1. Probing high scale SUSY
in low energy FCNC
Kei Yamamoto
（Niigata Univ. ⇒ KEK from this April）
Hiroshima Univ.
2015 Mar. 18
Collaborated with Morimitsu Tanimoto (Niigata Univ.)
arXiv: 1503.XXXX

2. Standard model has been established?
・Higgs discovery
[PDG 2014]
[CMS ]
質量と結合の関係
If　SM　Higgs,Source　for　all　particlesʼmass:
coupling/mass　=　VEV　(const.)
m_H
SM content
Mass VS. yukawa

3. Standard model has been established?
Flavor side
SM explains CP violation of K and B mesons successfully
⇒ see briefly
Also, no signals of lepton flavor
We examine the sensitivity of High Scale SUSY
in the CP violations of K and B mesons

4. CP violation CP symmetry : Symmetry between particle and antiparticle
C (charge) transformation
P (parity) transformation
CP symmetry is violated
CP violation have been observed in K and B mesons decays.
These neutral mesons oscillate between particle and antiparticle.
Box diagram of
Neutral meson mixing

5. CP violation CP asymmetry
If CP symmetry is conserved, the decay rate of neutral meson and
should be equal. 2
CP violation
: mixing
: decay
f : CP conjugate state
CP asymmetry
CP violation

6. CP violation in SM CKM matrix フレーバー固有状態と質量固有状態のずれ フレーバーを変える
Mass eigenstate basis
CKM matrix
(wolfenstein parametrization, λ(Cabbibo angle)~0.2)
Deviation between flavor eigenstate and mass eigenstate　⇒　change flavor
One complex phase　⇒　induce CP violation
フレーバー固有状態と質量固有状態のずれ　 フレーバーを変える
1つの複素位相　　CP対称性を破れを引き起こす

7. CP violation in SM CKM matrix The unitarity triangle Unitarity ：
Bs meson system（s-b system）
K meson system（d-s system）
UT6つ
B meson system（d-b system） Im Re
三辺が同オーダーのB中間子系が最も見やすい（Imが大きい）

8. CP violation in SM CKM matrix The unitarity triangle
These angles and lines of UT are determined by various measurements of
B and K meson
⇒ Belle, Babar,,
Unitarity ：
The unitarity triangle
Bs meson system（s-b system）
K meson system（d-s system）
UT6つ
B meson system（d-b system） Im Re
三辺が同オーダーのB中間子系が最も見やすい（Imが大きい）

9. Standard model has been established?
SM explains CP violation of K and B mesons successfully
No significant deviation, but
- a number of tensions
- future measurements can
improve a lot
New Physics
contributions to loop processes
are still possible
Also, no signals of lepton flavor
We examine the sensitivity of High Scale SUSY
in the CP violations of K and B mesons

10. Physics beyond SM We need new physics(NP) beyond SM
Neutrino oscillations
Dark matter（25% of the Universe）
Dark energy
Baryon asymmetry of universe
Hierarchy problem
あるはず　示唆
Gauge symmetryから出てくものではない　（color, charge はsymmetry）
We need new physics(NP) beyond SM
・大統一理論
・暗黒物質の存在
・宇宙のバリオン数非対称性
・ニュートリノ質量
・階層性問題 ・…

11. Example of NP : Supersymmetry (SUSY)
Symmetry between fermion and boson
Spin 0
Spin 1/2
Spin 1/2
Spin 1
Spin 0
Spin 1/2
assuming no CP violation in the Higgs potential,
lighter and heavier CP-even Higgs bosons (denoted as h and H, respectively), CP-odd (pseudo-scalar) Higgs A, and charged Higgs H±
Squark
Slepton
Gluino
Bino
Wino
Higgsino
Neutralino
Chargino }
2HDM 19 8
レプトン
スクォーク S-
Spin /
グルイーノ
- ino
Spin / 2

12. How to search NP Direct search (e.g. ATLAS, CMS) @ High energy
Produce new particle directly with high energy collider
High
Energy
Indirect search (e.g. LHCb, Low energy
Probe the effect NP in low energy physics induced by quantum correction
Low
Energy

13. How to search NP ⇒ Indirect search for NP is important
Direct search (e.g. ATLAS, High energy
Produce new particle directly with high energy collider
High
Energy
There are no evidence for new physics
Indirect search (e.g. LHCb, Low energy
Probe the effect NP in low energy physics induced by quantum correction
Low
Energy
⇒　Indirect search for NP is important

