Dark Energy density in Split SUSY models inspired by degenerate - PowerPoint PPT Presentation

Dark Energy density in Split SUSY models inspired by degenerate vacua Roman Nevzorov University of Hawaii , USA in collaboration with C.D.Froggatt and H.B.Nielsen SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 1/16

Outline Introduction No–scale supergravity MPP inspired SUGRA model Cosmological constant in Split SUSY models inspired by degenerate vacua Conclusions Based on: C. D. Froggatt, R. Nevzorov and H. B. Nielsen, arXiv:1103.2146 [hep-ph]; C. D. Froggatt, R. Nevzorov and H. B. Nielsen, Nucl. Phys. B 743 (2006) 133; C. D. Froggatt, L. V. Laperashvili, R. Nevzorov and H. B. Nielsen, Phys. Atom. Nucl. 67 (2004) 582 [arXiv:hep-ph/0310127]. SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 2/16

Introduction Astrophysical and cosmological observations indicate that there is a dark energy spread all over the Universe which constitutes 70% − 73% of its energy density Z ∼ (10 − 3 eV ) 4 . ρ Λ ∼ 10 − 123 M 4 Pl ∼ 10 − 55 M 4 In the SM much larger contributions to ρ Λ must come from gluon condensate and EW symmetry breaking ρ EW ∼ v 4 ≃ 10 − 62 M 4 ρ QCD ∼ Λ 4 QCD ≃ 10 − 74 M 4 Pl , Pl . But the contribution of zero–modes is expected to push total vacuum energy density even higher up to M 4 Pl , i.e. ω b ω f � � ρ Λ ≃ 2 − 2 = b f � d 3 � � Λ �� k � � k | 2 + m 2 k | 2 + m 2 | � � | � 2(2 π ) 3 ≃ − Λ 4 . = b − f 0 b f SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 3/16

Because of the enormous cancellation between the contributions of different condensates to ρ Λ the smallness of the cosmological constant should be regarded as a fine–tuning problem. An exact global supersymmetry ensures zero value for the vacuum energy density. But supersymmetry must be broken. The breakdown of SUSY induces a huge and positive contribution to ρ Λ ρ Λ ∼ Λ 4 SUSY , where Λ SUSY is a SUSY breaking scale. The non–observation of squarks and sleptons implies that Λ SUSY >> 100 GeV. SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 4/16

No–scale supergravity The scalar potential in ( N = 1) SUGRA models is specified in terms of the K ¨ a hler function M ) + ln | W ( φ M ) | 2 . G ( φ M , φ ∗ M ) = K ( φ M , φ ∗ The SUGRA scalar potential is given by + 1 N e G � � a ( D a ) 2 , G M G M ¯ N G ¯ M ) = � � V ( φ M , φ ∗ N − 3 M, ¯ 2 N = G − 1 G M ¯ G M ≡ ∂G/∂φ M , G ¯ M ≡ ∂G/∂φ ∗ M , NM , ¯ D a = g a G i T a � � � ij φ j . i, j SUGRA models include singlet fields which form hidden sector that gives rise to the breaking of local SUSY and induces non-zero gravitino mass m 3 / 2 = < e G/ 2 > In SUGRA models ρ Λ ∼ − < e G > . SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 5/16

The Lagrangian of the simplest no–scale SUGRA model is invariant under imaginary translations T → T + iβ , ϕ σ → ϕ σ and dilatations T → α 2 T , ϕ σ → α ϕ σ . The invariance under imaginary translations and dilatations constrain K ¨ a hler function � � 1 � � ζ σ | ϕ σ | 2 K = − 3 ln T + T − , W = 6 Y σλγ ϕ σ ϕ λ ϕ γ . σ σ,λ,γ Global symmetries ensure the vanishing of vacuum energy density in the no–scale SUGRA models. These symmetries also preserve supersymmetry in all vacua. SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 6/16

MPP inspired SUGRA model In order to achieve the appropriate breakdown of local supersymmetry dilatation invariance must be broken. Let us consider SUGRA model with two hidden sector fields that transform differently under the dilatations T → α 2 T , z → α z and imaginary translations T → T + iβ , z → z . We allow the breakdown of dilatation invariance in the superpotential of the hidden sector ∞ � � 1 z 3 + µ 0 z 2 + � � c n z n W ( z, ϕ α ) = κ + 6 Y σλγ ϕ σ ϕ λ ϕ γ , n =4 σ,λ,γ where µ 0 and c n ∼ 1 . SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 7/16

