B. Dutta

Texas A&M University

SO(10) model, Flavor Violation and Proton Decay

Phys. Rev. D69:115014,2004; D72:075009,2005; D75:015006,2007;. Phys. Rev. Lett. 94:091804,2005; 97:241802,2006;arXiv: 0708.3080 (Phys Rev D, Rapid Communication); arXiv:0712.1206; To appear

Outline

A Minimal SO(10) Model

Proton decay

Fermion masses, mixings and predictions

Lepton Flavor Violation

Conclusion

Bs- Bs, D0-D0 mixings and predictions (new results from Tevatron, BABAR, BELLE)

Gauge coupling unification

The Model…

The Yukawa superpotential involves the couplings of 16-dimensional matter spinors : All SM fields+ RWY =1/2 hijψiψjH +1/2 fijψiψj +1/2 h′ijψiψjD.

ψi (i denotes a generation index) with 10 (H), 126 (), and 120 (D) dim. Higgs fields:h and f are symmetric matrices and h′ is an anti-symmetric matrix due to the SO(10) symmetry.

The Higgs doublet fields not only exist in H, , D, but also in other Higgs fields (e.g., 210) which are needed in the model.

The Model…

SO(10)

SU(5)

Flipped SU(5),SU(5)X U(1)

SM (SU(3) x SU(2) X U(1))

Pati-Salam

Pati-Salam:SU(2)LxSU(2)RXSU(4)C

SU(3) x SU(2)xSU(2) X U(1)

210, 45, 54, 126, 126,

SO(10) gets broken by the following Higgs Fields:

WH=1/2 m1 (12+32

2+632)+m2+1(2

3+3132+623

2) +2 (1+32+63)

1(1,1,1)=-m1/1x(1-5x2)/(1-x)2

After solving the flat directions

2(15,1,1)=-m1/1x(1-2x-x2)/(1-x)

3(15,1,3)=m1/1x

Different values of x lead to different symmetry breaking chain, e.g., x=1/2,-1 : SU(5) , x=0 leads to 2231 etc.

SO(10)…

[In (4,2,2) notation]

i’s belong to 210

belong to 126, 126

m12/(12)x(1+x2)(1-3x)/(1-x)2

In the SU(5) case, X,Y gauge bosons remain massless…

The Model…

Altogether, we have six pairs of Higgs doublets: d = (H10

d , D1d, D2

d, d, d, d), u = (H10

u , D1u, D2

u, u, u, u),where superscripts 1, 2 of Du,d stand for SU(4) singlet and adjoint pieces under the G422 =SU(4)×SU(2)×SU(2) decomposition. The mass term of the Higgs doublets : (d)a(MD)ab(u)b, The lightest Higgs pair (MSSM doublets) has masses of the order of the weak scale.

210 Higgs multiplet (): is employed to break the SO(10) symmetry down to the standard model126 Higgs multiplet () : introduced as a vector-like pair and this field also contains a Higgs doublet.The VEV of this pair reduces the rank of SO(10) group, keep supersymmetry unbroken down to the weak scale.

MSSM Higgs doublet is here

The Model…

The above Yukawa interaction includes mass terms of thequark and lepton fields as follows (using 10+120+126 Higgs fields):

Using WY =1/2 hijψiψjH +1/2 fijψiψj +1/2 h′ijψiψjD.

Wmass Y = hH10 d (qdc + ℓec) + hH10u (quc + ℓνc)+

1/√3 f d(qdc − 3ℓec) +1/√3 f u(quc − 3ℓνc) + √2 fνcνc R + √2 fℓℓL + h′D1

d(qdc + ℓec) + h′D1u(quc + ℓνc) +

1/√3 h′D2d(qdc − 3ℓec) −1√3 h′D2 u(quc − 3ℓνc),

where q, uc, dc, ℓ, ec, ν c are the quark and lepton fields for the standard model, which are all unified into one spinor representation of SO(10).

