kiasworkshop.kias.re.kr/pheno2/downloads/2012_kias_pheno_pko.pdf · 2012-09-14 · hidden sector ?...

A Few General Aspects of Higgs-portal DM models and Higgs phenomenology

Pyungwon Ko (KIAS)

12년 9월 11일 화

Contents

• Motivations (Hidden sector DM)• Singlet scalar messenger (Strongly Interacting

Hidden Sector, Singlet fermion CDM)

• New vector boson messenger for PAMELA• A few generic aspects of Higgs-portal DM• Comments on the effective lagrangian approach• Conclusions

12년 9월 11일 화

Motivations

• EWPT and CKMology put strong constraints on new particles with nonzero SM charges @ EW scale

• No evidence of new particles @ LHC so far• SM singlets @ EW scale still possible• CDM can be a phenomenological motivation for

a new singlet particle @ EW scale

• Any other theoretical motivations ?

12년 9월 11일 화

SM singlet @ EW scale ?

• Hidden sector is generic in SUSY and superstring models

• There could be light degrees of freedom in a hidden sector, as there are many light d.o.f.’s in the visible sector

• Could be useful for multicomponent CDM’s• What would be the generic signatures ?? • Existence of a hidden sector is eventually an

experimental question

12년 9월 11일 화

Hidden Sector

• They are all SM singlets• Can have their own gauge interactions• Need messenger between the SM sector and

the hidden sector

• Gravitational messenger was considered in mid 80’s right after the 1st string revolution

• Here we consider Higgs portal and/or new gauge interactions as messengers

12년 9월 11일 화

Hidden sector ?

• Usually the hidden sector breaks SUSY spontaneously, and then does nothing else

• Could play an important role in phenomenology at TeV scale, especially in Higgs phenomenology (Invisible Higgs decay into a pair of CDM’s)

• Many possibilities for the choice of gauge groups and matter contents of the hidden sector (e.g.# of colors and flavors in the hidden QCD) and mediators between the SM and a hidden sector

12년 9월 11일 화

Related Works & Talks(as of 2007)

• Foot, Volkas, et al (Mirror World)• Berezhiani et al (Mirror World)• Strassler, Zurek, et al (Hidden Valley)• Wilczek (Higgs portal & Phantom)• Cheung, Ng, et al (Shadow)• Ko et al (Hidden Sector strong interaction)• Many works after 2007

12년 9월 11일 화

SM Hidden QCDSinglet

Scalar S’sSM Hidden sector

• Taeil Hur, D.W. Jung, P. Ko, J. Lee : Strongly interacting hidden sector

• S. Baek, P. Ko, W.I. Park : singlet fermion DM

12년 9월 11일 화

SM Hidden QCD

New gauge interactions

SM Hidden sector

• Both SM and hidden sector are charged under new gauge interaction

• B , L , B-L , Li - Lj , ... etc.

• More interesting collider signatures

• Gondolo, Ko, Omura, U(1)B, PRD

• mu-tau gauge int. for PAMELA (Baek & Ko) 12년 9월 11일 화

EWSB and CDM from Strongly Interacting Hidden Sector

12년 9월 11일 화

Contents

• Motivations• Toy model: Hidden Sector Pion as CDM• Model I with a scalar messenger• Model II with extra U(1) gauge boson messenger• Conclusions

12년 9월 11일 화

• the stability of DM without ad hoc Z2 symmetry ?

• the generation of mass scales from quantum mechanics ?

• the effects of a hidden sector, if it exists ?• Answer to these seemingly unrelated

questions is YES !

Can we understand

12년 9월 11일 화

Stability of DM

• Usually guaranteed by ad hoc Z2 symmetry• Or life time of DM made very long by fine

tuning of couplings

• Note that quark flavor is conserved within renormalizable QCD (accidental symmetry)

• Can we find a similar reason for the DM stability ?

12년 9월 11일 화

Can we understand the origin of all the masses ?

• In massless QCD, all the masses originate from dimensional transmutation

• Proton mass dynamically generated by quarks and gluons, not by the quark masses

• A similar mechanism for elementary particles ?• Questions by Coleman and Weinberg, Wilczek, C.

Hill, W. Bardeen, ......

12년 9월 11일 화

Weakly Interacting Hidden Sector

• Perturbation applicable & easy to analyze, • Gauge boson mass is generated by Higgs mechanism• Origin of mass scale remains unclear, just like in SM• Will discuss a Leptophilic Dirac Fermion DM and a

singlet fermion DM

12년 9월 11일 화

Strongly Interacting Hiddens Sector

• Perturbation not applicable & difficult to analyze• Construct relevant Effective Field Theory (EFT)

depending on the physics problems

• Can address dynamical generation of mass scale, like in massless QCD

• Chiral lagrangian technique for the Nambu-Goldstone boson (the hidden sector pion = CDM)

(arXiv:0709.1218 with T.Hur, D.W.Jung and J.Y.Lee)

12년 9월 11일 화

Nicety of QCD• Renormalizable : Valid to very high energy scale • Asymtotic feedom : No Landau pole below • QM dimensional transmutation :

• Trace anomaly breaks scale sym. of massless QCD• Chiral symmetry breaking (spontaneous & explicit)• Light hadron mass dominantly from chiral sym

breaking

• Flavor conservation : accidental symmetry of QCD

gs ⇥ �QCD �MPlanck

MPlanck

12년 9월 11일 화

Can we build a model for EWSB and CDM

similar to QCD ?

12년 9월 11일 화

Can we build a model for EWSB and CDM

similar to QCD ?

Yes !

12년 9월 11일 화

Toy Model

12년 9월 11일 화

Hidden Sector Pion as a CDM

• CDM in most models stable due to ad hoc Z2 symmetry

• In our models I&II, the hidden sector pion is stable due to flavor conservation in hQCD (accidental symmetry of the underlying gauge theory), which is a very nice aspect of our model

• Remember pion is stable under strong interaction in ordinary hadronic world, decays only through em or


12년 9월 11일 화

!"#$%%&'(!&)*+,

"&--&'.&,

/0-$)(1$)*2,&

!$3$40,(*+(+,%$'0,5(678


12년 9월 11일 화

Warming up with a toy model

• Reinterpretation of 2 Higgs doublet model• Consider a hidden sector with QCD like new

strong interaction, with two light flavors

• Approximate SU(2)L X SU(2)R chiral symmetry, which is broken spontaneously

• Lightest meson : Nambu-Goldstone boson -> Chiral lagrangian applicable

• Flavor conservation makes stable -> CDM

�h

�h

12년 9월 11일 화

Model-I

Potential for H1 and H2

V (H1, H2) = −µ21(H

†1H1) +

λ12

(H†1H1)2 − µ22(H

†2H2)

+λ22

(H†2H2)2 + λ3(H

†1H1)(H

†2H2) +

av322

σh

Stability : λ1,2 > 0 and λ1 + λ2 + 2λ3 > 0

Consider the following phase:

H1 =

(

0v1+hSM√

2

)

, H2 =

(

π+hv2+σh+iπ

0h√

2

)

Correct EWSB : λ1(λ2 + a/2) ≡ λ1λ′2 > λ23

– p.34/50

Not present in the two-Higgs Doublet model

12년 9월 11일 화

• H2 : SM singlet, no contribution to W,Z, or fermion masses -> Less problem with EWPT or Higgs mediated CPV