We also assume that the dilatation invariance is broken in the K ¨ a hler potential of the observable sector � � � η σλ � ξ σ | ϕ σ | 2 . � � � T + T −| z | 2 − ζ σ | ϕ σ | 2 K = − 3 ln + 2 ϕ σ ϕ λ + h.c. + σ σ σ,λ Such breakdown of global symmetry preserves a zero value of the energy density in all vacua. The scalar potential of the hidden sector takes a form 2 � � 1 ∂W ( z ) � � V ( T, z ) = . � � 3( T + T − | z | 2 ) 2 ∂z � � When c n = 0 this SUGRA scalar potential has two minima with zero vacuum energy density z = − 2 µ 0 z = 0 , 3 . SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 8/16

In the vacuum where z = − 2 µ 0 3 local supersymmetry is broken and gravitino gets a non–zero mass: 4 κ µ 3 0 m 3 / 2 = � 3 / 2 � . T + T − 4 µ 2 �� 0 27 9 At low energies the interactions of observable superfields ˆ y α in this vacuum are described by the effective superpotential µ αβ h αβγ W eff = � y β + � y α ˆ ˆ y α ˆ ˆ y β ˆ y γ , α, β α, β, γ 2 6 Y αβγ ( C α C β C γ ) − 1 / 2 m 3 / 2 η αβ µ αβ = ( C α C β ) 1 / 2 , h αβγ = < ( T + T − | z | 2 ) 3 / 2 > , x α = ξ α < ( T + T − | z | 2 ) > � � 1 + 1 C α = ξ α , . x α 3 ζ α The effective scalar potential of the observable sector is given by 2 � � ∂W eff ( y β ) + 1 x α � � a ( D a ) 2 , V eff ≃ � � + m α y ∗ m α = m 3 / 2 (1 + x α ) . � α � α ∂y α 2 � � SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 9/16

In the vacuum with z = 0 local SUSY remains intact and the low–energy limit of this theory is described by a pure SUSY model in flat Minkowski space. If the high order terms c n z n are present in the superpotential, V ( T, z ) may have many degenerate vacua with broken and unbroken SUSY which energy density vanishes. Then the vanishing of ρ Λ can be considered as a result of degeneracy of all possible vacua in the considered theory, one of which is supersymmetric with < W > = 0 . Thus the breakdown of global symmetries that ensures the vanishing of ρ Λ leads to the natural realization of the multiple point principle (MPP). SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 10/16

MPP postulates the existence of many phases with the same energy density which are allowed by a given theory. Being applied to supergravity MPP implies the existence of a phase with global SUSY in flat Minkowski space. Such vacuum is realised only if SUGRA scalar potential has a minimum where the following conditions are satisfied � � � ∂ W ( z i ) � W ( z 0 i ) = = 0 , ∂z j z i = z 0 i that requires an extra fine-tuning in general. In the SUGRA models based on the weakly broken dilatation invariance the MPP conditions are fulfilled without any extra fine-tuning. SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 11/16

Cosmological constant According to MPP the physical and supersymmetric vacua have the same energy density. Since the vacuum energy density of supersymmetric states in flat Minkowski space is zero ρ Λ in the physical vacuum vanishes in the leading approximation. However non–perturbative effects in the observable sector may lead to the breakdown of SUSY in the supersymmetric phase. In SUSY phase α 3 ( Q ) increases in the infrared region enhancing a role of non–perturbative effects. Top quark Yukawa coupling grows with increasing of α 3 ( Q ) that may induce top quark condensate at the scale Λ SQCD . Top quark condensate breaks SUSY resulting in positive value of the cosmological constant ρ Λ ≃ Λ 4 SQCD . SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 12/16

We assume that at high energy scale the gauge and Yukawa couplings are the same in both vacua. Since f a ( T, z ) ≃ const the gauginos are substantially lighter than scalar particles, i.e. M a ≪ m α . Such a hierarchical structure of the particle spectrum appears in the models with Split Supersymmetry. In the supersymmetric vacuum the QCD interaction becomes strong at � � 2 π Λ SQCD = M S exp , b 3 α (2) 3 ( M S ) ˜ 4 π ln M 2 4 π ln M 2 1 1 b 3 − b ′ g 3 S = − , M 2 α (2) α (1) M 2 3 ( M S ) 3 ( M Z ) g Z where ˜ b 3 = − 7 , b 3 = − 3 and b ′ 3 = − 5 are the beta functions of α 3 ( Q ) in the SM, MSSM and Split SUSY, while M g is a gluino mass. SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 13/16

For α 3 ( M Z ) = 0 . 116 − 0 . 121 and M g = 500 − 2500 GeV the measured value of the cosmological constant is reproduced when M S = 0 . 2 − 3 · 10 10 GeV. log[Λ SQCD /M P l ] � 26 � 28 � 30 � 32 � 34 � 36 � 38 � 40 4 6 8 10 log[ M S ] SUSY11, Fermilab, Batavia IL, USA, August 28 — September 2, 2011 – p. 14/16