minimal’susy’su(5)’gut’ inhighscale’susyhomepages.spa.umn.edu/~nagata/20130430.pdf ·...

Minimal SUSY SU(5) GUT in High-‐scale SUSY

Natsumi Nagata

Based on J. Hisano, T. Kuwahara, N. Nagata, 1302.2194 . J. Hisano, D. Kobayashi, T. Kuwahara, N. Nagata, 1304.3651 .

30 April, 2013 KEK

Nagoya University

Outline

1.  Introduc6on

2.  GUT scale mass spectrum in high-‐scale SUSY

3.  Proton decay in high-‐scale SUSY

4.  Summary

1. Introduc?on

SUSY SM

Supersymmetric (SUSY) Standard Model (SM)

scale

EW

TeV

SM par6cles

SUSY par6cles

SUSY SM


scale

EW

TeV

SM par6cles

SUSY par6cles

[GeV]0m500 1000 1500 2000 2500 3000 3500 4000

[GeV

]1/

2m

200

300

400

500

600

700

(600)g~

(800)g~

(1000)g~

(1200)g~

(600)q~

(1000)q ~

(1400)q ~

(1800)q ~

>0µ= 0, 0

= 10, A!MSUGRA/CMSSM: tan

=7 TeVs, -1 L dt = 4.7 fb"Combined

ATLAS

Combined)theory

SUSY#1 ±Observed limit (

)exp#1 ±Expected limit (

-1, 1.04 fb710 (2012) 67-85PLB

LSP$%

LEP Chargino

No EWSB

Direct search

SUSY SM


scale

EW

TeV

SM par6cles

SUSY par6cles

Even

ts /

2 G

eV

500

1000

1500

2000

2500

3000

3500 ATLAS

H

DataSig+Bkg FitBkg (4th order polynomial)

-1Ldt=4.8fb=7 TeV, s-1Ldt=5.9fb=8 TeV, s

(a)

=126.5 GeV)H

(m

Even

ts -

Bkg

-200-100

0100200

(b)

wei

ghts

/ 2

GeV

20

40

60

80

100Data S/B WeightedSig+Bkg FitBkg (4th order polynomial)

=126.5 GeV)H

(m

(c)

[GeV]m100 110 120 130 140 150 160

w

eigh

ts -

Bkg

-8-4048

(d)

126 GeV Higgs boson

[GeV]0m500 1000 1500 2000 2500 3000 3500 4000

[GeV

]1/

2m

200

300

400

500

600

700

(600)g~

(800)g~

(1000)g~

(1200)g~

(600)q~

(1000)q ~

(1400)q ~

(1800)q ~

>0µ= 0, 0



ATLAS

Combined)theory



-1, 1.04 fb710 (2012) 67-85PLB

LSP$%

LEP Chargino

No EWSB

Direct search

SUSY SM


High-‐scale SUSY ??

scale

EW

TeV

SM par6cles

SUSY par6cles

Even

ts /

2 G

eV

500

1000

1500

2000

2500

3000

3500 ATLAS

H

DataSig+Bkg FitBkg (4th order polynomial)

-1Ldt=4.8fb=7 TeV, s-1Ldt=5.9fb=8 TeV, s

(a)

=126.5 GeV)H

(m

Even

ts -

Bkg

-200-100

0100200

(b)

wei

ghts

/ 2

GeV

20

40

60

80

100Data S/B WeightedSig+Bkg FitBkg (4th order polynomial)

=126.5 GeV)H

(m

(c)

[GeV]m100 110 120 130 140 150 160

w

eigh

ts -

Bkg

-8-4048

(d)

126 GeV Higgs boson

[GeV]0m500 1000 1500 2000 2500 3000 3500 4000

[GeV

]1/

2m

200

300

400

500

600

700

(600)g~

(800)g~

(1000)g~

(1200)g~

(600)q~

(1000)q ~

(1400)q ~

(1800)q ~

>0µ= 0, 0



ATLAS

Combined)theory



-1, 1.04 fb710 (2012) 67-85PLB

LSP$%

LEP Chargino

No EWSB

Direct search

APrac6ve features

High-‐scale SUSY scenario has a lot of fascina6ng aspects from a phenomenological point of view.