-

-

- -

Imposing that the Lagrangian is invariant under a CP conjugation, the Yukawa couplings, hij , fij and h′ij and all masses and couplings in the Higgs superpotential are all real.The mixing of the lightest Higgs doublets with the Higgs doublets present in 120 involves a pure imaginary coefficient (VEV of 45) which will make the fermion masses hermitian in this model

Very interesting property!

Solves the EDM problems of SUSY models

A solution to strong CP problem

The Model…

The Model…The Yukawa coupling matrices for fermions:Yu = h + r2 f + r3 h′, Yd = r1(h + f +h′), Ye = r1(h − 3 f + ce h′), Y = h − 3r2 f + cvh′,

where the subscripts u, d, e, ν denotes for up-type quark, down-type quark, charged-lepton, and Dirac neutrino Yukawa couplings, respectively,

h= V11h, f = U14/(√3 r1)f, h′ = (U12 + U13/√3)/r1h′, r1 =U11/V11 r2 = r1 V15 /U14 , r3 = r1 (V12 − V13/√3)/(U12 + U13/√3);ce =(U12 − √3U13)/(U12 + U13/√3),c = r1(V12 + √3V13)/( U12 + U13/√3).

U, V : UMDV T = MD diag Mass of the lightest pair of doublet is ~ weak scale (assume)

Note: In the SU(5) vacuum,U14=0; r2=infinity; r3=0;f=0; ce=-1

Need to explain all observed fermion masses and mixings

The VEVs of the fields R : (1, 1, 3) and L : (1, 3, 1) give neutrino Majorana masses.

The light neutrino mass is obtained as m

light = ML −MD M−1

R (MD)T

where MD = Yh<Hu>, ML = 2√2f <L>, MR

=2√2f<R>.

Neutrino Mass

Pure type II: ML (In this talk) Lazarides, Shafi, Wetterich,81, Mohapatra, Senjanovic,81

Type I: Minkowski’77;Yanagida’79,Gellman, Ramond,Slansky’79; Glashow’79;Mohapatra, Senjanovic’80

Seesaw: EW scale2/GUT scale ~ eV

Proton Decay

• Generic prediction of most Grand Unified Theories

• Lifetime > 1033 yr! 0

e+

ProtonProton

Proton Decay

Proton Decay

• The amplitudes mediated by GUT bosons (dimension 6 operators) become small

Amp =u d 1/MHc 1/MSUSY s/2

• processes mediated by the triplet higgsino emerge (dim. 5 operators)

Λ is the cutoff scale for the Standard Model: MGUT

MHc : Mass of colored Higgsino ~ MGUT

Next-generation water Cherenkov detectors

• Conceptual idea of next-generation water Cherenkov detectors – 1999: Concept of UNO & Hyper-K– 2002?: Concept of the European detector

• Time line of each detector– UNO @ SUSEL/DUSEL

• DUSEL proposal• Construction: 10 years, wish to start as soon as possible

– Hyper-K @ Tochibora Mine (Kamioka)• Some years after start-up of T2K-1• Construction: 10 years, hopefully 2013 – 2022

– European detector @ Frejus Tunnel• CERN-based Super and beta beams hopefully ready before

2020• Contruction: hopefully 2010 – 2019 (first module 2017)

Nucleon decay• Reach of lifetime

– p→e+0 up to ～ 1035 yrs with ～ Mton water Cherenkov (present SK limit: 5.4 x 1033 yrs)

– p→K+ up to ～ a few x 1034 yrs with ～ 100 kton liq. Ar and ～ 50 kton liq. scintillator (present SK limit: 2.0 x 1033 yrs)

• There is a lot of life in proton decay•

• Next step is significant!

Proton decay Summary for SO(10)

Models of SO(10); Mohapatra et al, Raby et al, Pati and Babu, Senjanovic et al, Okada et al, Nath et al

SO(10) allows only small tan and very large values of SUSY masses

Situation is as bad as in SU(5)

Small tan is not preferred by Higgs mass and large values of SUSY masses also mean problem!

