Slides - Fermilab Center for Particle Astrophysics

Weak and strong CP, axions, 

and DM 

Jih Jihn EE. Kim Ki 

Seoul National University 

Seattle, 29 July 2011 

Yale, 1 August g 2011 

Fermilab, 2 Aug 2011 

Ohio State, 4 Aug 2011

What can be there beyond SM? 

New CP? Axions? SUSY? String? 

11. Th The weak k CP violation, i l ti and d th the 

strong g CP conservation 

22. Axions 

3. Dark matter 

J E Kim Weak and Strong CP, Axions and DM USA 2011

11. The weak CP violation violation, and the 

strong CP conservation 

The P violation in weak interactions is ultimately given at low 

energy perspective i by b the h Gl Glashow-Salam-Weinberg h S l W i b chiral hi l 

model of weak interactions: the standard model. 

3 /75

Dark matter in the universe is the most looked-for particle(s) 

iin cosmology l and d at LHC LHC, and d also l at llow temperature llabs. b 

The 100 GeV scale DM and the10-1000 micro eV axion are 

the most promising candidates candidates. 

Neutrinos Light bosons 

4/75

A rough sketch of 

masses and d cross 

sections. Bosonic 

DM with collective 

motion is always 

CDM. 

J E Kim Weak and Strong CP, Axions and DM USA 2011 5 /75

The weak CP violation 

The charge conjugation C and parity P have been known as 

exact symmetries in atomic physics, i.e. in electromagnetic 

interactions. 

1924: Atomic wave functions are either 

symmetric y or antisymmetric: y 

Laporte rule 

1927: Nature is parity symmetric, symmetric Wigner: 

Laporte rule = parity symmetric 

6/75

Quantum mechanics was developed after the atomic rule 

of Laporte was known known. It is based on the 

SYMMETRY PRINCIPLE !!!! 

In QM, these symmetry operations are represented by unitary 

operators. For continuous symmetries, we represent them by 

generators 

U 

where F is a set of generators. 

e 

ii 

F 

For discrete symmetries, we use U directly like 

P, C, CP, etc. 

7 /75

CP violation observed in the neutral K-meson 

system (and now from B-meson system) needed to 

iintroduce d a CP violation i l i iin the h SM SM. IIt was given i bby the h 

Kobayashi-Maskawa model. 

8 /75

The CKM matrix has been written by y many y since the 

KM paper, 

Kobayashi-Maskawa, Prog. Theor. Phys. 49 (1973) 652 

using N. Cabibbo, PRL10 (1963) 531 

Maiani, PLB 62 (1976) 183 

Chau-Keung, PRL 53 (1984) 1802 

Wolfenstein, PRL 51 (1983) 1945 : Approximate form 

Qi Qin-Ma, M PLB 695 (2011) 194 : AApproximate i t fform 

RRecently, l SSeo and d I wrote an exact CKM matrix i 

replacing the Wolfenstein form. Another complification in lit.? 

or reaching to the end of the road of writing the CKM matrix? 

9/75

CP violation books contain basics: 

GG. C. C Branco, B L. L Lavoura L and d JJ. PP. Sil Silva, 

CP Violation, Int. Ser. Monogr. Phys 103 (1999). 

II. I. I Bigi and A. A I. I Sanda, Sanda CP violation, violation Cambridge 

Monographs on Particle Phys. and Cosmology (2009) 

SStill, ill I would ld like lik to repeat the h ( (probably) b bl ) kknowns about b 

the CKM matrix V(CKM): 

11. Det Det. V(CKM) is better to be real ! 

2. 3x3 V(CKM) is complex to describe CP violation 

3. If any y among g 9 elements is zero, , then there is no 

weak CP violation. 

4. λ is a good expansion parameter (Wolfenstein) . 

5. (31)∙(22)·(13) is the barometer of weak CP violation. 

6. Eventually, V(CKM) is derivable from the Yukawa 

texture. 

10 /75

1. Det. V(CKM) is better to be real ! 

If not not, then Arg. Arg Det Det. M Mq is not zero. zero Usually, Usually we remove 

this to define a good quark basis. The PQ symmetry? 

Or calculable models? 

