No-Scale Supergravity

in the Light of LHC and Planck

Dimitri it i V. Nanopoulos

International School of Subnuclear Physics – 51 st

REFLECTIONS ON THE NEXT STEP FOR LHC

Erice, Sicily, Italy

24 June – 3 July 2013

Crossing the Scalar Rubicon:

Once or Twice?

Cosmological lInflation in Light of fPlanck

• A scalar in the sky? Higgs? Supersymmetry?

Unofficial Combination of Higgs Search

Data from March 6th

Is this the

Higgs Boson?

No

Higgs

here!

No Higgs here!

Scalars Come of Age

• A new boson discovered at the LHC

– A scalar, beyond any reasonable doubt

– Consistent with the Higgs of the Standard Model

• Circumstantial evidence for scalar inflaton

– No sign of non-Gaussianity, strings, defects, …

– Tilt in spectrum of scalar perturbations

• Dt Data consistent t with simplest Wess-Zumino model dl

• Also compatible with Starobinsky (R + R 2 ) model

• Similar predictions in Higgs inflation

• No-scale supergravity with WZ = Starobinsky!

Minimal Supergravity (mSUGRA)

M 0

M 1/2

μ

A 0

B 0

tan β

Universal soft scalar mass

Universal soft gaugino mass

Higgsino Mixing Parameter

Universal Trilinear Coupling

Higgs Bilinear Coupling

Ratio of Higgs VEVs

|μ| and B 0 term can be determined by the requirement for REWSB,

so we are left with only five parameters:

M 0 0, M 1/2, , A 0 0, tan β, and dsg sgn(μ)

No‐scale Supergravity (nSUGRA)

Choose a specific form for the Kähler potential:

K = -3ln(T + T * - Σφ i* φ i )

i

V = 0 At the tree‐level

SUGRA

Furthermore the gaugino mass m 1/2 remains undetermined. Thus, the

soft terms are not fixed (at the classical level) close to the Planck scale.

So, m 1/2 =m 1/2 (T i )

with determined by radiative corrections.

m 1/2 , m 0 = 0, A 0 = 0, B = 0

Thus, in principle all soft‐terms may be determined in terms

of only one‐parameter, m 1/2

The One‐Parameter Model

i

Relation to String Theory

The no‐scale structure emerges naturally as the

infrared limit of string theory.

In particular,

• Heterotic M‐theory compactifications

i

•Type IIB flux compactifications – Flipped SU(5)

• F‐theory compactifications (non‐pertubative ti limit it

of Type IIB)

The nSUGRA ‘One‐Parameter Model’

Strict No‐scale Moduli Scenario: m 0 = A = B = 0

Special Dilaton Scenario:

m

m 1/2

A=−m

2 m

= 1/2

0 = 1/2 B

3

3

These ansatz combined with the no‐scale condition define the so‐called

one‐parameter model since the soft‐terms are now all defined in terms m 1/2

Subset of the mSUGRA parameter space

Highly constrained, but

predictive!

______________________________________________________________

Ellis, Kounnas, and DVN, Nucl.Phys.B247:373‐395,1984

Lopez, DVN, and Zichichi, Phys.Lett.B319:451‐456,1993

Lopez, DVN, and Zichichi, Int.J.Mod.Phys.A10:4241‐4264,1995

Lopez, DVN, and Zichichi, h Phys.Rev.D52:4178‐4182,1995

Inflationary Models in Light of Planck

• Planck CMB observations consistent with inflation

• Tilted scalar perturbation spectrum:

n s = 0.9603 ± 0073 0.073

• BUT strengthen upper limit on tensor

perturbations: r < 0.10

• Challenge for monomial

inflationary models

• Starobinsky R 2 ? Higgs?

• No-ScaleWess-Zumino to rescue?

Starobinsky Model

• Non-minimal general relativity (singularity-free

cosmology):

• Inflationary interpretation, calculation of

Starobinsky, 1980

perturbations:

Mukhanov & Chibisov, 1981

• Conformally equivalent to scalar field model:

Whitt, 1984

Higgs Inflation

Bezrukov & Shaposhnikov, arXiv:0710.3755

• Standard Model with non-minimal coupling to

gravity:

• Consider case

: in Einstein frame

• With potential:

Similar to Starobinsky, but not identical

• Successful inflationary potential at

Inflation Cries out tfor Supersymmetry

• Want “elementary” scalar field

(at least looks elementary at energies

No-Scale Supergravity Inflation

• The only good symmetry is a local symmetry

• Early Universe cosmology needs gravity

• Supergravity

• BUT: potentials in generic supergravity models

have potential ‘holes’ with depths ~ – M

4

P

• Exception: No-Scale supergravity

– Appears in compactifications of string

– Flat directions, scalar potential ~ global model +

controlled corrections

No-Scale Supergravity Inflation

• Simplest SU(2,1)/U(1) example:

• Kähler potential:

• Superpotential:

• Assume modulus T = c/2 fixed by ‘string dynamics’

• Effective Lagrangian for inflaton:

• Modifications to globally supersymmetric case

• Good inflation possible …

:

JE, Nanopoulos & Olive, arXiv:1305.1247

No-Scale Supergravity Inflation

• In terms of canonical field χ:

• Define , , choose

• Dynamics prefers y = 0:

JE, Nanopoulos & Olive, arXiv:1305.1247

No-Scale Supergravity Inflation

• Inflationary potential for

Similar to global case

Special case

JE, Nanopoulos & Olive, arXiv:1305.1247

No-Scale Supergravity Inflation

• Good inflation for

Looks like R 2 model

JE, Nanopoulos & Olive, arXiv:1305.1247

Is If there it looks some and smells profound like Starobinsky… connection?

• Starobinsky model:

• After conformal transformation:

ti

• Effective potential:

• Identical with the No-Scale Wess-Zumino

model for the case

… it actually IS Starobinsky

JE, Nanopoulos & Olive, arXiv:1305.1247

Discovery of No‐Scale F‐SU(5) Signal at LHC

No‐Scale F‐SU(5) with vectorlike particles (b 3 = 0) SUSY spectrum

M~ t1 < M g ~ < M~

q

Prominent decay channels have high multiplicity of third‐generation quarks:

~ ~ ~ 0

~

χ

+ −

χ

0

g → t t → tt

1

→ W W bb

1

~ ~ ~ ~

~

χ

± ±

τν

±

g → t t → bt → W bb → W bb

τν χ

1

Pair produced gluinos generate events rich with jets and tau.

Considered excellent channel for discovery during early LHC run.

S t dLHC l i t f 5 10fb 1 @7T V ≥ 9 jt

Suggested LHC early run signatures for 5‐10fb ‐1 @7TeV: ≥ 9 jets

≥1τ & ≥ 3 b‐jets

0

1

Summary

• The dawn of the scalar era:

– AHi Higgs boson at the LHC

– A cosmological inflaton (?) ()

• Both would welcome supersymmetry

– Hierarchy, mass and couplings of Higgs

– Planck ☺ No-Scale Wess-Zumino inflationary model

• It seems that we must learn to live with (fairly)

elementary scalar fields

• Can supersymmetry be far behind?

Basic Inflationary Formulae

• Strength of perturbations:

• Slow-roll parameters:

• Tilt of scalar perturbations:

• Tensor-to-scalar ratio:

• Number of e-folds:

Cosmological lInflation in Light of fPlanck

• Planck CMB observations consistent with inflation

• Small tilt in spectrum of scalar perturbations

• No hint of non-Gaussianity, strings …