• “a” term gives hidden sector pion mass ->CDM• Charges of hidden pion : Not electric charge, but

the hidden sector isospin (I3)

Similar to the usual two-Higgs

doublet model, except that

12년 9월 11일 화

Model-I

h and H are mixtures of hSM and σh: partially composite

h(H) − V − V couplings : the same as the HSM − V − Vcouplings modulo cos α and sin α

the same is true for the h(H)− f − f̄ with SM fermions fcouplings

Productions of h and H at colliders are suppressed bycos2 α and sin2 α, relative to the production of the SMHiggs with the same mass

h(H) − πh − πh couplings contribute to the invisibledecays h(H) → πhπh

4 parameters for µ21 = 0: tan β, mπh, λ1 and λ2 or tradethe last two with mh and mH

– p.36/5012년 9월 11일 화

Br of h and HModel-I : Spectra and branching ratios

10-4

10-3

10-2

10-1

100

0 50 100 150 200 250 300

Br(

h)

mπh

bb

ττggcc

γZγγss

µµ

πhπh

tan β = 1mh = 120 GeVmH = 300 GeV

10-4

10-3

10-2

10-1

100

0 50 100 150 200 250 300 350 400

Br(

H)

mπh [GeV]

hhWW

ZZ

bbgg

ττ

πhπh

tan β = 1mh = 120 GeVmH = 300 GeV

Branching ratios of h and H as functions of mπh fortan β = 1, mh = 120 GeV and mH = 300 GeV.

h,H → πhπh : invisible decay branching ratios makedifficult to detect them at colliders

– p.25/38

12년 9월 11일 화

Relic DensityModel-I : Relic density of πh

-8-6-4-2 0 2 4 6 8

mh [GeV]

mπ

h [

GeV

]

tan β = 1mH = 500 GeV

60 80 100 120 140 160 180 200 220

0

50

100

150

200

250

300

350

400

450

500

-6-4-2 0 2 4 6 8

mh [GeV]

mπ

h [

GeV

]

tan β = 1mH = 500 GeV

60 80 100 120 140 160 180 200 220

0

50

100

150

200

250

300

350

400

450

500

Ωπhh2 in the (mh1 ,mπh) plane for tan β = 1 and mH = 500

GeV

Labels are in the log10

Can easily accommodate the relic density in our model

– p.27/3812년 9월 11일 화

Model-I : Direct detection rate

10-54

10-52

10-50

10-48

10-46

10-44

10-42

10-40

10 100 1000

σ (

πh N

→ π

h N

) [c

m2]

mπh [GeV]

Ω h2 < 0.096

0.096 < Ω h2 < 0.122

CDMS II

CDMS 2007 projected

XENON 10 2007

XMASS

super CDMS-1 ton10-48

10-47

10-46

10-45

10-44

10-43

10-42

10-41

10-40

100 200 300 400 500 600 700 800 900 1000

σ (

πh N

→ π

h N

) [c

m2]

mπh [GeV]

Ω h2 < 0.096

0.096 < Ω h2 < 0.122 CDMS-II

ZENON

σSI(πhp → πhp) as functions of mπh for tan β = 1 andtan β = 5.

σSI for tan β = 1 is very interesting, partly excluded bythe CDMS-II and XENON 10, and als can be probed byfuture experiments, such as XMASS and super CDMS

tan β = 5 case can be probed to some extent at SuperCDMS

–p.28/38

Model-I : Direct detection rate

10-54

10-52

10-50

10-48

10-46

10-44

10-42

10-40

10 100 1000

σ (

πh N

→ π

h N

) [c

m2]

mπh [GeV]

Ω h2 < 0.096

0.096 < Ω h2 < 0.122

CDMS II

CDMS 2007 projected

XENON 10 2007

XMASS

super CDMS-1 ton10-48

10-47

10-46

10-45

10-44

10-43

10-42

10-41

10-40

100 200 300 400 500 600 700 800 900 1000

σ (

πh N

→ π

h N

) [c

m2]

mπh [GeV]

Ω h2 < 0.096

0.096 < Ω h2 < 0.122 CDMS-II

ZENON

σSI(πhp → πhp) as functions of mπh for tan β = 1 andtan β = 5.

σSI for tan β = 1 is very interesting, partly excluded bythe CDMS-II and XENON 10, and als can be probed byfuture experiments, such as XMASS and super CDMS

tan β = 5 case can be probed to some extent at SuperCDMS

–p.28/38

12년 9월 11일 화

Model I : Scalar Messenger

PRL 2011 (with Taeil Hur)and work in preparation

12년 9월 11일 화

Model I (Scalar Messenger)

• SM - Messenger - Hidden Sector QCD• Assume classically scale invariant lagrangian --> No

mass scale in the beginning

• Chiral Symmetry Breaking in the hQCD generates a mass scale, which is injected to the SM by “S”

SM Hidden QCD

Singlet Scalar S

12년 9월 11일 화

Model-II

Introduce a real singlet scalar S

Modified SM with classical scale symmetry

LSM = Lkin −λH4

(H†H)2 −λSH

2S2 H†H −

λS4

S4

+(

QiHY Dij D

j + QiH̃Y Uij U

j + LiHY Eij E

j

+ LiH̃Y Nij N

j + SN iT CY Mij Nj + h.c.

)

Hidden sector lagrangian with new strong interaction

Lhidden = −1

4GµνG

µν +NHF∑

k=1

Qk(iD · γ − λkS)Qk

– p.42/50

Model-II

Introduce a real singlet scalar S

Modified SM with classical scale symmetry

LSM = Lkin −λH4

(H†H)2 −λSH

2S2 H†H −

λS4

S4

+(

QiHY Dij D

j + QiH̃Y Uij U

j + LiHY Eij E

j

+ LiH̃Y Nij N

j + SN iT CY Mij Nj + h.c.

)

Hidden sector lagrangian with new strong interaction

Lhidden = −1

4GµνG

µν +NHF∑

k=1

Qk(iD · γ − λkS)Qk

– p.42/5012년 9월 11일 화

• Hidden sector condensate develops a linear potential for S -> Nonzero VEV for S

• Hidden sector quarks get massive by • Nonzero Higgs mass parameter form • EWSB occurs if the sign is correct• Therefore, all the mass scales from hidden sector

quark condensates

• Construct effective chiral lagrangian for the hidden sector pion

• Calculate the relic density, (in)direct detection rate etc.