KM model has a phase. MCK do not have a phase. 

If it has a phase, then 

L L( 

quark - gauge int. ) L( 

Higgs boson) 

 

2 

32 

2 

gc ~ 

GG 

 

 

 

 

2 ~ 

gc GG 

2 

32 

The neutron EDM has the problem. Fine-tuning. So, 

the CKM matrix having Det=0 is a good choice. 

But it is not absolutely necessary necessary. 

11/75

4. λ is a good expansion parameter (Wolfenstein) . 

We expand in terms of θ 1 since θ 2 and θ 3 are of order θ 1 2 . 


Satisfying y g all the requirements, q , we write an exact CKM matrix, , 

(31)(22)(13) is i 2 

2 2 2 

e i 

 

s 

1 

s 

2 

s 

3 

J E Kim Weak and Strong CP, Axions and DM USA 2011 13 /75 

c 

1 

c 

2 

c 

3 

 

s 

1 

s 

2 

s 

3

The elements of Det. V(CKM) ( ) is, , 

All elements have the same imaginary part part, due to our 

good choice of Det. being real. But, the individual part 

describes CP violating processes. 

J E Kim Weak and Strong CP, Axions and DM USA 2011 14/75

The approximate pp form is, , 

κb, or κt , or δ being zero washes out the CP violation, 

in the exact or in the approximate pp form. 


The Jarlskog g triangles g are 

These can be read directly from V(CKM). 



With our exact V(CKM), R=1 and R=L give 

Useful textures to find symmetries behind Yukawa couplings 

at the fundamental scale scale. BUT 

18 /75

In any case case, either Det V is real or there must be 

an axion. Both of them solves the strong CP 

problem. 

Consider, for example, there is no axion and Det 

V is not real real. But But, there is no dangerous NEDM 

diagram. Since Det V is not real, try that it has 

a phase 3φ 

Can φ appear as a physical one? Seems not not. 


Consider the NEDM diagram 

V 

* 

13 

V 

32 

V 

* 

21 

appear 

The 

overall 

is 

V * 

13 

d 

(11) 

simple 

s s 

photon 

V V * 

V 32 

in the 

element 

phase 

t u 

determinan 

does 

enough to 

makes 

not 

see 

t with 

it 

appear. 

the 

real, 

V 21 

V 11 

d 

m d 

phase 

so 

But 

essence. 

e 

the 

 

d 

3i 0 

. 

21 /75

The CP violation is an intereferance 

phenomenon 

Here the 4 couplings are related. The CKM 

matrix and the Jarlskog determinant encode 

these. 

What is the origin of weak CP? 


The CP origin g is from scalar interactions 

1. Complex p Yukawa couplings. p g The KM idea. 

2. Higgs interactions. T. D. Lee and S. Weinberg 

In any case, we must use the mass eigenstate quarks. 

Then, , Case 1 gives g the CKM matrix. That’s all for KM. 

But Case 2 can have additional CP violating interactions 

through Higgs exchange exchange. 


The strong CP invariance 

The existence of instanton solution in nonabelian gauge 

theories needs θ vacuum [CDG, JR]. It introduces the 

θ term, 

1 

F F 

32 2 

2 

 

 

32 

2 

 

, 

QCD 

weak 

weak 

~ 

FF arg.Det. M 

Here theta-bar is the final value taking into 

account the electroweak CP violation. For QCD 

to become a correct theory describing the CP 

conserving strong interaction phenomena, this 

CP violation must be sufficiently suppressed. 


q

• The neutron mass term 

g 

NN 

i / 

mne 

m 

n 

i i 

/ f f 

The NMDM and NEDM terms 

The mass term and the NMDM 

term have the same chiral 

transformation property. So, 

(b)s are simultaneously removed. 

(a) So, d(proton)= - d(neutron). 

is the NEDM contribution. 

In our study, the VEV of pi-zero 

determine the size of NEDM. 

25 /75

It is an order of magnitude larger than 

Crewther et al bound bound. 


We used C A Baker et al, PRL 97, 131801 (06), to 

obtain →|θ|< 0 7x10-11 obtain →|θ|< 0.7x10 11 

Why is this so small? : Strong CP problem. 