14. How to search NP indirectly
１：See processes forbidden or suppressed in SM
・　Rare decay、CPV
・　μ→ｅγ、τ→μγ、τ→ｅγ、
・　Electric magnetic moment（EDM）　de、dN
・　Proton decay
2：Precise measurement
・　Lepton universality
・　（g−2）μ
・　EW precision test
Flavor physics
王道2：精密測定による標準模型との差

15. How to search NP indirectly
１：See processes forbidden or suppressed in SM
・　Rare decay、CPV
・　μ→ｅγ、τ→μγ、τ→ｅγ、
・　Electric magnetic moment（EDM）　de、dN
・　Proton decay
2：Precise measurement
・　Lepton universality
・　（g−2）μ
・　EW precision test
Flavor physics

16. Progress of B physics measurements
The LHCb collaboration has reported new data of the CP violation of Bs meson.
Time dependent CP asymmetry in βs Bs
SM consistent
NPが強く制限される
Experimental situations
This is the first measurement of the CP violating phase in the Bs->phiphi decay.
----- 会議メモ (2015/03/16 17:07) -----
LHCbのスライドを入れる
Exp. ] SM
[The CKMfitter,2011]
Time dependent CP asymmetry in
Exp. ] SM
[M. Bartsch et al ]

17. Progress of B physics measurements
Rare decay of Bs meson
In SM,
　　- loop suppressed
- CKM suppressed :BR |Vtb*Vtq|2　
- helicity suppressed :BR mμ2/mBs2
BsはPseudoscalar -> no photon penguin
CPSはCPとCSの線形和
⇒ Rare decay：BR(Bs→μμ)SM 〜 10-9
BR(B→μμ)SM 〜 10−10

18. Progress of B physics measurements
Rare decay of Bs meson
[Bobeth et al ]
[LHCb+CMS]
SM consistent
BsはPseudoscalar -> no photon penguin
CPSはCPとCSの線形和

19. Progress of B physics measurements
Rare decay of Bs meson
New data of CP violation of Bs are consistent with SM.
[Bobeth et al ]
⇒　Constrain to NP
[LHCb+CMS]
SM consistent
BsはPseudoscalar -> no photon penguin
CPSはCPとCSの線形和

20. ＮＰへの感度 Sensitivity to NP Loop processSM
loop suppressed
CKM suppressed NP
----- 会議メモ (2014/12/06 14:36) -----
シンプルに　KMのようなフレーバー抑制がないとすれば
It has sensitivity to high scale NP

21. Sensitivity to NP NP Neutral meson mixing SM NP model depend
----- 会議メモ (2014/12/06 14:36) -----
シンプルに　KMのようなフレーバー抑制がないとすれば

22. Effective Theory
By integrating out heavy particle which mediate, B transition is described
in terms of interaction between light particles.
ex) b → cud -
Searching for SUSY particle at LHC b c - d u W b c d - u g
Intermediate state
Transision amplitude
Dim.6 quark operator , which is expressed in terms of initial and final state quarks.
Wilson coefficient
Dim.6 Local operator

23. 49 9
Effective Theory
By integrating out heavy particle which mediate, B transition is described
in terms of interaction between light particles.
ex) b → cud -
Searching for SUSY particle at LHC b c - d u W b c d - u g
Wilson coefficients have both contributions, SM and New physics.
Dim.6 quark operator
Wilson coefficient
Dim.6 Local operator

24. Effective Hamiltonian
Effective Theory
Effective Hamiltonian
Ex)
i : index of mode
Decay amplitude
Hadronic matrix element

25. SUSY search and Flavor physics
No evidence of SUSY, and SUSY scale may be much higher than 1 TeV
Indirect Search for SUSY is needed ⇒　Flavor physics
Our motivation
We examine the sensitivity of High Scale SUSY in the CP violations of K and B mesons
Flavor physics　 ⇔　 SUSY search by LHC
CP asymmetry in B0 meson
Time dependent CP asymmetry
Semileptonic CP asymmetry
εK (CPV of K meson)
Kaon rare decay
Neutron EDM
High scale SUSY
SUSY is not observed
-> Indirect search by B and K decays
It is known epsilonK is poweful in 10 TeV scale.
wolfgang figure (rough estimate)
mass eigen state
epsilonK is powerful at collerate to K to pinunu ~
mq , mg = 10 TeV & 50 TeV
KL→ π0νν εK
K+→ π+νν

26. Contents SUSY setup Squark flavor mixing Squark mass spectrum
Numerical analysis
CP asymmetry in B meson decays
chrome EDM of the strange quark
εK and Kaon rare decay ←new

27. Contents SUSY setup Squark flavor mixing Squark mass spectrum
Numerical analysis
CP asymmetry in B meson decays
chrome EDM of the strange quark
εK and Kaon rare decay ←new