12년 9월 11일 화

Model-II

Effective lagrangian far below Λh,χ ≈ 4πΛh

Lfull = Leffhidden + LSM + Lmixing

Leffhidden =v2h4

Tr[∂µΣh∂µΣ†h] +

v2h2

Tr[λSµh(Σh + Σ†h)]

LSM = −λ12

(H†1H1)2 −

λ1S2

H†1H1S2 −

λS8

S4

Lmixing = −v2hΛ

2h

[

κHH†1H1

Λ2h+ κS

S2

Λ2h+ κ′S

S

Λh

+ O(SH†1H1

Λ3h,S3

Λ3h)

]

≈ −v2h

[

κHH†1H1 + κSS

2 + Λhκ′SS

]

– p.43/50

12년 9월 11일 화

Br for lighter Higgs hModel-II: Branching ratios of h

[GeV]hπM

210

310

Br(

h)

-510

-410

-310

-210

-110

1 = 500 GeV

hv

= 1βtan

= 120 GeVhM

hπ

hπ→h

bb→h cc→h

ss→h

ττ→h

µµ→h

WW→h

ZZ→h

γγ→h

gg→h

γZ→h

[GeV]hπM

210

310

Br(

h)

-510

-410

-310

-210

-110

1 = 1 TeV

hv

= 2βtan

= 120 GeVhM

hπ

hπ→h

bb→h cc→h

ss→h

ττ→h

µµ→h

WW→h

ZZ→h

γγ→h

gg→h

γZ→h

Br’s of h owith mh = 120 GeV as functions of mπh for(a)vh = 500 GeV and tan β = 1

(b) vh = 1 TeV and tan β = 2.

– p.45/50

12년 9월 11일 화

Relic densityModel-II: Relic densities of Ωπhh2

Ωπhh2 in the (mh1 ,mπh) plane for

(a) vh = 500 GeV and tan β = 1,

(b) vh = 1 TeV and tan β = 2.

– p.46/50

12년 9월 11일 화

Direct Detection RateModel-II: Direct detection rates

[GeV]hπM

102

103

10

]2[c

mS

Iσ

-4910

-4610

-4310

-4010

-3710

-3410

< 0.096 2hΩ

0.122 ≤ 2hΩ ≤ 0.096 CDMS-II(2004+2005)

XENON10(136kg-d)

CDMS-2007 projected

XMASS

super CDMS-1 ton

= 1 TeVh

v

= 500 GeVh

v

σSI(πhp → πhp) as functions of mπh.the upper one: vh = 500 GeV and tan β = 1,

the lower one: vh = 1 TeV and tan β = 2.

– p.47/5012년 9월 11일 화

Hidden World

SMExtra U(1)

gauge boson

Model II & III (Extra U(1))

• We consider two models• U(1) model by Strassler et al. (Hidden valley

scenario) : with hidden sector QCD

• Leptophilic U(1) motivated by PAMELA and FERMI data (Baek and Ko) : with hidden sector DM Dirac fermion

12년 9월 11일 화

U(1) model by Strassler et al. (Hidden Valley)

Work in preparation(with S. Baek & Taeil Hur)

12년 9월 11일 화

Model II with Extra U(1)

• Assume extra U(1) under which both SM and hQCD matters are charged [Hidden Valley Scenarios by Strassler et al.]

• Hidden sector pion as CDM [Cassel, Ghilencea, Ross]• hidden-Higgs and SM Higgs mix with each other• Relic density of CDM is dominated by Higgs

exchanges

• Direct Detection Rates close to the current/future experiments

12년 9월 11일 화

Therefore we do not try to extimate thermal relic density of the hidden sector baryon,keeping in mind that they could also contribute to the observed CDM density.

This paper is organized as follows. In Sec. 2, we describe the model lagrangian, and theeffective chiral lagrangian that describes dynamics of the hidden sector pions, a candidatefor the CDM. In Sec. 3, we show the particle spectra and collider phenomenology. In Sec. 4,we calculate thermal relic density of the hidden sector pion, and the spin-independentscattering cross section of the hidden sector pion on proton. In Sec. 5, we summarize ourresults. The detailed expressions for the model lagrangians and the relations between theinteraction eigenstates and the physical states are collected in Appendix.

2. Model

In this section, we recapitulate the U(1)X model by Strassler and his collaborators. Inthe model the SM is extended by new gauge groups SU(Nh)×U(1)X and new SM-singletfields: hidden quarks Qh, right-handed neutrino NR, complex scalar φ. The hidden quarks,which are SM singlets, are charged under the strong gauge group SU(Nh) while the otherfields are not. The U(1)X charges of the fields are chosen by anomaly-free condition. Allfield contents and their charge assignment are given in Table. 1.

2.1 Lagrangian above Λh

The full renormalizable Lagrangian above the confinement scale Λh is given by

L = L′SM + LKinetichidden + LYukawahidden + LScalarhidden (2.1)

LKinetichidden = −14[(Fh)aµν(Fh)

aµν ] − 14X̂µνX̂

µν − sinχ2

X̂µνB̂µν

+(DµΦ∗)(DµΦ) + i NRiD/ NRi+i UhLD/ UhL + i UhRD/ UhR + i DhLD/ DhL + i DhRD/ DhR (2.2)

LYukawahidden = −yNRLNRiH̃†#Lj + h.c.

−yUhUhRUhLΦ− yDhDhRDhLΦ∗ − yNRijN cRiNRjΦ

∗ + h.c. (2.3)

LScalarhidden = +µ22Φ∗Φ− λ12(H†H)(Φ∗Φ) −λ22

(Φ∗Φ)2, (2.4)

where (Fh)µν , X̂µν and Bµν are field strength tensors of SU(Nh), U(1)X and U(1)Ygroups, respectively. L′SM is same with Standard Model Lagrangian except that U(1)Xcontribution is added to the covariant derivative of each field : DµφSM ≡ (DµSM +iĝXQ̂X [φSM ]X̂µ)φSM for all SM fields.

The kinetic mixing term − sin χ2 X̂µνB̂µν can be removed by field redefinition X̂µ, B̂µ

→ Xµ, Bµ with transformation

(B̂µX̂µ

)=

(1 − tanχ0 1/ cos χ

)(BµXµ

). (2.5)

– 3 –

qLi uRi dRi !Li eRi NRi UhL UhR DhL DhR H ΦSU(3) 3 3 3 1 1 1 1 1 1 1 1 1SU(2) 2 1 1 2 1 1 1 1 1 1 2 1U(1)Y 16

23 −

13 −

12 −1 0 0 0 0 0

12 0

U(1)X −1515 −

35

35

15 1 q+ −q− −q+ q−

25 2

SU(nh) 1 1 1 1 1 1 nh nh nh nh 1 1# of gen. 3 3 3 3 3 3 1 1 1 1 1 1

Table 1: Charge assignments for the model : q+ + q− = −2

After this redefinition, the covariant derivative transforms

Dµ = ∂µ + igXQXX̂µ + igY QY B̂µ + · · · (2.6)

= ∂µ +igXcos χ

(QX −gYgX

QY sin χ)Xµ + igY QY Bµ + · · · . (2.7)

2.2 Chiral lagrangian for the hidden sector pions (πh’s)

In the low energy below Λh scale, the Lagrangian involving hidden sector quarks Qh canbe replaced by

Leffchial =v2h4

Tr[DµΣhDµΣ†h] +

v2h2

Tr[µh(MQhΣh + Σ†hM

†Qh

], (2.8)

where

Σh(x) = e2iΠ(x)/vh , Π(x) = πaσa2

=

(π0

2π+√

2π−√

2−π02

). (2.9)

The mass matrix of hidden quarks is given by

MQh =

(yUhΦ 0

0 yDhΦ∗

). (2.10)

The covariant derivative of Σ field is defined by

DµΣh = ∂µΣh + igX

cos χ(QLΣh − ΣhQR)Xµ, (2.11)

where

QL =

(q+ 00 −q+

)and QR =

(−q− 0

0 q−

). (2.12)

We ignore these terms :

