hidden impact on grand unification*gut : grand unified theory unification of fundamental forces...
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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