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**Kiwoon Choi PQ-invariant multi-singlet NMSSM**

with anomalous U(1) gauge symmetry Kiwoon Choi The IBS Center for Theoretical Physics of the Universe KIAS-NCTS Workshop 2014

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**Outline 2. Singlet extension of the MSSM with U(1)PQ originating from**

1. Introduction and motivation 2. Singlet extension of the MSSM with U(1)PQ originating from an anomalous U(1) gauge symmetry: * 126 GeV Higgs boson with a minimal fine tuning * Generation of an intermediate PQ scale: * Natural solution to - SUSY flavor problem - μ problem - Cosmological moduli problem 3. A specific form of the minimal model with two singlets 4. Conclusion

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**Introduction and motivation**

The Standard Model (SM) of particle physics is now completed, however it is certain that the SM is not the final story, but merely a low energy effective theory of certain form of more fundamental theory. Empirical evidences for physics beyond the SM (BSM physics): * Non-baryonic dark matter * Matter-antimatter asymmetry in our Universe * Neutrino masses * Inflation in the early Universe Incomplete or unnatural features of the SM: * Lack of the unification & quantum gravity * Fine-tuning problems: - Gauge hierarchy problem: - Strong CP problem:

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**What is the next energy scale of BSM physics?**

Unfortunately, empirical evidences for BSM physics do not provide yet a useful hint to this question. Either there are so many different possibilities, or the suggested scale of BSM physics is too high to be experimentally probed. * Dark matter: 10-22 eV (Clumping within galaxy) < mDM < 1060 eV (MACHO search) Long list of the candidates with a vast range of the interaction rate: WIMP, Axions, Fuzzy CDM, Gravitinos, Axinos, Higgs-portal, Q-balls, WIMPzillas, Branons, Primordial Black Holes, …. * Neutrino masses: ΛBSM ≤ 1015 GeV * Matter-antimatter asymmetry: ΛBSM ≤ 1016 GeV * Early Universe inflation: ΛBSM ≤ 1016 GeV

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What to do? * Search for the rare signals of the SM particles, reflecting the next BSM scale: Precision measurement of the Higgs and EW gauge bosons: EDM and (g-2): Flavor changing processes: * Search for new particles This requires a guideline, and at the moment, the best motivated new particles are those associated with the solutions of the fine tuning problems of the SM: Gauge hierarchy problem and Strong CP problem SUSY particles (including the WIMP DM) and axion DM

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**Gauge hierarchy problem:**

* 𝑆𝑈 5 ⊃𝑆𝑈(3)×𝑆𝑈(2)×𝑈 1 Grand unification at MGUT ~ 1014 – 1016 GeV * Non-renormalizable gravitational interactions: Quantum gravity at scales around MPlanck ~ 1018 GeV Radiative corrections to the Higgs boson mass when nothing happens between mH and MGUT : This requires a fine-tuning of UV physics H at the level of Then why mH << MGUT , MPlanck ?

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**Strong CP problem: CP violation in the SM: (η’ meson mass) ,**

, (neutron EDM) |θQCD+ Arg Det(yq)| < 10-10 Why |θQCD+ Arg Det(yq)| < 10-10, while δKM ~ Arg (yq) ~ 1 ?

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**SUSY as a solution to the gauge hierarchy problem**

Supersymmetry SUSY particles Fermi-Bose cancellation in the Higgs boson self energy: mSUSY = SUSY particle masses, particularly mstop and mgluino With SUSY, the Higgs boson mass can be as light as mSUSY without a fine-tuning of UV physics.

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**Implications of the recent LHC results for SUSY **

* Discovery of the SM-like 126 GeV Higgs boson * No sign of SUSY yet

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*** EWSB condition in SUSY model:**

mSUSY = SUSY-breaking mstop or mgluino μ = SUSY-preserving mhiggsino mstop,gluino ≫ MZ , so even with SUSY, we need a fine-tuning of parameters at the level of , which is at least about a few % fine-tuning. To minimize this fine-tuning, mstop and mgluino need to be close to the present LHC limit ~ 1 TeV.