Lmixing = −v2hΛ2h[κHH†1H1Λ2h

+ κSS2

Λ2h+ κ′S

S

Λh+ O(

SH†1H1Λ3h

,S3

Λ3h)]

≈ −v2h[κHH†1H1 + κSS

2 + Λhκ′SS] (2.13)

– 4 –

12년 9월 11일 화

qLi uRi dRi !Li eRi NRi UhL UhR DhL DhR H ΦSU(3) 3 3 3 1 1 1 1 1 1 1 1 1SU(2) 2 1 1 2 1 1 1 1 1 1 2 1U(1)Y 16

23 −

13 −

12 −1 0 0 0 0 0

12 0

U(1)X −1515 −

35

35

15 1 q+ −q− −q+ q−

25 2

SU(nh) 1 1 1 1 1 1 nh nh nh nh 1 1# of gen. 3 3 3 3 3 3 1 1 1 1 1 1

Table 1: Charge assignments for the model : q+ + q− = −2

After this redefinition, the covariant derivative transforms

Dµ = ∂µ + igXQXX̂µ + igY QY B̂µ + · · · (2.6)

= ∂µ +igXcos χ

(QX −gYgX

QY sin χ)Xµ + igY QY Bµ + · · · . (2.7)

2.2 Chiral lagrangian for the hidden sector pions (πh’s)

In the low energy below Λh scale, the Lagrangian involving hidden sector quarks Qh canbe replaced by

Leffchial =v2h4

Tr[DµΣhDµΣ†h] +

v2h2

Tr[µh(MQhΣh + Σ†hM

†Qh

], (2.8)

where

Σh(x) = e2iΠ(x)/vh , Π(x) = πaσa2

=

(π0

2π+√

2π−√

2−π02

). (2.9)

The mass matrix of hidden quarks is given by

MQh =

(yUhΦ 0

0 yDhΦ∗

). (2.10)

The covariant derivative of Σ field is defined by

DµΣh = ∂µΣh + igX

cos χ(QLΣh − ΣhQR)Xµ, (2.11)

where

QL =

(q+ 00 −q+

)and QR =

(−q− 0

0 q−

). (2.12)

We ignore these terms :

Lmixing = −v2hΛ2h[κHH†1H1Λ2h

+ κSS2

Λ2h+ κ′S

S

Λh+ O(

SH†1H1Λ3h

,S3

Λ3h)]

≈ −v2h[κHH†1H1 + κSS

2 + Λhκ′SS] (2.13)

– 4 –

12년 9월 11일 화

2.3 Scalar Potential

The scalar potential is given by

V (H, Φ) = −µ21H†H − µ22Φ∗Φ + ρ3(Φ∗ + Φ)/√

2 (2.14)

+λ12

(H†H)2 +λ22

(Φ∗Φ)2 + λ12(H†H)(Φ∗Φ). (2.15)

The coefficient of the linear terms, which come from the second term of Eq. 2.8, is definedby ρ3 ≡ −(yUh + yDh)µhv2h/

√2. If we define components of the scalar fields like this :

H =

(0

(h + v1)/√

2

), Φ = (φ + v2 + iφI)/

√2, (2.16)

The conditions for minimization are given by

µ21 =12(λ1v21 + λ12v

22) (2.17)

µ22 =12(λ2v22 + λ12v

21) + ρ

3/v2. (2.18)

Then the nonvanishing mass terms can be written as

Vmass =12

(h φ

) ( λ1v21 λ12v1v2λ12v1v2 λ2v22 − ρ3/v2

)(h

φ

)− 1

2ρ3

v2φ2I . (2.19)

We note that φI is not a pseudo-Goldstone boson in this particular choice of U(1)X gauge.We’ll see that a linear combination of φI and π0 becomes massless and is eaten by the Z ′

gauge boson. The mass eigenstates h1 and h2 are linear combination of φ and h :(

h1h2

)=

(cos α sinα− sinα cos α

)(h

φ

). (2.20)

The corresponding masses and the mixing angle are

tan 2α =−2λ12v1v2

λ2v22 − λ1v21 − ρ3/v2(2.21)

M2H1,H2 =λ1v21 + λ2v22 − ρ3/v2 ∓

√(λ1v21 − λ2v22 + ρ3/v2)2 + 4λ212v21v22

2. (2.22)

In this paper, we take the physical Higgs masses MH1,2 and mixing angle α as theinput parameters. Then the coupling constants in the Higgs potential are obtained as

λ1 =1v21

(M2H1 cos

2 α + M2H2 sin2 α

)

λ2 =1v22

(M2H1 sin

2 α + M2H2 cos2 α + ρ3/v2

)

λ12 =1

v1v2

(M2H1 − M

2H2

)cos α sinα (2.23)

– 5 –

2.5 Xµ∂µφI and Xµ∂µπ0 terms

If we expand the Lagrangian about the VEVs of the scalar fields, there are mixing termsXµ∂µφI and Xµ∂µπ0. After the orthonormal transformation

φI′ = cos απ0φI + sinαπ0π0 (2.31)

π0′ = − sinαπ0φI + cos απ0π0 (2.32)

with απ0 = tan−1((q++q−) vhQX [Φ] v2

) = − tan−1(vhv2 ), only Xµ∂µφI

′ term remains, and the fieldφI

′ will eaten by the gauge bosons. This can be seen also from their mass matrix:

(M2)φI−π0 =

(−ρ3/v2 −ρ3/vh−ρ3/vh −v2ρ3/v2h

). (2.33)

Then the mass of physical field π0′ is given by

M2π0′ = M2π±(1 + v

2h/v

22), (2.34)

where M2π± = µh(MUh + MDh) = µh(yUh + yDh)v2/√

2.

3. Particle spectra and collider phenomenology

• 2 scalar higgs : h1 and h2 ( mixture of h and φ )The mixing angle is defined in Eq. 2.20.

• new Z ′ gauge boson

• one unstable pseudo-scalar π′0 ( mixture of π0 and A which is imaginary componentof the singlet field Φ = (φ + v2 + iφI)/

√2 )

π′0 = − sinαπ0φI + cos απ0π0 (3.1)

If vh # v2, then π′0 ∼ π0. If v2 # vh, then π′0 ∼ A.

Decay channel : π′0 → h1Z1, h1Z2, h2Z1, h2Z2 → ...

• Stable hidden-sector charged pion π±

M2π± = µh(MUh + MDh) = µh(yUh + yDh)v2/√

2 (3.2)

4. Numerical calculation

For simplicity, we assume yNR = 0 (ignore neutrino part), µh = vh, and MUh = MDh . Theremaining free parameters are gX , χ, q+, α, tanβ ≡ v2v1 , MZ′ , Mπ± , MH1 , MH2 .

To see the effect of MZ′ and MH1,2 on the relic density and the direct detection crosssection, we make various choices of gX , q+, tanβ, MZ′ . We show the results in Figures 1.We fixed the other free parameters to be χ = 0, α = π/4, MH1 = 300 GeV, MH2 = 3, 000GeV.