Proton Decay in SO(10) ModelThe proton decay is mediated by the colored Higgs triplets: T + T : ((3, 1,−1/3) + c.c.) (CL operator); C + C : ((3, 1,−4/3) + c.c.) (CR operator);

These Higgs triplets appear in: 10+120+126+126+210 multiplets. We generate both LLLL (CL) and RRRR (CR) operators:−W5 =Cijkl

L qkqlqiℓj + CijklR ec

kucl uc

i dcj

These operators are obtained by integrating out the triplet Higgs fields, T = (HT ,DT ,D′T ,T ,T ,′T ,T ) The fields with ‘′’ are decuplet, and the others are sextet or 15-plet under SU(4) decomposition.C = (DC,C).

Proton Decay…

CijklL = c hijhkl + x1fijfkl + x2hijfkl + x3fijhkl + x4h′ijhkl +x5h

′ijfkl, Cijkl

R = c hijhkl + y1fijfkl + y2hijfkl + y3fijhkl + y4h′ijhkl + …c = (MT

−1 )11, and the other coefficients xi, yi are also given by the components of MT

−1.

The proton decay amplitude: A = α2βp/(4πMTmSUSY )Ax, where

Ax = cAhh + x1 Aff + x2 Ahf + x3 Afh + x4 Ah′h + x5 Ah′f +...

WtripY = hHT (qℓ + ucdc) + hHT (1/2qq + ecuc) + fT (qℓ −

ucdc) + …Same h, f and h’ which appear in the Yukawa couplings

One way to suppress the decay amplitude is by demanding cancellation among different terms.

In order to achieve that, we need a cancellationamong h, f and h′ to have small couplings

The best way to avoid the cancellation is to choose smaller values of r2,3.

However, we also need cancellation among the same set of couplings to generate the large mass hierarchy among the quark masses

Proton Decay (1st solution) …The current nucleon decay bounds, |Ap→K| 10−8, | An→| 2 · 10−8 and|An→K| 5 ·10−8 for colored Higgsino mass is 2 ·1016 GeV, and squark and wino masses : 1 TeV and 250 GeV

Understanding the solutions:

h, f, h’ combine together to produce the fermion masses

We need small numbers in this combination to reproduce the first generation fermion masses

Two ways: (1) Big h element+ Big f element + Big h’ element = Small element (2) small h element+ small f element + small h’ element = Small element

Small elements are preferred to solve proton decay problem!

If the couplings are small then the amplitudes are small

To suppress Ahh, the elements h11 and h22

(in h-diagonal basis) are needed to be suppressed rather than the up- and charm-quark Yukawa couplings, respectively. As a result, we need Yukawa texture to be h ≃ diag(~0,~0,O(1)).

Once h is fixed, the other matrices f and h′ are almost determined as

where λ ~ 0.2.

223

22

3

0~

0~0~

0

0

0

23

23

33

if= h′=

Proton Decay…

One example for numerical fit for tan β(MZ) = 50, h = diag(0, 0, 0.638),

The coefficients, xi, yi, involve the colored Higgs mixings, which can be suppressed by our choice of the vacuum expectation values and the Higgs couplings.

The Ahh for p → Kνμ mode is ~ 2 · 10−11.

r1 = 0.966, r2 = 0.135, r3 = 0, |ce| = 0.987.

0071.00101.000208.0

0101.000945.00044.0

00208.00044.00~

00181.000046.0

0181.000022.0

00046.00022.00

ih′=f=

Proton Decay…

r2 0 to produce correct charm mass

[ SU(5) like vacuum]

B.D.,Y. Mimura, R. Mohapatra, Phys.Rev.Lett.94:091804,05; Phys.Rev.D72:075009,2005.

Proton Decay…

Any fine tuning in the solution?

CijklL = c hijhkl + x1fijfkl + x2hijfkl + x3fijhkl + x4h′ijhkl +x5h

′ijfkl, Cijkl

R = c hijhkl + y1fijfkl + y2hijfkl + y3fijhkl + y4h′ijhkl + …

The coefficients, x1, x2, etc need to be small

These coefficients arise from the Higgs mass matrix, depend on Masses and Yukawa couplings

In this process we induce fine tuning of the order of a few percent level

The Model Predictions

The number of parameters in the models is 17 3 (h), 6(f), 3(h′) and 5 Higgs parameters (r1,2,3, ce,c).