  126 GeV Higgs boson can be achieved

  SUSY flavor & CP problems are relaxed

  Gravi6no problem is avoided

  DM candidates

(sufficient radia6ve correc6ons)

(suppressed by sfermion masses)

(heavy gravi6no)

w/ light fermions (chiral symmetries)

(wino/higgsino)

Today’s topic

(i) Gauge coupling unifica6on is improved.

Addi6onal features of high-‐scale SUSY in the context of grand unified theories (GUTs):

(ii) Proton decay problem in the minimal SUSY SU(5) GUT is avoided.

Defects in the GUTs with low-scale SUSY

Shortcomings of low-‐scale SUSY GUTs:

(i) Large threshold correc6ons at the GUT scale are required to realize the gauge coupling unifica6on.

(ii) Protons decay too fast (Proton decay problem). Some addi6onal mechanism is required to suppress the proton decay.

Gauge coupling unification in low-scale SUSY

10 14 10 15 1016

1.8 x 10

1.6 x 10

2.1 x 10

16

16

16

H

GU

T

Colored Higgs Mass vs. GUT Scale

M (GeV)

M

(

GeV

)

C

In low-‐energy SUSY, the mass of color-‐triplet Higgs mul6plet is found to be much lower than the GUT scale (RGE analysis).

Errors are from input parameters.

68%, 90%

H. Murayama and A. Pierce (2001)

This implies that the threshold correc6ons to the gauge coupling constants are s6ll not small, even in the SUSY GUTs.

Defects in the GUTs with low-scale SUSY

Shortcomings of low-‐scale SUSY GUTs:

(i) Large threshold correc6ons at the GUT scale are required to realize the gauge coupling unifica6on.

(ii) Protons decay too fast (Proton decay problem). Some addi6onal mechanism is required to suppress the proton decay rate.

Proton decay in low-scale SUSY Proton decay is induced by the exchanges of

  SU(5) gauge bosons (X-‐bosons)   Color-‐triplet Higgs mul6plets

Dim-‐6 operators Dim-‐5 operators

yield dominant decay modes, such as

Predicted life6me (in low-‐scale SUSY):

Experimental constraints:

T. Goto and T. Nihei (1999), H. Murayama and A. Pierce (2001).

Super-‐Kamiokande, arXiv: 1109.3262.

•  Minimal SUSY GUT is excluded

•  needs some extensions to suppress the dim-‐5 proton decay (PQ symmetry, higher-‐dimensional models, etc.)

Today’s topic

(i) Gauge coupling unifica6on is improved

Addi6onal features of high-‐scale SUSY:

(ii) Proton decay problem in the minimal SUSY SU(5) GUT is avoided

All of the superheavy par6cles in the minimal SUSY GUT can lie around the GUT scale.

Small threshold correc6ons are required.

Simple solu6on. No need for addi6onal mechanism.

Decoupling can revive the minimal SUSY SU(5) GUT

Assump6on

A chiral supermul6plet X responsible for SUSY is charged under some symmetry.

SUSY is transferred via operators involving X† X

Soi masses of the scalar par6cles arise from

(MPl: the reduced Planck scale)

VEV of X field Scalar/gravi6no mass

Gaugino mass

Anomaly media6on L. Randall and R. Sundrum (1998) G.F. Giudice, M.A. Luty, H. Murayama, R. Rattazzi (1998)

Wino is the lightest in the gaugino sector

Since the field X is charged under some symmetry, the gaugino mass terms are not given by the X field linear terms.

In this case, the gaugino masses are generated by

Higgsinos

We regard the higgsino mass as a free parameter in the following discussion.