– 7 –

2.3 Scalar Potential

The scalar potential is given by

V (H, Φ) = −µ21H†H − µ22Φ∗Φ + ρ3(Φ∗ + Φ)/√

2 (2.14)

+λ12

(H†H)2 +λ22

(Φ∗Φ)2 + λ12(H†H)(Φ∗Φ). (2.15)

The coefficient of the linear terms, which come from the second term of Eq. 2.8, is definedby ρ3 ≡ −(yUh + yDh)µhv2h/

√2. If we define components of the scalar fields like this :

H =

(0

(h + v1)/√

2

), Φ = (φ + v2 + iφI)/

√2, (2.16)

The conditions for minimization are given by

µ21 =12(λ1v21 + λ12v

22) (2.17)

µ22 =12(λ2v22 + λ12v

21) + ρ

3/v2. (2.18)

Then the nonvanishing mass terms can be written as

Vmass =12

(h φ

) ( λ1v21 λ12v1v2λ12v1v2 λ2v22 − ρ3/v2

)(h

φ

)− 1

2ρ3

v2φ2I . (2.19)

We note that φI is not a pseudo-Goldstone boson in this particular choice of U(1)X gauge.We’ll see that a linear combination of φI and π0 becomes massless and is eaten by the Z ′

gauge boson. The mass eigenstates h1 and h2 are linear combination of φ and h :(

h1h2

)=

(cos α sinα− sinα cos α

)(h

φ

). (2.20)

The corresponding masses and the mixing angle are

tan 2α =−2λ12v1v2

λ2v22 − λ1v21 − ρ3/v2(2.21)

M2H1,H2 =λ1v21 + λ2v22 − ρ3/v2 ∓

√(λ1v21 − λ2v22 + ρ3/v2)2 + 4λ212v21v22

2. (2.22)

In this paper, we take the physical Higgs masses MH1,2 and mixing angle α as theinput parameters. Then the coupling constants in the Higgs potential are obtained as

λ1 =1v21

(M2H1 cos

2 α + M2H2 sin2 α

)

λ2 =1v22

(M2H1 sin

2 α + M2H2 cos2 α + ρ3/v2

)

λ12 =1

v1v2

(M2H1 − M

2H2

)cos α sinα (2.23)

– 5 –

12년 9월 11일 화

(GeV)±!M1 10

210

310

410

!1210

!1010

!810

!610

!410

!210

1

210

410

610

810

910

Relic Density tb==1

MZ2==120

MZ2==400

MZ2==600

MZ2==1200

MZ2==1800

MZ2==3000

MZ2==6000

MZ2==10000

Relic Density tb==1

(GeV)±!M1 10

210

310

410

!5010

!4910

!4810

!4710

!4610

!4510

!4410

!4310

!4210

!4110

!4010

Direct Detection[pb] (proton)Direct Detection[pb] (proton)

(GeV)±!M1 10

210

310

410

!610

!510

!410

!310

!210

!110

1

)|Z!Z’

"|sin( )|Z!Z’

"|sin(

(GeV)±!M1 10

210

310

410

1

10

210

310

410

510

610

710

0!M

0!M

Figure 1: The DM relic density, the spin-independent cross section of the DM scattering off aproton, the neutral pion mass, and the sine of the Z − Z ′ mixing angle (clockwise from the upperleft panel) as a function of the DM mass Mπ± for various choices of the Z ′ masses as indicated in thelegend for tanβ = 1, q+ − q− = 2. We fixed gX = 0.1121,χ = 0,α = π/4,MH1 = 300(GeV), MH2 =3000(GeV).

In Figure 1, we show the dependences of the relic density of dark matter, spin inde-pendent cross section for the dark matter scattering off a proton, the sine of Z −Z ′ mixingangle, and the “neutral” pion mass on the Mπ± . We choose gX = 0.1121(αX = 10−3) ,tanβ = 1, q+ = 0, and several values of MZ′ . Since the U(1)X charge of the hidden sectordark matter is q+ − q− = 2 in this case, we have both Z ′ contribution and Higgs bosoncontribution to the relic density. As the DM mass Mπ± increases more decay channelsopen and the ΩDMh2 decreases. The blue line (MZ′ = 120 GeV) shows both the SM Z andthe hidden sector Z ′ resonance effects near Mπ± = 45, 60 GeV, respectively. For heavierMZ′ we cannot clearly see the dips due to Z ′ resonances because their decay widths are

– 8 –

(GeV)±!M1 10

210

310

410

!1210

!1010

!810

!610

!410

!210

1

210

410

610

810

910

Relic Density tb==1

MZ2==120

MZ2==400

MZ2==600

MZ2==1200

MZ2==1800

MZ2==3000

MZ2==6000

MZ2==10000

Relic Density tb==1

(GeV)±!M1 10

210

310

410

!5010

!4910

!4810

!4710

!4610

!4510

!4410

!4310

!4210

!4110

!4010


(GeV)±!M1 10

210

310

410

!610

!510

!410

!310

!210

!110

1

)|Z!Z’

"|sin( )|Z!Z’

"|sin(

(GeV)±!M1 10

210

310

410

1

10

210

310

410

510

610

710

0!M

0!M


In Figure 1, we show the dependences of the relic density of dark matter, spin inde-pendent cross section for the dark matter scattering off a proton, the sine of Z −Z ′ mixingangle, and the “neutral” pion mass on the Mπ± . We choose gX = 0.1121(αX = 10−3) ,tanβ = 1, q+ = 0, and several values of MZ′ . Since the U(1)X charge of the hidden sectordark matter is q+ − q− = 2 in this case, we have both Z ′ contribution and Higgs bosoncontribution to the relic density. As the DM mass Mπ± increases more decay channelsopen and the ΩDMh2 decreases. The blue line (MZ′ = 120 GeV) shows both the SM Z andthe hidden sector Z ′ resonance effects near Mπ± = 45, 60 GeV, respectively. For heavierMZ′ we cannot clearly see the dips due to Z ′ resonances because their decay widths are

– 8 –

12년 9월 11일 화

(GeV)±!M1 10

210

310

410

!1210

!1010

!810

!610

!410

!210

1

210

410

610

810

910

Relic Density tb==1

MZ2==120

MZ2==400

MZ2==600

MZ2==1200

MZ2==1800

MZ2==3000

MZ2==6000

MZ2==10000

Relic Density tb==1

(GeV)±!M1 10

210

310

410

!5010

!4910

!4810

!4710

!4610

!4510

!4410

!4310

!4210

!4110

!4010


(GeV)±!M1 10

210

310

410

!610

!510

!410

!310

!210

!110

1

)|Z!Z’

"|sin( )|Z!Z’

"|sin(

(GeV)±!M1 10

210

310

410

1

10

210

310

410

510

610

710

0!M

0!M


too large. We can also see the resonces due to H1 near Mπ± = 150 GeV. Near Mπ± = 300GeV the π+π− → 2H1 channel opens and the ΩDMh2 abruptly decreases.

The cross section for the direct detection is dominated by the Z ′ contribution. Thecase with MZ′ = 120 GeV gives too large cross section and is already ruled out by thecurrent experiments.

In Figure 2, we turned off the Z ′ coupling to the DM pairs by setting q+ = −1(q+−q− =0). We can see that all the gauge boson contribution has disappeared and only the Higgsboson contributions remain. As a consequence, the direct production predictions lie wellbelow the current experimental bound.

