1. Beyond the Standard Model with SUSY and Axions
Kiwoon Choi (KAIST)
PLANCK 2013
May 24, Bonn

2. the best motivated and perhaps the most promising candidates for
Beyond the SM physics
Although more than 30 years old now, SUSY and axions are still
the best motivated and perhaps the most promising candidates for
BSM physics.
Introduced to solve the two major fine-tuning problems of the SM:
* Gauge hierarchy problem  SUSY around the weak scale
* Strong CP problem  QCD axion
and provide attractive DM candidate.
In this talk, I will discuss the present status of these two compelling
candidates for BSM physics in light of recent progress, as well as
the prospect for experimental discoveries in the future.
Cf: BSM in cosmology (L. Covi), flavor physics (A. Masiero)
and string theory (L. Ibanez)

3. 1) Implications of the 126 GeV Higgs boson for SUSY
Outline
1) Implications of the 126 GeV Higgs boson for SUSY
Where is SUSY ? mSUSY
* MSSM: Maximal stop-mixing, Minimally split SUSY, High scale SUSY
* Natural NMSSM as a model for minimal fine-tuning &
Warped NMSSM as its UV completion
2) QCD Axion
Where is axion ? fa
* EDM, Axion dark matter, Axion dark radiation, …
3) Conclusion

4. * 126 GeV Higgs boson
A new boson with mh = 126 GeV has been discovered at the LHC, which
looks very much like the SM Higgs boson:
pp  h + X & h  ZZ, WW, γγ, bb, ττ
Although the data fit very well to the minimal SM Higgs boson, a variety of
BSM physics models are also compatible with the data:
Modification of Higgs boson
couplings by BSM physics:

5. * Current LHC limits on SUSY (colored superparticles)
mstop > 600 GeV mgluino > 1.3 TeV
mgluino ~ msquark > 1.5 TeV

6. as a mechanism for natural EWSB, in particular for models with high
Direct search limits begin to threaten the original motivation for SUSY
as a mechanism for natural EWSB, in particular for models with high
mediation scale of SUSY breaking.
EWSB in SUSY model:
( Λ = mediation scale of SUSY breaking )
High mediation scale, e.g. Λ ~ MGUT:
 fine-tuning of < 1 %
(mstop > 600 GeV, mgluino > 1.3 TeV )
Low mediation scale, e.g. Λ ~ TeV,
Fine-tuning can be ameliorated to be about 10 %.

9. Can arise naturally from many SUSY breaking scheme
* Minimally Split SUSY : mgaugino ~ msfermion/8π2
Can arise naturally from many SUSY breaking scheme
1) SUSY breaking F-component: FZ ~ m3/2MPl (for vanishing C.C)
2) Sfermion masses by gravity mediation:
 msfermion ~ FZ/MPl ~ m3/2
3) Gauge multiplet can be easily sequestered from the SUSY breaking by Z:
: No gaugino mass from FZ
(Approximate symmetry, Geometric separation, …)
However, usually there exists a gauge coupling modulus fa = T whose
F-component contributes to the gaugino masses.

11. * High scale SUSY with shift symmetry
tanβ = 1  Highest SUSY scale compatible with mh = 126 GeV
Shift symmetry at compactification scale mcom:
at mcom
Pseudo-Goldstone Higgs model: Inoue et al (1986)
Heterotic string orbifold: Antoniadis et al (1994); Lopes Cardoso et al (1994)
Gauge-Higgs unification model: KC et al (2004); Hebecker et al (2009)
Shift symmetry is broken by the top Yukawa coupling, but still tanβ at SUSY
breaking scale can be close to 1:
 mSUSY ~ 109 – 1011 GeV
Hebecker, Knochel, Weigand (2012)
Theoretically interesting in principle, however huge fine-tuning for EWSB and
no hope to see SUSY at the LHC.

