1. The LHC Diphoton Excess & F-Theory LRS
Models
JOHAR M. ASHFAQUE
University of Liverpool
Work In Progress
2016
JOHAR M. ASHFAQUE STRING PHENO 2016

2. Motivated By The Diphoton Signal...
E8 Ñ E6 ¢SUp3qu
E6 Ñ SOp10q¢Up1q Flipped SOp10q
SOp10q Ñ SUp5q¢Up1q Flipped SUp5q
SUp5q Ñ SUp3q¢SUp2q¢Up1q
see e.g.
G. K. Leontaris, Q. Shafi (2016)
A. Karozas, S. F. King, G. K. Leontaris, A. K. Meadowcroft (2016)
JOHAR M. ASHFAQUE STRING PHENO 2016

3. Aim Is Twofold
Search for LRS Models from F-Theoretic E6
Exploring the connection between F-Theory Phenomenology
and the LHC Diphoton Excess
JOHAR M. ASHFAQUE STRING PHENO 2016

4. Model Building Elements in F-Theory
Each lower-dimensional subspace provides an important model
building element
Dimension Ingredient Complex Enhancements
Codimension
8D Gauge Theory 1 -
6D Matter 2 Rank 1
4D Yukawa Couplings 3 Rank 2
JOHAR M. ASHFAQUE STRING PHENO 2016

5. The SUp5q GUT: Pictorially
The six extra dimensions are compactified on B3 whereas the
SUp5q degrees of freedom are localized on the submanifold SGUT .
The gauge bosons live on the bulk of SGUT but the chiral
multiplets are localized on complex matter curves. At the
intersection of two matter curves with a Higgs curve a Yukawa
coupling develops.
JOHAR M. ASHFAQUE STRING PHENO 2016

6. Non-Trivial Gauge Flux
The preferred GUT breaking method is turning on a non-trivial
gauge flux which will break the gauge group.
The hypercharge flux is an important ingredient which provides an
elegant mechanism for breaking the GUT group.
JOHAR M. ASHFAQUE STRING PHENO 2016

7. The E6 Subgroups
E6 Ñ SOp10q¢Up1q Ñ SUp5q¢Up1q2
E6 Ñ SOp10q¢Up1q Ñ SUp4q¢SUp2q¢SUp2q¢Up1q
E6 Ñ SUp6q¢SUp2q Ñ SUp5q¢SUp2q¢Up1q
E6 Ñ SUp6q¢SUp2q Ñ SUp4q¢SUp2q¢SUp2q¢Up1q
E6 Ñ SUp6q¢SUp2q Ñ SUp3q¢SUp3q¢SUp2q¢Up1q
E6 Ñ SUp3q¢SUp3q¢SUp3q
JOHAR M. ASHFAQUE STRING PHENO 2016

8. The Two Extended Rank 6 MSSM Models
In all the known instances
E6 Ñ SUp3q¢SUp2q¢rUp1q3
s
E6 Ñ SUp3q¢SUp2q¢rSUp2q¢Up1q2
s
which are equivalent up to linear transformations.
C. M. Chen, Y. C. Chung (2011)
JOHAR M. ASHFAQUE STRING PHENO 2016

9. What Seems To Be The Problem?
SUp3qC ¢SUp3qL ¢SUp3qR
UB¡L must not be identical to UY
UB¡L must be orthogonal to SUp3qC ¢SUp2qL
UB¡L w SUp3qR
see
J. Harada (2003)
JOHAR M. ASHFAQUE STRING PHENO 2016

10. A Body of Clay, A Mind Full of Play
A Second of Life - Thats Me
“We must think beyond the box if we are to broaden our horizons.”
J. M. A.
JOHAR M. ASHFAQUE STRING PHENO 2016

11. Work In Progress
SUp3qC ¢SUp2qL ¢Up1qY ¢Up1q¢Up1ql jh n
Up1q
λijk
D Si Dj
¯Dk λijk
H Si Hj
¯Hk λij
hSi Hj
¯h ηi
Dζi D ¯D ηi
hζi h¯h
see
J. M. A., L. Delle Rose, A. E. Faraggi, C. Marzo (2016)
JOHAR M. ASHFAQUE STRING PHENO 2016

12. The SM Embedding: E6 Ñ SOp10q¢Up1qζ
27
6
99999998
99999997
161
2
FL FR pQ, uc, dc, L, ec, Nq
Ñ
Q uc
ec
¨
dc
L
¨
N
10¡1 D h pD, D, H, Hq
Ñ
D
H
¨
D
H
¨
12 S Ñ S
Z2 Monodromy ô !
t1
t2
t3
$
(
)
θ12 θ21 θ0
θ23 θ13
θ32 θ31 Ø S
JOHAR M. ASHFAQUE STRING PHENO 2016

13. Making The Connection
D D, H
S
g
g
γ
γ
Figure: Vector-like representations (D Dq € 10 of SOp10q contribute to
the diphoton signal.
JOHAR M. ASHFAQUE STRING PHENO 2016

14. υχαριστω!!!
JOHAR M. ASHFAQUE STRING PHENO 2016