– 9 –

(GeV)±!M1 10

210

310

410

!1210

!1010

!810

!610

!410

!210

1

210

410

610

810

910

Relic Density tb==20

MZ2==1200

MZ2==1800

MZ2==3000

MZ2==6000

MZ2==10000

Relic Density tb==20

(GeV)±!M1 10

210

310

410

!5010

!4910

!4810

!4710

!4610

!4510

!4410

!4310

!4210

!4110

!4010


(GeV)±!M1 10

210

310

410

!610

!510

!410

!310

!210

!110

1

)|Z!Z’

"|sin( )|Z!Z’

"|sin(

(GeV)±!M1 10

210

310

410

1

10

210

310

410

510

610

710

0!M

0!M

Figure 3: The DM relic density, the spin-independent cross section of the DM scattering off aproton, the neutral pion mass, and the sine of the Z − Z ′ mixing angle (clockwise from the upperleft panel) as a function of the DM mass Mπ± for various choices of the Z ′ masses as indicated in thelegend for tanβ = 20, q+−q− = 2. We fixed gX = 0.1121,χ = 0,α = π/4,MH1 = 300(GeV), MH2 =3000(GeV).

For large tanβ the Higgs coupling to the DM pairs decreases and the abrupt changeof ΩDMh2 near the Higgs threshold no longer happens as can be seen from Figure 3.

Now we consider the relic density dependence on other parameters. In Figure 4,constant contour plots for ΩDMh2 = 0.1099 are shown in the (χ, Mπ±) plane. For the leftpanel where q+ = −1, the Z ′ contribution vanishes. And the DM annihilates throughπ+π− → H1H1(H2H2) almost 100 % for α = π/4(0). The dependence on χ arise becauseρ3(= −M2π±v

2h/v2) which enters the Higgs mass term in (2.22) is sensitive to vh which in

turn depends on the χ. This can be seen more clearly from the plot in the right panelwhere we take light MZ′ = 800GeV. As MZ′ becomes smaller, so does vh, and the χ

– 10 –

q+ - q- = 0No coupling between DM

and Z’

q+ - q- = 2Higgs coupling to DM

decreases for large tan(beta)

12년 9월 11일 화

A Leptophilic Model Motivated by PAMELA(Baek and Ko, arXiv:0811.1646, JCAP)

12년 9월 11일 화

PAMELA positron excess• PAMELA reports positron access @ high energy • PAMELA reports no access in antiproton• ATIC/PPB-BETS : excess in (e+ + e-) around

500-800 GeV

• Combining these observations, one can conclude• Leptophilic DM, OR• Very heavy DM (> 10 TeV) with dominant DM

+ DM -> W+ W- (and also into ZZ , HH)

12년 9월 11일 화

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DM with M ⌅ 10 TeV that annihilates intoW⇥W⇤

Figure 1: Three examples of fits of e+ (left), e+ + e� (center), p̄ (right) data, for M =150 GeV (upper row, excluded by p̄), M = 1 TeV (middle row, favored by data), M =10 TeV (lower row, disfavored by the current e+ + e� excess). Galactic DM profiles andpropagation models are varied to provide the best fit. See Sec. 4 for the discussion on thetreatment of the uncertain astrophysical background.

4

Cirelli, Strumia et al. NPB

e+, (e- + e+), pbar from left, center, and

right

12년 9월 11일 화

U(1)Lµ�L� model

• Anomaly free subgroup of SM : one of

• Least constrained one : • Foot, He, Volkas, et al. in late 80’s• Baek, Deshpande, Ko, He : muon g-2• PAMELA positron excess and collider signature

(Baek and Ko)

B � L , Le � Lµ , Lµ � L⇥ , Le � L⇥

Lµ � L⇥

12년 9월 11일 화

There are already many papers available studying the implications of the PAMELA data

in different models and/or context [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,

24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39].

The simplest model for the leptophilic (or hadrophobic) gauge interaction is to gauge

the global U(1)Lµ−Lτ symmetry of the standard model (SM), which is anomaly free [40,

41, 42, 43]. Within the SM, there are four global U(1) symmetries which are anomaly free:

Le − Lµ, Lµ − Lτ , Lτ − Le, B − L

One of these can be implemented to a local symmetry without anomaly. The most popu-

lar is the U(1)B−L, which can be easily implemented to grand unified theory. Two other

symmetry involving Le are tightly constrained by low energy and collider data. On the

other hand, the Lµ −Lτ symmetry is not so tightly constrained, and detailed phenomeno-

logical study is not available yet. Only the muon (g−2)µ and the phenomenology at muon

colliders have been discussed [43, 44]. This model can be extended by introducing three

right-handed neutrinos and generate the neutrino masses and mixings via seesaw mecha-

nism [41]. Also U(1)Lµ−Lτ can be embedded into a horizontal SU(2)H [41] acting on three

lepton generations. This may be related with some grand unification.

In this paper, we extend the existing U(1)Lµ−Lτ model by including a complex scalar

φ and a spin-1/2 Dirac fermion ψD, with U(1)Lµ−Lτ charge 1. There is no anomaly

regenerated in this case, since we introduced a vectorlike fermion. The complex scalar φ

gives a mass to the extra Z′

by ordinary Higgs mechanism. And the Dirac fermion ψDplays a role of the dark matter, whose pair annihilation into µ or τ explains the excess of

e+ and no p̄ excess as reported by PAMELA [2, 3]. Then we study the phenomenology of

the U(1)Lµ−Lτ model with Dirac fermion dark matter in detail.

In Sec. 2, we define the model and discuss the muon (g − 2)µ in our model. In Sec. 3,

we calculate the thermal relic density of the CDM ψD, and identify the parameter region

that is consistent with the data from cosmological observations. In Sec. 4, we study the

collider signatures of the model at various colliders (Tevatron, B factories, LEP(2), the Z0

pole and LHC), including production and decay of Z′

and Higgs phenomenology. Then our

results are summarized in Sec. 5. We note that this model was discussed briefly in Ref. [4]

in the context of the muon (g − 2)µ and the relic density. In this paper, we present the

quantitative analysis on these subjects in detail, as well as study the collider signatures at

colliders.

2. Model and the muon (g − 2)µ

The new gauge symmetry U(1)Lµ−Lτ affects only the 2nd and the 3rd generations of leptons.

We assume li=2(3)L , li=2(3)R (i: the generation index) carry Y

′

= 1(−1). We further introduce

a complex scalar φ with (1, 1, 0)(1) and a Dirac fermion ψD with (1, 1, 0)(1), where the first

and the second parentheses show the SM and the U(1)Lµ−Lτ quantum numbers of φ and

ψD, respectively. The covariant derivative is defined as

Dµ = ∂µ + ieQAµ + ie

sW cS(I3 − s

2W Q)Zµ + ig

′

Y′

Z′

µ (2.1)

– 2 –

The model lagrangian is given by 1

LModel = LSM + LNew (2.2)

LNew = −1

4Z

′

µνZ′µν + ψDiD · γψD − MψDψDψD + Dµφ

∗Dµφ (2.3)

−λφ(φ∗φ)2 − µ2φφ

∗φ − λHφφ∗φH†H.

