MSSM Inflation and the LHC Rouzbeh Allahverdi University of New - - PowerPoint PPT Presentation

MSSM Inflation and the LHC

Rouzbeh Allahverdi University of New Mexico University of New Mexico

GGI mini‐Workshop on “LHC and Dark Mattetr” GGI mini Workshop on LHC and Dark Mattetr 10 June 2010

Outline:

• Introduction
• Inflation in MSSM

Inflation in MSSM

• Properties, predictions, and parameter space
• Cosmology/phenomenology complementarity
• LHC role
• Summary

Summary

Introduction:

LHC-Cosmology connection studied in the context of WIMP dark matter:

• See the WIMP (missing energy) and measure its mass
• Make measurements and identify a point in the dark matter

allowed region for a given model (e.g., mSUGRA)

• Measure as many parameters as possible, and calculate

thermal relic density How about other connections between LHC & cosmology?

Inflation?

(Baryogenesis?)

Some connection between physics of inflation (or baryogenesis) and TeV scale physics must exist. ( y g ) p y

Example: Probing TeV scale leptogenesis at the LHC

C G 090 21 Blanchet, Chacko, Granor, Mohapatra arXiv:0904.2174

Key: Embedding inflation in TeV scale physics y g p y

Most direct connection: Inflation driven by the visible sector Inflation driven by the visible sector

R.A., Enqvist, Garcia-Bellido, Mazumdar PRL 97, 191304 (2006)

Less direct: Inflation driven by the SUSY breaking sector

R.A., Dutta, Sinha PRD 81, 083538 (2010)

Inflation in MSSM:

Inflation: a period of superluminal expansion o the universe. It is driven by a scalar field (inflaton):

φ

t s d e by a sca a e d ( ato )

) ( 3 = ′ + + φ φ φ V H & & &

φ

2 2

3 ) ( M V H φ =

Hubble expansion rate

2

3

P

M : H

Assumptions: Canonical kinetic terms, minimal coupling to gravity Inflation occurs in the slow-roll regime :

2 2

1 ⎟ ⎞ ⎜ ⎛ ′ V

V ′ ′

2

1 | | |, | << η ε

2

2 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ≡ V V M P ε

V V M P ≡

2

η

Inflation occurs within a field range :

) exp(

e

N a

∫

e

d V N

φ

φ 1

) , (

e i φ

φ

S l f t f th i

) exp(

tot i e

N a =

∫

′ =

i

d V M N

P tot φ

φ

2

: a

Scale factor of the universe needed to explain the isotropy and

) 60 30 ( ≈ ≥ N N

: a

needed to explain the isotropy and flatness problems of the big-bang model.

) 60 30 ( − ≈ ≥

COBE tot

N N

Observable: Density fluctuations (CMB temperature anisotropy).

2

1 H φ π δ & 5 1 H

H =

ε η 6 2 1 − + =

s

n

Amplitude Scalar spectral index (COBE) (WMAP7)

5

10 9 . 1

−

× ≈

024 . 963 . ±

MSSM has many scalar fields (Higgses, squarks, sleptons). Can MSSM lead to inflation? Answer (naive): s e ( a e) No, slow-roll conditions not satisfied. Hopeless effort? Hopeless effort? NO! Potential can be made sufficiently flat along various directions in the field space. p

Two such directions can lead to successful inflation.

R.A., Enqvist, Garcia-Bellido, Mazumdar PRL 97, 191304 (2006) R.A., Enqvist, Garcia-Bellido, Jokinen, Mazumdar JCAP 0706, 019 (2007)

Inflaton candidates in MSSM:

~ ~ ~ d d u + +

~ ~ ~ e L L + +

(family color and weak isospin indices omitted)

3 d d u + + = ϕ

3 = ϕ

(family, color, and weak isospin indices omitted) Flat directions: in MSSM with unbroken SUSY.