(e.g., Peccei-‐Quinn symmetry)

Origin of Higgsino mass is somewhat model-‐dependent.

  On the assump6on of a generic Kahler poten6al

  It can be suppressed by some symmetry.

Higgsinos can be much lighter than the gravi6no.

Gravi!noScalar Par!cles Higgsinos

Gauginos

Gluino

BinoWino

Mass spectrum

MS = 10(2-‐3) TeV

Thermal relic (2.7-‐3TeV)

Higgsinos can be light (addi6onal symmetries)

(Loop suppressed)

J. Hisano, S. Matsumoto, M. Nagai, O. Saito, M. Senami (2006).

Higgs mass

The 126 GeV Higgs boson mass is easily accounted.

mt= 173.2 ± 0.9 GeV M. Ibe, T.T. Yanagida (2012).

tanΒ�50

tanΒ�5

tanΒ�2

tanΒ�1 ΜH � MSUSY

10 100 1000 104110

115

120

125

130

135

140

MSUSY�TeV

mh�GeV

Small tanβ is favored

126GeV

2. GUT scale mass spectrum in high-‐scale SUSY

Minimal SUSY SU(5) GUT

MSSM maPer fields are embedded in a representa6on

MSSM Higgs fields are embedded into

Color-‐triplet Higgs mul6plets induce the baryon # viola6ng interac6ons

MSSM Higgs superfields (MHC : mass of color-‐triplet Higgs)

S. Dimopoulos and H. Georgi (1981) N. Sakai (1981)

Minimal SUSY SU(5) GUT

Gauge superfields

X bosons (mass: MX) MSSM gauge superfields

Adjoint Higgs superfields

induce baryon # viola6ng interac6ons

Adjoint Higgs (mass: MΣ) Longitudinal mode of X mul6plets SM singlet

SU(5) → SU(3)C × SU(2)L × U(1)Y

RGE analysis

The superheavy par6cles yield threshold correc6ons to the SM gauge couplings at the GUT scale (μGUT)

αi-‐1(μGUT) = αG

-‐1(μGUT) + threshold correc6ons

depending on the masses of superheavy par6cles

Unified gauge coupling

obtained through the renormaliza6on group equa6ons (RGEs)

By using the rela6on, we can es6mate the masses of superheavy par6cles at the GUT scale.

Indirect method

J. Hisano, H. Murayama, T. Yanagida (1992).

Threshold correc6ons @ GUT scale

Threshold correc6ons (1-‐loop in DR scheme)

Then, we have two rela6ons,

By using the rela6ons, we evaluate MHC and MGUT in the following analysis.

The GUT scale

1-‐loop results

First, we derive simpler formulae by using

  1-‐loop RGEs for gauge couplings   1-‐loop threshold correc6ons

Results

Features (MS : scalar mass, μH = MS)

  MHC gets larger as MS is taken to be higher.

It originates from the mass difference among the components of the fundamental Higgs mul6plets.

  MHC depends only on the ra6o of M2 and M3.

1-‐loop results

  MGUT is independent of MS

  MGUT is dependent on the scale of the gauginos

Since it results from the mass difference in the gauge vector mul6plets and the adjoint Higgs mul6plet.

(A part of which is included as the longitudinal mode of the gauge mul6plets)

  MGUT decreases when gaugino masses get larger

Owing to the opposite sign of the contribu6ons of the gauge fields to those of maPer fields.

c.f.) 1-‐loop gauge coupling beta func6on

MHC vs. SUSY scale

1015

1016

1017

1018

102 103

M Hc

MS (TeV)

M2 = 3TeV

M 3/M 2 = 3

M 3/M 2 = 9

M 3/M 2 = 30

tan! = 3

(MS : sfermion mass)

Errors come from the strong coupling constant

Low-‐energy SUSY case

J. Hisano, T. Kuwahara, N. Nagata (2013).

•  MHC increases as MS grows while it decreases when M3/M2 becomes large

•  MHC can be around ~1016 GeV in high-‐scale SUSY scenario

μH = MS

Interes6ng features

MHC can be around the GUT scale in the high-‐scale SUSY scenario.