In general, we have to include renormalizable kinetic mixing term for U(1)Y and U(1)Lµ−Lτgauge fields, which will lead to the mixing between Z and Z

′

. Then the dark matter pair

can annihilate into quarks through Z − Z′

mixing in our case, and the p̄ flux will be

somewhat enhanced, depending on the size the Z − Z′

mixing. However, electroweak

precision data and collider experiments give a strong constraint on the possible mixing

parameter, since the mixing induces the Z′

coupling to the quark sector. Furthermore, if

one assumes that the new U(1)Lµ−Lτ is embedded into a nonabelian gauge group such as

SU(2)H or SU(3)H , then the kinetic mixing term is forbidden by this nonabelian gauge

symmetry [41]. In this paper, we will assume that the kinetic mixing is zero to simplify the

discussion and to maximize the contrast between the positron and the antiproton fluxes

from the dark matter annihilations.

In this model, there are two phases for the extra U(1)Lµ−Lτ gauge symmetry depending

on the sign of µ2φ :

• Unbroken phase: exact with 〈φ〉 = 0, µ2φ > 0 and MZ′ = 0,

• Spontaneously broken phase: by µ2φ < 0, nonzero 〈φ〉 ≡ vφ %= 0, and MZ′ %= 0

In the unbroken phase, the massless Z′

contribute to the muon (g − 2)µ as in QED up to

the overall coupling:

∆aµ =α

′

2π. (2.4)

Currently there is about 3.4σ difference between the BNL data [47] and the SM predic-

tions [48] in (g − 2)µ:

∆aµ = aexpµ − a

SMµ = (302 ± 88) × 10

−11. (2.5)

The ∆aµ in (2.4) can explain this discrepancy, if α′

∼ 2 × 10−8. However, this coupling

is too small for the thermal relic density to satisfy the WMAP data. The resulting relic

density is too high by a several orders of magnitude. Also the collider signatures will be

highly suppressed. Therefore we do not consider this possibility any more, and consider

the massive Z′

case (broken phase) in the following.

In the broken phase, it is straightforward to calculate the Z′

contribution to ∆aµ. We

use the result obtained in Ref. [43]:

∆aµ =α

′

2π

∫ 1

0dx

2m2µx2(1 − x)

x2m2µ + (1 − x)M2Z

′

≈α

′

2π

2m2µ3M2

Z′

(2.6)

1Similar idea for the DM was considered in [45, 46] in the context of Stueckelberg U(1)X extension of

the SM model.

– 3 –

Here we ignored kinetic mixing for simplicity

We will study the following observables:Muon g-2, Leptophilc DM, Collider Signature

12년 9월 11일 화

Muon (g-2)



LNew = −1

4Z

′


∗Dµφ (2.3)




′





















∆aµ =α

′

2π. (2.4)


tions [48] in (g − 2)µ:


SMµ = (302 ± 88) × 10

−11. (2.5)






the massive Z′





∆aµ =α

′

2π

∫ 1

0dx

2m2µx2(1 − x)

x2m2µ + (1 − x)M2Z

′

≈α

′

2π

2m2µ3M2

Z′

(2.6)


the SM model.

– 3 –



LNew = −1

4Z

′


∗Dµφ (2.3)




′





















∆aµ =α

′

2π. (2.4)


tions [48] in (g − 2)µ:


SMµ = (302 ± 88) × 10

−11. (2.5)






the massive Z′





∆aµ =α

′

2π

∫ 1

0dx

2m2µx2(1 − x)

x2m2µ + (1 − x)M2Z

′

≈α

′

2π

2m2µ3M2

Z′

(2.6)


the SM model.

– 3 –

FIGURES

FIG. 1. Feynman diagram which generates a non-zero ∆aµ

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1000 1200

a

MZ’ (GeV)

FIG. 2. ∆aµ on the a vs. mZ′ plane in case b). The lines from left to right are for ∆aµ away

from its central value at +2σ,+1σ, 0,−1σ and −2σ, respectively.

9

12년 9월 11일 화

FIGURES

FIG. 1. Feynman diagram which generates a non-zero ∆aµ

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1000 1200

a

MZ’ (GeV)

FIG. 2. ∆aµ on the a vs. mZ′ plane in case b). The lines from left to right are for ∆aµ away

from its central value at +2σ,+1σ, 0,−1σ and −2σ, respectively.

9

Prediction for muon (g-2)

12년 9월 11일 화

Collider Signatures

The second approximate formula holds for mµ ! MZ′ . In Fig. 1, shown in the blue band

is the allowed region of MZ′ and α′

which is consistent with the BNL data on the muon

(g − 2)µ within 3 σ range. There is an ample parameter space where the discrepancy

between the BNL data and the SM prediction can be explained within the model.

3. Dark matter

The Dirac fermion ψD can play a role of the CDM. In our model, thermal relic density of

the CDM in our model is achieved through the DM annihilations into muon or tau leptons

or their neutrinos:

ψDψ̄D → Z′∗ → l+l−, νlν̄l

with l = µ or τ . We modified the micrOMEGAs [49] in order to calculate the relic density

of the U(1)−charged ψD CDM. It is easy to fulfil the WMAP data on ΩCDM for a wide

range of the DM mass, as shown in Fig. 1 in the black curves which represent constant

contours of Ωh2 = 0.106 in the (MZ′ ,α)-plane for MψD = 10, 100, 1000 GeV from below.

We can clearly see the s−channel resonance effect of Z′

→ ψDψ̄D near MZ′ ≈ 2MψD . If

100 GeV ! MψD ! 10 TeV, α " 10−3 and 100 GeV ! MZ′ ! 1 TeV, both the relic

density and ∆aµ can be easily satisfied while escaping the current collider searches. This

parameter space, however, can be probed by the LHC. These issues are covered in the

following section.

There would be no signal in direct DM detection experiments in this model, since the

messenger Z′

does not interact with electron, quarks or gluons inside nucleus. Also we

do not expect any excess in the antiproton flux in cosmic rays in the indirect search for

CDM. On the other hand, there could be excess in the positron signal consistent with the

PAMELA positron excess in our model.

4. Collider Signatures

New particles in this model are Z′

, s (the modulus of φ) and ψD, and they couple only

to muon, tau or their neutrinos. Let us discuss first the decay of Z′

gauge boson and its

productions at various colliders, and then Higgs phenomenology in our model.

In the broken phase with MZ′ %= 0, Z′

can decay through the following channels:

Z′

→ µ+µ−, τ+τ−, ναν̄α (with α = µ or τ), ψDψD ,

if they are kinematically allowed. Since these decays occur through U(1)Lµ−Lτ gauge

interactions, the branching ratio is completely fixed once particle masses are specified. In

particular,

Γ(Z′

→ µ+µ−) = Γ(Z′

→ τ+τ−) = 2Γ(Z′

→ νµν̄µ) = 2Γ(Z′

→ ντ ν̄τ ) = Γ(Z′

→ ψDψ̄D)

if MZ′ & mµ,mτ ,MDM. And the total decay rate of Z′

is approximately given by

Γtot(Z′

) =α

′

3MZ′ × 4(3) ≈

4(or 3)

3GeV

(

α′

10−2

)

(

MZ′

100GeV

)

– 4 –






3. Dark matter



or their neutrinos:











following section.


messenger Z′









gauge boson and its




Z′




particular,

Γ(Z′

→ µ+µ−) = Γ(Z′

→ τ+τ−) = 2Γ(Z′

→ νµν̄µ) = 2Γ(Z′

→ ντ ν̄τ ) = Γ(Z′

→ ψDψ̄D)



