Flavor violating Z from

Transcription

1 Flavor violating Z from SO(10) SUSY GUT model Yu Muramatsu( 村松祐 ) CCNU Junji Hisano(KMI, Nagoya U. & IPMU), Yuji Omura (KMI) & Yoshihiro Shigekami (Nagoya U.) Phys.Lett.B744 (2015) 395, and JHEP 1611 (2016) 018

2 Content 1. Introduction i. Short review for GUT ii. Z from GUT iii. Flavor violating Z 2. Flavor violating Z from SO(10) SUSY GUT model i. Problem of SO 10 GUT ii. Flavor violating Z 3. Phenomenology i. Flavor violating coupling ii. Phenomenology

3 1. Introduction 00/41 Content 1. Introduction i. Short review for GUT ii. Z from GUT iii. Flavor violating Z concept only forget mathematical difficulty

4 i. Short review for GUT GUT is marvelous!!! 01/41 Unification of forces(interactions) :SM :MSSM sparticle mass Λ SUSY GUT Λ SUSY GUT GeV unification of forces is one of the goals (dreams) of physics electric force magnetic force make simple, Occam s razor Maxwell s equations electromagnetic force gravity Einstein tried but not succeeded

5 i. Short review for GUT GUT is marvelous!!! 02/41 charge explanation SU(5) G SM SU(5) diagonal generator G SM diagonal generator esplecially U 1 Y charge = U 1 Y generator e.g. λ traceless SU(3) part SU(2) part 2: 3 = 1 3 : 1 2 Q Y (d R c ) Q Y (l L ) GUT explain SM charge anomaly free explanation SM charge is anomaly free =GUT explain why SM is anomaly free

6 i. Short review for GUT GUT is marvelous!!! 03/41 The SM is gauge theory Gauge groups describe not only interactions but also particles. Unification of particles Realize simultaneously!! Unification of SM fermions in SU(5) GUT model Unification of SM fermions in minimal SO(10) GUT model Unification of interactions and particles is great advantage of GUTs, but unification of particles makes some troubles

7 i. Short review for GUT Unification of particles 04/41 What will happen when particles are unified into samel representation? One of the SU(5) Yukawa terms SU(5) Yukawa GUT scale Unification of SM fermions in SU(5) GUT model Unified particles have same character (here mass) at GUT scale. m d = m e m s = m μ m b = m τ at GUT scale

8 Yukawa unification in SU(5) i. Short review for GUT z scale Does RG eq. effect from GUT scale to M z scale modify this scale RG eq. effect does not modify this problem.

9 non-renormalizable SU(5) GUT Yukawa unification in SU(5) i. Short review for GUT 06/41 GUT group breaking contribution or smaller non-renormalizable terms contribute to mass of the first- and second- generation particles. these non-renormalizable contributions solve this problem I will use this mechanism later

10 ii. Z from GUT Origin of additional Z 07/41 G SM U(1) origin of additional Z : Z gauge group rank G SM = SU 3 C SU 2 L U 1 Y 4(=2+1+1)+1=5 U(1) SU(5) minimal unification group 4 SO(10) 5 rank of SM group GUT is one of the famous candidates for additional Z. But light Z is allowed? Does proton decay restrict it?

11 ii. Z from GUT Light Z 08/41 origin of Z at GUT scale GeV constrained by proton decay light Z mass scale constrained by Z physics light Z is possible In this work we do not specify how to realize light Z. some cancelation and/or some additional symmetry is necessary

12 iii. Flavor violating Z Origin of flavor violating Z 09/41 Fermion gauge interaction from U(1) symmetry in interaction basis q i : U(1) charge for ψ i we have to transfer from interaction basis to mass basis to make Yukawa matrix diagonal interaction basis mass basis unitary transformation

13 iii. Flavor violating Z Origin of flavor violating Z 10/41 In SM Z interaction (q 1 = q 2 = q 3 = q) after unitary transformation flavor universal charge = identity matrix In some U(1) symmetry which has flavor nonuniversal charge (not q 1 = q 2 = q 3 ) non-diagonal matrix = flavor violating Z

14 iii. Flavor violating Z Z in GUT 11/41 but In some U(1) symmetry flavor non-universal charge is essential to realize anomaly cancelation. U(1) gauge symmetry comes from GUT symmetry no anomaly problem generation universal charge (q 1 = q 2 = q 3 ) summarizing the above GUT can be a origin of Z but this Z is flavor conserving

15 2. Flavor violating Z from Content SO 10 SUSY GUT model 11/41 2. Flavor violating Z from SO(10) SUSY GUT model i. Problem of SO 10 GUT ii. Flavor violating Z

16 i. Problem of SO(10) GUT Quark and lepton unification 12/41 In SO(10) GUT model advantage unify all quark and lepton but cause some trouble How to realize observed quark and lepton masses and mixings?

