A short review of axion and axino parameters

Transcription

1 A short review of axion and axino parameters Jihn E. Kim Seoul National University Gwangju Institute of Science and Technology Seattle, 25 April 2012

2 What can be there beyond SM? New CP? Axions? SUSY? String? 1. Strong CP and axions 2. Axino mass 3. Pseudoscalar boson at 125 GeV? J E Kim Axion and axino parameters, Seattle, 25 Apr /56

3 Dark matter Axion Supersymmetry observed in the Universe natural sol. of strong CP natural sol. of the iggs mass problem All three are related to this talk. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

4 1. Strong CP and axions Axion is a Goldstone boson arising when the PQ global symmetry is spontaneously broken. PQ symmetry: Wigner-Weyl realization Axion: Nambu-Goldstone realization The axion models have the spontaneous symmetry breaking scale V and the axion decay constant f a which are related by V =N DW f a. ere, I present the general idea on axions and its SUSY partner axino. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

5 A rough sketch of masses and cross sections. Bosonic DM with collective motion is always CDM. [Kim-Carosi, 2008] J E Kim Axion and axino parameters, Seattle, 25 Apr /56

6 The cosmic axion density is, 10 9 GeV < F a < {10 12 GeV?} Turner (86), Grin et al (07), Giudice-Kolb-Riotto (08), Bae-uh-K (JCAP 08, [arxiv: ]): recalculated including the anharmonic term carefully with the new data on light quark masses. It is the basis of using the anthropic argument for a large f a. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

7 Many lab. searches were made, and we hope the axion be discovered. The status was (Kim-Carosi, RMP, 2010) J E Kim Axion and axino parameters, Seattle, 25 Apr /56

8 Strong CP problem The instanton solution introduces the so-called θ term, and the resulting θ bound from NEDM. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

9 Look for the neutron mass term by CPV meson VEVs g πnn i m n m n e iπ / f π The NMDM and NEDM terms The mass term and the NMDM term have the same chiral transformation property. So, (b)s are simultaneously removed. (a) So, d(proton)= - d(neutron). is the NEDM contribution. In our study, so the VEV of pi-zero determine the size of NEDM. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

10 θ < It is an order of magnitude stronger than Crewther et al bound. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

11 The strong CP problem is solved by 1. Calculable, 2. Massless up quark (X) 3. Axion 1. Calculable The Nelson-Barr CP violation ere, the weak CP violation must be spontaneous so that θ0 must be 0. It can be achieved at high energy scale. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

12 2. Massless up quark Suppose that we chiral-transform a quark, q e iγ α 5 q: d d 4 4 θ x mqq + 32π x mqqe 2iγ α 5 2 ~ FF θ 2α ~ + FF 2 32π If m=0, it is equivalent to changing -2α. Thus, there exists a shift symmetry -2α. ere, is not physical, and there is no strong CP problem. The problem is, Is massless up quark phenomenologically viable? J E Kim Axion and axino parameters, Seattle, 25 Apr /56

13 m m u d = 0.5, m m u d = 2.5 1MeV, = 5.1± 1.5MeV (Manohar-Sachrajda) Excluding the lattice cal., this is convincing that m u =0 is not a solution now. Particle Data (2010) J E Kim Axion and axino parameters, Seattle, 25 Apr /56

14 3. Axions istorically, Peccei-Quinn tried to mimick the symmetry -2±, by the full electroweak theory. They found such a symmetry if u is coupled to up-type quarks and d couples to down-type quarks, + + = ), ( d u d R L u R L V d q u q L Eq. β=α achieves the same thing as the m=0 case. + FF d de e u ue e x d e q e q i i d i i u d u i d u i ~ 32 2 }:, { }, { : π α θ α γ β α γ β β α γ J E Kim Axion and axino parameters, Seattle, 25 Apr /56

15 The Lagrangian is invariant under changing -2±. Thus, it seems that is not physical, since it is a phase of the PQ transformation. But, is physical. At the Lagrangian level, there seems to be no strong CP problem. But < u > and < d > breaks the PQ global symmetry and there results a Goldstone boson, axion a [Weinberg,Wilczek]. Since is made field, the original cos dependence becomes the potential of the axion a. If its potential is of the cos form, always =a/fa can be chosen at 0 [Instanton physics,pq,vafa-witten]. So the PQ solution of the strong CP problem is that the vacuum chooses θ = 0 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

16 istorically: The Peccei-Quinn-Weinberg-Wilczek axion is short lived, and the so-called invisible axions [KSVZ, DFSZ] are searched for. KSVZ: L = Q Q S V S,, ) L R ( u d + Now the couplings of S determines the axion interaction. Because it is a Goldstone boson, the couplings are of the derivative form except the anomaly term. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

17 Let the PQ symmetry operator be: Γ When it is realized by the Wigner-Weyl manner, the PQ charged fields ϕ i have PQ quantum numbers, Γ i, Γ φ i = Γ i φ But for axion, we describe in the Nambu- Goldstone manner where Γ is not unitarilly implementable. Still the PQ quantum numbers Γ i of the fields ϕ i are useful since they are just numbers. i J E Kim Axion and axino parameters, Seattle, 25 Apr /56