12. 126 GeV Higgs boson in NMSSM
EWSB and mh = 126 GeV can be achieved in NMSSM with less fine-tuning:
Hall et al (2012), Ross et al (2012), King et al (2012), Kang et al (2012), Gherghetta et al (2012), …
Natural NMSSM: Hall, Pinner, Ruderman (2012); Gherghetta, Harling, Medina, Schmidt (2012)
* Small tanβ ~ 2, Large λ = 1-2 , Low mediation scale Λ ~ TeV,
* mstop < 1.2 TeV, mgluino < 3 TeV, mhiggsino < 300 GeV, mS < 1 TeV
 : About 10% tuning
So, there still exists a sizable room for SUSY to provide a good
solution to the hierarchy problem in the NMSSM.

13. * Warped NMSSM * Fine-tuning for EWSB in NMSSM
Fine-tuning for Λ ~ 10 TeV Hall, Pinner, Ruderman (2012)
Natural NMSSM:
NMSSM with large λ=1-2 and
low cutoff scales for
UV completion well below MGUT:
* Composite (Fat) Higgs with nearly
conformal new strong dynamics
Harnic, Kribs, Larson, Murayama (2004)
* Warped NMSSM
Birkedal, Chacko, Numura (2004);
Gherghetta, Harling, Setzer (2011)

14. * Warped NMSSM with Higgs sector at IR brane Slice of AdS5
UV Birkedal, Chako, Nomura (2004); Gherghetta, Harling, Setzer (2012)
Slice of AdS5 IR
k = AdS curvature
SUSY breaking Z Gauge multiplets & Radion T Higgs (Hu, Hd, S)
at UV boundary in bulk at IR boundary
Light fermions Moduli Top quark multiplets
quasi-localized near stabilization quasi-localized near
the UV boundary yielding the IR boundary
(Small Yukawa couplings, FT << FZ (Large Yukawa couplings,
Large soft masses) Small soft masses)
* Low cutoff scale ΛIR ~ e-kπRMPl for the Higgs and stops
* Effective SUSY with heavy 1st & 2nd generation sfermions, and
light Higgs, stops, gauginos & Higgsinos

16. * Higgs mixing in natural NMSSM
KC, Im, Jeong, Yamaguchi, arXiv: ; Cheung, McDermott, Zurek , arXiv: ;
Barbieri, Buttazzo, Kannike, Sala, Tesi, arXiv: ; Badziak, Olechowski, Pokorski, arXiv:
For λ = 1-2, all Higgs boson masses may not be so different from each other,
which would result in a sizable Higgs mixing.
126 GeV Higgs boson:
 with sizable θ1 and/or θ2
Such mixing results in a modification of the low energy couplings of the
(Singlet-doublet mixing & Higgsino Loop)

17. KC, Im, Jeong, Yamaguchi, arXiv:1211.0875
The mixing between the 126 GeV Higgs and the singlet S is not
severely constrained, so sin2θ2 can be as large as O(10)%.
KC, Im, Jeong, Yamaguchi, arXiv:
Significantly enhanced γγ rate ~ 1.5 x SM-rate, SM-like WW & ZZ events,
and depleted bb & ττ rates ~ 0.7 x SM-rate can be obtained with
= & sin2θ2 = O(10) %
which can be tested by the next round of LHC experiments.

18. (no anthropic reasoning)
QCD axion
* Strong CP problem
: Neutron EDM 
(no anthropic reasoning)
* Axion solution: Non-linearly realized U(1)PQ broken by the QCD anomaly
U(1)PQ: a  a + constant 
 Dynamical relaxation of θ

19. Generically the dynamical relaxation is not complete.
Small shift of axion VEV by
1) CP-Violation
2) Additional PQ-breaking by UV dynamics
(quantum gravity effects such as stringy instantons, gravitational wormholes, …)
* SM CPV 
* BSM CPV around TeV 
* Stringy instantons  
Even with axions, regardless of the existence of BSM physics near TeV,
can take any values below the experimental bound ~

20. * EDM as a probe for BSM physics
< e-cm
Future experiments may be able to measure some EDMs ~ e-cm:
Storage ring experiment for charged particle EDM: Y.K. Semertzidis (
Sensitivity: dproton, ddeutron ~ e-cm
 BSM physics at scales up to TeV
However, for a proper interpretation of the experimentally measured
EDM, it is necessary to have an accurate theoretical computation of
the EDMs from .

