Hidden Impact on Grand Unification

Joydeep ChakraborttyIIT Kanpur

XXI DAE-BRNS High Energy Physics Symposium 2014 — IIT Guwahati

*SM : Standard Model

Well Established Theory of Particle Physics*GUT : Grand Unified Theory

Unification of Fundamental Forces (Strong, Weak, Electromagnetic) apart from Gravity

*SUSY : Supersymmetry Symmetry among Fermions and Bosons

*SUGRA : Supergravity Local Supersymmetry

The new Physics may contain a larger symmetry as SM is expected to be embedded in that.

Many unanswered questions in the SM can be explained within this framework.

It is believed to have unified theory at some high scale and all the low energy Physics will evolve from that.

The new framework is expected to be constrained and contains lesser number of free parameters –

Attractive and Natural.

Beyond SM : GUT + SUSY

What is GUT?

Unified framework —

Gauge couplings are unifiedLeptons and Quarks belong to same representations

Predicts Proton decay ~ GUT Scale !Other BSM requirements are expected to be fulfilled !

Schematic view

N=1 Unified SUGRA framework

SUGRA Breaking and Generation of Soft Terms

N=1 Unified SUGRA framework

Gaugino: Supersymmetric partner of Gauge bosons

Gaugino Mass Operator is related to :

dimension-5 “Gauge Kinetic Operator”

Necessary things to do..

Define dimension-5 operators in Gauge Kinetic Sector.

Provide a Prescription to Calculate orientations of VEVs of Scalar fields.

Compute Non-Universal Gaugino Masses.

Gauge Kinetic term:

: matrix form of gauge field strength tensor

are the generators,

Normalised as:

when are in fundamental representation

Dimension-5 Operator:

is the D-dimensional Scalar, belongs to the symmetric product of adjoint representations.

parametrises the strength of this interaction.

�i

Lkin = � 1

4cTr(Fµ⌫F

µ⌫)

Fµ⌫ =X

�i.Fµ⌫i

Ldim�5 = � ⌘

MPl[1

4cTr(Fµ⌫�DFµ⌫)]

�i

⌘

�D

c =1

2

Tr(�i�j) = c�ij

Rank =4, Number of generators = 24

SU(5) � SU(3)C ⌦ SU(2)L ⌦ U(1)Y

SU(5) Representations �1 �2 �324 1/

p15 3/

p15 -2/

p15

75 4/

p3 -12/5

p3 -4/5

p3

200 1/

p21 1/5

p21 1/10

p21

5⌦ 5̄ = 1� 24

(24⌦ 24)symm = 1� 24� 75� 200

5 = (3, 1)�2 � (1, 2)3

< �24 >=v24p15

diag(1, 1, 1,�3/2,�3/2)

Non-Universal Gaugino MassesSU(5) Representations �1 �2 �3

24 1/

p15 3/

p15 -2/

p15

75 4/

p3 -12/5

p3 -4/5

p3

200 1/

p21 1/5

p21 1/10

p21

M1 : M2 : M3 = (A+ �1B) : (A+ �2B) : (A+ �3B)

F↵� = F1 �↵� + F2 d↵�� ��D

Gaugino Masses for SO(10) and E(6)

SO(10) : Dimension of adjoint representation is 45

E(6) : Dimension of adjoint representation is 78

(45⌦ 45)symm = 1� 54� 210� 770

(78⌦ 78)symm = 1� 650� 2430

What about the X-gauginos

GUT symmetry is broken to the MSSM gauge group at the GUT scale itself — not necessary!

Thus there are some broken generators.

X-Gauginos : related to those broken generators.

They also acquire masses in form: (A+ �XB)

Radiative Correction to Vacuum Energy

Vacuum Energy receives radiative correction from massive X-gauginos. [ Ellis et. al. Phys. Lett. B 155, Nucl. Phys. B 247]

This contribution is very large:

To avoid such catastrophe, this contribution must vanish.

This is possible if the X-gauginos are massless, i.e.,

O(m23/2M

2Pl)

A/B = ��X

Unique Gaugino Mass Ratio

Mi ⌘ M 0 [��X + �j ]

� 2 SU(5) �1 �2 �3 �X M1 : M2 : M3

24 1 3 -2 1/2 1/2 : 5/2 : -5/275 5 -3 -1 -2 7 : -1 : 1200 10 2 1 3/2 17/2 : 1/2 : -1/2

Status of flipped-models

� 2 SO(10) �5 �1 �X M5 : M1

210 -1 4 -1 0 : 5770 -1 -16 -1 0 : -15

� 2 E(6) �10 �1 �X M10 : M1

650 -6 30 -6 0 : 362430 4 108 4 0 : 104

E(6) ! SO(10)⌦ U(1)

SO(10) ! SU(5)⌦ U(1)

Phenomenological Issues

High Scale Boundary Conditions:

Different Non-universality in Gaugino Masses:

Low Scale Spectrum :

Collider and Low energy Constraints, Relic Density,Higgs Mass, Muon (g-2)

M0,M3, A0, tan �, sgn(µ)

M1 : M2 : M3

and Muon (g-2)M1 : M2 : M3

-3

-2

-1

0

1

2

3

-4 -2 0 2 4

M2/

M3

M1/M3

3σ Points2σ Points1σ Points

-1-0.8-0.6-0.4-0.2

0

-2 -1.5 -1 -0.5 0

Zoom

Relic 3σ Points

Conclusions and Views Radiative corrections to the vacuum energy need attention.

One solution : X-Gauginos need to be massless

Non-Universality in Gaugino masses is fixed now

Few models, specifically flipped-scenario, need special care

To explain Muon (g-2) the required pattern of are constrained within this framework

None of these existing single field models fits here

The impact hidden sector can not be ignored

M1 : M2 : M3