THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, Zurich, 2013 Graham Ross
THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC
Latsis symposium, Zurich, 2013
Graham Ross
The Higgs Era
The Standard Model after LHC 8
u Symmetries è Dynamics
SU(3)× SU(2)×U(1)
uidi
⎛
⎝⎜⎜
⎞
⎠⎟⎟L
, uiR , diR ,liν i
⎛
⎝⎜⎜
⎞
⎠⎟⎟L
, liR , ν iRChiral Matter
Higgs H +
H 0
⎛
⎝⎜
⎞
⎠⎟ →WL
± , ZL , h0
u Unanswered questions
Gauge bosons
- Gauge and multiplet structure?
- 18(27) parameters? - Charges?
- Baryogenesis? - Dark matter? - Strong CP problem?
- Neutrino masses?
SU (5) ⊃ SU (3)⊗ SU (2)⊗U (1) e.g. SO(10) ⊃
}
-‐uc uc u d uc u d
u d ec
(3)SU
} (2)SU?3 0
eQ Q −+ =
dc dc dc
e e
( )5 :L
( )10 :L
1/ 3cdQ =
(10(16 ) 1) ) (5 ( )L LL L+ += νe,L
c ≡νe,R
LH states SU(2) doublets
{
ν
Grand Unification (String Unification) u Unanswered questions
- Gauge and multiplet structure(?)
- 18 (27) parameters? - Charges
- Baryogenesis? - Dark matter? - Strong CP problem?
- Neutrino masses?
Georgi Glashow 1974
SU (5) ⊃ SU (3)⊗ SU (2)⊗U (1) e.g. SO(10) ⊃
}
-‐uc uc u d uc u d
u d ec
(3)SU
} (2)SU
dc dc dc
e e
( )5 :L
( )10 :L
(10(16 ) 1) ) (5 ( )L LL L+ +=
{
ν
Grand Unification (String Unification) u Unanswered questions
- Gauge and multiplet structure(?)
- 23 parameters? - Charges
- Baryogenesis - Dark matter? - Strong CP problem
- Neutrino masses g5 g3 g2 g1
Log 10 [Energy Scale (GeV)] 9 11 13 15 17
mνL
∝ < H >2
mνR
ml ,q
2
mνR
<H>
Lν Lν ν R
<H>
} (X,Y )µ , MX 1015−16GeV
45 24 12
Smirnov
BUT…
} ?
Doublet-Triplet splitting problem:
The Standard Model as an EFT:
H +
H 0
⎛
⎝⎜
⎞
⎠⎟Higgs doublet …but no SU(5) colour triplet partner ✔
H H H
H-‐
H0 _
Xµ
H
mh2 (Q2 ) = mh
2 +δmh2 (Q2 )
δmh2 ∝MX
2 ln Q2 +MX2
µ2
⎛⎝⎜
⎞⎠⎟=O(1015GeV )
Aµ ✔, Ψ ✔ H ✗
The hierarchy problem !
} ?
Doublet-Triplet splitting problem:
H +
H 0
⎛
⎝⎜
⎞
⎠⎟Higgs doublet …but no SU(5) colour triplet partner ✔
H H H
H-‐
H0 _
δmh2 ∝MSUSY
2 ln Q2 +MX2
µ2
⎛⎝⎜
⎞⎠⎟
Solution – Supersymmetric GUTs -
Xµ
H
X
H
MSUSY 1TeV
The Standard Model as an EFT:
mh2 (Q2 ) = mh
2 +δmh2 (Q2 )
Aµ ✔, Ψ ✔ H ✔
(5) (3) (2) (1)SU SU SU U⊃ ⊗ ⊗ e.g. SO(10) ⊃
}
-‐uc uc u d uc u d
u d ec
(3)SU
} (2)SU
dc dc dc e e
( )5 :L
( )10 :L
(16)L = (10)L + (5)L + (1)L
ν
g5 g3 g2 g1gauge coupling unifica3on
• Grand Unification, String Unification
MSUSY TeV
Dimopoulos. Georgi Ibanez, GGR Dimopoulos, Raby, Wilczek
LHC SUSY searches so far negative
[GeV]g~m500 600 700 800 900 1000 1100 1200 1300
[GeV
]10 r¾
m
200
400
600
800
1000
forbidden
10r¾t t
Ag~
not included.theorySUSYm95% CL limits.