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*** Physical Higgs boson mass in SUSY model:**

MSSM: mstop ~ TeV, which requires a fine tuning of O(10-4−10-6) Singlet extension of the MSSM: With λ ~ 1 and tanβ ~ 1, this can be large enough for the observed Higgs boson mass to be compatible with mstop ~ 1 TeV. Fine-tuning can be ameliorated to the minimal level ~ few %, which is a point strongly motivates this type of singlet extension of the MSSM.

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**Axion as a solution to the strong CP problem**

With a spontaneously broken anomalous global U(1) symmetry (Peccei-Quinn symmetry), θQCD becomes a dynamical field “axion” = Goldstone boson of the spontaneously broken U(1)PQ ( vPQ = PQ scale = Scale of the spontaneous breaking of U(1)PQ ) Dynamical relaxation of θQCD+ Arg Det(yq) = < a > / vPQ Low energy QCD dynamics develops an axion potential minimized at <a > = 0: a/vPQ

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**Most of the axion physics is determined by the PQ scale vPQ:**

Axion mass: Axion-photon couplings: (Astrophysical bound on gaγγ : vPQ > 109 GeV ) Cosmological relic axion mass density: Hiramatsu et al (2012) (PQ phase transition after the primordial inflation) PQ scale and the axion mass for axion DM: vPQ ~ 1010 − 1011 GeV ma ~ 5×10-5 − 5×10-4 eV

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**Axion search experiments are approaching to this region for axion DM.**

The new Center for Axion and Precision Physics (CAPP) in the Institute for Basic Science (IBS) of Korea will join soon this game searching for the axion DM!

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**ADMX (Axion Dark Matter eXperiment) vs CAPP (Y. Semertzidis)**

Current plan B-field High-Q B-field DM axion mass

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*** Low scale SUSY and the QCD axion are still the most compelling &**

interesting candidates for BSM physics. * They are introduced to understand some of the highly nontrivial hierarchical structures of the SM parameters: Scale hierarchy: (Gauge hierarchy problem) CP-angle hierarchy: (Strong CP problem) * They shed a light also on different questions such as the dark matter & unification. * They provide concrete predictions which can be tested experimentally in the foreseeable future. * There are many virtues of having them together!

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**Questions about the axion solution to the strong CP problem: **

Difficulties of low scale SUSY: * μ-problem * SUSY flavor problem * Cosmological moduli problem Questions about the axion solution to the strong CP problem: * Origin of U(1)PQ whose explicit breaking other than the QCD anomaly is extremely suppressed: Axion potential induced by generic high scale dynamics: * Origin of the intermediate PQ scale 109 GeV < vPQ < 1011 GeV Having SUSY together with U(1)PQ that originates from an anomalous U(1) gauge symmetry, all of these problems can be solved in a natural manner.

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**EWSB condition in SUSY model:**

* μ-problem EWSB condition in SUSY model: mSUSY = SUSY-breaking mstop or mgluino μ = SUSY-preserving mhiggsino Then why μ ≈ mSUSY, rather than μ ≈ MPlanck ? There may exist a symmetry, e.g. U(1)PQ or an R-symmetry, which forbids a bare μ ≈ MPlanck , but is spontaneously broken in a specific way to generate μ ≈ mSUSY . Kim, Nilles

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* SUSY flavor problem Non-observation of any BSM flavor-changing process = Deviation from flavor-degenerate sfermion masses Nearly flavor-degenerate sfermion masses or heavy ( ≥ 100 TeV) sfermions * Cosmological moduli problem Generic SUGRA or string models involve moduli fields with mmoduli ≤ mSUSY. Moduli-dominated Universe followed by late moduli decays: mSUSY ≥ 100 TeV Cosmological mechanism to wash out the moduli in the early universe

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**Two possible scenarios for SUSY:**

1) msfermion (∋ mstop) ~ 100 TeV: fine-tuning of O(10-6), with a mechanism to generate μ ~ msfermion (Still the gauginos may be around TeV: Minimally split-SUSY) 2) msfermion ~ mgaugino ~ 1 TeV: fine-tuning of O(few %), Price for the reduced fine-tuning: * singlet-extension in order to be compatible with mhiggs = 126 GeV * flavor-degenerate sfermion masses in order to be compatible with the non-observation of BSM flavor-changing process * cosmological mechanism to wash out the moduli in the early universe

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**SUSY models with an anomalous U(1) gauge symmetry can explain**

