Mirror World and Improved Naturalness

Transcription

1 Mirror World and Improved Naturalness Thomas Grégoire Boston University Based on hep-ph/ R. Barbieri, T.G., L. Hall

2 Mirror Worlds Motivations Originally introduced to restore parity Dark Matter could be made of Mirror particles Problems Cannot be at the same temperature at nucleosynthesis. Need different initial temperature, and baryon asymmetry.

3 Dark matter halo cool. LEP Paradox Electroweak precision constraints test physics at scales higher than 1 TeV: 7 10TeV vs We need new physics at 1 TeV to stabilize the weak scale

4 Setup Mirror world L = L SM (φ A ) + L SM (φ B ) Z 2 : φ A φ B Consistently with ɛ B µν Z 2, we could add A B Bµν + λ h A 2 h B 2 ɛ Dangerous : photon-photon mixing.

5 Bound on ɛ : From cosmology: ɛ < 10 8 Bounds on λ : Depends on the reheating temperature Another approach : break later Z 2, more on this We study the consequences of taking λ O(1)

6 A large λ does not re-introduced significant ɛ Separate charge conjugation in the two sectors Need more than 4-loops diagrams.

7 Higgs Potential: ( h A 2 + h B 2) + δ > 0 : symmetric phase. ( h A 2 + h B 2) 2 + ( h A 4 + h B 4) µ 2 λ δ h A = h B = v Z 2 unbroken.the two Higgses mix v 2 µ 2 = 2(2λ + δ) m 2 + = 2µ 2 = 4v 2 (2λ + δ) m 2 = 2µ 2 δ 2λ + δ = 4δv2

8 with: h + = 1/ 2(h A + h B ) h = 1/ 2(h A h B ) Naturalness Only µ 2 gets a quadratic divergence: Z 2 In the Standard Model Quadratic divergence from top quark : µ 2 = µ a t Λ 2 t a t = 3λ2 t 8π 2

9 The Higgs mass is given by: m 2 h = 2µ 2 Fine-tuning: D t = ln m2 h ln Λ 2 t = a t Λ 2 t µ 2 Cutoff: Λ t = 400GeV ( mh 115GeV ) D 1/2 t

10 In the mirror world: D t = ln v2 ln Λ 2 t = ln m2 ± ln Λ 2 t Λ M t = a t µ 2 2 cutoff: Λ M t = 2π 3λt m + D 1/2 t The higher, the higher the cutoff. Limit on from electroweak precision measurements. m + m +

11 h + h The SM result log m h becomes 1 2 log m log m The limit on the mirror world Higgs masses become: m + m < m 2 EW m EW = 207GeV is the SM limit on the Higgs mass

12 Λ M t = 2π ( ) 2 mew m D 1/2 t 3λt m m Identify with m h of the SM Cutoff-scale can be raised by a factor: Λ M t Λ SM t ( 120GeV 3 m ) 2 with D t 4, we get Λ M t 2.5TeV

13 Cutoff from Higgs self coupling: In Standard model µ 2 = µ 2 0 a H Λ 2 H a H = 3λ 8π 2 Λ M H = 4π 3 vd 1/2 H 1.3TeVD1/2 H Raising the Higgs mass means raising help λ : does not

14 Adding asymmetric term V (h A, h B ) Z2 + m 2 ( h A 2 h B 2) h A = ( 0 v A ) h B = ( 0 v B ) v 2 A + v 2 B = µ2 2λ + δ v 2 B v 2 A = 1 + y 1 y y = m2 2λ + δ µ 2 δ Hierarchy between v A and v B : fine-tune y

15 The mass eigenstates are: h + = sin θh A + cos θh B h = cos θh A sin θh B Naturalness: Expressions for a H and are the same as before Λ M t = tan θ = v A /v B m 2 + = 2µ 2 m 2 = µ 2 δ λ (1 y2 ) 2π 3λt m + D 1/2 t a t Λ M H = 4πv 1 + v2 B 5 va 2 D 1/2 H

16 But constraints from EWPT are different log m h cos 2 θ log m + sin 2 θ log m + SM Max for m + Mirror increase exponentially with m + < m ( mew m ) 1+ v 2 B v 2 A v B /v A Can push m + v B v A 2 high without too much fine-tuning: m + 1.7TeV Λ M t = 6.2TeVD 1/2 t

17 LHC Decay to invisible modes significant In the exact Z 2 case, λ A = λ B Br(h X invisible ) = 1 2 Br(h X) SM Br(h X visible ) = 1 2 Br(h X) SM Total width unchanged for h For h +, the channel h + h h might be open

18 Branching ratio WW 0.2 h- h- 0.1 t t m = 110GeV GeV m +

19 Cosmology There are light particle in the mirror world: photon, electron, neutrino : bad for nucleosynthesis Could be ok with very low reheating temperature. T reheat few GeV Ignatiev, Volkas

20 Break the Z 2 in the light Fermions sector. λ f A Ψ A f h AΨ A f +λ f B Ψ B f h BΨ B f f top A e, 3ν, g, γ, c, s, u, d 5 GeV A - B coupled A - B decoupled B 3ν, g, γ nucleosynthesis

21 Part of the particle content in the visible sector become non-relativistic and reheat the visible sector only At the end of the day, at nucleosynthesis: T A > T B In term of equivalent number of neutrino: Disfavored... N ν = 1.4

22 Dark matter Can the mirror world be the dark matter? If the lightest mirror fermions are: e B, u B, d B with mass above the Dark matter can be: QCD B scale N B (u B d B d B ), B (d Bd B d B )e + B, ++ B (u Bu B u B )e B e B

23 If the baryon asymmetries are the same: η A = η B and the mass scale of Right abundance N B + B B is 5 GeV Dark matter halo do not cool

24 Conlusions We studied a mirror world that communicate only through Higgs quartic coupling Naturalness can be improved with respect to the Standard Model Higgs physics at the LHC is very different Production of Higgs is reduced Invisible decay branching fraction significant

25 Cosmology: Breaking the exchange symmetry is good for nucleosynthesis (maybe not enough) Mirror world baryons could be the dark matter.