17 i. Problem of SO(10) GUT Mechanism to solve it 13/41 add new Higgs (e.g. 120 H ) In SO(10) group = 1 + new contribution, break GUT relation use SUSY threshold correction If tan β is large SUSY threshold corrections solve this problem. > 40 tan β

18 i. Problem of SO(10) GUT In this model 14/41 extend matter sector introduce three 10s of SO(10) MSSM matters heavy particles This mixing is useful to realize observed quark and lepton masses and mixings.

19 i. Problem of SO(10) GUT flavor violating Z 15/41 origin of Z e.g. MSSM matters heavy particles flavor non-universal charge origin of flavor violating Z

20 i. Problem of SO(10) GUT short summary 16/41 SO 10 unification group origin of Z mechanism to solve SO(10) GUT model make Z flavor violating one This model has following interesting features compatible with some high-scale (split) SUSY model distinctive flavor violation only for ഥ5 matters This SO(10) model is good origin of FV Z.

21 unitary condition ii. Flavor violating Z Flavor violating Z interaction 17/41 Flavor violating Z interaction in fermion mass basis Z gauge boson is interaction basis of course other fermions have flavor conserving interaction 6 6 unitary matrix

22 ii. Flavor violating Z Flavor violating Z interaction 18/41 Flavor violating Z interaction in fermion mass basis What we want to calculate this interaction by hand Z gauge boson mass : M Z gauge coupling : g Z Z Z mixing angle : θ mixing parameter : U 16 but O 100 TeV is interesting from gauge coupling unification from fermion masses and mixings

23 2. Phenomenology 18/41 Content 3. Phenomenology i. Flavor violating coupling ii. Phenomenology

24 i. Flavor violating coupling Flavor violating coupling calculation 19/41 down-quark charged-lepton Yukawa up-quark Yukawa make Yukawa matrix diagonal We use this relation in low energy scale. This relation is satisfied at GUT scale. mixing angle is ratio of Yukawa coupling and

25 i. Flavor violating coupling Flavor violating coupling calculation 20/41 To calculate flavor violating coupling we need up-type quark mass down-type quark mass charged-lepton mass CKM matrix : : : : u m i d m i l m i U CKM We can calculate these parameters at M Z scale if we assume particle contents. In this model we assumem Z = O(100) TeV.

26 i. Flavor violating coupling Particle content 21/41 at GUT scale GeV light Z mass scale = SUSY scale = O(100) TeV In this model we assume high-scale SUSY (split SUSY) O(100) TeV SUSY particles, but gaugino mass is O(1) TeV (loop induced) SUSY flavor contributions are negligible GUT scale (O(10 16 ) GeV) SUSY scale (O(100) TeV) gaugino scale (O(1) TeV) : GUT particles : Z, SUSY particles, vector particles (from 10 rep.) : gaugino

27 i. Flavor violating coupling Gauge coupling unification 22/41 high-scale SUSY O(1) TeV gauginos the residual SUSY particles mass is O 100 TeV advantage obtain 125 GeV Higgs mass satisfy SUSY flavor constraints more precise gauge coupling unification U(1) Y High-scale SUSY SU(2) L SU(3) C Low-scale SUSY from Hisano-san s slide

28 i. Flavor violating coupling Higgs mass in high-scale SUSY model 23/41 Giudice, Strumia (2012) tan β 3 is favored when stop mass is O(100) TeV.

29 i. Flavor violating coupling tan β in SO(10) model 24/41 In the minimal SO(10) SUSY GUT model m t Y t (v sin β) m b Y b (v cos β) In our SO(10) SUSY GUT model Y t = Y b tan β m t Τm b large tan β is favorable +extra 10s of SO(10) tan β m t Τm b Y t Y b small tan β is acceptable

30 i. Flavor violating coupling Yukawa relation 25/41 Introduce higher dimensional operator contribution (εc ij ) to realize observed fermion masses and mixings. From these relations we can calculate flavor violating coupling

31 i. Flavor violating coupling Flavor violating coupling 26/41 red : ε c ij d < 10 2 blue : ε c ij d < 10 3 d A sd ~ Re(A d ij ) Im(A d ij ) d A bd d A bs 1-2 generation 1-3 generation 2-3 generation K physics < B physics