28. 超対称標準模型でのCP対称性の破れ Squark flavor mixing ：complex
The origin of flavor violation
SM：The off diagonal elements in the CKM matrix
MSSM：The off diagonal elements in the squark mass matrices
↑ It contains the new CP-violating phase
　　　　　　　　：complex
　　⇒ new CP violating phase
※クォーク質量行列と同時対角化できるとは限らないので非対角成分が残る
ほぼうまく説明できている

29. Squark flavor mixing The origin of flavor violation
Horyuu The soft squark mass matrices contain the CP-violating phases, which contribute to the flavor changing neutral current (FCNC) with the CP violation.
Squark flavor mixing
The origin of flavor violation
SM：The off diagonal elements in the CKM matrix
MSSM：The off diagonal elements in the squark mass matrices
↑ It contains the new CP-violating phase
We work in the basis of mass eigenstate.
Mixing matrix
it is same at slepton case
30sで
M: super CKM basis
X parameter
new phase apear
※ 1st and 2nd family squarks are degenerate: s12=0
The magnitude of mixing parameters sij ⇨ The magnitude of the SUSY contributions

30. Squark flavor mixing Mass difference SM SUSY
Quark squark Gluino interaction

31. Squark mass spectrum Λ Q0 mH
We should consider SUSY particle spectrum, which is consistent with Higgs Discovery.
[M.Tanimoto and KY (2014)] Λ
SUSY breaking scale Λ = 1017GeV, 1016GeV
Taking universal soft parameters at SUSY breaking scale Λ
Running soft masses in SUSY
H1, H2 Q0
Lighter CP even higgs besom SM Higgs
Comment : not Minimal SUGRA
We forgive 10% off diagonal element
Gauge mediationだと分かれない
SM-SUSY matching scale Q0 =10, 50 TeV
Running Higgs coupling in SM λ, m2
HSM mH
SM scale mH, 126 GeV

32. RGE running result @Q0=10TeV
dL,R, sL,R bR bL
gluino H1 tR H2

33. Parameter squark and gaunino mass mixing parameters11 5
mg 〜 mq ~
m3 = mq ~
Parameter
squark and gaunino mass
[M.Tanimoto and KY (2014)] ※
6:2:1
Chargino :wino & higgsino
Neutralino :wino & bino
stop mass(hutatu),
sbottom mass,
gaugino mass
MFV では出てこないことは知られている ので
non-minimal FV でやります
----- 会議メモ (2015/03/08 14:58) -----
mass はこうしました
mixing
----- 会議メモ (2015/03/08 16:27) -----
M_1 M_2 M_3 bino wino
----- 会議メモ (2015/03/16 17:02) -----
本来ならckmによってdelta決まるはずだが、今　10％くらいフリーにしている
mixing parameters
：free parameter
For simplicity,
random
[Delgado, Garcia, Quiros, PRD90(2014)015016]
tanβ and L-R mixing angle :
mq [TeV]
tanβ ~ Xt θd θu
case1 : 0.5
case2 : λ (Cabibbo angle)

34. Parameter squark and gaunino mass tanβ and L-R mixing angle : mg 〜 mq11 5
mg 〜 mq ~
m3 = mq ~
Parameter
squark and gaunino mass
[M.Tanimoto and KY (2014)]
6:2:1
Chargino :wino & higgsino
Neutralino :wino & bino
stop mass(hutatu),
sbottom mass,
gaugino mass
MFV では出てこないことは知られている ので
non-minimal FV でやります
----- 会議メモ (2015/03/08 14:58) -----
mass はこうしました
mixing
----- 会議メモ (2015/03/08 16:27) -----
M_1 M_2 M_3 bino wino
----- 会議メモ (2015/03/16 17:02) -----
本来ならckmによってdelta決まるはずだが、今　10％くらいフリーにしている ※
[Delgado, Garcia, Quiros, PRD90(2014)015016]
tanβ and L-R mixing angle :
mq [TeV]
tanβ ~ Xt θd θu
case1 : 0.5
case2 : λ (Cabibbo angle)

35. Parameter

36. Parameter LR mixing angle mixing parameters 10TeV 50TeV θd θu θe
0.0061
0.0023
0.0137
mixing parameters
：free parameter
For simplicity,
random

37. Contents SUSY setup Squark flavor mixing Squark mass spectrum
Numerical analysis
CP asymmetry in B meson decays
chrome EDM of the strange quark
εK and Kaon rare decay