1. Calculable θ, , 2. Massless up pq quark ( (X) ) 

3. Axion 

Massless up quark 

Suppose that we chiral-transform a quark, 

Here, θ is not physical, and there is no strong CP 

problem. p The p problem is, , “Is massless up pqquark 

phenomenologically viable?” 

If m=0, it is equivalent 

to changing g g θ → θ -2α. 

Thus, there exists a 

shift symmetry θ → θ -2α. 

27 /75

The famous up/down quark mass ratio from chiral pert. 

calculation is originally given as 5/9 [Weinberg [Weinberg, 

Leutwyler] which is very similar to the recent compilation, 

m 

m 

u 0. 

5, 

d 

mu m md 2. 

51MeV, 

 

5 5. 1 1 

1 1. 

5 MeV 

(Manohar-Sachrajda) 

Excluding the lattice 

cal., this is convincing g 

that mu=0 is not a 

solution now. 

Particle Data (2010) 

J E Kim “Axions and cosmological constant”SNU CTP, 8 April 2010 

28 /75

So, , we need to consider axions and calculable 

models only. 

For calculable models, CP violation is absent in the 

Lagrangian That’s the definition of calculable models. 

Even if CP violation occurs through scalar interactions interactions, the 

complex Higgs couplings do not belong to calculable 

models. So, , calculable models start with 

REAL COUPLINGS. 

Namely, Lagrangian conserves CP, and theta=0 is chosen 

as the h symmetry point. i 

Then Then, CP violation must be spontaneous by generating 

complex VEVs. And we must build models forbidding 

theta term up to two loop level. 


22. Axions

Ki Kim-Carosi, C i arXiv:0807.3125 Xi 0807 3125 “A “Axions i and dth the strong t CP problem” bl ” 

(Rev. Mod. Phys. 82, 511 (2010)) 

Historically, Peccei-Quinn tried to mimick the symmetry θ → θ -2α, by 

the full electroweak theory. They found such a symmetry if H u is 

coupled to up-type quarks and H d couples to down-type quarks, 

d 

L q u H q d H V ( H , H ) 

L 

R 

u 

L 

R 

d 

( u d 

Eq. β=α 

achieves 

the same 

thing as the 

m=0 case. 


The Lagrangian g g is invariant under changing g g θ → θ -2α. 

Thus, it seems that θ is not physical, since it is a phase of 

the PQ transformation. But, θ is physical. At the 

Lagrangian level, there seems to be no strong CP 

problem. But and breaks the PQ global 

symmetry and there results a Goldstone boson boson, axion aa 

[Weinberg,Wilczek]. Since θ is made field, the original 

cosθ dependence p becomes the ppotential 

of the axion a. 

If its potential is of the cosθ form, always θ=a/Fa can be 

chosen at 0 [Instanton physics physics,PQ,Vafa PQ Vafa-Witten] Witten]. So the 

PQ solution of the strong CP problem is that the vacuum 

chooses 

0 


‘tt Hooft determinental interaction and the 

solution of the U(1) problem. If the story 

ends here, the axion is exactly massless. 

But,…. 


History: The Peccei-Quinn-Weinber-Wilczek axion is 

ruled out early in one year [Peccei, 1978]. The PQ 

symmetry can be incorporated by heavy quarks, using 

a singlet Higgs field [KSVZ axion] 

L 

Q Q S V 

S, 

H , H ) 

L 

R 

( u d 

 

Here, Higgs doublets are neutral under PQ. If they are 

not neutral, neutral then it is not necessary to introduce heavy 

quarks [DFSZ]. In any case, the axion is the phase of 

the SM singlet S, S, if the VEV of SS is much above the 

electroweak scale. 

Now the couplings of S determines the axion interaction. 

Because it is a Goldstone boson, the couplings are of the 

derivative form except the anomaly term. 


Namely, the parameter theta-bar is made dynamical, i.e. 

