THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, - - PowerPoint PPT Presentation

▶
the dream of grand unified theories and the lhc latsis
SMART_READER_LITE
LIVE PREVIEW

THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, - - PowerPoint PPT Presentation

Sep 11, 2023 115 likes •407 views

THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, Zurich, 2013 Graham Ross The Standard Model after LHC 8 u Symmetries Dynamics Gauge SU (3) SU (2) U (1) bosons u i l i Chiral , l iR , iR

slide-1
SLIDE 1

THE DREAM OF GRAND UNIFIED THEORIES AND THE LHC Latsis symposium, Zurich, 2013

Graham Ross

slide-2
SLIDE 2

The Higgs Era

The Standard Model after LHC 8

u Symmetries è Dynamics

SU(3)× SU(2)×U(1)

ui di ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟

L

, uiR, diR, li νi ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟

L

, liR, νiR

Chiral 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?
slide-3
SLIDE 3

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

e

Q Q − + =

dc dc dc e

e

( )

5 :

L

( )

10 :

L

1/3

c

d

Q =

(10 (16 ) 1 ) ) (5 ( )

L L L 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

slide-4
SLIDE 4

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 L L 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

¡ ¡ m

ν L ∝ < H >2

m

ν R

 ml,q

2

m

ν R

<H> ¡

L

ν

L

ν ν R

<H> ¡

} ¡

(X,Y )µ, M X 1015−16GeV

45 24 12 ¡

Smirnov

slide-5
SLIDE 5

BUT…

slide-6
SLIDE 6

} ¡?

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

mh

2(Q2) = mh 2 +δmh 2(Q2)

δmh

2 ∝ M X 2 ln Q2 + M X 2

µ2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = O(1015GeV)

Aµ ✔, Ψ ✔ H ✗ The hierarchy problem !

slide-7
SLIDE 7

} ¡?

Doublet-Triplet splitting problem:

H + H 0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

Higgs doublet …but no SU(5) colour triplet partner ✔ ¡

H H H H-­‑ H0

_

δmh

2 ∝ M SUSY 2

ln Q2 + M X

2

µ2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

Solution – Supersymmetric GUTs -

Xµ

H

X

H

M SUSY 1TeV

The Standard Model as an EFT: mh

2(Q2) = mh 2 +δmh 2(Q2)

Aµ ✔, Ψ ✔ H ✔

slide-8
SLIDE 8

(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 g1

gauge ¡coupling ¡ unifica3on ¡

  • Grand Unification, String Unification

MSUSY  TeV

  • Dimopoulos. Georgi

Ibanez, GGR Dimopoulos, Raby, Wilczek

slide-9
SLIDE 9

LHC SUSY searches so far negative

[GeV] g ~ m 500 600 700 800 900 1000 1100 1200 1300 [GeV] 1
  • m
200 400 600 800 1000 f
  • r
b i d d e n 1
  • t
t
  • g
~ not included. theory SUSY
  • 95% CL limits.
= 8 TeV s , 1
  • t
t
  • g
~ production, g ~
  • g
~ Status: LHCP 2013 Preliminary ATLAS Expected Observed Expected Observed Expected Observed Expected Observed 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 fb int [L ]
  • 1
= 12.8 fb int [L ]
  • 1
= 12.8 fb int [L ]
  • 1
= 20.7 fb int [L

SUSY@TeV ?

gluino mass [GeV] 500 600 700 800 900 1000 1100 1200 1300 1400 1500 LSP mass [GeV] 100 200 300 400 500 600 700 800 Observed SUSY theory σ Observed -1 Expected m ( g l u i n
  • )
  • m
( L S P ) = 2 m ( t
  • p
) LHCP 2013 = 8 TeV s CMS Preliminary 1 χ ∼ t t → g ~ production, g ~
  • g
~
  • 1
) 19.4 fb T +H T E SUS-12-024 0-lep (
  • 1
6) 19.4 fb ≥ jets SUS-13-007 1-lep (n
  • 1
SUS-12-017 2-lep (SS+b) 10.5 fb
  • 1
SUS-13-008 3-lep (3l+b) 19.5 fb

mg

, q  >1−1.5 GeV

Significance? –Fine tuning measure Δ (not optional in likelihood fit!)

δmh

2 

ai m

 i

2 q

,l

∑

+ bi M

 i

2 g

,W

,B

∑

+..., ai,bi ∝ log M

X

mh ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

(C)GNMSSM

Δ ≈ δmh,i

2

mh

2

δmh

2

( )i

mh

2

≥ 20 still room for SUSY!

