Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
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