 

 

gc 

a 

L Fa 

GG, 

a Fa 

F 

~ 

2 

1 2 

 

2 

2 

32 32 

F 

There is no potential p for the field a , but at very y low 

energy below the QCD chiral symmetry breaking scale, 

the potential consistent with the symmetry of the anomaly 

term is generated, 

V 

 

a 

 

4 

cos 

 

QCD 0 

 

Fa 

 

F 

a 

35/75

In most studies, a specific example is 

discussed discussed. Here Here, we consider an effective 

theory just above the QCD scale. All heavy 

fields are integrated out. out 

Kim-Carosi, RMP82, 557 (2010) 

[arXiv:0807 [arXiv:0807.3125] 3125] 

In axion physics physics, heavy fermions carrying 

color charges are special. So consider the 

following Lagrangian 


Heavy Q’s 

integrated 

out 

The axion mass depends only on the combination of 

(c2+c3). 




The interaction 

 

m 

u 

 

3 

 

 

0 

1 

2 

32 

2 

4 

mum d 

Z 2 2 

V [ a ] f m ( 1 cos 

2 

( 1 Z ) 

a 

F 

a 

1 

 

2 

 

F 

a Z f 

m 

cos ma 

 

F 11 

Z F 

a 

a 

 

F 

a 

F 

a 

) 

 

 

a 

F 

a 

~ 

{ FF} 

7 

10 GeV 

0. 

6[ 

eV ] 

F 

J E Kim Weak and Strong CP, Axions and DM USA 2011 40/75 

a

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

CP conserving point 

In the evolving universe universe, at some temperature temperature, say T T1, aa 

starts to roll down to end at the CP conserving point 

sufficiently closely. This analysis constrains the axion decay 

constant (upper bound) and the initial VEV of at T1. J E Kim Weak and Strong CP, Axions and DM USA 2011 41 /75

Bae-Huh-Kim, JCAP0809, 005 

m q 

Λ QCD 


If we do not take into account the overshoot factor 

and the anharmonic correction, 

Inclusion of these 

showed the region, 

prev. figure 


The relevant axion interactions are presnt presnt, 

Interaction 

em 

a ~ a 

: ca FemFem, 

ye 

ei 

5e 

a Fa 

8 8 

F 

F 

a 

a 

The Primakoff term is always present present, but the electron term 

is present only when the Higgs coupling to leptons carry the 

PQ charge. 

In a full theory, one must look into all the PQ charges of 

fermions. 


Above the electroweak scale, we integrate out heavy 

fi fields. ld If colored l d quarks k are integrated i d out, iits effect ff is i 

appearing as the coefficient of the gluon anomaly. If only 

bosons are integrated out out, there is no anomaly term term. 

Thus, we have 

KSVZ: c1=0, c2=0, c3=nonzero 

DFSZ DFSZ: c1=0, 0 c2=nonzero, c3=00 

PQWW: similar to DFSZ 


It depends on 

models models. 

There are not many 

calculations in 

string models. 

46 /75

White dwarf bound 

(1st (1 hint at the center of the axion window) 

st hint at the center of the axion window) 


2. 

24 

10 

13 

 

F 

a 

0.510 

10 

GeV 

for 

Bae Bae, Huh Huh, JEK, JEK Kyae Kyae, Viollier Viollier, NPB 817, 817 58 (2009) 

N 

DW 

 

Isern, 

7 th PATRAS 

2011 

1 

2 

48 /75

ADMX Phase II & ADMX-HF Coverage 

van a Bibber bbe aat ASK S 2011 0 

V -1 g ga 

[GeV ] 

10 -12 

10-13 10 

10 -14 

10 -15 

10-16 10-16 f (GHz) 

이미지를 표시할 수 없습니다. 컴퓨터 메모리가 부족하여 이미지를 열 수 없거나 이미지가 손상되었습니다. 컴퓨터를 다시 시작한 후 파일을 다시 여십시오. 여전히 빨간색 x가 나타나면 이미지를 삭제한 다음 다시 삽입해야 합니다. 

0.5 1 2 5 10 20 

ADMX 

(complete) 

ADMX 

(Ph (Phase II) 

ADMX 

(Higher TM) 

ADMX - HF 

a ~ 023 0.23 

KVSZ 

DFSZ 

1 10 100 

m a (eV) 

49/75

3. Dark matter 

Here Here, I skip WIMPs and other Z2 odd cases cases, but 

simply comment on axionic DM difference from 

others. 

