1. Cosmological implication on naturalness and supersymmetry
Natsumi Nagata
E-ken Summer school
September 04, 2012

2. Difficult ! Task 発表は、M１にも分かる内容を混ぜつつ、新しい内容まで発表することが目標です。
あまり、基礎だけにならず、スタッフも楽しめる内容を！
Difficult !

3. Cosmological constant
Outline
Definition of ``Naturalness”
Cosmological hints for new TeV scale
Cosmological hints for the existence of fine-tuning
A model of fine-tuned SUSY and its phenomenology
Summary
WIMP miracle
Cosmological constant

4. 1. Definition of Naturalness

5. Effective interactions @ a low energy scale μ1
Philosophy
It is unlikely that the microscopic equations contain various free parameters that are carefully adjusted by Nature to give cancelling effects such that the macroscopic systems have some special properties.
Effective a low energy scale μ1
A a high energy scale μ2
Various different μ2 should not be adjusted
with an accuracy of 0(μ1/μ2).
Unnatural !

6. Definition of naturalness
On the other hand, if some μ2 would be small, then this may still be natural, provided that this property would not be spoilt by any higher order effects.
Naturalness
At any energy scale μ, a physical parameter or set of physical parameters αi is allowed to be very small only if the replacement αi = 0 would increase the symmetry of the system.
G. ‘t Hooft (1979).

7. Example of natural parameters
Electron mass
At mZ scale,
very small
Additional chiral symmetry
Separate conservation of left/right handed electrons
This guarantees that all renormalizations of me are proportional to me itself.

8. Example of unnatural parameters
Symmetry is not enhanced
※ Conformal symmetry is violated at the quantum level.
However, we can take both m and λ to be small,
φ(x) → φ(x) + Λ　　　　　Λ： const
Let us assume that this is an approximate symmetry of
a new underlying theory

9. Naturalness Breakdown Mass Scale (NBMS)
Symmetry breaking effect
ε (dimensionless)
μ０：symmetry breaking scale
If any “natural” underlying theory is to describe the scalar particle whose effective Lagrangian at low energies is given above, then the breaking scale lies around
c.f.) strong scale
※ Naturalness breaks down beyond μ0

10. an order of magnitude discussion
Naturalness Breakdown Mass Scale (NBMS)
Note that this is just
an order of magnitude discussion
Additional factors: π, O(1) constants…
A few factor is fine, 10 times allowed ? How about 100? 1000? …?

11. Then, how about the Standard Model ?
Is it natural ??

12. The Higgs squared-mass parameter QCD Θ-term
Naturalness in the SM
The Standard Model (SM) (possibly) has two unnatural parameters:
The Higgs squared-mass parameter
QCD Θ-term

13. Higgs mass TeV scale new physics !
The difficulties with the unnatural mass parameters only occur in theories with scalar fields. Higgs boson is the only scalar particle in the SM. Its squared mass is unnatural.
NBMS in terms of the quadratic divergence
TeV scale new physics !
V. F. Weisskopf (1939).

14. Physics beyond the SM Symmetry No scalar No high-energy scale
Many possible directions of physics beyond the SM have been proposed.
Symmetry
No scalar
No high-energy scale
Supersymmetry, a pseudo-NG boson, …
Technicolor
Extra dimension

15. Physics beyond the SM Symmetry No scalar No high-energy scale
Many possible directions of physics beyond the SM have been proposed.
Symmetry
No scalar
No high-energy scale
Supersymmetry, a pseudo-NG boson, …
This talk and
Technicolor
Extra dimension

16. Physics beyond the SM Symmetry No scalar No high-energy scale
Many possible directions of physics beyond the SM have been proposed.
Symmetry
No scalar
No high-energy scale
Supersymmetry, a pseudo-NG boson, …
Technicolor
Extra dimension

17. Supersymmetry Fermion mass Chiral symmetry Scalar mass
Ask other symmetries in the SM to keep the Higgs mass parameter from being much heavier than the EW scale.
Fermion mass
Chiral symmetry
protect
Scalar mass
Allowed to be light
Naturalness is controlled by the order parameter of SUSY (soft SUSY parameters).