= 8 TeVs, 10
r¾t tAg~ production, g~-g~ Status: LHCP 2013
PreliminaryATLAS
ExpectedObservedExpectedObservedExpectedObservedExpectedObserved
10 jets*0-lepton, 7 -
3 b-jets*0-lepton,
4 jets*3-leptons,
3 b-jets*2-SS-leptons, 0 -
ATLAS-CONF-2013-054
ATLAS-CONF-2012-145
ATLAS-CONF-2012-151
ATLAS-CONF-2013-007
]-1 = 20.3 fbint
[L
]-1 = 12.8 fbint
[L
]-1 = 12.8 fbint
[L
]-1 = 20.7 fbint
[L
SUSY@TeV ?
gluino mass [GeV]500 600 700 800 900 1000 1100 1200 1300 1400 1500
LSP
mas
s [G
eV]
0
100
200
300
400
500
600
700
800
ObservedSUSYtheoryσObserved -1
Expected
m(gluin
o) - m
(LSP) =
2 m(to
p)
LHCP 2013 = 8 TeVs
CMS Preliminary10χ∼ t t →g~ production, g~-g~
-1) 19.4 fbT+HTESUS-12-024 0-lep (-1 6) 19.4 fb≥
jetsSUS-13-007 1-lep (n
-1SUS-12-017 2-lep (SS+b) 10.5 fb-1SUS-13-008 3-lep (3l+b) 19.5 fb
mg , q >1−1.5GeV
Significance? –Fine tuning measure Δ (not optional in likelihood fit!)
δmh
2 aim i2
q ,l∑ + biM i
2
g ,W ,B∑ + ..., ai ,bi ∝ log
MX
mh
⎛⎝⎜
⎞⎠⎟
(C)GNMSSM
Δ ≈δmh,i
2
mh2δmh
2( )imh2 ≥ 20 still room for SUSY!
Ghilencea, GGR
Casas et al
Kaminska, GGR, Schmidt-‐Hoberg
-uc uc u d uc u d
u d ec
dc
dc
dc
e
e
( )5 :L
( )10 :L
(5) (3) (2) (1)SU SU SU U⊃ ⊗ ⊗
} : New lepto-quark gauge interactions X µ
XM
} u
u
dc
e+ X µ
τ ∝ M X4 ,
τ
p→e+π 0 >1×1034 yrs, M X >1016GeV
0p eπ +→
GUTs - Nucleon decay
SUSY GUTS – Nucleon decay 1ΛQQQL F
τ
p→e+π 0 >1×1034 yrs, M X >1016GeV τp→K +ν
> 3.3×1033yrs
Λ >1027GeV , 109MPlanck
Raby Murayama et al
SUSY GUTS – Nucleon decay 1ΛQQQL F
τ
p→e+π 0 >1×1034 yrs, M X >1016GeV τp→K +ν
> 3.3×1033yrs, Λ >1027GeV , 108MPlanck
Recent developments:
GUT SU(5), SO(10)
µ-term small (Higgsino mass)
Anomaly free (discrete) symmetry
Discrete R-symmetry Z4R ...
Split multiplets (Higgs)
Higher dimension e.g.string unification
⇒
No D=5 ✔
††
† Doublet – Triplet splitting
Lee et al
Ratz et al
Doublet-Triplet splitting from higher dimensions
W = P exp −i T aAma dxm
γ∫
⎛
⎝⎜
⎞
⎠⎟
Compactification: K = K0 /H
freely acting discrete group
Wilson line breaking:
embedding of H into gauge group G
W : H ⊂ G
Massless states: H ⊗H singlets
e.g. SU(5) : H = Z3, H = Diag(α ,α ,α ,1,1), α = e2iπ /3
R⊗ R( ) : (1⊗ 5)→ H −
H0
⎛
⎝⎜
⎞
⎠⎟1
, 3,5( )→ eνe
⎛
⎝⎜
⎞
⎠⎟1
⊕dc
dc
dc
⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟α 2
, Matter → 3,5 +10( )
Breit, Ovrut, Segre
I
sin2θW = 0.23116(12) (Expt)
2sin 0.2312 0.0002Wθ = ±
α s = 0.134 ± 0.01− 4(sin2θW − 0.23116) c. f . 0.1184(7) (Expt)?
SUSY-GUT gauge coupling unification
Ghilencea, GGR
Mstring = gstring .M Planck = 3.6 ×1017 GeV
c.f. String Unification - Weakly Coupled Heterotic String
10 24 3
4( ...)' '
HSeff i
iL d x ge R Trk Fφ
α α−= + +∫
2' 1/ only scalestringMα =110α−
}
4d xV∫
}
4 310 10 '' ',64 16 4
StringN String NG G
V Vα αα α α αα
π π= = =
1gi
2( MZ )=
ki
gstring2 + bi ln
Mstring
MZ
⎛
⎝⎜
⎞
⎠⎟ + Δ i
Kaplunovsky
Gross, Harvey,Martinec, Rohm
I
GGR, D.Ghilencea
16(2.5 2).10UM GeV= ±
E 10 -60
MP
173.6 10 ?WCHSUM GeV= ×
String unification with gravity
Δ i ?