Ghilencea, GGR Casas et al Kaminska, ¡GGR, ¡Schmidt-­‑Hoberg ¡

slide-10
SLIDE 10
  • 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

X

M

} ¡

u u dc e+

X µ

τ ∝ M X

4,

τ p→e+π 0 >1×1034 yrs, M X >1016GeV

p e π

+

→

GUTs - Nucleon decay

slide-11
SLIDE 11

SUSY GUTS – Nucleon decay

1 Λ QQQL F τ p→e+π 0 >1×1034 yrs, M X >1016GeV

τ p→K +ν > 3.3×1033yrs

Λ >1027GeV, 109 M Planck

Raby Murayama et al

slide-12
SLIDE 12

SUSY GUTS – Nucleon decay

1 Λ QQQL F τ p→e+π 0 >1×1034 yrs, M X >1016GeV

τ p→K +ν > 3.3×1033yrs, Λ >1027GeV, 108 M Planck

Recent developments:

GUT SU(5), SO(10) µ-term small (Higgsino mass) Anomaly free (discrete) symmetry Discrete R-symmetry Z4

R...

Split multiplets (Higgs) Higher dimension e.g.string unification

⇒

No D=5 ✔ ¡

† † †

Doublet – Triplet splitting

Lee et al Ratz et al

slide-13
SLIDE 13

Doublet-Triplet splitting from higher dimensions

W = P exp −i T aAm

a 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 − H ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

1

, 3,5

( )→

e νe ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

1

⊕ d c d c d c ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟

α 2

, Matter → 3,5 +10

( )

Breit, Ovrut, Segre

slide-14
SLIDE 14

I

sin2θW = 0.23116(12) (Expt)

2

sin 0.2312 0.0002

W

θ = ±

α s = 0.134 ± 0.01− 4(sin2θW − 0.23116)

  • c. f .

0.1184(7) (Expt)? SUSY-GUT gauge coupling unification

Ghilencea, GGR

slide-15
SLIDE 15

Mstring = gstring.M Planck = 3.6 ×1017GeV

c.f. String Unification - Weakly Coupled Heterotic String

10 2 4 3

4 ( ...) ' '

HS eff i i

L d x ge R Tr k F

φ

α α

−

= + +

∫

2

' 1/

  • nly scale

string

M α =

1 10

α −

} ¡

4

d x V

∫

} ¡

4 3 10 10

' ' ' , 64 16 4

String N String N

G G V V α α α α α α α π π = = = 1 gi

2(MZ ) =

ki gstring

2

+ bi ln Mstring MZ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + Δi

Kaplunovsky Gross, Harvey,Martinec, Rohm

slide-16
SLIDE 16

I

GGR, D.Ghilencea

16

(2.5 2).10

U

M GeV = ± E

10

  • 60

MP

17

3.6 10 ?

WCHS U

M GeV = ×

¡ ¡

String unification with gravity

Δi ?

..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)

slide-17
SLIDE 17

( )

, (5 2 ) 2

log( ) log( ) ( ) ( l ( ) 4 4

  • g

)

X Y SU i i

m m m β σ β σ ρ β π ρ ρ π − + + − = − .

(3) (2) 1) ) ( (5 S SU U SU U ⊗ ⊗ →

2 2 2 2

1 ( ) ( )

n

M n R

σ

σ χ ρ = + +

1 n = ± n =

. . .

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

Δi

GGR Raby Ratz

slide-18
SLIDE 18

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 MU

WCHS = 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

slide-19
SLIDE 19

Summary

Gauge, matter multiplets

⇒ GUT SU(5), SO(10),…

  • Hierarchy problem

⇒ SUSY GUT

µ-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[M d] = Det[Ml]

slide-20
SLIDE 20

Summary

Gauge, matter multiplets

⇒ GUT SU(5), SO(10),…

  • Hierarchy problem

⇒ SUSY GUT

µ-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[M d] = Det[Ml]

Soft masses – radiative breaking

Ibanez,GGR

slide-21
SLIDE 21

Outlook – indirect signals

  • Nucleon decay D=6 operators

τ p→e+π 0

SuperK >1×1034 yrs

Hadronic matrix element

  • c. f . MU = (2.5± 2).1016GeV

Operator renormalisation

Giudice, ¡Romanino ¡

slide-22
SLIDE 22
  • 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: m

ν L ∝ < H >2

m

ν R

 ml,q

2

m

ν R

slide-23
SLIDE 23
  • FCNC
  • Neutrino masses – see-saw

Outlook – indirect signals

  • Nucleon decay D=6 operators

q

, l

,ν

mixing

Beneke

Egede

slide-24
SLIDE 24

mL

2

( )ij 

1 8π 2 3m0

2 + A0 2

( ) fν

† fν

( )ij log mνR

MU

L = fleRLh1 + fνν RLh2 + mνRν Rν R e.g. Lepton FCNC:

Borzumati, Masiero

Γ µ → eγ

( ) ∝ mL

2

( )12

slide-25
SLIDE 25
  • 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 ¡

slide-26
SLIDE 26
  • 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!

slide-27
SLIDE 27
slide-28
SLIDE 28

¡ ¡ ¡ ¡ ¡ ¡ ¡

¡ ¡

¡

¡

¡

¡

¡

¡

¡

¡

¡ ¡

¡

Unification in split SUSY

Giudice, Romanino