* the origin of U(1)PQ, * the origin of the intermediate PQ-scale 109 GeV < vPQ < 1011 GeV, * why μ ≈ mSUSY , rather than μ ≈ MPlanck ? and also provide a natural mechanism to * wash out the cosmological moduli, * generate flavor-degenerate sfermion masses. KC, S.H. Im, M.S. Seo (in preparation) We are interested in such SUSY models yielding a singlet-extension of the MSSM in the low energy limit: * compatible with mhiggs = 126 GeV with a minimal fine tuning of O(few %)

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**compactification, and it is broken often by the Stuckelberg mechanism: **

* Origin of U(1)PQ : Anomalous U(1)A gauge symmetry is a nearly generic feature of realistic string compactification, and it is broken often by the Stuckelberg mechanism: -Stuckelberg mechanism: Gauge boson gains a heavy mass without breaking the global part of U(1)A. U(1)PQ = Unbroken global part of U(1)A * Origin of the intermediate PQ-breaking scale: Spontaneous PQ-breaking by a balance between SUSY-breaking effect (by the D-term of U(1)A) and Planck-scale suppressed effect: Murayama, Suzuki, Yanagida ( )

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* μ-problem: Bare μ ≈ MPlanck is forbidden by U(1)PQ , but a correct value of μ ≈ mSUSY is generated by the spontaneous PQ-breaking: Kim, Nilles ( ) * Cosmological mechanism to wash out the moduli PQ phase transition takes place at T ~ mSUSY , rather than T ~ vPQ. Vacuum-energy dominated universe at a temperature Present universe with broken PQ-symmetry Thermal inflation to wash out the cosmological moduli Lyth, Stewart; KC, Chun, Kim

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*** Flavor-degenerate sfermions masses**

SUSY breaking in models with anomalous U(1)A gauge symmetry: KC, Jeong, Okumura, Yamaguchi (Flavor-degenerate DA always dominates over the potentially dangerous flavor-non-degenerate gravity mediation.) There can be additional gauge-mediated SUSY breaking induced by the PQ-breaking sector, which is comparable to DA. Sfermion masses are determined mostly by the flavor-degenerate U(1)A D-term and gauge mediation. and

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** Just two minimal models whose low energy limits at the TeV scale**

* Singlet extension of the MSSM with U(1)PQ originating from an anomalous U(1) gauge symmetry Most general singlet extension of the MSSM around the TeV scale: Generalized μ-problem: Why μ , μij , ξi1/2 ~ mSUSY (or smaller)? All mass parameters in this effective superpotential should be generated by the spontaneous breaking of U(1)PQ . Attempts to get phenomenologically viable singlet-extension with a reasonably simple PQ-breaking sector and tanβ ~ 1: KC, S.H. Im, M.S. Seo, arXiv:1402.xxxx Just two minimal models whose low energy limits at the TeV scale are described by

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**Among those two models, the one with**

is particularly interesting as it allows a limit where the singlet sector is parametrically lighter than the MSSM sector without causing any further fine-tuning: For instance, we can consider a limit which has a variety of interesting implications for the Higgs and DM physics, as well as the collider signatures of the model. KC, S.H. Im, M.S. Seo (in preparation)

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**candidate for BSM physics:**

Conclusion 1. Low scale SUSY and the QCD axion are still the most compelling candidate for BSM physics: -Solve the gauge hierarchy problem & the strong CP problem -Provide attractive DM candidates: axions and/or neutralinos -Fit nicely with the unification and also with string theory -Phenomenological consequences which are within the reach of experimental tests in the foreseeable future 2. Singlet-extension of the MSSM at the TeV scale is well motivated by the observed Higgs boson mass mhiggs=126 GeV and a request for the minimal fine-tuning.

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**3. Attempts to understand - the origin of the PQ-symmetry**

- the origin of the intermediate PQ-breaking scale - the μ-problem: why μ ≈ mSUSY, rather than μ ≈ Mplanck ? - flavor-degenerate sfermion masses - the cosmological moduli problem point to SUSY models with an anomalous U(1) gauge symmetry at high scales. 4. Attempt to get phenomenologically viable singlet-extension of the MSSM from such high scale models yields a specific form of two-singlet NMSSM at the TeV scale, which can have interesting implications for the Higgs and DM physics, as well as the collider signatures of SUSY particles.

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