..close..but not close enough!
..string threshold corrections,
sin2θW = 0.23116(12) (Expt)
α s = 0.134 ± 0.01− 4(sin2θW − 0.23116) c. f . 0.1184(7) (Expt)
( ), (5
2)
2log( ) log( )( ) ( l ()4 4
og )X Y SUi im m mβ σ β σρ β
πρ ρ
π−+ + − = − .
(3) (2) 1)) ((5S SUU SU U⊗ ⊗→
2 2 22
1( ) ( )nM nR σσ χ ρ= + +1n = ±
0n =
.
.
.
Reduction in X,Y boson contribution - equivalent to reduction in unification scale.
,X Y
3,2,1 }
3,2,1
String threshold effects, : Wilson line breaking Δ iGGR Raby Ratz
I
GGR, D.Ghilencea
MU = (2.5± 2).1016GeV
E 10 -60
MP
String unification with gravity Precision Unification possible
+ Wilson line breaking
e.g. Z3 : SU (5)→ SM
MUWCHS = 6.1016GeV ,
δ (α s ) = −0.008
sin2θW = 0.23116(12) (Expt)
α s = 0.126 ± 0.01− 4(sin2θW − 0.23116) c. f . 0.1184(7) (Expt)?
GGR
Summary
Gauge, matter multiplets ⇒ GUT SU(5), SO(10),…•
•
Hierarchy problem ⇒ SUSY GUTµ-term ⇒ Z4
R ⊂ Lorentz symmetry D>4
Doublet-triplet splitting ⇒ Wilson line breaking
Precision gauge and gravity coupling unification possible
α s = 0.126 ± 0.01− 4(sin2θW − 0.23116) MU = (2.5± 2).1016GeV
• Family replication and masses String compactification
Family symmetries (?)
GUT relations mb = mτ , Det[Md ]= Det[Ml ]
Summary
Gauge, matter multiplets ⇒ GUT SU(5), SO(10),…•
•
Hierarchy problem ⇒ SUSY GUTµ-term ⇒ Z4
R ⊂ Lorentz symmetry D>4
Doublet-triplet splitting ⇒ Wilson line breaking
Precision gauge and gravity coupling unification possible
α s = 0.126 ± 0.01− 4(sin2θW − 0.23116) MU = (2.5± 2).1016GeV
• Family replication and masses String compactification
Family symmetries (?)
GUT relations mb = mτ , Det[Md ]= Det[Ml ]
Soft masses – radiative breaking Ibanez,GGR
Outlook – indirect signals
• Nucleon decay D=6 operators
τ
p→e+π 0SuperK >1×1034 yrs
Hadronic matrix element
c. f . MU = (2.5± 2).1016GeV
Operator renormalisation
Giudice, Romanino
• Neutrino masses – see-saw
Baryogenesis – via Leptogenesis – νR decay:
Thermal leptogenesis
⇒ mν < 0.1eV , mνR1> 4 ×108GeV
Buchmuller review
Outlook – indirect signals
• Nucleon decay D=6 operators
Majorana mass – L violation: mνL
∝ < H >2
mνR
ml ,q
2
mνR
• FCNC
• Neutrino masses – see-saw
Outlook – indirect signals
• Nucleon decay D=6 operators
q, l,ν mixing
Beneke Egede
mL
2( )ij 18π 2 3m0
2 + A02( ) fν
† fν( )ij logmνR
MU
L = fl eRLh1 + fνν RLh2 +mνRνRνR
e.g. Lepton FCNC:
Borzumati, Masiero
Γ µ→ eγ( )∝ mL
2( )12
• SUSY @ LHC, SUSY Higgs
• Dark Matter SUSY WIMP, Axions
• FCNC
faxion >109GeV
• Neutrino masses – see-saw
Outlook – indirect signals
• Nucleon decay D=6 operators
q, l,ν mixing
Sphicas
Sarkar, Aprile
• SUSY @ LHC, SUSY Higgs
• Dark Matter SUSY WIMP, Axions
• FCNC
faxion >109GeV
• Neutrino masses – see-saw
Outlook – indirect signals
• Nucleon decay D=6 operators
q, l,ν mixing
Sphicas
Sarkar, Aprile
LHC 14!
Unification in split SUSY Giudice, Romanino