A natural solution of the μ problem and QCD axion Jihn E. Kim Kyung Hee University (GIST until Feb.) Seoul National University Yong Pyong Workshop Feb. 26, 2013 J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

1. Introduction on the μ problem 2. Higgs-flavor democracy 3. Generation of TeV scale μ 4. Invisible axion 5. On the GUT and string models J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February 2013

1. Introduction on μ J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February 2013

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J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

But the fundamental scalar Higgs boson is needed at the TeV scale: V= -μ 2 Φ*Φ + λ(Φ*Φ) 2 There is no good symmetry to forbid the mass term. So, to have the TeV scale Higgs boson mass parameter, one needs for μ 2 a fine-tuning of order For fermions, there is a chiral symmetry to have a zero mass fermion. So, N=1 SUSY has been introduced, pairing every known particle and its super-partner. We need two Higgs doublets H u and H d to give masses to up- and down-type quarks: J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

With SUSY, two Higgs doublets H u and H d can be light if their SUSY partner Higgsinos are light. But, the chiral symmetry does not work for H u and H d since they form a vector-like representation of the gauge group: Under SU(3)xSU(2)xU(1), So, H u H d is an SU(3)xSU(2)xU(1) singlet and it is allowed. It is the mu term J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

By the survival hypothesis, μ is the GUT scale. Then, SU(2)xU(1) cannot be broken by the VEVs of Higgs doublets. μ must be of order TeV to break the SU(2)xU(1) symmetry of the SM. This is the fine-tuning problem of μ [Kim-Nilles (1984)]: μ/M GUT = When a term is needed to be small, a symmetry is a good starting point to have the term zero. Examples: Gell-Mann-Okubo mass formula: Isospin symmetry Almost zero pion mass squared: chiral symmetry SU(2) L xSU(2) R Almost zero QCD vacuum angle: PQ symmetry J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

For the μ term, a symmetry can be the PQ symmetry. The PQ symmetry is defined by But, we can consider the PQ symmetry preserving term, μ is generated when the PQ symmetry is broken. Kim-Nilles (1984) Chun-K-Nilles (1992) J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

The dim=2 Kaehler potential But, W must preserve the PQ symmetry also, So, KN and GM are related in most cases. Kim-Nilles (1984) Giudice-Masiero (1988) J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

String models do not allow global symmetries, except that of the shift symmetry of the MI axion. Gravitational interaction seems not respecting global symmetries, typically by the wormholes taking out the global charges, effectively breaking the global symmetries. [Barr-Seckel (1992), Kamionkowski-March- Russel (1992), Holman-Hsu-Kephart-Kolb-Watkins- Widrow (1992)] On the other hand, discrete symmetries are allowed in string models. And discrete gauge symmetries can be a subgroup of the gauge symmetries. [Krauss-Wilczek (1989) ] J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

The first step toward obtaining a small mu from a symmetry principle is to have zero value at the lowest order. The next step is to have the corrected value of TeV scale. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

2. Higgs-flavor democracy J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February 2013

H. Harari, H. Haut and J. Weyers, Quark masses and Cabibbo angles, PLB78 (1978) 459; Y. Chikashige, G. Gelmini, R. D. Peccei, and M. Roncadelli, Horizontal symmetries, dynamical symmetry breaking and neutrino masses, PLB94 (1980) 499; P. Kaus and S. Meshkov, A BCS quark mass matrix, MPLA3 (1988) 1251, A4 (1989) 603 (E); H. Fritzsch and J. Plankl, Flavor democracy and the lepton-quark hierarchy, PLB237 (1990) 451. Rank 1 mass matrix : The flavor-democracy leads to masses m t, 0, 0. It was used to obtain a very large top quark mass. We use this idea to obtain a massless Higgs doublet. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

There can be many Higgs doublets. To have the democracy, we extend it with SUSY. So, consider SSM, with many Higgs doublet pairs. To have just one massless doublet pair, we consider models with just two pairs of Higgs doublets: [J. E. Kim, to appear 1303.xxxx] So, the above Higgs-flavor-democracy leads to masses M G, 0. It is the first example obtaining 0 mass pair of Higgs doublets without using a global symmetry. Kim-Nilles and Giudice-Masiero use the PQ symmetry or R symmetry, but no discrete symmetry. We anticipate the following. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

There have been arguments that gravitational interaction does not respect the needed Peccei-Quinn symmetry: S. M. Barr and D. Seckel, Planck scale corrections to axion models, PRD46 (1992) 539; M. Kamionkowski and J. March-Russell, Planck scale physics and the Peccei-Quinn mechanism, PLB282 (1992) 137; R. Holman, S. D. H. Hsu, T. W. Kephart, E. W. Kolb, R. Watkins, and L. M. Widrow, Solutions to the strong CP problem in a world with gravity, PLB282 (1992) 132; S. Ghigna, M. Lusignoli and M. Roncadelli, Instability of the invisible axion, PLB283 (1992) 278; B. A. Dobrescu, The strong CP problem versus Planck scale physics, PRD55 (1997) In addition, strings do not allow global symmetries except that implied by the MI axion. The MI axion decay constant is larger than GeV [CK, PLB154 (1984) 393]. It cannot be the QCD axion whose decay constant is near GeV. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

The S 2 xS 2 symmetry seems needed. So, fermions are the Key. With SUSY, we can relate the Higgs mass to S 2 xS 2. S 2 has singlets as representations. Two singlets can have symmetric and anti-symmetric products. So, the mass term is expected as, Or the superpotential can be written as J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