) ( = ϕ V

SUSY breaking+ Higher order terms: Dine, Randall, Thomas

NPB 458, 291 (1996)

g

( )

6 10 2 3 6 2 2

) 6 cos( 2 1 ) ( M M A m V φ λ φ θ λ φ ϕ

φ

+ + =

6 3

2

P P

M M

φ

) exp( θ φ ϕ i =

) ( ~ TeV O A m

soft mass A-term

) exp( 2 θ ϕ i =

) ( , TeV O A m

φ

Minimizing the potential along :

10 2 6 2 2

1 ) ( A V φ λ φ λ φ φ

θ

6 2 3 2 2

2 ) (

P P

M M A m V φ λ φ λ φ φ

φ

+ − =

A point of inflection exists in the potential:

φ

4 1 3

⎟ ⎟ ⎞ ⎜ ⎜ ⎛ ≅ φ

φ P

M m 10 ⎟ ⎟ ⎠ ⎜ ⎜ ⎝ ≅ λ φ

Provided that:

2

A

2 2

4 1 40 α

φ

+ ≡ m A ) 1 ( << α

inflation

V

inflation

V φ

φ

Inflection point

φ

) (

0 =

′ ′ φ V

4

2 2

4 ) ( φ α φ

φ

m V = ′

2 2

15 4 ) ( φ φ

φ

m V =

Properties, Predictions, and Parameter Space:

Density perturbations: Density perturbations:

Bueno-Sanchez, Dimopoulos, Lyth JCAP 0701, 015 (2007) R.A., Enqvist, Garcia-Bellido, Jokinen, Mazumdar JCAP 0706, 019 (2007) , q , , , , ( )

[ ]

Δ Δ ≈

COBE P H

N M m

2 2 2

sin 1 5 8 φ π δ

φ

Δ 5 φ π

[ ]

Δ Δ − =

COBE s

N n cot 4 1

⎟ ⎟ ⎞ ⎜ ⎜ ⎛ +

0 )

( l 1 9 66 V N φ

2

⎞ ⎛ M

⎟ ⎟ ⎠ ⎜ ⎜ ⎝ + ≈

4 0 )

( ln 4 9 . 66

P COBE

M N φ

2

A

30 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ≡ Δ φ α

P COBE

M N

2 2

4 1 40 α

φ

+ ≡ m A

Allowed parameter space to generate acceptable perturbations:

) 024 . 963 . , 10 9 . 1 (

5

± = × ≈

− s H

n δ ) , (

s H 700 800 700 800 600 700 600 700

6

10− ≤ Δ

400 500 [1012 GeV] 400 500 [1012 GeV]

10 , ≤ Δ

200 300 φ0 [10 200 300 φ0 [10 100 200 100 200 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV]

Important properties: 1)

within the whole range allowed by WMAP can be generated (unlike other models of inflation).

s

n

2) Creation of matter after inflation is guaranteed, and can be treated reliably (inflaton is a linear combination of sparticles). 3) CMB data alone cannot pinpoint the inflaton parameters (unlike other models of inflation). ( ) Two observables: Three parameters: (can be traded for )

s H n

, δ Δ φ

φ

m λ A m

Three parameters: (can be traded for )

Oth i t i d t fi i fl t t

Δ , , φ

φ

m λ

φ

, , A m

Other experiments required to fix inflaton parameters

Cosmology/Phenomenology Complementarity:

The inflaton mass can be connected to low energy masses The inflaton mass can be connected to low energy masses

• r input masses via RGEs.

~ ~

2 2 2

3 ~ ~ ~ d d u + + = φ 3

2 ~ 2 ~ 2 ~ 2 d d u

m m m m + + = ⇒

φ

~ ~ 3 ~ ~ ~ e L L + + = φ 3

2 ~ 2 ~ 2 ~ 2 e L L

m m m m + + = ⇒

φ

gaugino masses

: , ,

3 2 1

M M M

3

g g gauge couplings

, ,

3 2 1

: , ,

3 2 1

g g g

: 3 ~ ~ ~ d d u + + = φ

R.A., Dutta, Mazumdar PRD 75, 075018 (2007)

3

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − =

2 1 2 1 2 3 2 3 2 2

5 2 4 6 1 g M g M d dm π μ μ

φ

⎠ ⎝ 5 6 d π μ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − =

2 1 1 2 3 3 2

5 8 3 16 4 1 g M g M d dA π μ μ

~ ~ ~ e L L + +

⎠ ⎝ μ

: 3 e L L + + = φ

⎞ ⎛

2

9 3 1 dm ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − =

2 1 2 1 2 2 2 2 2

10 9 2 3 6 1 g M g M d dm π μ μ

φ

⎞ ⎛ 9 3 1 dA ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − =

2 1 1 2 2 2 2

5 9 2 3 4 1 g M g M d dA π μ μ

mSUGRA-udd, tan β=10, A =0, >0 mSUGRA-udd, tan β=10, A =0, >0 mSUGRA-udd, tan β=10, A =0, >0 mSUGRA-udd, tan β=10, A =0, >0 mSUGRA-udd, tan β=10, A =0, >0 mSUGRA-udd, tan β=10, A =0, >0

