¯L
12dRg̃g̃

d¯RIm[12dL

12dL ] =Im[sR
12dR

12dR ]Breaking of C-inv. : EW & Yukawa interactions
13年12月8日日曜日

Breaking of SO(10) relation
Dominant SUSY contribution comes from22md˜ ,33 = md˜ ,33LR32dRsRb̃R
12dLd¯Ld¯R

13dRg̃

(RG eﬀect through top Yukawa)

sRg̃

g̃

sLd¯L

13dLSUSYK

13年12月8日日曜日

Im[12 m2dL ]b̃Lm2b̃

m2SUSYRb̃L

32dLg̃

sLtan

1332dR dR
m2SUSYd¯R

12dR

1030
50dL ,33dR ,33

0.7
0.7
0.5

1
0.8
0.5

2 mixing
2 ∗ parameterKaon
ase with Md˜ ! Md˜ (except for 33 elements)LR|ij | = 0.1

maximal phase

Excluded (2-σ)

With SO(10) relation,
SUSY
K

is signiﬁcantly
reduced

YesAnarchy

NoUniversalEnough?

13年12月8日日曜日

LFV in High-scale SUSY models (Anarchy)• Anarchy ... large oﬀ-diagonal elements are given at tree-level

MEG (2013 result)

MEG (upgrade)

13年12月8日日曜日

• µ → 3e: Br(µ → 3e) " 7 × 10× Br(µ → e−3LFVinHigh-scale
SUSYmodels(Anarchy)• µ-e conversion: R ∼ (a few) × 10 × Bµe

In SUSY models, there is strong correlations btw Br(μ→e γ), Br(μ→eee ) and RμeComparison (just for fun)

Future experimental limits can be converted to that of Br(µe )MEG (obsolete)
MEG (2013 result)
Mu3e (Phase I)
MEG (upgrade)

~±l o

Mu2e
Mu3e (Phase II)COMET

2PRISMBr

m4SUSY±μ

13年12月8日日曜日

χ0 oElectron EDM in High-scale SUSY models
M1µ taneL ẽLẽR eRCurrent bound31

13eL ẽL ˜L ˜R ẽR eR
2deNew Limit: de < 8.7
13年12月8日日曜日

10 29

m2SUSY

ACME colaboration (2013)

LFV in high scale SUSY models (universal)[Moroi, MN, Ynagida (2013)]• Universal ... oﬀ-diagonal elements are generated by radiative corrections
In the see-saw model, with keeping the explanation ofHiggs mass, is it possible to detect the LFV signals?
mSUGRAmh126 GeVMRMGUT (ymeasurable
LFV rates

13年12月8日日曜日

1)

LFV in high scale SUSY models (universal)• Large neutrino Yukawa coupling is also useful to enlarge theparameter spaces with successful EWSB
Anomaly-med

m0 , it becomes
For Midiﬃcult to achieve
successful EWSB
cf. focus point

y2mHu

MN = 31015 GeV

MN = 1011 GeV

13年12月8日日曜日
igure2: Br(µ → eγ) as functions of m and tan β for M = 3 × 1015 GeV and m = mLFV in high scale SUSY models (universal)• Large neutrino Yukawa coupling is also useful to enlarge theparameter spaces with successful EWSBmSUGRA

mh126 GeVFor smaller gaugino
masses, large neutrino
Yukawa is required

13年12月8日日曜日

Summary✓近年 LHC実験 結果(、O(10) TeV✓振動SUSY模型
破質量、SUSY粒子 未発見) 踏重 SUSY模型 興味深破湯川結合 通証拠、重観測可能 荷電Kaon mixing

制限 緩生✓SO(10) relation✓EDM 実験 面白✓大13年12月8日日曜日

湯川結合 EWSB 助役立Back up

13年12月8日日曜日

Importance of double-mass insertionin high-scale SUSY models (Anarchy)

12eL

2vsY

13eL

32eR m/mµsingle mass insertion
2Br

m4SUSYdouble mass insertion
4Brgure2: Br(µ → eγ) as a function of the slepton mixing parameter ∆l̃ (which is the absolute
13年12月8日日曜日

m4SUSY