The S 2 xS 2 symmetry: S 2 (L)xS 2 (R) or S 2 (H u )xS 2 (H d ). Use just S 2 (H u ) : H (1) u  H (2) u, H (2) u  H (1) u, H (1) d  H (1) d, H (2) d  H (2) d, So, we obtain m E = m O, and the democratic form is obtained. S 2 xS 2 symmetry is crucial. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

Now we obtainedNext we try to obtain J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

3. Generationtion of TeV scale μ J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February 2013

In the basis The mass matrix is diagonalized to The new basis are related to the old one by J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

The S 2 symmetry is so powerful that the zero mass state cannot be raised to a massive one if it is not broken. To raise the mass, one has to break the S 2 symmetry, otherwise one cannot raise it. A common S 2 symmetry is needed. Then S 2 symmetry of Higgs doublets can be related to the S 2 symmetry of the X fields. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

We do not need to introduce the tadpole term of X. Somehow a parity may be needed. Then, the following the S 2 xS 2 symmetric term can be considered. To generate the VEVs of X fields, consider the following [Kim, PLB136 (1984) 378, global symmetry breaking W] J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

Possible vaccua: Then, the S 2 xS 2 symmetry can be spontaneously broken. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

So, we can consider the following effective interaction At low energy: Since H (1) u, H (2) u, H (1) d, H (2) d fields couple to the light quarks, they carry the PQ charges. So, X 1 and X 1 -bar fields carry the PQ charge, and at F a the PQ symmetry is broken. With the intermediate scale F a, the mu term is of correct order. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

At low energy, mu is generated, and the mass matrix is J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

We realize the 3 rd column of Fig. For this, we used the same intermediate scale, i.e. F a and μ are related. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

Note that the following diagram is the definition of the effective PQ symmetry at low energy. It is the mu term. The next order correction is J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

So, the 2 nd diagram breaks the PQ symmetry. It is of order: So, the theta parameter is sufficiently small. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

4. Invisible axion J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February 2013

Since H (1) u, H (2) u, H (1) d, H (2) d fields couple to the light quarks, they carry the PQ charges. So, X 1 and X 1 -bar fields carry the PQ charge, and at F a the PQ symmetry is broken. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

Possible vaccua: Then, the S 2 xS 2 symmetry can be spontaneously broken. And mu is raised. And the PQ symmetry is broken at the scale F a. It is the choice of a vacuum, a spontaneous symmetry breaking. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

So, the experimental bound seems very strong and the vacuum angle in must be very small. The idea of very light axion with a sufficiently long lifetime satisfies the particle physics constraints. It means very weak couplings with photon and can contribute the plasma production of axions in stars, and axions survived by now if its mass is below 24 eV. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

The 100 GeV scale DM(WIMP) and the micro eV axion are the most promising candidates for CDM. Neutrinos Light bosons J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

In the evolving universe, at some temperature, say T 1, a starts to roll down to end at the CP conserving point sufficiently closely. This analysis constrains the axion decay constant (upper bound) and the initial VEV of a at T 1. It is very flat if the axion decay constant is large, CP conserving point J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

Bae-Huh-Kim, JCAP0809, 005 mqmq Λ QCD J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

Georg Raffelt, MPI Physics, Munich Axion Cosmophysics, KEK, Tsukuba, 6–9 Nov 2012 Axion Bounds and Searches Directsearches Too much CDM (misalignment) (misalignment) TelescopeExperiments Globular clusters (a-  -coupling) SN 1987A Too many events Too much energy loss Too much hot dark matter CAST ADMX (Seattle & Yale) [GeV] f a eVkeVmeV  eV mama neV Globular clusters (He ignition), WD cooling (a-e coupling) Too much cold dark matter Too much cold dark matter (re-alignment with  i = 1) (re-alignment with  i = 1)String/DWdecay AnthropicRange Axions with meV-range masses? Dark matter Dark matter Cooling of white dwarfs, neutron stars Cooling of white dwarfs, neutron stars Diffuse axion background from SN emission Diffuse axion background from SN emission

By discovering the axion, QCD is completed satisfactorily. If the axion is ruled out at the window, Either, its mass is too small to be detected, or the small-θ problem remains as a fine-tuning. J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45

J E Kim μ and QCD axion, “Workshops”, Yong Pyong & Busan, 26 & 28 Feb On the GUT and string models

J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45 Indeed, there exist models with two pairs of Higgs doublets From string model building. Braun-He-Ovrut-Pantev, JHEP 0605 (2006) 043 Ji-Hun Kim, JEK, B. Kyae, JHEP 0706 (2007) 034 The KKK model gives a GUT based on the flipped SU(5): SU(5)xU(1) X

J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45 SU(5)xU(1) X

J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45 When SU(5) is involved, the doublet-triplet splitting problem exists. It is a chief problem. We also need X=10 1 and X-bar= bar pair, for the GUT breaking. Ellis et al: But the mass matrix in our case will take the form, for colored triplets T, Det=0, and one T mass is vanishing. D-T splitting is not achieved. We must break S 2 xS 2. It can be done.

J E Kim μ and QCD axion, “Workshops”, Yong Pyong & Busan, 26 & 28 Feb Conclusion

J E Kim μ and QCD axion, “Workshops”, Yong Pyong, 26 February /45 1. We achieved 2. We obtained the approximate PQ symmetry and very light axion from a discrete symmetry. Solved the old gravity objection problem. 3. String model with the flipped SU(5) possible. We realize the 3 rd column. For this, we used the same intermediate scale, i.e. F a and μ are related.

J E Kim μ and QCD axion, “Workshops”, Yong Pyong & Busan, 26 & 28 Feb Epilogue: This idea can be applied to the cosmological constant problem. [Choi-Kim-Kyae]