Jihn E. Kim Seoul National University. Padova, J. E. Kim

Transcription

1 Jihn E. Kim Seoul National University Padova,

2 1. Introduction 2. The LSP is the most popular these days. I pres ent the axion contribution to CDM, which is an yway needed for a strong CP solution. 3. Axions, axions from stars and the universe 4. SUSY extension and axino (related to neutr.) 5. Conclusion

3 compared to X-ray images(red) Gravitational lensing

4 WIMP was was first discussed by B. W. Lee and S. Weinberg (1977) ju st two months before Ben was killed by a traffic accident. They considered a heavy neutrino, which implies that the usage weak is involved. The LSP interaction is weak if interaction mediat ors (SUSY particles) are in the 100 GeV range as W boson. That s t he reason we talk about WIMP. Now it almost means the LSP. 100 ev 2 GeV m

5 A rough sketch of masses and cross sections. Bosonic DM with collective motion is always CDM.

6 There are several particle physics candidates for CDM: WIMP: LSP, LKP and other hypothetical heavy particles appearing with Z 2. Others: axion, axino, gravitino Some of these are related to axion which resulted for a solution of the strong CP problem. Strong interaction preserves CP. NEDM exists if CP is broken.

7 The existence of instanton solution in nonabelian gauge theories needs vacuum [CDG, JR]. It introduces the term, Here theta-bar is the final value taking into account the electroweak CP violation. For QCD to become a correct theory, this CP violation must be sufficiently suppressed.

8 2. Strong CP problem Let us start with the axion s role in the sol ution of the strong CP problem. Its attra ctive strong CP solution is the bottom lin e in every past and future axion search experiments. So, let us start with the str ong CP problem. The instanton solution introduces the so-called term, and the resulting NEDM.

9 The neutron mass term 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) is the NEDM contribution. So, d(proton)= - d(neutron). The VEV of pi-zero determine the size of NEDM.

10 It is an order of magnitude larger than Crewther et al bound.

11 We used C A Baker et al, PRL 97, (06), to o btain < 0.7x10-11 Why is this so small? : Strong CP problem. 1. Calculable, 2. Massless up quark (X) 3. Axion [as a new section] 1. Calculable The Nelson-Barr CP violation is done by introducing vectorlike heavy quarks at high energy. This model produces the KM type weak CP violation at low energy. Still, at one loop the appearance of must be forbidden, and a two-loop generation is acceptable. The weak CP violation must be spontaneous so that 0 must be 0.

12 2. Massless up quark Suppose that we chiral-transform a quark, If m=0, it is equivalent to changing -2. Thus, there exists a shift symmetry -2. Here, is not physical, and there is no strong CP problem. The problem is, Is massless up quark phenomenologically viable?

13 The famous up/down quark mass ratio from chiral pert. calculation is originally given as 5/9 [Weinberg, Leutwyler] which is very similar to the recent compilation, (Manohar-Sachrajda) Excluding the lattice cal., this is convincing that m u =0 is not a solution now. Particle Data (2006), p.510

14 3. Axions Kim-Carosi, arxiv: Axions and the strong CP problem (Rev. Mod. Phys. Submitted) Historically, Peccei-Quinn tried to mimick the symmetry -2, by the full electroweak theory. They found such a symmetry if H u is coupled to up-type quarks and H d couples to down-type quarks, Eq. = achieves the same thing as the m=0 case.

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, which can be seen from the free energy dependence on cos. At the Lagrangian level, there seems to be no strong CP problem. But <H u > and <H 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

16 t Hooft determinental interaction and the solution of the U(1) problem. If the story ends here, the axion is exactly massless. But,.

17 History: The Peccei-Quinn-Weinber-Wilczek axion is ruled out early in one year [Peccei, 1978]. The PQ symmet ry can be incorporated by heavy quarks, using a singl et Higgs field [KSVZ axion] Here, Higgs doublets are neutral under PQ. If they are not neutral, then it is not necessary to introduce heavy quarks [DFSZ]. In any case, the axion is the phase of t he SM singlet S, if the VEV of S is much above the ele ctroweak scale. 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.

18 In most studies, a specific example is discuss ed. Here, consider an effective theory just abo ve the QCD scale. All heavy fields are integrat ed out. [Kim-Carosi, arxiv: ] In axion physics, heavy fermions carrying colo r charges are special. So consider the followin g Lagrangian

19 The axion mass depends only on the combination of (c2+c3).

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22 The potential arising from the anomaly term after integrating out the gluon field is the axion potential. Two properties: (i) periodic potential with 2 F a period (Pontryagin) (ii) minimum is at a=0, 2 F a,, 4 F a,, [PQ, VW] The interaction

23 Leading to the cos form determines the axion mass The instanton contribution is included by Delta. Numerically, we use

24 The essence of the axion solution is that <a> seeks =0 whatever happened before. In this sense it is a cosmological solution. The height of the potential is the s cale of the nonabelian gauge interaction.

