dark energy and qcd axion from approximate u(1) de & u(1) pq jek, phys. rev. lett. 111 (2013)...

Dark energy and QCD axion from approximate U(1)de & U(1)PQ

JEK, Phys. Rev. Lett. 111 (2013) 031801;JEK, Phys. Lett. B726 (2013) 450;JEK+H. P. Nilles, Phys. Lett. B730 (2014) 53 ;JEK, JKPS 64 (2014)795 [arXiv:1311.4545[hep-ph] ].

Jihn E. Kim Kyung Hee Univ. & Seoul National Univ.

KASI, 16 April 2014

Sure, data needs more crayons!Or, color generating computer!

All colors are constructed with three

fundamental ones! (She may be a theorist)

1. Introduction 2. Axions and the strong CP problem 3. QCD axion from discrete

symmetries 4. Dark energy from U(1)de

1. Introduction

CCFollows thecold darkmatter

Responsible forgalaxy formation

Cosmic pie

We discuss DE of order 10-47 GeV4 and CDM axion.

A rough sketch ofWIMP masses and cross sections.

[Baer-Choi-Kim-Roszkowski,Soon appearing[arXiv:1404.xxxx]]

J E Kim “Dark energy and QCD axion”, KASI, 16 April 2014 6/40

★ Because DE is a property of potential energy, bosonic coherent motion (BCM) can account for it. BCM such as axion also accounts for CDM.

★ Higgs boson is a fundamental scalar.

In the age of fundamental scalars, can these explain both DE and CDM?

Higgs portal:

The Higgs fields know the fundamental scalars contributing to CDM and DE. THEN, GLOBAL SYMMETRIES, AS FOR THE AXION, IS BETTER TO BE CONSIDERED.

In the age of GUT scale vacuum energy observed, can these explain all of DE and CDM and inflation-finish?


★ But quantum gravity effects are known to break global symmetries: the Planck scale wormholes connect observable universe O to the shadow world S. They can take out the global charges from O.

(i) The discrete symmetry arises as a part of a gauge symmetry.

[Krauss-Wilczek, PRL 62 (1989) 1211]

(ii) The string selection rules directly give the discrete symmetry. [JEK, PRL 111 (2013) 031801]

★ We can think of two possibilities of discrete symmetries realized from string compactification, below MP:

★ So, we start with discrete gauge symmetries.

Quantum gravity problem


Vertical, exact sym.:gauged U(1),or string dictated.

A few low order W’s respected by discrete symmetry definesa global symmetry.

The global symmetry violating terms.

Exact and approximate symmetries


2. Axions and Strong CP

The strongly interacting θ(Gluon)μν (Gluon-dual)μν termgives a nEDM. Neutron EDM is measured very accurately.

dnth = (1.2-14.5)x10-16 θe cm

dn

exp = 2.9 x10-26 e cm, Baker et al (2006)

Strong CP

10102.4)-(0.2 || “Why is nEDM so small?”is the strong CP problem.

J E Kim “Dark energy and QCD axion”, KASI, 16 April y 2014 1140

For gauge symmetrybreaking, exactly flat.

]2,0[ aDWfNa For global symmetrybreaking, a potentialis generated: Approximate

af

)O( 4QCD


In the evolving universe, at some temperature, say T1, a starts to roll down to end at the CP conserving point sufficiently closely. This analysis constrains the axion decayconstant (upper bound) and the initial VEV of a at T1.

It is very flat if the axion decay constant is large,

CP conserving point

The axion oscillation is just one example of Bosonic Coherent Motion (BCM).

Still oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim-Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991), Hong-Kim-Nam-Semertzdis, 1403.1576. Graham et al, 1101.2691, Budker et al, 1306.6089, Sikivie et al, 1310.8545.

10-20


The Lagrangian is invariant under changing θ → θ

-2α. But θ becomes dynamical and the θ=a/ Fa potential becomes

0

d

u

a mm

ZFa

Z

mfZV

,cos1

)1(

2

22

The true vacuum chooses θ=a/ Fa at


A recent calculation of the cosmic axion density is,

109 GeV < Fa < {1012 GeV ?}

Turner (86), Grin et al (07), Giudice-Kolb-Riotto (08),

Bae-Huh-K (JCAP 08, [arXiv:0806.0497]): recalculated including the anharmonic term carefully with the new data on light quark masses.It is the basis of using the anthropicargument for a large Fa.

