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 Blanchet, Chacko, Granor, Mohapatra C G arXiv:0904.2174 090 21 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. φ φ It is driven by a scalar field (inflaton): t s d e by a sca a e d ( ato ) φ ( ) V & & H & ′ φ + φ + φ = = 2 3 ( ) 0 V H 2 2 3 3 M M : P H Hubble expansion rate Assumptions: Canonical kinetic terms, minimal coupling to gravity ε η << | |, | | 1 Inflation occurs in the slow-roll regime : V ′ ′ ′ 2 ⎛ ⎛ ⎞ ⎞ 1 1 V V V η ≡ ε ≡ ⎜ ⎜ ⎟ ⎟ 2 2 2 2 M P M P ⎝ ⎠ 2 V V

φ i φ ( , ) Inflation occurs within a field range : e φ a 1 e V ∫ ∫ a = = φ φ e e exp( exp( ) ) N N N N d d ′ tot tot 2 M V φ i P i : : a a S Scale factor of the universe l f t f th i ≥ ≥ N ≈ ≈ − ( ( 30 30 60 60 ) ) N N N needed to explain the isotropy and needed to explain the isotropy and tot COBE flatness problems of the big-bang model. Observable: Density fluctuations (CMB temperature anisotropy). 2 1 H 1 H δ H = = + η − ε 1 2 6 n & π φ s 5 Amplitude Scalar spectral index − ≈ × ± 5 1 . 9 10 0 . 963 0 . 024 (COBE) (WMAP7)

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: ~ ~ ~ ~ ~ ~ + + + + + + L L e u u d d d d ϕ = ϕ = 3 3 (family color and weak isospin indices omitted) (family, color, and weak isospin indices omitted) ϕ = Flat directions: ( ) 0 in MSSM with unbroken SUSY. V SUSY breaking+ Higher order terms: Dine, Randall, Thomas g NPB 458, 291 (1996) ( ) φ φ 6 10 1 ϕ = φ + λ θ + λ 2 2 2 ( ) cos( 6 ) V m A φ φ 3 3 6 6 2 2 M M M M P P φ ϕ ϕ = = exp( θ θ , ~ ( ( ) ) exp( ) ) m m A A O O TeV TeV i i φ 2 soft mass A-term

θ Minimizing the potential along : φ φ φ φ 6 10 1 φ φ = φ φ − λ λ + λ λ 2 2 2 2 2 2 ( ( ) ) V V m A A φ 3 6 2 M M P P φ A point of inflection exists in the potential: 0 1 ⎛ ⎞ 3 4 m M ⎜ ⎜ ⎟ ⎟ φ φ φ ≅ ≅ P ⎜ ⎜ ⎟ ⎟ 0 λ 10 ⎝ ⎠ Provided that: 2 A A α << ≡ + α 2 ( 1 ) 1 4 2 40 m φ

inflation inflation V V φ φ φ 0 0 ′ φ ′ 0 = ( ) 0 V Inflection point ′ φ = α φ 2 2 ( ) 4 V m φ 0 0 4 4 φ = φ 2 2 ( ) V m φ 0 0 15

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 , , , , ( ) m M 8 1 [ ] φ δ ≈ Δ P 2 sin N φ φ Δ Δ H π π COBE 2 2 5 5 0 [ ] = − Δ Δ 1 4 cot n N s COBE ⎛ ⎞ φ φ 1 ( ( 0 ) 0 ) V ⎜ ⎜ ⎟ ⎟ ≈ + + 66 66 . 9 9 ln l N N ⎜ ⎜ ⎟ ⎟ COBE 4 4 ⎝ ⎠ M P 2 ⎛ M ⎛ ⎞ ⎞ 2 A A M ≡ + α ⎜ ⎟ Δ ≡ α 2 1 4 P 30 N ⎜ ⎟ φ 2 COBE 40 m ⎝ ⎠ φ 0

Allowed parameter space to generate acceptable perturbations: − δ ≈ × = ± 5 ( ( 1 . 9 10 , , 0 . 963 0 . 024 ) ) n H H s s 800 800 700 700 700 700 600 600 500 500 [10 12 GeV] [10 12 GeV] 10 − Δ Δ ≤ ≤ 6 400 400 , 10 φ 0 [10 φ 0 [10 300 300 200 200 200 200 100 100 0 0 0 0 500 500 1000 1000 1500 1500 2000 2000 m φ [GeV] m φ [GeV]