18. QCD Θ-term violates P & T (CP). Neutron Electric Dipole Moment (nEDM)
J. Hisano, J. Y. Lee, N.N., Y. Shimizu (2012)
Experimental constraint (Institut Laue-Langevin)
Phys.Rev.Lett. 97, (2006).
strong CP problem

19. Experimental constraint on nEDM
〜 1 fm
〜 fm

20. Peccei-Quinn (PQ) mechanism
Θ → a(x) … axion field
fa : the axion decay const
The axion VEV makes the Θ-term vanish
R. D. Peccei and H. R. Quinn (1977)

21. Does the naturalness argument require the TeV-scale new physics ?
Problems
In this talk, I’d like to discuss the following problems:
Does the naturalness argument require
the TeV-scale new physics ?
Are there any other hints for the TeV-scale physics ?
Do all the theoretical parameters except for the above 2 parameters satisfy the naturalness condition ?
Is it possible that the new physics is fine-tuned and has the TeV-scale new physics? Couldn’t it be natural ?

22. Not necessarily… Does the naturalness argument require
the TeV-scale new physics ?
If you adopt ‘t Hooft’s naturalness conjecture,
Not necessarily…

23. 2. Cosmological hints for TeV-scale physics
WIMP DM

24. Yes !! Weakly Interacting Massive Particles (WIMPs)
Are there any other hints for the TeV-scale physics ?
Yes !!
Weakly Interacting Massive Particles
(WIMPs)

25. Evidence for dark matter (DM)
Galactic scale
Scale of galaxy clusters
Begeman et. al. (1991).
Clowe et. al. (2006).
Cosmological scale
About 80% of the matter in the Universe is nonbaryonic dark matter.
Komatsu et. al. (2010).

26. Rotational Curve Cold neutral hydrogen gas
v(r)
c.f.) CMB: 2.7 K r
By measuring the amount of Doppler shifts, you can determine the rotation speed.

27. Bullet Cluster
X-ray
Gravitational Lensing
Clowe et. al. (2006).

28. Bullet Cluster
X-ray
Gravitational Lensing
Clowe et. al. (2006).

29. Cosmic Microwave Background (CMB)
(COBE)
T = 2.7 K
J. Mather & G. Smoot
Nobel Prize 2006

30. Cosmic Microwave Background (CMB)
(WMAP)
Komatsu et. al. (2010)

31. Weakly Interacting Massive Particles
WIMPs
One of the most promising candidates for dark matter is
Weakly Interacting Massive Particles
(WIMPs)
have masses roughly between 10 GeV ~ a few TeV.
interact only through weak and gravitational interactions.
Their thermal relic abundance is naturally consistent with the cosmological observations [thermal relic scenario].
appear in models beyond the Standard Model.

32. Thermal relic scenario
When T > mDM
WIMPs were created as much as any other particles.
(in the thermal bath)
Temperature dropped as the universe expanded.
T < mDM
WIMPs annihilated each other into the SM particles.
Temperature still dropping
The Universe kept expanding
# density of WIMPs became fewer and fewer…

33. Thermal relic scenario
Eventually, WIMPs stopped finding each other.
# of WIMPs was fixed.
(Freeze-out)
Large annihilating rate
Small relic density

34. Numerical coincidence ? WIMP miracle ??
Relic abundance
By solving the Boltzmann Equation, we obtain
c.f.)
for M 〜 100 GeV
Typical quantity of the EW scale physics
Numerical coincidence ? WIMP miracle ??