The RGEs can be used to map mSUGRA parameter space into plane: R.A., Dutta, Santoso arXiv:1004.2741

φ

φ −

m

500 mSUGRA-udd, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-udd, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-udd, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-udd, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-udd, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-udd, tan β=10, A0=0, µ>0 10-8pb 400 ] stau-coan n , δ 10-8pb 400 ] stau-coan n , δ 10-8pb 400 ] stau-coan n , δ 10-8pb 400 ] stau-coan n , δ 10-8pb 400 ] stau-coan n , δ 10-8pb 400 ] stau-coan n , δ 10-8pb 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 200 φ0 [10 10-9pb 200 φ0 [10 10-9pb 200 φ0 [10 10-9pb 200 φ0 [10 10-9pb 200 φ0 [10 10-9pb 200 φ0 [10 10-9pb 100 10-9pb 100 10-9pb 100 10-9pb 100 10-9pb gµ-2 bound (T) gµ-2 bound (D) 100 10-9pb 100 10-9pb 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] gµ-2 bound (D) 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV]

mSUGRA-LLe, tan β=10, A =0, >0 mSUGRA-LLe, tan β=10, A =0, >0 mSUGRA-LLe, tan β=10, A =0, >0 mSUGRA-LLe, tan β=10, A =0, >0 mSUGRA-LLe, tan β=10, A =0, >0 mSUGRA-LLe, tan β=10, A =0, >0

(T):Teubner, et al arXiv:1001.5401 (D): Davier, et al arXiv:1004.2741

500 mSUGRA-LLe, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-LLe, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-LLe, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-LLe, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-LLe, tan β=10, A0=0, µ>0 10-8pb 500 mSUGRA-LLe, tan β=10, A0=0, µ>0 10-8pb 400 ] stau-coan ns, δH 10-8pb 400 ] stau-coan ns, δH 10-8pb 400 ] stau-coan ns, δH 10-8pb 400 ] stau-coan ns, δH 10-8pb 400 ] stau-coan ns, δH 10-8pb 400 ] stau-coan ns, δH 10-8pb 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 300 [1012 GeV] excluded ns, δH 200 φ0 [1 10-9pb 200 φ0 [1 10-9pb 200 φ0 [1 10-9pb 200 φ0 [1 10-9pb 200 φ0 [1 10-9pb 200 φ0 [1 10-9pb 100 10 pb 100 10 pb 100 10 pb 100 10 pb gµ-2 bound (T) gµ-2 bound (D) 100 10 pb 100 10 pb 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV]

500 mSUGRA-udd, tan β=10, A0=0, µ>0 500 mSUGRA-udd, tan β=10, A0=0, µ>0 500 mSUGRA-udd, tan β=10, A0=0, µ>0 500 mSUGRA-udd, tan β=10, A0=0, µ>0 500 mSUGRA-udd, tan β=10, A0=0, µ>0 500 mSUGRA-udd, tan β=10, A0=0, µ>0

(Focus point region not shown)

400 500 stau-coan 10-8pb 400 500 stau-coan 10-8pb 400 500 stau-coan 10-8pb 400 500 stau-coan 10-8pb 400 500 stau-coan 10-8pb 400 500 stau-coan 10-8pb 300 400 V] stau-coan ns, δH 10 pb 300 400 V] stau-coan ns, δH 10 pb 300 400 V] stau-coan ns, δH 10 pb 300 400 V] stau-coan ns, δH 10 pb 300 400 V] stau-coan ns, δH 10 pb 300 400 V] stau-coan ns, δH 10 pb 200 300 [1012 GeV] excluded ns, H 200 300 [1012 GeV] excluded ns, H 200 300 [1012 GeV] excluded ns, H 200 300 [1012 GeV] excluded ns, H 200 300 [1012 GeV] excluded ns, H 200 300 [1012 GeV] excluded ns, H 100 200 φ0 [ 10-9pb 100 200 φ0 [ 10-9pb 100 200 φ0 [ 10-9pb 100 200 φ0 [ 10-9pb 100 200 φ0 [ 10-9pb 100 200 φ0 [ 10-9pb 100 10 pb 100 10 pb 100 10 pb 100 10 pb gµ-2 bound (T) gµ-2 bound (D) 100 10 pb 100 10 pb 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV]

µ

100 200 300 400 500 600 700 800 mφ [GeV] 100 200 300 400 500 600 700 800 mφ [GeV]