Without string radiation

All these three figures,Baer-Choi-Kim-Roszkowski,“Nonthermal DM”, to appear.


L. Rosenbergand G. Rybka in front of theADMX apparatus.Science 343, 552 ,1 November 2013. CAPP at KAIST(Y.Semertzdis) will dofor a larger axion mass and more.

Xe tank at XMASSbefore completingfilling water30 October 2013.

Science Vol. 343, 552 (2013): 1 November 2013, Focus

Solve technical problemin theory of strongnuclear force

Explain dark matter

Bounce off atomic nucleiTurn into photons instrong magnetic field

Solve more than oneproblem; allow fordecisive test.

Follow naturally fromsupersymmetry; providemany models and multipleavenues of detection

Year invented1977 by Lee-Weinberg;SUSY WIMP 1983 Gold.

1979 invisible axion1982 CDM

symmetry PQ the define

1or,~

32

ninteractio Effective

2XXHH

MGG du

G parity-R Exact

cationcompactifi

string from motivated

approach down-Top

Many lab.searcheswere made,and we hopethe axion bediscovered .

Graham et al, 1101.2691, Budker et al, 1306.6089, Sikivie et al, 1310.8545. Oscillating nEDM was suggested to be measured 20 years ago: Hong-Kim-Sikivie, PRD42, 1847 (1990), Hong-Kim PLB265, 197 (1991), Hong-Kim-Nam-Semertzidis, arXiv:1403.1576[hep-ph].


KSVZ axion: The Peccei-Quinn symmetry by renormalizable couplings to heavy quarks.

),,( duRL HHSVSQQL

Here, Higgs doublets are neutral under PQ. If they are not neutral, then it is not necessary to introduce heavy quarks [DFSZ axion]. In any case, the axion is the phase of the SM singlet S, if the VEV of S is much above the electroweak scale.

Because Fa can be in the intermediate scale, axionscan live up to now (m<24 eV) and constitute DM of theUniverse.

Why are we restrictedto renormalizableinteractions onlyat the EW scale?Definition of a globalsymmetry can be non-renormalizable termsalso: DFSZ.

XXHHM

W duPG

1

,

Kim-Nilles term


The axion is created at T=Fa, but the universe (<a>)does

not roll until 3H=ma (T=0.92 GeV [Bae-Huh-Kim]). From

then on, the classical field <a> starts to oscillate. harmonic oscillator motion:ma

2 Fa2 = energy density = ma x number density =

like CDM.See, Bae-Huh-Kim, arXiv:0806.0497 [JCAP09 (2009)

005],Figure will be given with correct coefficients and

new dataBaer-Choi-Kim-Roszkowski, “Nonthermal DM”, to

appear.

109 GeV < Fa <10 12 GeV,


3. QCD axion from discrete symmetries

S2(L) x S2(R) symmetric fermion masses can arise from

The fermion mass matrix will be

h.c. ) (2m

- (2)R

(2)L

(1)R

(2)L

(2)R

(1)L

(1)R

(1)L L

22

220

mm

mm

M

m

M

0

00

The first step for the solution of the μ-problem.[JEK, arXiv:1303.1822].


[JEK, PRL111, 031801 arXiv:1303.1822].

In string theory, matter fields are from E8 x E8 representations. Not from BMN .Kim-Nilles μ-term arises from

Where do X and X–bar belong?

duHH 2

PM

XXW

Anyway,BMN fields: decay constant is very largeF>1016 GeV[Choi-Kim (1984),Svrcek-Witten(2006)]

)2,1(

0

)2,1(

0

,

i

d

d

d

bd

gd

rd

i

u

u

u

bu

gu

ru

X

H

H

T

T

T

X

H

H

T

T

T

Probably, in matter reps.


How can we break S2(L) x S2(R) symmetry ?