35. 3. Cosmological hints for fine-tuned world
Cosmological constant, cosmic coincidence

36. Cosmological constant
Do all the theoretical parameters except for the above 2 parameters satisfy the naturalness condition ?
No !!
Cosmological constant

37. Luminosity distance
Given a candle with luminosity L and its flux f, you can define the distance from it, called luminosity distance, as
Matter dominant (Ωm = 1)
Cosmological constant dominant (ΩΛ = 1)

38. Type Ia Supernovae
When the mass of the white dwarf exceeds 1.4 times the mass
of Sun, the white dwarf collapses and explodes !!
Peak luminosity is approximately constant
Standard Candle

39. Existence of Dark Energy
Non zero cosmological constant
is observed in 1998 !
A.G. Riess, B.P. Schmidt, S. Perlmutter
arXiv:
Nobel Prize 2011

40. ρΛ 〜 (10-3 eV)4 Cosmological constant is unnatural
If the observed dark energy is explained by the energy of
vacuum (cosmological constant), its energy density is
ρΛ 〜 (10-3 eV)4
Isn’t it too small provided that naïve estimates tell us its natural value is around MP4 ??
Probably, (246 GeV)4 or (1 TeV)4…
Anyway, the observed value seems to be too small !

41. Cosmological constant is unnatural
Putting it equal to zero does not seem to increase the symmetry
Assumption
Only gravitational effects violate naturalness
Quantum gravity is not understood anyhow so we exclude it from our naturalness requirement
G. ‘t Hooft (1979).

42. Cosmic coincidence problem
Why now ??
N. Arkani-Hamed, L.J. Hall, C. Kolda, H. Murayama (2000).

43. Multiverse String landscape Eternal inflation Anthropic principle
It is possible to observe small but non-zero cosmological constant on the condition that someone actually observe it.
Theoretical support ??
Multiverse
String landscape
Eternal inflation

44. Note
Multiverse does not say we don’t need any mechanism to explain what looks unnatural.
In fact, we have no idea what condition we should apply to realize the existence of observers.
e.g.) Strong CP Problem
The neutron EDM seems to be too small.

45. So, how about the naturalness for the EW scale ?
Natural ?? Or fine-tuned ??

46. Maybe, it’s just unlucky.
LHC will soon find new physics beyond the SM
and it accounts for the naturalness of the EW.

47. Possibly, it’s just nature’s mischief.
First, the effective theory (the SM) appears to
be unnatural, but, once you obtain the high-energy theory beyond it, you conclude the it is natural.
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2011年度 勝率
.353
(2011年4月15日)

48. (instead of using it to explain something…)
Or, nature is fine-tuned.
Multiverse ??
I think it is interesting to imagine how we can do if the multiverse description is realized.
(instead of using it to explain something…)

49. 4. Fine-tuned SUSY and its phenomenology

50. Let me show you an example.
Is it possible that the new physics is fine-tuned and has the TeV-scale new physics?
Let me show you an example.

51. And more attractive features
Supersymmetry ??
Even if the weak scale is fine-tuned, the underlying theory may still be supersymmetric.
In order to satisfy ‘t Hooft’s conjecture
Consistency of string theory
And more attractive features

52. Assumption A chiral supermultiplet X responsible for SUSY is charged
under some symmetry.
[(e.g.) PQ symmetry]
SUSY is transferred via operators involving X† X
Scalar masses arise from
(M*: the scale at which SUSY is mediated)
VEV of X field

53. Gravitino mass/Higgsino mass
(〜 0.01 for M* = MGUT)
Higgsino mass
[G.F. Giudice, A. Masiero (1988)]
Note
There might be an additional suppression due to
an approximate PQ symmetry.

54. Anomal-mediated supersymmetry breaking (AMSB)
Gaugino mass
Anomal-mediated supersymmetry breaking (AMSB)
L. Randall and R. Sundrum (1998)
G.F. Giudice, M.A. Luty, H. Murayama, R. Rattazzi (1998)
Wino is the lightest SUSY particle (LSP)

55. Mass spectrum

56. Then, what determines the SUSY scale ??
Wino dark matter
Then, what determines the SUSY scale ??
(Naturalness for the EW scale is not in our hand, any more)
The amount of dark matter abundance !!
J. Hisano, S. Matsumoto, M. Nagai, O. Saito, M. Senami (2006).

57. Wino dark matter
Anthropic selection??
L. J. Hall, Y. Nomura.

58. Mass spectrum
105 TeV
103 TeV
30 TeV
3 TeV
10 TeV

59. This model has a lot of attractive features
from phenomenological point of view

60. OK !! Split SUSY The SUSY scale is much higher than the EW scale.
The spectrum below the SUSY scale contains
The SM particles (1 Higgs douplet)
Bino
Wino
Gluino
Higgsino
Gauge coupling unification
Existence of DM
SUSY Flavor/CP problem
OK !!
N. Arkani-Hamed, S. Dimopoulos (2004).