Explanation of the proton decay fix some parameters.We choose h11,22 = 0 and r3 = 0.

Since we will be working pure type II seesaw, i.e., M=f vL, c is redundant in fitting fermion masses and mixings. This reduces the number of parameters to 13.

13 input parameters: up-type quark masses, charged lepton masses, the CKM angles and the phase, the ratio of the squared of neutrino mass differences (m2 sol/m2 A), and the bi-maximal mixings as input parameters.The down-type quark masses, Ue3 and δMNSP etc are the predictions of this model.

The predicted value of strange quark mass has twoseparate regions, roughly ms ~ 1/3mμ(1±O(λ2)). The negative sign corresponds to a strange quark mass: ms(μ = 2GeV) =120−130 MeV. lattice derived value, ms(μ = 2GeV) = (105 ± 25) MeVThe positive signature gives the following value of the strange quark mass, ms(μ = 2GeV) =155 − 165 MeV

Strange Quark Mass

ms/md=17-18, 19-20.5

[18.9 0.8, Leutwyler’00]

We get the following approximate relation for Ue3: |Ue3|2 ≈ tan2 θsol /(1− tan4 θsol) m2

sol/m2A

We also have the following relation since Ue3 is related to the ratio : |Ue3| ≈1/√2|Vub/Vcb|

.

|Ue3|

The MNSP phase is is given by the approximate expression: sin δMNSP ~1/√2 sin θe

12sin θ13sin(tan−1 ceh′12/ (3

f12))

MNSP Phase

B.D.,Y. Mimura, R. Mohapatra, Phys.Rev.Lett.94:091804,05; Phys.Rev.D72:075009,2005.

The location of δMNSP in the 2nd or 4th quadrant has impact on the probability of νμ to νe oscillation (Pμ→e) which will be measured at the T2K experiment and at Tokai-to-Korea experiments.

This probability depends on sine and cosine of δMNSP, distance (L), energy of the neutrino beam, mass squared differences (m2

13, m212), 3

mixing angles,and matter density.

MNSP Phase

We take the energy of the beam is 0.7 GeV and the values of mass squared differences: m2

13 = 2.5 × 10−3 eV2, m2

12 = 8 × 10−5 eV2 and Ue3 = 0.1. The probability for δ = 330o is about 1.8 timesbigger compared to the probability for δ = 135o when the beam arrives at Kamioka from Tokai(L = 295 km). The difference is magnified much more if we have a detector installed at Korea (L = 1000 km).

MNSP Phase…

Lepton Flavor Violation

Lepton flavor violating processes, e.g., μ → eγ, τ→ μγ etc. The operator for li → lj + γ :

Lli→lj =i(e/2ml) lj σμq (alPL + arPR) li · Aμ+ h.c.

li → lj + γ = mμ (e2 /64π)(|al|2 + |ar|2)

.The right handed masses have hierarchies and therefore get decoupled at different scales. The flavor-violating pieces present in Y induces flavor violations into the charged lepton couplings and into the soft SUSY breaking masses through the RGEs:

dYe/dt =(1/16π2 )(YY † + · · ·)Ye

dm2LL/dt =(1/16π2 )(YY † m2

LL + m2LL YY † +

· · ·)

Lepton Flavor Violation…B

r(-

>e)

Br(

->

)

>0 >0

Gauge Coupling Unification

Recent claim: The minimal SO(10) model is ruled out When gauge coupling unification is required.

Fermion mass hierarchies plus the SO(10) breaking vacuum causes problem to gauge coupling unification

Proton decay also applies strong constraint

Soln.: Extension is needed, extra 120, 10 etc.