Small threshold correc6ons are required to realize gauge coupling unifica6on.

Gauge coupling unifica6on is improved !!

10

20

30

40

50

106 108 1010 1012 1014 1016

!"1

Scale (GeV)

25

26

27

28

1016

!"1

Scale (GeV)Zoom

U(1)

SU(2)

SU(3) Low-‐scale SUSY

High-‐scale SUSY

MGUT vs. gluino mass

1016

101

M GUT

M3 (TeV)

M2 = 300GeV

M2 = 3TeV

MS = 103TeVtan! = 3

Errors come from



•  The GUT scale MGUT has liPle dependence on the gaugino masses.

•  MGUT gets lower when the gaugino masses become larger.

μH = MS

Interes6ng features

The GUT scale becomes lower in the high-‐scale SUSY scenario.

Proton decay via the X-‐boson exchange is enhanced. e+

d

X

uc

u

e+

u

Y

uc

dsensi6ve to the X-‐boson mass

1.0

1.2

1.4

1.6

1.8

2.0

103 104 105 106

Lifet

ime

(1035

year

s) 1 TeV3 TeV

10 TeV

M (GeV)S

gaugino threshold

M = 1.0 ! 10 (GeV)X 16

J. Hisano, D. Kobayashi, N. Nagata (2013).

Life6me

(MX = 1.0 × 1016 GeV)

(MX = 0.8 × 1016 GeV) c.f.) Hyper-‐Kamiokande with 10 years exposure

[arXiv: 1109.3262]

3. Proton decay in high-‐scale SUSY

Yukawa interac6ons

Yukawa coupling terms in superpoten6al

(i,j: genera6ons, a,b,…: SU(5) indices)

D.O.F. Field re-‐defini6ons

2 × 6 + 2 × 9 − 9 × 2 = 6 + 4 + 2 quark masses CKM extra phases

(Real D.O.F.)

Parameteriza6on

(Vij: CKM matrix) Constraint

(Two of them are independent)

Dim-‐5 effec6ve operators

HC HC

Qi

Qi

Qk

Ll

U i

Ej

Uk

Dl

HC HC

Exchanges of color-‐triplet Higgs mul6plets induce the dimension-‐five baryon-‐number viola6ng operators. Effec6ve superpoten6al

LLLL

LLLL

RRRR

RRRR


Effec6ve Lagrangian (dim-‐5)

LLLL RRRR

Sfermions are integrated out below the SUSY breaking scale (MS)

•  LLLL operator

•  RRRR operator Charged higgsino exchange Charged wino exchange

Other contribu6ons (e.g., neutral wino, neutral higgsino, gluino…) are found to be negligible in our scenario.


(a)

qL

qL

qL (lL)

lL (qL)

W̃

q̃L l̃L (q̃L)

(b)

uRdR (sR)

(!!)L

"̃Rt̃R

sL (dL)

H̃u H̃d

LLLL RRRR

Although it is induced in the flavor changing process, its contribu6on is sizable because of the large Yukawa couplings of the third genera6on fermions

T. Goto and T. Nihei (1999) V. Lucas and S. Raby (1997)

Loop func6on

Chiral flip [M = wino mass (M2) or higgsino mass (μH)]

Suppressed by sfermion mass (decoupling)

In the case of μH >> M2, the higgsino exchange contribu6on dominates the wino exchange one.

Proton decay life6me

For μH = MS, the proton life6me is approximately given as

Renormaliza6on factors

The proton life6me is significantly reduced with large tanβ.

The life6me can be well above the current experimental limit:

Decoupling can revive the minimal SUSY SU(5) GUT !