61. Good enough !! Gauge coupling unification sfermions SU(5) multiplets
α-1
Good enough !!
N. Arkani-Hamed, S. Dimopoulos (2004).
sfermions
SU(5) multiplets
・・・
do not affect 1-loop
(The other Higgs doublet makes a small contribution)

62. The 125 GeV Higgs boson mass is easily accounted.
Higgs mass
The 125 GeV Higgs boson mass is easily accounted.
125 GeV
error はmt, alpha_s
Small tanβ is favored
mt= ± 0.9 GeV
M. Ibe, T.T. Yanagida (2012).

63. SUSY search
Consistent

64. what can we do ?? We cannot find the new physics at all ??
If the nature adopts this scenario,
what can we do ??
We cannot find the new physics at all ??

65. Direct detection experiments
arXiv:

66. Direct detection of wino DM
We have wino DM flying around us. Let us catch it !
But…
All of these tree diagrams are suppressed.
The Wino-nucleon scattering process is dominated by loop diagrams

67. Direct detection of wino DM
1-loop diagrams:
They are not suppressed even if MDM >> mW
2-loop diagrams:
Mass fractions for proton

68. Direct detection of wino DM
The SI cross section of Wino DM with a proton
Small cross section
(due to an accidental cancellation…)
J. Hisano, K. Ishiwata, and N. Nagata, Phys. Lett. B 690 (2010) 311.

69. ? Indirect detection of wino DM
The indirect detection of wino DM from annihilation to photons is promising. ?
M. Ibe, S. Matsumoto, T.T. Yanagida (2012).
J. Hisano, S. Matsumoto, M.M. Nojiri, O. Saito (2004).

70. χ± → χ0 π+ Collider searches
Wino is a (and possibly the only ) the LHC.
χ± → χ0 π+
Δm 〜 160 MeV
cτ 〜 O(10) cm

71. Collider searches
Disappearing charged tracks can be used for triggering
13 LHC
Wino mass
10 fb-1
350 GeV
100 fb-1
550 GeV

72. Other possibilities
CP, flavor physics ??
Light Higgsino
e.t.c. …

73. Summary

74. It is possible that the EW scale is (looks) fine-tuned.
Conclusion
It is possible that the EW scale is (looks) fine-tuned.
High-scale SUSY is attractive, though.
We have a chance to find out new particles.
We have an opportunity to study new idea for challenging the scenario.

75. Backup

76. The Higgs field would become unphysical
Naturalness in the SM Higgs sector
Is there an approximate symmetry if m → 0 ??
How about
・・・ ☆
However we also had the local gauge transformations:
For the symmetry group to be closed, we also have invariance
under
But then it becomes possible to transform Φ(x) away completely.
The Higgs field would become unphysical

77. Naturalness in the SM Higgs sector
Symmetry under ☆ should be broken by all interactions
that have to do with the gauge transformations.
So, the symmetry is broken at best by O(g2/4π).
Also the λφ4 term breaks this symmetry.
Therefore,
Note
This is just an “order of magnitude” argument

78. CMB l 〜200 (Habble distance @ last scattering) (Curvature negative)
(Curvature positive)
l 〜200 (Habble last scattering)

79. CMB
W. Hu, M. White (1996).

80. Sachs-Wolfe effect

81. MACHO
Gravitational microlensing effects
EROS-2 (2006) arXiv:

82. protons decay into neutrons
Anthropic weak scale
Changing the Higgs VEV by a factor of a few will lead to
drastic changes of the universe.
V. Agrawal, S.M. Barr, J.F. Donoghue, D. Seckel (1998)
T. Damour and J.F. Donoghue (2008)
If v < 0.5 × (246 GeV)
protons decay into neutrons
No atoms
If v > 5 × (246 GeV)
neutrons decay into protons inside nuclei
No atoms except proton

83. An evidence for high scale SUSY