18 And we use the Nambu-Goldstone fields a i. Let the axion field be in the phase of ϕ which was a linear combination of axion components a i which were in the phase: φ = Σ i c φ The PQ transformation here is the shift of the Nambu-Goldstone fields, i i δa = faδθ J E Kim Axion and axino parameters, Seattle, 25 Apr /56

19 The PQ transformation here is the shift of the Nambu- Goldstone fields, δa = faδθ δa = Γ faδθ i i We obtain the relation, considering the δθ coefficient, to encode the shift symmetry in the Namu-Goldstone phase, e ia / f a Σc i Γ i (number) e iγ i a / f a Where the number is VEV of some field operator. Let the field be ϕ(x) J E Kim Axion and axino parameters, Seattle, 25 Apr /56

20 So, axion a is defined as with < φ > = N DW f a : Φ = ϕ e ia / f [ NG] We use only one a a i c ϕ e i i iγθ i [ WW ] because we need one Γ PQ: WW, axion:ng Two real fields are needed to describe axion with ϕ, a, and ϕ = N f, a = 0. DW If the VEV of a were not zero, it breaks the CP symmetry. a J E Kim Axion and axino parameters, Seattle, 25 Apr /56

21 eavy Q s are Integrated out The axion mass depends only on the combination of (c2+c3). The hadronic axion usually means c1=0, c2=0, c3 0. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

22 t ooft determinental interaction and the solution of the U(1) problem. If the story ends here, the axion is exactly massless. But,. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

23 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

24 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

25 a a a a u F GeV ev F m f Z Z m F a m ] 0.6[ 1 cos = + = Λ π π ) ( = a a F m f Z Z m π π The instanton contribution is included by Δ. Numerically, we use J E Kim Axion and axino parameters, Seattle, 25 Apr /56

26 Axion couplings Above the electroweak scale, we integrate out heavy fields. If colored quarks are integrated out, its effect is appearing as the coefficient of the gluon anomaly. If only bosons are integrated out, there is no anomaly term. Thus, we have KSVZ: c1=0, c2=0, c3=nonzero : hadronic DFSZ: c1=0, c2=nonzero, c3=0 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

27 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

28 adronic coupling is important for the study of supernovae: The chiral symmetry breaking is properly taken into account, using the reparametrization invariance so that c3 =0. KSVZ: DFSZ: The KSVZ axion has been extensively studied. Now the DFSZ axion can be studied, too. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

29 For axion detection, we need to know the axionphoton-photon coupling strength which is parametrized by c aγ γ J E Kim Axion and axino parameters, Seattle, 25 Apr /56

30 String models give definite numbers. [I-W Kim-K] There exist only one calculation in string compactification, In a model explaining all MSSM phenomenology. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

31 Axions in the universe The axion potential is of the form The vacuum stays there for a long time, and oscillates when the ubble time(1/) is larger than the oscillation period(1/m a ) 3 < m a This occurs when the temperature is about 0.92 GeV. [Preskill-Wise-Wilczek; Dine-Fischler, Abbott-Sikivie, 1983] J E Kim Axion and axino parameters, Seattle, 25 Apr /56

32 Bae-uh-Kim, arxiv: [JCAP09 (2009) 005] There is an overshoot factor of 1.8. So we use theta2, rather than theta1. If F a is large(> GeV), then the axion energy density dominates. Since the energy density is proportional to the number density, it behaves like a CDM, but 10 9 GeV < F a <10 12 GeV, J E Kim Axion and axino parameters, Seattle, 25 Apr /56

33 The axion field evolution eq. and time-varying Lagrangian 1 θ + 3 θ + V '( θ ) = 0 2 Fa L = R ( F θ V ( θ )) V = a m 2 a F 2 a (1 cosθ ) The adiabatic condition:, m a m a The adiabatic invariant quantity: θ 2 2 f1( θ ) = dθ ' cosθ ' πθ θ cosθ R 3 2 m a θ f1( θ ) J E Kim Axion and axino parameters, Seattle, 25 Apr /56

34 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

35 Bae-uh-Kim, JCAP0809, 005 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

36 2. Axino mass J E Kim Axion and axino parameters, Seattle, 25 Apr /56

37 Each real field is made SUSY multiplets with ϕ ϕ chiral, a chiral A, The axion a was defined as with < φ > = f a : A/ f v a i A/ fa ΓAϕ Ae = Γiϕ i e, ϕi = vi + ρi V i a ϕ A = V, A = 0. a J E Kim Axion and axino parameters, Seattle, 25 Apr /56

38 The axion is defined in SUSY as 1 N DW v A/ f i ϕ A e Γϕ i i i Va e A/ a f a ϕ ϕ i A = v i = V, a, A = 0 To preserve the shift symmetry of A, SUSY couplings in the Kaehler potential and W are K= function of (A+A*), W(A)=0. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