25 For models, the complex SU(2) singlet scalar field S ma y contain very tiny SU(2) doublet components (<10-7 ), and practically we can consider the axion as the pha se of S (DFSZ), Since the DW number appears in the phase of S, F a can be in general equal to or smaller than <2 1/2 S>.

26 Axion is directly related to. Its birth was from the P Q symmetry whose spontaneous breaking introd uced a boson. However, we can define axion as a pseudoscalar a without potential except that ar ising from the theta term Then this nonrenor. term can arise in several ways F a From string theory or M-theory : Planck scale Large extra dimensions, cf. M Pl =M D (R/M D )n/2 Depends on R From composite models : Comp. scale From renormalizable theories: Goldstone boson(global symm.) coupl. Glob. sym. break. scale to the one-loop gluon anomaly.

27 A similar axion-photon-photon ae B term is present in any axion model with a coefficient Old lab bounds: Meson decays J/ a+, a, K + +a, Beam dump experiments p(e - )N ax, a, e + e - Nuclear deexcitation N* Na, a, e + e -

28 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 DFSZ: c1=0, c2=nonzero, c3=0 PQWW: similar to DFSZ

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30 Hadronic 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.

31 General very light axion: Axial vector couplings:

32 Axion mixing Even if we lowered some F a, we must consider hidden sector also. In this case, axion mixing must be considered. There is an impo rtant theorem. Cross theorem on decay constant and condensation scales [K99]: Suppose two axions a 1 with F 1 and a 2 with F 2 (F 1 <<F 2 ) couples to two nonabelian groups whose scales have a hierarchy, 1 << 2. Then, diagonalization process chooses the larger condensation scale 2 chooses smaller decay constant F 1, smaller condensation scale 1 chooses larger decay constant F 2. So, just obtaining a small decay constant is not enough. Hidden se ctor may steal the smaller decay constant. It is likely that the QC D axion chooses the larger decay constant. [See also, I.-W. Kim -K, PLB, 2006]

33 In this regard, we point out that the MI-axion with anomalous U(1) always has a large decay constant since all fields are charged under this anomalous U(1). Phenomenologically successful axion must need the approximate PQ. An approximate PQ global symmetry with discrete symmetr y in SUGRA was pointed out long time ago: for Z 9 give n by [L-P-Shafi]. Z 9 is not possible in orbifold compactific ation. May need Z 3 xz 3 orbifold.

34 String models g ive definite num bers. [I-W Kim- K]

35 Lab. experiments can perform more than just the enegy loss mech anism. The early Tokyo experiment could not give a more stringent bound than the supernova limit, but the CAST(CERN axion solar t elescope) could compete with the supernova bound.

36 In the hot plasma in stars, axions once produced most probably escape the core of the star and take out energy. This contributes to the energy loss mechanism of star and should not dominate the luminocity. The Primakoff process: a (present in any model) g a < 0.6x GeV -1 or F a > 10 7 GeV 0.4eV < m a < 200 kev ruled out beyond this, too heavy to produce Compton-like scattering: e ae (DFSZ axion has aee coupling) g aee < 2.5x eV < m a < 200 kev (cf. DAMA: 3.9x10 11 m a = 3.2 kev) SN1987A: NN NNa 3x10-10 < g ann < 3x 10-7 Fa > 0.6x 10 9 GeV The improved supernova(gl. cl.) limit is 10 9 GeV.

37 CAST Coll. ( Andriamonje et a l.). JCAP 0704:01 0,2007 The coupling depends on axion models. The numbers are given u sually in field theoretic as sumptions. Fa> 0.5x10^9 GeV at ma<0.39 ev. Biljana Lakic (CAST), nex t talk CAST. This can compete with SN1987A constraint.

38 The vacuum stays there for a long time, and oscillates when the Hubble time(1/h) is larger than the oscillation period(1/m a ) 3H < m a This occurs when the temperature is about 0.92 GeV.