The minimal SO(10) superpotential is used, i.e., 210, 10 and 126 [K. Babu, R. Mohapatra, Phys.Rev.Lett.70:2845,1993]

S. Bertolini et al, Phys.Rev.D73:115012,2006.

We can solve this puzzle using 120 or even with an additional 10’ Higgs extension

If we choose SU(5) vacuum, 75 or 24 (of 210) is light

It is possible to use the 75 VEV around the GUT scale to break SU(5) The SO(10) symmetry breaks at around 1017-18 GeV

Fragments of 75 are distributed between the SU(5) breaking and the SO(10) breaking scale

We also need the colored Higgs masses to be at the string scale for successful unification

This automatically solves proton decay problem.

Gauge Coupling Unification…

For flipped SU(5) like vacuum 50+50 is light

126+126

It is possible to do a general analysis instead of just the SU(5) vacuum

The lighter multiplets which can move the gauge coupling unification to 1017-18 GeV are the followings:(8,1,0); (8,2,1/2)+cc; (6,1,1/3)+cc; (6,2,-1/6)+cc [210,126+126]

The colored Higgs masses are of the string scaleproton decay is suppressed.

Gauge Coupling Unification…

The strategy is to find the lighter multiplets for any value of x to keep the gauge coupling unification at the string scale

The new multiplets can be around 1015-16 GeV and the unification scale is the string scaleFlavor violation due to the majorana couplings [when the fields from 126+126 are light].

Proton decay amplitudes are reduced, since the Cutoff scale are high

Gauge Coupling Unification and Proton Decay

u d 1/MHc 1/MSUSY s/2

MH3 becomes large

The unification of the three gauge couplings provides two independent relations on the particle mass spectrum below the symmetry breaking scale

NIA= 2T3(φI ) − 3T2(φI ) + T1(φI ) and NI

B=2T3(φI ) + 3T2(φI ) − 5T1(φI )

Proton Decay (2nd solution) …

Case 1: SU(5) case: full multiplet ( disappears) MHc ~1015 GeV: bad for proton decay

Case 2: with broken multiplets; MHc can be large (using positive NIs): good for proton decay

SU(5) got ruled out…

We rescue SO(10)…

How general are these solutions?

Can we rescue any SO(10)?

Yes, we can! Provided we have the following multiplets around 1016 GeV

Only these four fields can rescue SO(10)

The Unification

Gauge Coupling Unification…

3

2

Y

(8,2,1/2)+cc are around 1016 GeV

Log10[scale]

Since the colored Higgsfields can be heavier than 1017 GeV and the current nucleon decay bounds can be satisfied

If tan β is large enough >20, the proton decay via dimension five operator (such as p → K¯ν) can be observable in the megaton class detector

However, the proton decay via the dimensionsix operator (such as p → πe) may not be observed

Status of Proton Decay in the new scenario

Flavor violations:

If (8, 2, 1/2) and/or (6, 1, 1/3) ismuch lighter than the SO(10) breaking scale, a sizableflavor violation can be generated since those fields originatefrom 126 or 120 which couple to fermions

The couplings can be written as f qucφ(8,2,1/2) + qdcφ(8,2,−1/2) + f qqφ(6,1,−1/3)+f ucdcφ(6,1,1/3)

If (8, 2, 1/2) field is light, it cangenerate off-diagonal elements for both left- and right handedsquark mass matrices If the light (6, 1,−1/3) field comes form 126, it can generateoff-diagonal elements only for left-handed squarks.

If both left- and right-handed squark mass matriceshave sizable off-diagonal elements, the meson mixing viabox diagram is enhanced and thus, it can have impacton D-¯D , Bs-¯Bs mixings etc

The gluino Box diagram dominates.In the mass insertion approximation :

...)()(])()[(32RR32LL

2

32RR

2

32LL

12

~

12 dddd

SM

g

baM

M

SUSY contributions in Bs-Bs mixing

b

X X

s

s

b

M=2|M12|

3-2: Mixing among second-third generation squarks)

2

,

2~

d

RRLL,

~/)( mMRRLLd

Where a,b depend on squark, gluino masses. b~O(100), a~O(1) for mSUSY~ 1 TeV

d32 can affect Bs-Bs mixing amplitude.

m~ is the average squark mass

SUSY contributions in Bs-Bs mixing …

Similarly we can have mixings among other generations as well!