21. To make sure the existence of BSM physics, we need to measure
EDMs from
Bsaisou, Hanhart, Liebig, Meiβner, Nogga, Wirzba, arXiv: ;
Guo, Meiβner, arXiv:
(χPT + Lattice)
To make sure the existence of BSM physics, we need to measure
both dn & dp, together with an improvement of the theoretical
computation of dn(θ) & dp(θ).
Although the electron EDM by itself can probe BSM physics directly,
the observable most sensitive to de is the EDM of paramagnetic atoms,
which are affected by θ even more complicate way:
( )

24. * QCD axion from closed string modes
Axion scales suggested by theory
* QCD axion from closed string modes
KC, Kim (1985);
Svrcek, Witten (2006)
(U(1)PQ is non-linearly realized during inflation)
* Axion scale generated by SUSY breaking effects
 Kim, Nilles (1984)
(PQ phase transition after primordial inflation)

25. * PQ phase transition after inflation:
Axion DM
* PQ phase transition after inflation: 
(fa can be larger in case with late entropy production)
Axion DM search with resonant cavity:
may be here!

27. Stringy realization: U(1)PQ from anomalous U(1) gauge symmetry with
Axions with SUSY
1) Nearly inevitable component of string theory
2) Natural generation of an intermediate axion scale
Stringy realization: U(1)PQ from anomalous U(1) gauge symmetry with
FI=0 in SUSY limit KC, Jeong, Okumura, Yamaguchi (2011)
3) Interesting cosmology due to axino & saxion
* Axino DM: Covi, Kim, Roszkowski (1999)
See J. E. Kim’s talk
* Axion dark radiation: KC, Chun, Kim (1997)
Late decaying saxions (moduli) 
(Nearly generic feature of SUSY axion models)
See J. Conlon’s talk

28. SUSY may be here! Then we will discover her in the next round
Conclusion
Where is SUSY ?
* Natural NMSSM still provides a good solution to the fine-tuning
problem in EWSB, and the natural parameter region (~ 10% fine-tuning)
can be extended to mstop = 1.2 TeV, mgluino = 3 TeV.
Stop Gluino
1.2 TeV TeV
SUSY may be here! Then we will discover her in the next round
of LHC experiments.

29. * Sizable modification (~ O(10)%) of the low energy couplings of
126 GeV Higgs boson is a plausible possibility in natural NMSSM.
Expected 1-σ precision Higgs measurements at LHC (14 TeV, 300 fb-1)
Deviation Peskin,
of arXiv:
Higgs couplings
We may be able to see some deviations from the SM in the next
round of LHC experiments.

30. * With the proposed level of sensitivity, EDMs will make it possible to
access BSM physics even at scales above the LHC scale.
Storage ring experiment for charged particle EDM:
Sensitivity of dproton, ddeutron ~ e-cm
To utilize this exciting possibility, we will need a more precise theoretical
computation of the EDMs from .

31. Where is axion?
* In near future, detection of axion DM with fa ~ few x (1011 – 1012) GeV
will be a real possibility.
On the other hand, we will need new technique to reach the region
fa ~ 3 x 1010 GeV, giving Ωah2 ~ 0.1 in a minimal cosmological scenario.
It may be possible to test fa ~ 1016 GeV with molecular interferrometry
or a tensor mode in density perturbation.

32. Flavor, Neutrino CMB, LSS, Cosmic Rays
In summary, to make a further progress, we will need a guide from
experiments.
It may come soon from some of our on-going (or planned) efforts
to search for BSM physics with LHC, flavors, DM, CMB, EDM, ….
Dark matter, Inflation,
Baryon Asymmetry,  BSM Physics
Naturalness, Unification
Quantum Gravity, …
Flavor, Neutrino CMB, LSS, Cosmic Rays
p-decays, EDM, LHC, DM, …
(Higgs, MET, …) (WIMP, Axion,…)
Exciting discoveries may be waiting for us!

33. Thank you for
your attention!