1. 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

2. 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

3. 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:

4. 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

5. 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

6. 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 ?

7. 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 ?

8. 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.

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

10. * 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.

11. * 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.

12. 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

13. 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

14. 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!

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

16. * 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!

17. 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.

18. 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

19. * 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

20. 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

21. 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 %)

22. 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
 ( )

23. * 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

24. * 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

25.  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

26. 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)

27. 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.

28. 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.