We get Bs-Bs mixing and

Grand unified models and ...

It is possible to generate large 23 mixing terms in squarks and slepton masses in SU(5) and SO(10) models (due to large neutrino mixing) via Dirac and Majorana couplings.

T. Goto etal ‘95

12, 13 mixings are also generated: e, e, k , D0-D0, Bd

0- Bd0 mixings get new

contributions. (Depends on the neutrino mass (Dirac and Majorana) hierarchies, Ue3 etc.)

Grand unified models and ...

Down quarks (Dc) and Leptons (L):

In SU(5): W: H

c

HdHuN 55551010105

5

Dc and L are coupled to Nc: flavor violation in the quark sector

Q, Uc and Ec : 10, Right-Neutrino: Nc

explains neutrino mixing, assume M diagonal. (Majorana mass of Nc)

We get large dRR (squarks).

Grand unified models and ...

Even if we start with diagonal squark slepton masses, we get large flavor mixings in both squark, slepton masses.

Soft masses at the GUT scale:

)(2

0

222

5

kImmmmLDc

)/Mln(M /m3(8/1G

*2

0

2

0

2 Ak M* : string scale/Planck scale,

MG: GUT scale

SU(5) Model

The soft SUSY breaking masses at MG:

*

2

0

222

5

0

0

00

mmmm

ld c Immmm cc euQ

2

0

222

,CKM

VdiagT

CKMVV uPuqeLu

TV

diagV

qeRdP

dqeLd ,

diagePee

This boundary condition is in the basis:

At the weak scale we use the basis where d,e are real, diagonal; We assume minimal SU(5)

VqeR= VqeL=1

arises due to

;

SO(10) Model

In SO(10): The quarks and leptons are unified in 16 (flavor violating effects are larger since both left and right quarks, leptons feel the neutrino Yukawa coupling)

Same effects exist in SO(10)

The Higgs fields are in 10, 126

We also have Majorana couplings:

f 1616 126

SO(10) Model ...

Majorana neutrino coupling (f) introduces flavor violation in both left- and right squark mass matrices

f explains the neutrino masses and mixings in the case when m=f vL.

The scalar masses at MG with f:

)f f (2

0

22222 kImmmmmmLEDQU ccc

SO(10) Model…

*

2

0

2

16

0

0

00

mm

,T

VCKM

VdiagT

CKMVV

qeLuPuqeLu

In the case of 10, 126 Higgs, the Yukawa couplings are symmetric

This boundary condition is in the basis:

),,,( bsidi

deeeP We assume VqeL=1;,

diagePee

TV

diagV

qeLdP

dqeLd

Both dRR and d

LL are large.

(No large fine tuning in the mass fit)

ΔM2[off−diag](MG) = U|fdiag|2U†.

Previously we show that minimalrenormalizable SO(10) models need 120 Higgs field to satisfy proton decay constraint

The Yukawa couplings are not symmetric anymore, we can choose them to be hermitian: Solves SUSY CP problem

2*2*22*2

LEDQUmmmmm ccc

The soft scalar masses at the GUT scale:

A realistic SO(10) scenario:

Dutta, Mimura, Mohapatra’04

In both SU(5) and SO(10):

2-3 mixing in the slepton masses will introduce

2-3 mixing in the squark masses will introduce new contribution to Bs mixing

The phases, s,b enters into Bs mixing and can generate large Bs

Summary:

Bs-Bs and in grand unified models

2

td

ts

B

B

d

s

V

V

M

M

d

s ddss BBBB

fB/fB = 1.23 ± 0.06

M1/2=300GeV

tan10

We include , |Vts/Vtd| errors

Ms/Md

BR

(

)

B.D.,Y. Mimura, Phys.Rev.Lett.97:241802,06

Bs-Bs mixing and in grand unified…

Expt. band

Re-Im plot for 2M12(Bs) when Br( ) saturates the experimental bound.