32 1-3 generation 2-3 generation i. Flavor violating coupling Flavor violating coupling 27/41 Indeed A ij ψ mi ψ mj ψ A l ij /A d kl m i l m j l /m k d m l d 1-2 generation

33 ii. Phenomenology Prediction 28/41 From here I show prediction of this model 100 TeV M Z = ቊ 36 TeV g Z = e.g. K 0 d R s R ҧ s R ҧ d R ഥK 0

34 ii. Phenomenology K ഥK mixing 29/41 deviation from SM prediction real part imaginary part current limit future limit CKM fitter group Belle II O 30 % O 20 %

35 ii. Phenomenology K ഥK mixing 30/41 red : ε c ij d < 10 2 blue : ε c ij d < 10 3 M Z = 100 TeV M Z = 36 TeV

36 ii. Phenomenology B (s) ഥB (s) mixing 31/41 especially B s തB s mixing A d bs > A d d bd, A sd but SM contribution is relatively large indeed we can neglect these contribution current limit O 10 %

37 ii. Phenomenology B (s) ഥB (s) mixing 32/41 red : ε c ij d < 10 2 blue : ε c ij d < 10 3 M Z = 100 TeV M Z = 36 TeV all points satisfy δε K 0.3

38 ii. Phenomenology other quark flavor process 32/41 sadly other quark flavor violating processes are negligible e.g. K L π 0 νν, ҧ K + π + νν, ҧ K L l i l j, K L π 0 l i l j, B s μ + μ, B μ + μ

39 ii. Phenomenology 33/41 μ 3e BR(μ 3e) current limit future limit SINDRUM Mu3e O O key In this model μ must be left-handed.

40 ii. Phenomenology 34/41 μ 3e SINDRUM Mu3e red : ε c ij d < 10 2 blue : ε c ij d < 10 3 M Z = 100 TeV M Z = 36 TeV candidate for signal

41 ii. Phenomenology 35/41 μ-e conversion BR(μN en) (especially N=Au, Al) μ-e transition in Nuclei quark Nuclei again current limit future limit key SINDRUM N=Au O COMET-I N=Al O COMET-II O In this model μ must be left-handed.

42 ii. Phenomenology 36/41 μ-e conversion SINDRUM red : ε c ij d < 10 2 blue : ε c ij d < 10 3 M Z = 100 TeV M Z = 36 TeV

43 ii. Phenomenology 37/41 μ-e conversion COMET-I COMET-II red : ε c ij d < 10 2 blue : ε c ij d < 10 3 M Z = 100 TeV candidate for signal M Z = 36 TeV

44 ii. Phenomenology 38/41 τ decay τ decay A d bs l A τμ l A τe /A d bd > A d d bd, A sd d > 1 /A bs l d, A μe /A sd < 1 l A τμ l l A τe, A μe large τ μ decay?

45 ii. Phenomenology 39/41 τ decay Surely τ μ decay is large. But sadly τ experimental bounds are not restrict.

46 summary 40/41 Summary SO 10 SUSY GUT model signal of model is flavor violation mechanism to solve problem of GUT model induces flavor violation distinctive flavor violation compatible with high-scale SUSY scenario lepton flavor violation can be a signal of this model

47 future prospect 41/41 In GUT model (not only this model) flavor physics (especially if we can get information of chirality) is very important e.g. charged-lepton sector only LFV from left-handed charged lepton is detected (no signal from right-handed charged lepton) FV from right-handed down quark is expected SU(5) like models are favored

48 60 m Guan Yu( 関羽 )

49 Back up

50 Theory

51 Input parameter for calculation

52 Input parameter for calculation

53 approximate expressions for flavor violating coupling when ε 1

54 inverse seesaw original inverse seesaw mechanism Mohapatra (1986) MSSM Higgs VEV extend this mechanism

55 Dim-5 proton decay The constraint from dim-5 proton decay excludes the minimal SU(5) SUSY GUT model. Goto, Nihei (1998) Decoupling Can Revive Minimal Supersymmetric SU(5) in the high-scale SUSY scenario Hisano, Kobayashi, Kuwahara, Nagata (2013) This model is SO(10) GUT model There are many particles around GUT scale. SO(10) GUT models have mechanisms to suppress dim- 5 proton decay. Dimopoulous Wilczek adjoint VEV form

56 Dark matter candidate LSP is Wino (anomaly mediation) Axion introduce U 1 PQ symmetry breaking scale is around GeV explain correct relic density Preskill, Wise, Wilczek (1983) and so on