Important properties: n 1) within the whole range allowed by WMAP can be generated s (unlike other models of inflation). 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). ( ) δ , H n Two observables: s φ φ Δ Δ λ λ , , , A , m m m m A Three parameters: Three parameters: (can be traded for ) (can be traded for ) φ φ φ 0 0 Oth Other experiments required to fix inflaton parameters i t i d t fi i fl t t

Cosmology/Phenomenology Complementarity: The inflaton mass can be connected to low energy masses The inflaton mass can be connected to low energy masses or input masses via RGEs. ~ ~ ~ ~ + + ~ 2 2 2 2 2 2 + + m m m u d d ~ ~ ~ ⇒ = φ = 2 u d d m φ 3 3 ~ ~ ~ ~ ~ + + + + 2 2 2 m m m L L e ~ ~ ~ φ = ⇒ = 2 e L L m φ 3 3 3 , , , , : M M M gaugino masses g g 1 1 2 2 3 3 , , : g g g gauge couplings 1 2 3

~ ~ ~ + + u d d φ = : R.A., Dutta, Mazumdar PRD 75, 075018 (2007) 3 3 2 ⎛ ⎞ dm 1 2 φ μ = − + ⎜ ⎟ 2 2 2 2 4 M g M g μ μ π π 3 3 1 1 2 ⎝ ⎝ ⎠ ⎠ 6 6 5 5 d d ⎛ ⎞ 1 16 8 dA μ = − + ⎜ ⎟ 2 2 M g M g μ μ π 3 3 1 1 2 ⎝ ⎝ ⎠ ⎠ 4 3 5 d ~ ~ ~ + + + + L L L L e e φ = : 3 2 ⎛ ⎛ ⎞ ⎞ dm dm 1 1 3 3 9 9 φ μ = − + ⎜ ⎟ 2 2 2 2 M g M g μ π 2 2 1 1 2 ⎝ ⎠ 6 2 10 d ⎛ ⎛ ⎞ ⎞ 1 1 3 3 9 9 dA dA μ = − + ⎜ ⎟ 2 2 M g M g μ π 2 2 1 1 2 ⎝ ⎠ 4 2 5 d

The RGEs can be used to map mSUGRA parameter space into φ − φ m plane: R.A., Dutta, Santoso arXiv:1004.2741 0 mSUGRA-udd, tan β =10, A 0 =0, µ >0 mSUGRA-udd, tan β =10, A 0 =0, µ >0 mSUGRA-udd, tan β =10, A 0 =0, µ >0 mSUGRA-udd, tan β =10, A 0 =0, µ >0 mSUGRA-udd, tan β =10, A 0 =0, µ >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 mSUGRA-udd, tan β =10, A =0, >0 mSUGRA-udd, tan β =10, A 0 =0, µ >0 500 500 500 500 500 500 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 10 -8 pb 400 400 400 400 400 400 stau-coan stau-coan stau-coan stau-coan stau-coan stau-coan n , δ n s , δ H n s , δ H n s , δ H n s , δ H n s , δ H n s , δ H n , δ n , δ n , δ n , δ n , δ [10 12 GeV] [10 12 GeV] [10 12 GeV] [10 12 GeV] [10 12 GeV] [10 12 GeV] ] ] ] ] ] ] 300 300 300 300 300 300 excluded excluded excluded excluded excluded excluded φ 0 [10 φ 0 [10 φ 0 [10 φ 0 [10 φ 0 [10 φ 0 [10 200 200 200 200 200 200 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 10 -9 pb 100 100 100 100 100 100 g µ -2 bound (T) g µ -2 bound (D) g µ -2 bound (D) 0 0 0 0 0 0 0 0 0 0 0 0 100 100 100 100 100 100 200 200 200 200 200 200 300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500 600 600 600 600 600 600 700 700 700 700 700 700 800 800 800 800 800 800 m φ [GeV] m φ [GeV] m φ [GeV] m φ [GeV] m φ [GeV] m φ [GeV]