M=2|M12|

Bs-Bs mixing phase and future

The phase Bs is large for SO(10)This phase can be measured in the CP asymmetry of Bs CP asymmtry of semileptonic Bs decays

(degrees)

SM

s

full

si

Bs BM

BMeC Bs

)(

)(

12

122

Max(2Bs)

Br(

)

B.D.,Y. Mimura, Phys.Rev.Lett.97:241802,06

seff(s-Bs)=(-23 16)0 : D0 result

Sin2 and Vub measurement

Recent measurements:

Sin20.668 0.026WA)

Vub=(4.49 0.19 0.27)x 10-3 (Inclusive)

Exclusive determination has large theoretical error (WA): x10-3 [PDG]

Vub=(3.49 0.17)x10-3 using sin2 (WA)

[HFAG 07]

[Kowelewski 06]

67.049.084.3

With |Vtd/Vts|=008.0

006.0206.0

Sin2 and Vub measurement

There exists tension in the fit.

• Can SUSY grand unified models explain this discrepancy?

• What are the predictions?

• We need 13 terms - mixing between first-third generations in the scalar mass

matrices to modify Sin2.

sin2effsin2eff

Br(

)

Br(

)

Br() vs sin2 in SO(10) and SU(5)

Experimental world average

Vub=0.0041 Vub=0.00449

Br(e) is around 10-12 by our choice of Ue3 and k2

We choose m0=1 TeV, m1/2=300 GeV tan=10, A0=0

k2 and Ue3 are free for SU(5), Ue3~0.02 for SO(10)

Recent result shows that (BaBar and Belle)

The mass difference of D0-D0 mixing:

This new data can constrain new physics such as supersymmetry (SUSY) in the similar way as the traditional constraint from the K meson mixing data

D0-D0 mixing

xD =

yD = 31.2

1.2 10 x 6.6

30.34.3 10 x 78.8

xD =MD/D

yD =D/2D

D is the average decay width of two neutral D meson mass eigenstates

-1110 x )5.04.1(M

The SUSY contribution to the Bs mixing is related to the 2-3 off-diagonal elements of the squark mass matrices, which maybe large since it can be related to the large atmospheric mixing.

It is hard to predict the amount of the SUSY contribution to the K mixing and D mixings due to cancellation.

we can show that cancellations for both K and D mixings are not allowed simultaneously when the non-universal terms in squark mass matrices originate from left-right symmetric models.

Consequently, the recent observation of the D mass difference restricts the amount of SUSY contribution.

D0-D0 mixing

D0-D0 mixing

The main SUSY contribution comes from the u12 (in

the u diagonal basis)

u12 is proportional to d

12+Vus d22 upto the phase pu

The phase freedom is not important for D since there is no cancellation between the SM and SUSY (the short-distance SM contribution is small)

Therefore, when sin2 23 is large, both K mixing

(12d) and D mixing (12

u) SUSY contribution cannot be cancelled away

D0-D0 mixing and K0-K0 mixing simultaneously

Cancellation of the two mixing amplitudes happen for two different regions of sin

13

We use sin2 θ23 = 1/2, tan2 θ

12 =0.4

B.D.,Y. Mimura, arXiv:0708.3080

Since all solutions of the K mixing providerestriction to the phases of the SUSY contributions, phases of the SUSY contribution for Bd,s

mixings are restricted for large SUSY contribution

We choose CKM parameters as sin 2SM ~ 0.77

B.D.,Y. Mimura, arXiv:0708.3080

Conclusion

This model also will be detected in the upcoming results of BS +- . This BR is large since t~b~.

We have constructed a realistic minimal SO(10) model

The model suppresses proton decay naturally

The fermion masses can be fit and the model has many predictions

Ue3 is about 0.1 (without fine tuning) in this model

The model has interesting predictions for T2K experiments

The SO(10) model with 120 or extra 10 can have gauge coupling unification (we can have correct fermion fitting, proton decay allowed for any tanMinimal SO(10) model is ruled out

The non-universal squark and slepton masses get generated due to neutrino sector

The D0 mixing can be large in this model.

Conclusion…

Large Bs mixing phase can occur – under experimental investigation [phase of Bs J/

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