39 The axion is created at T=F a, but the universe (<a>)does not roll until 3H=m a (T=0.92 GeV [Bae-Huh-Kim]). From the n, the classical field <a> starts to oscillate. Harmonic oscillator m a 2 F a 2 = energy density = m a x number density = like CDM. See, Bae-Huh-Kim, 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 9 GeV < F a <10 12 GeV,

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42 Bae-Huh-Kim

43 If we do not take into account the overshoot factor and the anharmonic correction, Inclusion of these showed the region

44 x=(l/380 MeV) -1

45 QCD phase transition effect is not important.

46 Anthropic argument [Pi(84), Tegmark-Aguirre-Rees-Wilczek(05 )] Axion field values right after inflation can take any value between [0, ]. So a may be at the required value by an appropriate misalignment angle for any F a in the new inflation scenario. [Pi(84)] Tegmark et al studied the landscape scenario for 31 dimensionless pa rameters and some dimensionful parameters with which habitable pl anets are constrained. They argue that for axion the prior probability function is calculable for axion models, which is rather obvious. Equally probable to sit anywhere here They considered astrophysical conditions and nuclear phy sics conditions. For axion, one relevant figure is Q(scalar fluctuation) vs (matter density per CMB photon). If axio n is the sole candidate for CDM, the decay constant is sh own before. But there may be more favored heavy WIMP candidates in which case axions supply the extra neede d CDM amount.

47 Tegmark, Aguirre, Rees, Wilczek, PRD (2005) Q=scalar fluctuation amplitude H on horizon, (2 0.2)x10-5 WIMP may be dominantly CDM, and the rest is provided by axion.

48 The anthropic region with a GUT scale infl ation studied by Hertzberg, Tegmark, Wilczek,

49 Cosmic axion search If axion is the CDM component of the universe, then they can be detected. K. van Bibber s talk. The feeble coupling can be compensated by a huge number of axions. The number density ~ F a2, and the cross section ~ 1/F a2, and there is a hope to detect [10-5 ev range]. Positive for 1 HQ

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51 From local density with f a E B Future ADMX will cover the interesting region.

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53 4. SUSY extension and axino The gravitino constraint: gravitinos produced thermall y after inflation decays very late in cosmic time sc ale (>10 3 sec) and can dissociate the light nuclei b y its decay products. Not to have too many gravitin os, the reheating temperature must be bounded, T R < 10 9 GeV(old), or 10 7 GeV(recent) Thus, in SUSY theories we must consider the relatively small reheating temperature. Strong CP solution and SUSY: axion : implies a superpartner axino

54 The LSP seems the most attractive candidate for DM simply because the TeV order SUSY breaking scale i ntroduces the LSP as a WIMP. This scenario needs an ex act or effective R-parity for it to be sufficiently long lived. Story changes if one wants to solve the strong CP prob. For axino to be LSP, it must be lighter than the lightest neutralino. The axino mass is of prime importance. The co nclusion is that there is no theoretical upper bound on the axino mass. For axino to be CDM, it must be stable or pr actically stable. KeV axinos can be warm DM (90s) [Rajagopal-Turner-Wilczek] GeV axinos can be CDM (00s) [Covi-H. B. Kim-K-Roszkowski]

55 Gravitino problem is resolved if gravitino is NLSP, since the TP gravitinos would decay to axino and axion which do not affect BBN produced light elements. [Ellis et al, Moroi et al] On the other hand, if is NLSP(=LOSP), the TP mechanism restricts the reheating temperature after inflation. At high reheating temperature, TP contributes dominantly in the axino production.if the reheating temperature is below c. energy density line, there still exists the CDM possibility by the NTP axinos. [Covi et al] NTP for

56 Covi-JEK- H B Kim- Roszkowski Low re-heating Temperature

57 In this figure, NTP axinos can be CDM for relatively low reheating temperature < 10 TeV, in the region NTP axino as CDM possibility The shaded region corresponds to the MSSM models with h 2 < 10 4, but a small axino mass renders the possibility of axino closing the universe or just 30 % of the energy density. If all SUSY mass parameters are below 1 TeV, then h 2 <100 and sufficient axino energy density requires If LHC does not detect the neutralino needed for closing the universe, the axino closing is a possibility.

58 If the axino is heavier than the neutralino, we have a different region of the allowed parameter space [Choi-Kim-Lee-Seto, PRD77, (2008)],

59 5. Conclusion The CDM candidates are WIMPs and very light axions. We k now that they must fill the universe based on the observati onal grounds and we exist here in a galaxy. There may be ways to distinguish them (WMAP haze?). Direct searches for WIMPs in the universe use the seasonal modulation of WIMP cross section in our environment. Th e LHC machine will tell whether the neutralino mass falls i n the CDM needed range or not. The strong CP sol. needs a very light axion. Whether it is the dominant DCM component or not, it is believed that it exist s. In this framework, the axino plays a crucial role in cosmology, but more difficult to be detected at LHC.

60 I reviewed axion and related issues on: 1. Solutions of the strong CP problem: Nelson-Barr, m u =0 r uled out now, axion. 2. Axions can contribute to CDM. Maybe solar axions are e asier to detect. Then, axion is not the dominant compon ent of CDM. Most exciting is, its discovery confirms insta nton physics of QCD by experiments. 3. With SUSY extension, O(GeV) axino can be CDM. It is d ifficult to detect this axino from the DM search, but possib le to detect at the LHC as missing energy.