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