39 So, the axino mass can be calculated when the Kaehler geometry is completely known. But, we can guess its form, m a~ = ξgoldstino + + ξ gaugino a m terms in Wint ξ gaugino a anomalous I m 3/ 2 If the gravitino mass is not dominating, the axino mass can be calculated in the GMSB scenario. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

40 In the KSVZ model, a two loop diagram can be drawn The axino mass is estimated as We can take it as GeV mass. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

41 In the DFSZ model, a two loop diagram with the top mass gives a much smaller axino mass m m t a~ m, DFSZ a~, KSVZ mq We can take it as about 10 ev mass. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

42 3. iggs boson at 125 GeV? J E Kim Axion and axino parameters, Seattle, 25 Apr /56

43 It seems that there is something new particle is present around 125 GeV. Most probably, it looks like a iggs boson. The SM iggs boson or the lightest or the next lightest scalar iggs boson, or something else? It has to be determined. In SUSY models, many models with a singlet X is introduced. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

44 We point out that a pseudoscalar boson with a singlet X is of general phenomenon. The pseudoscalar possibility of the 125 GeV two photon mode is discussed. In addition, the strong CP problem must be solved. The MSSM cannot do it because μ u d breaks the PQ symmetry. Strong CP solution in NMSSM pseudoscalar at EW JEK+Nilles+Seo, arxiv: J E Kim Axion and axino parameters, Seattle, 25 Apr /56

45 This is a typical example, leading to the EW scale singlet, starting with the PQ symmetry. After the PQ symmetry is broken at the intermediate scale of GeV, there exist the invisible axion. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

46 The invisible axion not explicitly written, ) ( ) ( ' ' ' F S S Z F S S Z X X m X XS mxx X W d u d u = ξ η + + = ew 2 ew EW ~ X f X W d u h d u µ µ Suvives down to the EW scale J E Kim Axion and axino parameters, Seattle, 25 Apr /56

47 In our new language, X ew is the φ type field. It must survive down to the EW scale. The surviving fields are just A and the φ type field. W EW ~ 2 = µ + µ ϕ f ϕ u d h u d + We showed in a specific model that tilde-mu=0. But, the mu term is present and a TeV scale by the Kim- Nilles[PLB 138, 150]. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

48 Remember that SUSY models have no A dependence in the superpotential. Any global symmetry realized at low energy in NG manner includes A. What is the other? In supersymmetrizing its nonsusy part, we double the degrees: supersymmetrize the φ type field and also a field. W = R( S 1 S 2 f 2 a ) S 1 : 2 components S 2 :2 components J E Kim Axion and axino parameters, Seattle, 25 Apr /56

49 Doubling S1 and S2 by φ 1, φ 2, A 1, A 2 Each carries two components. To have the NG global symmetry, we need A= A 1-A 2 in the exponent should not appear. But A = A 1+A 2 in the exponent can appear. It is superheavy and removed at low energy. The same remark applies to φ 1 and φ 2, and only X ew is survives to low energy. This is the counting of degrees in the NG realization of the four components. JEK+Nilles+Seo, arxiv: : A does not appear in W, but X ew appears as X ew u d. And mu-term. If X ew 3 appears, I will be very much surprised. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

50 Now, the EW scale Lagrangian has an additional symmetry, EW X ew f W d u h d u = µ Suvives down to the EW scale Treating mu s as a perturbation, there exists a symmetry ew i ew d i d u i u X e X e e δ δ δ 2, J E Kim Axion and axino parameters, Seattle, 25 Apr /56

51 The chargino (more generally the iggsino pair) has the anomaly current, J 5 µ = ~ γ µ γ 5 ~ µ J 5 µ = α 2 em π F em µν ~ F µν em + 2 µ ~ γ µ γ 5 ~ KNS symmetry from the PQ symmetry: An EW scale light pseudoscalar J E Kim Axion and axino parameters, Seattle, 25 Apr /56

52 The weak gauge boson fusion gives a correct order of the two photon mode. Still solves the strong CP problem by the invisible axion discussed earlier. J E Kim Axion and axino parameters, Seattle, 25 Apr /56

53 J E Kim Axion and axino parameters, Seattle, 25 Apr /56

54 With a singlet X, the scalars take the following mass matrix. With the off-diagonal term, the lightest iggs boson mass can be raised: Without the off-diagonal term, the maximum value of the lightest scalar mass is smaller than that of the MSSM limit M Z (Weinberg s limit). M. Drees, IJMP A4, 3635 (1989) J E Kim Axion and axino parameters, Seattle, 25 Apr /56

55 With the off-diagonal term, the lightest iggs boson mass can be raised: J E Kim Axion and axino parameters, Seattle, 25 Apr /56

56 Conclusion 1. Strong CP solution completes QCD s theoretical ends. 2. Invisible axion, working for DM and can be detected. 3. Axino mass can arise from many sources. 4. Some comments on the LC physics, and set the axion to the recent LC finding. i.e., out of the MSSM. 5. A new approximate anomalous symmetry at the EW scale: iggsino symmetry An EW scale light pseudoscalar for LC, not necessarily for 125 GeV. Watch this!!! J E Kim Axion and axino parameters, Seattle, 25 Apr /56