Spontaneously by

0, )2()2()1()1( XXFXX a

The massless (0) fields, and superheavy (G) fields

)(2

1

)(2

1

)2(

,

)1(

,

)(),0(

,

)2()1()(),0(

dudu

G

du

G

HHH

XXX


GeV 200 Then,

10 gives ,10MM

),10(GeV, 10

MM

,2

3-

E

P212)0(

E

P)0()0()0()0(

P

OfX

ffHHXXM hexedu

c

This defines the PQcharges of X and H.


★ Quantum gravity effects occurring at the Planck scale connect the observable universe O to the shadow world S via the Planck size wormholes. The discrete symmetry is a part of a gauge symmetry.

How did we succeed?


The global symmetry violating terms.

A few low order W’s are respected by discrete symmetry.

)terms 5(1

)terms 4( DM

DP

The d=5 examples are Weinberg operatorand KN operator(with SUSY).

etc.Minkowski,

saw-see:alizationRe

mass defines

1

operator Weinberg

uuHHM

L

DFSZ:nRealizatio

symm PQ defines

1

operator Nilles-Kim

duHHXXM

W

The d=4 example is the θ termof Callan-Dashen-Gross andJackiw-Rebbi.

KSVZ:nRealizatio

couplingdefines

~32

operator CDG/JR

2

FFL


The PQ breaking diagram is


But the dominant breaking is by the QCD anomaly term:


4. Dark energy from U(1)de

DE magnitude

★ There exists a tiny DE of order 10-47 GeV4.

★ We propose to relate this DE scale to a pseudo-Goldstone boson mass scale.

★ The breaking scale of U(1)de is trans-Planckian, and the intermediate scale PQ symmetry breaking of U(1)de just adds the decay constant only by a tiny amount.


) (

P

) (

P

) (

P

) (

P

WM

WM

WM

WW

DM

D

63

52

43 111

W, potential-super from )terms 5(1

)terms 4(

★ The discrete and global symmetries below MP are the consequence of the full W. So, the exact symmetries related to a discrete gauge symmetry or to string compactification are respected by the full W. Considering only W(3), we can consider approximate symmetries too. In particular, the approximate PQ symmetry.

★ In string compactification, the bottom-up approach constraints [Lee et al, NPB 850, 1] toward a discrete gauge symmetry need not be considered. They are automatically satisfied with suitable massless singlets.

★ For the MSSM interactions supplied by R-parity, one needs to know all the SM singlet spectrum. Z2 needed for a WIMP candidate.


★ Because the Higgs scalar is known to be a fundamental scalar, fundamental SM singlet scalar VEVs at the PQ symmetry breaking scale are considered,

The DE potential height is

The singlets must couple to Hu Hd : Then, to remove the U(1)de-QCD anomaly , U(1)PQ must be introduced for one linear combination is free of the QCD anomaly. The needed discrete symmetry must be of high order such that some low order W are forbidden.

7

2)0(

2)0(6

2/3446

5

82/38 GeV1010

G

ew

G

ew

M

vm

M

vm

: and )0()0( dede ff constant decay DE

2)0(2


★ A related comment is on the dilatonic symmetry:

The dilatonic symmetry is spontaneously broken at the Planck scale.So, the dilaton is created without potential. It appears in the exponent.

How do we raise the height of the dilaton potential? Another VEV suchas <Hu> and <Hd> cannot render a potential for the dilaton.Maybe a confining force can do it. So, dilaton may have a severe problemaccounting the scale of DE.


★ But, if QCD anomaly coupling to U(1)de is present, then we have the usual QCD axion.

★ U(1)de should not have QCD anomaly.

★ We need one more U(1) such that one linear combination U(1)de does not have the QCD anomaly. We must introduce to global U(1)s, of course approximate: U(1)de and U(1)PQ .

★ We have the scheme to explain both 68% of DE and 28% of CDM via approximate global symmetries. With SUSY, axino may contribute to CDM also.

Hilltop inflation


★ The discrete symmetry Z10R charges are the gauge charges of the mother U(1) gauge symmetry.