50 /75

B. M. Demirkoez (ATLAS), 7th B. M. Demirkoez (ATLAS), 7 PATRAS, Mykonos, 1 July 2011 

51/75

squark to jets jets, or 

gluinos to jets 

52 /75

q ~ q 

q 

~ 

0 

1 

This gives the above LHC bound for the R-parity 

conserving CMSSM. 

If the R-parity conserved, also the axino or 

gravitino LSP models are not free from this LHC problem. 

For Fa=1011 GeV and 1 TeV squark mass, the vertex is 

shifted by a few mm order order, which is swamped by decays 

to NLSPs. 

q ~ 

q 

a~ 

, or g~ 

3 / 

2 

53 /75

The lepton modes are not accurate enough to compete 

with this (MET) + jets. 

q 

l 

q ~ q 

0 

0 

1 

~ ~ 

~ 

l 

2, 

3 

 

l 

 

~ 

54 /75

Direct detection 

Axion detection 

Colliders 

1. Complementarity with the 

assumption ti ρWIMP/ρ / a 

2. Identification of dark matter 

3. Interplay with astrophysics 

Indirect detection 


EE. AAprile, il 

1 July 2011 

7th PATRAS 

Mykonos 


The flat rotation curve hints the existence of DM in our 

galaxy galaxy. 


mass 

vel. disper. p 

coh. length 

Dark matter candidates 

 

 

m 

v 

 

m m v 

axion WIMP sterile 

10 

10 

10 

5 

17 

eV 

c 

cm 

100 GeV 

10 

10 

12 

c 

cm 

10 

10 

10 

keV 

8 

17 5 

1 

The axion and WIMP both behave as CDM at the time of 

forming galaxies galaxies. They differ in spin and coherence lengths lengths. 

Sikivie and Yang pointed out that for axions there is a 

possibility of BEC. [PRL 103 (2009) 111301] 

Sikivie comments that axion is better in explaining the 

inner caustics and angluar momentum of galaxies. 


c 

cm

Tidal torque theory with axion BEC 

Not irrotational: 

net overall rotation 

Sikivie: Talkat7th Sikivie: Talk at 7 PATRAS 2011 

th PATRAS, 2011 

By BEC 

By BEC 

Net overall rotation is obtained because, in the lowest energy state, 

all axions fall with the same angular g momentum. Two distinctive behaviors 

before the dark matter falls into galactic halos. WIMPs have an irrotational 

velocity field whereas axions fall in with net overall rotation. Axions do this 

because they go to the lowest energy state for given angular momentum 

BEFORE FORMING GALAXIES. That state has net overall rotation. 


Why BEC ? by yielding their energy to the non-condensed 

particles, the total entropy is increased. 

Pre BEC BEC 

 

To same p and same E 


neighboring 

protogalaxy l 

 

v 0 

Tidal torque theory 

with ordinary CDM 

the velocity field remains irrotational 


Sikivie: the caustics are different in the two cases: 

Caustic rings for axions and `tent-like' caustics for WIMPs. 

Th The evidence id my collaborators ll b t and d I ffound d ffor caustic ti 

rings is only consistent with axions. 

So the bulk of dark matter must be axions. 


ATLAS on SUSY 

SUSY confronts data 

CMS on Z’ Z 

The squark and gluinos are excluded roughly below 1 TeV TeV, 

and extra Z’ below 1.6 TeV (1.9 TeV without SUSY). 

Regarding this I comment my recent works. 


GUT gauge g g ggroup p : SU(6) ( ) GUT 

Flavor unification: JEK JEK, PLB107 (1982) 69 

This GUT contains the previous SU(3) WW. So So, if we succed 

in unification with SU(3) c, then the needed flavor symmetry 

will result. In F-theory, we succeeded. 


For diagonal subgroups of E6, any U(1) generator can be 

a li linear combination bi i of f CCartan subgroup b of f E E6. SSo, 

we 

prove in terms of the Cartan subgroup of SU(6)xSU(2). 

F 3, F 8, T 3, Y, Y 6, X 3 

Leptons p and Higgs gg doublets do not carry y the baryon y 

number. 

B aY bY 

cX 

 

6 3 

dR 

No solution. 