800 mSUGRA-LLe, tan β=50, A0=0, µ>0 800 mSUGRA-LLe, tan β=50, A0=0, µ>0 800 mSUGRA-LLe, tan β=50, A0=0, µ>0 800 mSUGRA-LLe, tan β=50, A0=0, µ>0 800 mSUGRA-LLe, tan β=50, A0=0, µ>0 800 mSUGRA-LLe, tan β=50, A0=0, µ>0 800 mSUGRA-LLe, tan β=50, A0=0, µ>0

(Focus point region not shown)

700 800 funnel 10-8pb 700 800 funnel 10-8pb 700 800 funnel 10-8pb 700 800 funnel 10-8pb 700 800 funnel 10-8pb 700 800 funnel 10-8pb 700 800 funnel 10-8pb 500 600 eV] luded stau-coan ns, δH 500 600 eV] luded stau-coan ns, δH 500 600 eV] luded stau-coan ns, δH 500 600 eV] luded stau-coan ns, δH 500 600 eV] luded stau-coan ns, δH 500 600 eV] luded stau-coan ns, δH 500 600 eV] luded stau-coan ns, δH 300 400

0 [1012 GeV

excluded 300 400

0 [1012 GeV

excluded 300 400

0 [1012 GeV

excluded 300 400

0 [1012 GeV

excluded 300 400

0 [1012 GeV

excluded 300 400

0 [1012 GeV

excluded 300 400

0 [1012 GeV

excluded 200 300 φ0 10-9pb 200 300 φ0 10-9pb 200 300 φ0 10-9pb 200 300 φ0 10-9pb 200 300 φ0 10-9pb 200 300 φ0 10-9pb 200 300 φ0 10-9pb 100 10 pb 100 10 pb 100 10 pb 100 10 pb 100 10 pb 100 10 pb 100 10 pb gµ-2 bound (T) gµ-2 bound (D) 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV] 500 1000 1500 2000 mφ [GeV]

Mass measurements at the LHC can also be used to constrain

LHC Role:

Mass measurements at the LHC can also be used to constrain plane.

φ

φ −

m

Consider a SUSY reference point in the co-annihilation region Consider a SUSY reference point in the co annihilation region (all masses are in GeV):

, 40 tan , 350 , 210

2 / 1

= = = = A m m β 329 , 3 . 151 , 7 . 140

2 1

~ ~

= = = ⇒

τ τ χ

m m m

With

• f data LHC can determine high energy parameters:

1

10

−

fb

2 1 1

τ τ χ

With of data, LHC can determine high energy parameters:

16 , 1 40 tan , 4 350 , 4 210

2 / 1

± = ± = ± = ± = A m m β

10 fb

Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback PRL 100, 231802 (2006)

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

R.A., Dutta, Santoso arXiv:1004.2741

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

100 200 300 200 250 300

mφ[GeV] φ0[× 10

12 GeV] udd LLe

General approach: 1) Fi d SUSY 1) Find SUSY. 2) Measure as many masses as possible (sparticles 2) Measure as many masses as possible (sparticles, gauginos). 3) Use RGEs to extrapolate the inflaton mass to high scales. 4) Narrow down the allowed region in plane.

φ

φ −

m

5) Use this to find .

A , λ

(Information about the underlying physics giving rise to higher

• rder term, SUSY breaking sector?)

• MSSM can lead to inflation provides the first example of

Summary:

• MSSM can lead to inflation, provides the first example of

LHC-inflation connection.

• MSSM inflation has three underlying parameters. CMB

measurements alone cannot pinpoint them.

• Particle physics experiments are needed to determine the

parameters.

• Dark matter plus muon can significantly narrow down

the allowed parameter space.

2 − g

• Mass measurements at the LHC are important. Combined

LHC/ILC and PLANCK data can lead to precise determination p

• f the parameters.

1.75 2 1.5 1.75 A2 1 1.25

2n1A

0.75 1 8 m2n 0.25 0.5 13 14 15 16 Log Μ 0.25

300 250 200 150 = mφ

Log Μ

• GeV
• 1600

300 , 250 , 200 , 150 = = A mφ

1.75 2 1.5 1.75 1 1.25 0 m2A2 0.75 1 40 m 0.25 0.5 13 14 15 16 Μ 0.25

2200 2000 1800 1600 A

Log Μ

• GeV
• 400

2200 , 2000 , 1800 , 1600 = =

φ

m A

0.8 0.6 0.8 A2 0.6 0 m2A2 0.4 40 m 0.2 12.5 13 13.5 14 14.5 15 15.5 16 Μ Log Μ

• GeV