★ The height of the potential is highly suppressed and we can obtain 10-47 GeV4 from discrete symmetry Z10R, without the gravity spoil of the global symmetry breaking term.

★ As a byproduct of the Mexican hat potential, Fig. (b), we also have a model of inflation, the so-called ‘hilltop inflation’. It is a small field inflation, consistent with the recent PLANCK data.

Typical example


★ The simplest orbifold is Z(12-I), since there are only 3 fixed points. Note Z(3) has 27 fixed points. The model of [Huh-Kim-Kyae, PRD 80, 115012] has the Higgs with two units of discrete charge.

★ For example, the Z10 is a subgroup of one U(1) direction

Z10 = (0 0 0 0 0 4 2 0) (0 0 0 0 0 -8, 4, 0)’ (A)

★ For the MSSM interactions supplied by R-parity, one needs to know all the SM singlet spectrum. Z2 needed for a WIMP candidate.


★ Some singlets have the even discrete charges. For example, s9 and s13 have Z10 quantum number magnitude 10.

★ The VEVs of s9 and s13 break U(1) gauge symmetry direction (A) to Z10 . Even if Higgs doublets obtain VEVs, the resulting discrete group is Z2. From this direction, we can obtain Z10 if d=3 superpotential term contains Z10 =0 terms. We obtain Z10R if d=3 superpotential term does not contain Z10 =0 terms, but contains Z10 =2, 12, 22, etc. terms. For Z10 or Z10R , the d=2 μ Hu Hd term is not allowed.

★ In conclusion, it is so simple to obtain the desired ZN or ZnR symmetry if we know all the SM singlets. We presented it in a Z(12-I) model.

We find the method very useful for model building. And we can obtain an approximate PQ global symmetry as discussed in [JEK, PRL 111, 031801 (2013)] for the case of S2xS2. .


5. Gravity waves from U(1)de

DE magnitude

★ There exists a tiny DE of order 10-47 GeV4.

★ We propose to relate this DE scale to a pseudo-Goldstone boson mass scale.

★ The breaking scale of U(1)de is trans-Planckian, and the intermediate scale PQ symmetry breaking of U(1)de just adds the decay constant only by a tiny amount. The height is (GUT scale)4

★ It is by closing the green circle of (a):

evenscos

)(s

42DE

24

mf

V

★ What is the form of the U(1)de breaking V?


★ We obtain

2812

201

811

rrs

sr

nn ss

[0.96, 0.008]

VV s4 cos

0')'( with V

New type (chaoton)

hybrid inflation


Natural inflation startingat π is here.Freese-Kinney:1403.5277.

Natural inflation startingat 0 is here.


★ One condition to have a large e-folding is the Lyth bound, in our case

fDE > 15 MP [D. Lyth, PRL 78 (1997) 1861]

★ It is possible if the potential energy density is lower than MP

4 ..

One method is natural inflation: [Freese-Frieman-Olinto,PRL 65 (1990) 3233]. But, trans-Planckian needed twoAxions at least: [Kim-Nilles-Peloso, JCAP 01 (2005) 005]


Kim-Nilles,PLB 730 (2014) 53 [arXiv:1311.0012].

Kim [arXiv:1404.4022].


U(1)de inflation with‘chaoton’ X, more range.

Conclusion

★ BCM is one possibility of CDM.

★ Global symmetry U(1)PQ needed.

★ For CDM, it must live sufficiently long.

★ Invisible axion is a CDM candidate.

★ Higgs portal, or anomaly portal always give U(1)PQ –gluon-gluon anomaly.

★ U(1)de can give anomaly–free pseudo- Goldstone boson for the observed DE.

City of Daejeon, Yusung Prefecture

KAISTCampus

Head QCampus

3 km

Center for Axion andPrecision Physics:Yannis Semertzidis

Center for UndergroundPhysics: Young Duk Kim

Center for Theoretical Physicsof the Universe(hep-ph, -th, nucl-th, astro-ph[CO]):Kiwoon Choi

dark energy and qcd axion from approximate u(1) de & u(1) pq jek, phys. rev. lett. 111 (2013)...

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