38. Meson mixing & Time dependent CP asymmetry
ΔF=2 process
The gluino-sbottom-quark interaction
Meson mixing & Time dependent CP asymmetry
K-K, B-B , Bs-Bs mixing: ―
Standard model +
observed value is very sensitive, so it becomes a severe constraint.
Time dependent CP asymmetry :
SM + SUSY
The cEDM of the strange quark $d_{s}^C$ is given
in terms of the gluino-sbottom-quark interactions as seen in Appendix C.
The upper bound of the cEDM of the strange quark is given
by the experimental upper bound of the neutron EDM as

39. ΔMB /ΔMB ΔMBs /ΔMBs Sin(2Φs)SUSY/Sin(2Φs)SUSY+SM
We scan δij randomly in the region of 0　～ 0.5
We scan sij randomly in the region of 0 ～ 0.5 with taking |sijL|= |sijR|
ΔMB /ΔMB
SUSY
SUSY+SM
ΔMBs /ΔMBs
SUSY
SUSY+SM 6%
0.4%
S13
S23
Sin(2Φ1)SUSY/Sin(2Φ1)SUSY+SM
Sin(2Φs)SUSY/Sin(2Φs)SUSY+SM
φ1=β 8% 6%
small
----- 会議メモ (2015/03/16 17:02) -----
maximam にとってもBには効かない
S13
S23

40. εK /εK
SUSY
SUSY+SM
40%
sensitive
S13S23
We scan δij randomly in the region of 0　～ 0.5
SM component
Taking account
of Gluino squark
interaction ⇒

41. Time dependent CP asymmetry
SM prediction
Both CP violations come from CP phase
in the mixing.
SUSY contribution
[S. Khalil ,E. Kou(2003), A.L. Kagan(2002), M.Endo,S.Mishima,M.Yamaguchi (2005)]
depends on S23
Difference of sign comes from parity of final state
Experimental results
[HFAG,2012]

42. C8g/C8g Time dependent CP asymmetry SηK vs. SΦK SΦK/Sη’K 0.2% S23 S23SM
Our predictions
SηK vs. SΦK
Time dependent CP asymmetry
C8g/C8g
SUSY SM
SΦK/Sη’K
0.2%
S23
S23
insensitive…
Q0=10 TeV
tanβ=10

43. Semi-leptonic CP asymmetry
CP asymmetry in the semileptonic decay in
mixing
SM + SUSY
Experimental results
[LHCb ]
SM predictions
Experimental results
[PDG 2012]
[A.Lenz and U.Nierste, arXiv: [hep -ph]]
fomula
depend on , depend on

44. asl asl vs. asl Semi-leptonic CP asymmetryd
Semi-leptonic CP asymmetry
asl vs. asl s d
Our predictions SM
asld < 1×10-3, 　asls < 5 × 10-5
insensitive…

45. Chromo-EDM of strange quark
Q0=50 TeV tanβ=3
Chromo-EDM of strange quark
[K.Fuyuto, J.Hisano and N.Nagata, 2013]
|dsC|< 4 × cm
Phase 構造の違いで、εが小さくてもedmは大九九なり得る
sensitive
Upper bound
S23 45

46. Chromo-EDM of strange quark vs. εK
Q0=50 TeV tanβ=3
Chromo-EDM of strange quark vs. εK
Phase 構造の違いで、εが小さくてもedmは大九九なり得る 46

47. Chromo-EDM of strange quark vs. εK
Q0=10TeV ➡　Q0=50TeV
@ Q0=50TeV
二桁実験バウンドより小さい
Edmはleft right mixing is supressed large mass def.
Order supressed
Esilonl is not supressed because it is insensitive left-right mixing
----- 会議メモ (2015/03/16 17:07) -----
edmよりepsilonのほうがよく効くよ 47

48. Contents SUSY setup Squark flavor mixing Squark mass spectrum
Numerical analysis
CP asymmetry in B meson decays
chrome EDM of the strange quark
εK and Kaon rare decay

49. ⇒ Sensitive to New Physics
KL → π0νν and K+ → π+νν
Rare decay : BRSM 〜10-11
Clean theoretically : theoretical uncertainty 〜2％
[Buras et all, 2006]
理論的不定性が小さい
Forn factorがよくわかっている
----- 会議メモ (2015/03/07 18:39) -----
rare decay of k meson decay is powerful NP probe.
One example is K to pinunu decay
KL topi0nunu is CP violatog decay
----- 会議メモ (2015/03/08 14:57) -----
prove のみ
----- 会議メモ (2015/03/16 17:07) -----
kotoのスライド
⇒ Sensitive to New Physics