JEK+S. Shin, 

1104 1104.5500 5500 


For leptophobic Z’, we may try 

1 5 

1 

1 

1 

 

Y' 

Y6 

Y , , , 0, 

0, 

1 

3 6 6 

3 3 3 

Hu carries a nonvanishing Y’. So, N has a novanishing Y’ 

and singlet neutrino mass scale is the Z’ Z mass scale. scale 

So, we consider Z’ coupling both to B and L. 

For Z6 hexality, we consider SU(6)xSU(2). 


Still, we studied the Z-Z’ mass in the SU(6)xSU(2) model 

with fine tuned coupling constants constants. 

So, we consider SU(6)xSU(2) 

In this study, y we assume of 

course the lepton coupling 

to Z’. Then, the LEP2 

precision ii experiment i t 

bound on the rho 

parameter is crucial to 

constrain the model. 


Effective SUSY 

CCohen-Kaplan-Nelson, h K l N l PLB 388 388, 588 (1996) 

The first two family sfermions are heavy, but the third family 

sfermions are at TeV TeV. 

To obtain this kind, we assign different quantum 

numbers to the third family members. The mediation 

mechanism is Z’ meditation. Langacker et al., PRL 100, 041802 (2008); 

Mohapatra+Nandi, PRL 79, 181 (1997) 

It is different from the 

E6 GUT. 

Jeong+JEK+Seo, 

1107 1107.5613 5613 


Z’ mediation to effSUSY 



Three quark families appear as 

3(3 3 (3c, 3 3W) ) 

At low energy, we must 

hhave nine i 3* W tto cancel l SU(3) W 

anomaly. 

d u X + 

d u X + 

3Hu + 3 lep+3 H 1d N 0 

3 3 6 

Both H Hu and H d appear from 3* 3 . 

It is in contrast to the other 

cases such as in SU(5) or SO(10). 

Now, the Hu and Hd coupling must 

come from 3* W 3* W 3* W coupling. 

D H 0 H + e- ν 

(H- ) (H0 ) 

There remain three pairs of 3* W(H + ) and 3* W(H- ) plus 

three families of 3W(quark) and 3* W(lepton) 


Th Thus, there th appears the th LLevi-Civita i Ci it symbol b l and d ttwo epsilons il are 

appearing, in SU(3) W space, a, b, c and in flavor space, I, J, …. 

Therefore, in the flavor space the Hu-Hd mass matrix is antisymmetric and 

hence its determinant is zero. 

Introduction of flavor in the Higgs sector: 

Lee-Weinberg g SU(3)-weak ( ) gives g 

3*-3*-3* SU(3)-weak singlet = antisymmetric gives 

antisymmetric bosonic flavor symmetry (SUSY)! 

and d one pair i of f Hi Higgs ddoublets bl t iis massless. l 


The hierarchy of SUSY partner masses are 

M a 

M 

~ 

Z ' 

g g 

( ) 

 

( 16 

) 

2 

gY 

' '2 

F 

Y 2 

16 16 M 

2 2 

Y ' a M 2 2 Z 'log 

mess 

mess 

 

 

M 

Z ' 

 

 

 

M 

g 

Y 

' 

Y ' 

~ 

q~ 

, l 

~ ~ ( ) 

M 

, 

' 

log 

 

q Z 

1, 

2 l1, 

2 

M Z ' 

4 

 

 

 

 


3/2

1. In fact, this kind of model is already present in 

string compactification compactification. [JEK [JEK, plb 656 656, 207 (2007) 

[arXiv:0707.3292]] 

2. One Higgs doublet pair. 

3. Quantum numbers of extra U(1)’ charges as needed 

in the U(1)’ mediation. 


Conclusion 

Here, I talked a few topics beyond the SM paying attention 

to my recent papers. 

1. A useful suggestion for the CKM matrix. 

2. Weak CP and strong CP, and axions. 

3. There is no Z’ below 10 TeV from E6, otherwise our 

wisdom to the standard model is in trouble trouble. 

4. U(1) U(1)’ mediation possible consistent with the recent LHC 

data. For example, in flavor unification models, not 

in E6 GUT.

Slides - Fermilab Center for Particle Astrophysics

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