1. J. E. Kim Axion theory Jihn E. Kim Seoul National University DESY, Hamburg, 30. 09. 2008

2. J. E. Kim 1.Introduction 2. The LSP is the most popular CDM these days. I present the axion contribution to CDM, which is anyway needed for a strong CP solution. 3. Axions (axions from stars and the universe) 4. SUSY extension and axino (related to neutralino), very brief 2/60

3. J. E. Kim compared to X-ray images(red) Gravitational lensing

4. J. E. Kim WIMP was was first discussed by B. W. Lee and S. Weinberg (1977) just 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 mediators (SUSY particles) are in the 100 GeV range as W boson. That’s the reason we talk about WIMP. Now to many it almost means the LSP. ρ 100 eV 2 GeV m

5. J. E. Kim A rough sketch of masses and cross sections. Bosonic DM with collective motion is always CDM. [Roszkowski, modified]

6. J. E. Kim There are several particle physics candidates for CDM: WIMP: LSP, LKP and other hypothetical heavy particles appearing with Z 2. With the PAMELA data, this class seems the case. But others also exist: axion, axino, gravitino Some of these are related to axion which resulted for a solution of the strong CP problem. It comes from the bound on NEDM which exists if CP is broken. 1

7. J. E. Kim The existence of instanton solution in nonabelian gauge theories needs θ vacuum [CDG, JR]. It introduces the θ 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. 7

8. J. E. Kim 2. Strong CP problem Axion’s attractive strong CP solution is the bottom line in every past and future axion search experiments. So, let us start with the strong CP problem. The instanton solution introduces the so-called θ term, and the resulting NEDM. 8

9. J. E. Kim 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)So, d(proton)= - d(neutron). is the NEDM contribution. In our study, the VEV of pi-zero determine the size of NEDM.

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

11. J. E. Kim We used C A Baker et al, PRL 97, 131801 (06), to obtain → | θ |< 0.7x10 -11 Why is this so small? : Strong CP problem. 1.Calculable θ, 2. Massless up quark (X) 3. Axion [as a new section] 1. Calculable θ 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 θ must be forbidden, and a two-loop generation is acceptable. The weak CP violation must be spontaneous so that θ 0 must be 0. 11

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

13. J. E. Kim 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, Particle Data (2006), p.510 (Manohar-Sachrajda) Excluding the lattice cal., this is convincing that m u =0 is not a solution now.

14. J. E. Kim 3. Axions Kim-Carosi, arXiv:0807.3125 “Axions and the strong CP problem” (Rev. Mod. Phys. Submitted) Historically, Peccei-Quinn tried to mimick the symmetry θ → θ -2α, 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. β=α achieves the same thing as the m=0 case. 14

15. J. E. Kim The Lagrangian is invariant under changing θ → θ -2 α. Thus, it seems that θ is not physical, since it is a phase of the PQ transformation. But, θ is physical. At the Lagrangian level, there seems to be no strong CP problem. But and breaks the PQ global symmetry and there results a Goldstone boson, axion a [Weinberg,Wilczek]. Since θ is made field, the original cos θ dependence becomes the potential of the axion a. If its potential is of the cos θ form, always θ =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 15

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

17. J. E. Kim History: The Peccei-Quinn-Weinber-Wilczek axion is ruled out early in one year [Peccei, 1978]. The PQ symmetry can be incorporated by heavy quarks, using a singlet 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 the SM singlet S, if the VEV of S is much above the electroweak 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. 17

18. J. E. Kim In most studies, a specific example is discussed. Here, we consider an effective theory just above the QCD scale. All heavy fields are integrated out. [Kim-Carosi, arXiv:0807.3125] In axion physics, heavy fermions carrying color charges are special. So consider the following Lagrangian

19. J. E. Kim The axion mass depends only on the combination of (c 2 +c 3 ).

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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): a def. (ii) minimum is at a=0, 2  F a,, 4  F a,, … [PQ, VW] depending on the identification of S in field space The interaction 22

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

24. J. E. Kim The essence of the axion solution is that seeks  =0 whatever happened before. In this sense it is a cosmological solution. The height of the potential is the scale Λ of the nonabelian gauge interaction.

25. J. E. Kim 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: c 1 =0, c 2 =0, c 3 =nonzero DFSZ: c 1 =0, c 2 =nonzero, c 3 =0 PQWW: similar to DFSZ 28

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27. Hadronic coupling is important for the study of supernovae: The chiral symmetry breaking is properly taken into account, using the reparametrization invariance so that c 3 ’=0. KSVZ: DFSZ: The KSVZ axion has been extensively studied. Now the DFSZ axion can be studied, too. 30

28. J. E. Kim General very light axion: Axial vector couplings:

29. J. E. Kim Even if we lowered some F a, we must consider hidden sector also. In this case, axion mixing must be considered. There is an important 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, Λ 1 << Λ 2. Then, diagonalization process chooses the larger condensation scale Λ 2 chooses smaller decay constant F 1, smaller condensation scale Λ 1 chooses larger decay constant F 2. So, just obtaining a small decay constant is not enough. Hidden sector may steal the smaller decay constant. It is likely that the QCD axion chooses the larger decay constant. [See also, I.-W. Kim-K, PLB, 2006] Axion mixing in view of hidden sector 32

30. J. E. Kim An approximate PQ global symmetry with discrete symmetry in SUGRA was pointed out long time ago: for Z 9 given by [L-P-Shafi]. Z 9 is not possible in orbifold compactification. May need Z 3 xZ 3 orbifold. 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.