50. K → πνν in SM KL→ π0νν K+→ π+νν Direct CPV K to pinunu Relation
理論的不定性が小さい
Forn factorがよくわかっている
----- 会議メモ (2015/03/07 18:43) -----
pure imaginaly part
neglecting CPV KK mixing
K^+ CP conserve
K+→ π+νν
K to pinunu Relation
Direct CPV
Hadronic matrix element, isospin relation
K to pinunu deference

51. K → πνν in SM η ρ K+→ π+νν KL→ π0νν KL→ π0νν K+→ π+νν Direct CPV
Future (20XX)
CP -
CP +
KL→ π0νν
Direct CPV
理論的不定性が小さい
Forn factorがよくわかっている
----- 会議メモ (2015/03/07 18:43) -----
height
K+→ π+νν
K to pinunu Relation
Hadronic matrix element, isospin relation
K to pinunu deference

52. ⇒ Sensitive to New Physics
KL → π0νν and K+ → π+νν
Rare decay : BRSM 〜10-11
Clean theoretically : theoretical uncertainty 〜2％
[Buras et all, 2006]
理論的不定性が小さい
Forn factorがよくわかっている
----- 会議メモ (2015/03/07 18:39) -----
rare decay of k meson decay is powerful NP probe.
One example is K to pinunu decay
KL topi0nunu is CP violatog decay
----- 会議メモ (2015/03/08 14:57) -----
prove のみ
----- 会議メモ (2015/03/16 17:07) -----
kotoのスライド
⇒ Sensitive to New Physics
Experiment
←KOTO

53. [yamanaka, Flavor in new physics @ J-PARC (2015) ]

54. [yamanaka, Flavor in new physics @ J-PARC (2015) ]

55. K → πνν and εK in MSSM MSSM MSSM
It is known there are no large enhancement in K → πνν decay in the Minimal flavor violation(MFV) scheme
SUGRA model with MFV
[T.Goto, Y,Okada and Y.Shimizu(1998)]
@ Squark mass < 600 GeV, Gaugino mass < 600 GeV
with non-MFV
[A.J.Buras,et al (2005)]
@ Squark mass = 600 GeV, Gluino mass = 1 TeV, δ13, δ23 ~ 0.3
Goto: SUGRA and Minimal flavor violation(universal soft parameter) 小さい
数％、susy region 書く
MFV: the flavor and CP violation are governed by the CKM matrix, the so-called MFV
MSSM
MSSM
It is known there are no large enhancement in K → πνν decay in the Minimal flavor violation(MFV) scheme

56. K → πνν and εK in MSSM In the MSSM SM exchange exchange exchange
Dominant term comes from 長い
chargino + gluino 1

57. Numerical analysis results @ Q0=10 TeV
K→πνν : Chargino dominant
εK : Gluino dominant
epsilon_K constraint
chargino contribution in the unit of the SM

58. Numerical analysis results @ Q0=10 TeV
@sd=su=0.1
with 90%C.L. |εK|exp constraint
Grossman-Nir bound
〜 8 × SM
〜 3 × SM SM
1σ exp. bound
@sd=su=0.1
@sd=0, su=0.1
----- 会議メモ (2015/03/07 19:02) -----
epsilon_K constraint
at most 30%
at most 3%

59. Numerical analysis results @ Q0=10 TeV
sd & su dependense
〜 100 × SM
〜 20 × SM
1σ exp. bound
----- 会議メモ (2015/03/07 19:09) -----
＊K+に実験値のライン入れる

60. Numerical analysis results @ Q0=50 TeV
@sd=su=0.3
Grossman-Nir bound
〜 2 × SM
〜 2 × SM SM
1σ exp. bound
@sd=su=0.3
@sd=0, su=0.3
at most 10%
at most 1.5%

61. Summary
We have studied the contribution of the high-scale SUSY to B and K meson systems
We consider the high-scale SUSY at TeV scale in the framework of the mass eigenstate basis of the SUSY particles assuming the non-minimal squark (slepton) flavor mixing
As results,
is most sensitive even if the SUSY scale is higher than 50 TeV
Chrome EDM has a sensitivity at SUSY scale 10-50TeV
CP asymmetry and mass difference of B meson are insensitive to high scale SUSY
To prove the high scale SUSY
We also assume that AX , MgX , and mu are all real parameters to avoid a large electric dipole mo- ment of the neutron
If large NP contribution to both and come out, it may suggest the contribution of chargino and gluino are comparable.
Even if the NP contribution to is small, can be enhanced.
We expect the measurement of these processes will be improved by the J-PARC KOTO experiment (and CERN NA62 experiment) in the near future.

62. Summary Intensity frontier is crucial to probe BSM !
[Iijima, Flavor of new J-PARC (2015) ]