MHC can be around 1016 GeV (as discussed above)

Results

1033

1034

1035

1036

102 103 104 105

lifetim

e (ye

ars)

MS (TeV)tan! =

50

tan! =

3 tan! =

5 tan! =

10

tan! =

30

M = "S HM = 3 TeV2 M = 1.0 # 10 GeVHc 16

Experimental limit

J. Hisano, D. Kobayashi, T. Kuwahara, N. Nagata (2013).

Proton decay life6me in high-‐scale SUSY scenario can evade the experimental constraints, especially for small tanβ.

Results

Experimental limit


1033

1034

1035

1036

101 102 103

lifetim

e (ye

ars)

tan! = 10 tan! = 30

tan! = 50

tan! = 5

(TeV)"H

M = 10 TeVS 3

M = 3 TeV2 M = 1.0 # 10 GeVHc 16

We take the new phases so that they yield the maximal amplitude for the proton decay rate.

We are to obtain severe limits on the parameters

We have found that the higgsino contribu6on is dominant in a wide range of parameter region.

5. Summary

Summary

•  We discuss the minimal SUSY SU(5) GUT in the high-‐scale SUSY scenario

•  The gauge coupling unifica6on can be improved with high SUSY breaking scale

•  The GUT scale is slightly reduced, and thus the dimension-‐6 proton decay might be promising

•  Dimension-‐5 proton decay can evade the current experimental limits

•  We look forward to future proton decay experiments

Backup

Yukawa interac6ons

Yukawa coupling terms in superpoten6al

Mass and gauge eigenstates

where primes represent the mass eigenstates.

Superheavy masses

Superpoten6al of Higgs sector

VEV of adjoint Higgs

Doublet-‐triplet mass spli�ng

mH is fine-‐tuned as Superheavy masses

MHC vs. gluino mass

Errors come from the strong coupling constant



•  MHC decreases when M3/M2 becomes large

•  MHC can be around ~1016 GeV in high-‐scale SUSY scenario

1015

1016

1017

1018

101

M Hc

M3 (TeV)

M2 = 300GeV

M2 = 3TeV

MS = 103TeVtan! = 3

Effec6ve 4-‐Fermi operators

(AR(i,j), AR : renormaliza6on factors)

Loop func6on

Renormaliza6on factors

0.3

0.32

0.34

0.36

0.38

0.4

102 103 104 105

tan! = 3

(i,j)=(2,2)(i,j)=(2,3)(i,j)=(3,2)(i,j)=(3,3)

M = !S HM = 3 TeV2 M = 1.0 " 10 GeVHc 16

MS (TeV)

A(i, j)

R

0.3

0.32

0.34

0.36

0.38

0.4

102 103 104 105

A(2,2

)R

MS (TeV)

M = !S HM = 3 TeV2 M = 1.0 " 10 GeVHc 16

tan! =3tan! =5

tan! =10tan! =30tan! =50

0.09

0.1

0.11

0.12

0.13

0.14

0.15

102 103 104 105

tan! =3tan! =5

tan! =10tan! =30tan! =50

M = !S HM = 3 TeV2 M = 1.0 " 10 GeVHc 16

MS (TeV)

A R Renormaliza6on factors are reduced as the SUSY scale gets higher.

Hadron matrix elements

(MB : baryon mass parameter)

Low-‐energy constants

(@ μ = 2 GeV)

Y. Aoki et al. [RBC-‐UKQCD Collabora6on] (2008).

Decay width

Results

Experimental limit


1033

1034

1035

1036

102 103 104 105

lifetim

e (ye

ars)

MS (TeV)tan! =

10

tan! =

5 tan! =

3

tan! =

30

M = "S HM = 3 TeV2 M = 1.0 # 10 GeVHc 15

Results

Experimental limit


1033

1034

1035

1036

100 101 102

lifetim

e (ye

ars)

tan! = 10

tan! = 30

tan! = 5

tan! = 3

(TeV)"H

M = 10 TeVS 2

M = 300 GeV2 M = 1.0 # 10 GeVHc 16

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