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

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

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:

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

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

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 ?

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 ?

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.

Implications of the recent LHC results for SUSY * Discovery of the SM-like 126 GeV Higgs boson  * No sign of SUSY yet

* 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.

* Physical Higgs boson mass in SUSY model: MSSM: mstop ~ 10 - 100 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.

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

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

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!

ADMX (Axion Dark Matter eXperiment) vs CAPP (Y. Semertzidis) Current plan B-field High-Q B-field DM axion mass

* 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!

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.

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

* 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

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

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 %)

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  ( )

* 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

* 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

 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

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)

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.

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.