31. J. E. Kim String models give definite numbers. [I-W Kim-K] 34

32. J. E. Kim Axions from stars  Axion couplings: to e, p, n, and photon. The Primakoff process using the following coupling, Lab. experiments can perform more than just the enegy loss mechanism. The early Tokyo experiment could not give a more stringent bound than the supernova limit, but the CAST(CERN axion solar telescope) could compete with the supernova bound. 35

33. J. E. Kim Compton-like scattering: γe → ae (DFSZ axion has aee coupling) g aee < 2.5x10 –13 0.01eV < m a < 200 keV (cf. DAMA: 3.9x10 –11 m a = 3.2 keV) Hadronic axion window around 2 eV: hot DM constraint with neutrino 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: γ → a (present in any model) g aγγ 10 7 GeV 0.4eV < m a < 200 keV ruled out beyond this, too heavy to produce SN1987A: NN → NNa 3x10 -10 0.6x 10 9 GeV The improved supernova(gl. cl.) limit is 10 9 GeV.

34. J. E. Kim CAST Coll. ( Andriamonje et al.). JCAP 0704:010,2007 Andriamonje et al. The coupling depends on axion models. The numbers are given usually in field theoretic assumptions. F a > 0.5x10^9 GeV at m a <0.39 eV. This can compete with SN1987A constraint. 37

35. J. E. Kim Axions in the universe The axion potential is of the form 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.

36. J. E. Kim The axion is created at T=F a, but the universe  ( )does not roll until 3H=m a (T=0.92 GeV [Bae-Huh-Kim]). From then, the classical field 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 theta 2, rather than theta 1. If F a is large(> 10 12 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,

37. J. E. Kim The axion field evolution eq. and time-varying Lagrangian The adiabatic condition: The adiabatic invariant quantity:

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39. Bae-Huh-Kim, JCAP0809, 005

40. J. E. Kim If we do not take into account the overshoot factor and the anharmonic correction, Inclusion of these showed the region

41. J. E. Kim x=(L/380 MeV) -1

42. J. E. Kim QCD phase transition effect is not important.

43. J. E. Kim Anthropic argument [Pi(84), Tegmark-Aguirre-Rees- Wilczek(05)] Axion field values right after inflation can take any value between [0,π]. So Ω 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 parameters and some dimensionful parameters with which habitable planets 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 physics conditions. For axion, one relevant figure is Q(scalar fluctuation) vs ξ(matter density per CMB photon). If axion is the sole candidate for CDM, the decay constant is shown before. But there may be more favored heavy WIMP candidates pinpointed by PP in which case axions supply the extra needed CDM amount. 46

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

45. J. E. Kim The anthropic region with a GUT scale inflation studied by Hertzberg, Tegmark, Wilczek, 0807.1726

46. J. E. Kim Cosmic axion search If axion is the CDM component of the universe, then they can be detected. K. van Bibber’s efforts. The feeble coupling can be compensated by a huge number of axions. The number density ~ F a 2, and the cross section ~ 1/F a 2, and there is a hope to detect [10 -5 eV range]. Positive for 1 HQ 49

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48. From local density with f aγγ E∙B Future ADMX will cover the interesting region.

49. J. E. Kim Raffelt’s type cartoon

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

51. J. E. Kim The LSP seems the most attractive candidate for DM simply because the TeV order SUSY breaking scale introduces the LSP as a WIMP. This scenario needs an exact 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 conclusion is that there is no theoretical upper bound on the axino mass. For axino to be CDM, it must be stable or practically stable. KeV axinos can be warm DM (90s) [Rajagopal-Turner-Wilczek] GeV axinos can be CDM (00s) [Covi-H. B. Kim-K-Roszkowski]

52. J. E. Kim 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 χ 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

53. J. E. Kim Covi-JEK- H B Kim- Roszkowski Low re-heating Temperature

54. J. E. Kim 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 Ω χ 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 Ωχ 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. 57

55. J. E. Kim If the NLSP is stau with the axino or gravitino LSP, the previously forbidden stau LSP region is erased [Brandenburg, Covi, Hamaguchi, Roszkowski, Steffen]. In this case, the CDM axino is similar to the bino LSP case but it is easier to detect the stau signal due to its em charge at the LHC.

56. J. E. Kim If the axino is heavier than the neutralino, we have a different region of the allowed parameter space [Choi-Kim-Lee-Seto, PRD77, 123501 (2008)], With PAMELA, this possibility is more Important for axino.

57. J. E. Kim 5. Conclusion I reviewed axion and related issues on: 1. Solutions of the strong CP problem: Nelson-Barr, m u =0 ruled out now, axion. 2. Axions can contribute to CDM. Maybe solar axions are easier to detect. Then, axion is not the dominant component of CDM. Most exciting is, its discovery confirms instanton physics of QCD by experiments. 3. With SUSY extension, O(GeV) axino can be CDM. It is difficult to detect this axino from the DM search, but possible to detect at the LHC as missing energy. 4. In any case, to understand the strong CP with axions in SUSY framework the axino must be considered to the CDM discussion.