Γtot(Z′

) =α

′

3MZ′ × 4(3) ≈

4(or 3)

3GeV

(

α′

10−2

)

(

MZ′

100GeV

)

– 4 –






3. Dark matter



or their neutrinos:











following section.


messenger Z′









gauge boson and its




Z′




particular,

Γ(Z′

→ µ+µ−) = Γ(Z′

→ τ+τ−) = 2Γ(Z′

→ νµν̄µ) = 2Γ(Z′

→ ντ ν̄τ ) = Γ(Z′

→ ψDψ̄D)



Γtot(Z′

) =α

′

3MZ′ × 4(3) ≈

4(or 3)

3GeV

(

α′

10−2

)

(

MZ′

100GeV

)

– 4 –

MΨD"10GeV

MΨD"100GeV

MΨD"1000GeV

1fb

10fb

100fb

1fb

10fb

0 1 2 3 4

#6

#5

#4

#3

#2

#1

log10!M

Z’ "GeV#

log 10!Α’#

Figure 1: The relic density of CDM (black), the muon (g − 2)µ (blue band), the production crosssection at B factories (1 fb, red dotted), Tevatron (10 fb, green dotdashed), LEP (10 fb, pinkdotted), LEP2 (10 fb, orange dotted), LHC (1 fb, 10 fb, 100 fb, blue dashed) and the Z0 decaywidth (2.5 ×10−6 GeV, brown dotted) in the (log10 α

′

, log10 MZ′ ) plane. For the relic density, weshow three contours with Ωh2 = 0.106 for MψD = 10 GeV, 100 GeV and 1000 GeV. The blue bandis allowed by ∆aµ = (302 ± 88) × 10−11 within 3 σ.

if the channel Z′

→ ψDψ̄D is open (or closed). Therefore Z′

will decay immediately inside

the detector for a reasonable range of α′

and MZ′ .

Z ′ can be produced at a muon collider as resonances in the µµ or ττ channel [43] via

µ+µ− → Z′∗ → µ+µ−(τ+τ−).

The LHC can also observe the Z ′ which gives the right amount of the relic density as can

be seen in Fig. 1. Its signal is the excess of multi-muon (tau) events without the excess of

multi-e events.

The dominant mechanisms of Z′

productions at available colliders are

qq̄ (or e+e−) → γ∗, Z∗ → µ+µ−Z′

, τ+τ−Z′

→ Z∗ → νµν̄µZ′

, ντντZ′

There are also vector boson fusion processes such as

W+W− → νµν̄µZ′

(or µ+µ−Z′

), etc.

Z0Z0 → νµν̄µZ′

(or µ+µ−Z′

), etc.

W+Z0 → νµµ̄Z′

(or µ+µ−Z′

), etc.

– 5 –

12년 9월 11일 화

0 100 200 300 400 500 600 700

10!6

10!4

0.01

1

MH1!GeV"

BR

Α#5$, tanΒ#1

0 100 200 300 400 500 600 700

10!7

10!5

0.001

0.1

MH2!GeV"

BR

Α#5$, tanΒ#1

0 100 200 300 400 500 600 700

10!6

10!4

0.01

1

MH1!GeV"

BR

Α#40$, tanΒ#1

0 100 200 300 400 500 600 700

10!6

10!4

0.01

1

MH2!GeV"

BR

Α#40$, tanΒ#1

0 100 200 300 400 500 600 700

10!8

10!6

10!4

0.01

1

MH1!GeV"

BR

Α#40$, tanΒ#0.1

0 100 200 300 400 500 600 70010!9

10!7

10!5

0.001

0.1

MH2!GeV"

BR

Α#40$, tanΒ#0.1

Figure 2: In the left (right) column are shown the branching ratios of the lighter (heavier) HiggsH1(2) into two particles in the final states: tt̄ (solid in red), bb̄ (dashed red), cc̄ (dotted red), ss̄(dot-dashed red), τ τ̄ (solid orange), µµ̄ (dashed orange), WW (dashed blue), ZZ (dotted blue) andZ

′

Z′

(solid blue) for difference values of the mixing angle α and tanβ. We fixed MZ′ = 300 GeV.We also fixed MH2 = 700 GeV (MH1 = 150 GeV) for the plots of the left (right) column.

model is constrained by the muon (g − 2)µ and the collider search for a vector boson

decaying into µ+µ− at the Tevatron, LEP(2) and B factories. The collider constraints

favors ψDM heavier than ∼ 100 GeV. We calculated the relic density of the CDM with

these constraints, and still find that the thermal relic density could be easily within the

WMAP range. We also considered the production cross section of the new gauge boson Z′

at the LHC, which could be 1 fb –1000 fb. This is clearly within the discovery range at

the LHC with enough integrated luminosity ! 50fb−1. It is remained to be seen whether

– 7 –

0 100 200 300 400 500 600 700

10!6

10!4

0.01

1

MH1!GeV"

BR

Α#5$, tanΒ#1

0 100 200 300 400 500 600 700

10!7

10!5

0.001

0.1

MH2!GeV"

BR

Α#5$, tanΒ#1

0 100 200 300 400 500 600 700

10!6

10!4

0.01

1

MH1!GeV"

BR

Α#40$, tanΒ#1

0 100 200 300 400 500 600 700

10!6

10!4

0.01

1

MH2!GeV"

BR

Α#40$, tanΒ#1

0 100 200 300 400 500 600 700

10!8

10!6

10!4

0.01

1

MH1!GeV"

BR

Α#40$, tanΒ#0.1

0 100 200 300 400 500 600 70010!9

10!7

10!5

0.001

0.1

MH2!GeV"

BR

Α#40$, tanΒ#0.1

Figure 2: In the left (right) column are shown the branching ratios of the lighter (heavier) HiggsH1(2) into two particles in the final states: tt̄ (solid in red), bb̄ (dashed red), cc̄ (dotted red), ss̄(dot-dashed red), τ τ̄ (solid orange), µµ̄ (dashed orange), WW (dashed blue), ZZ (dotted blue) andZ

′

Z′

(solid blue) for difference values of the mixing angle α and tanβ. We fixed MZ′ = 300 GeV.We also fixed MH2 = 700 GeV (MH1 = 150 GeV) for the plots of the left (right) column.

model is constrained by the muon (g − 2)µ and the collider search for a vector boson

decaying into µ+µ− at the Tevatron, LEP(2) and B factories. The collider constraints

favors ψDM heavier than ∼ 100 GeV. We calculated the relic density of the CDM with

these constraints, and still find that the thermal relic density could be easily within the

WMAP range. We also considered the production cross section of the new gauge boson Z′

at the LHC, which could be 1 fb –1000 fb. This is clearly within the discovery range at

the LHC with enough integrated luminosity ! 50fb−1. It is remained to be seen whether

– 7 –

12년 9월 11일 화

MΨD"10GeV

MΨD"100GeV

MΨD"1000GeV

1fb

10fb

100fb

1fb

10fb

0 1 2 3 4

#6

#5

#4

#3

#2

#1

log10!M

Z’ "GeV#

log 10!Α’ #

Figure 1: The relic density of CDM (black), the muon (g − 2)µ (blue band), the production crosssection at B factories (1 fb, red dotted), Tevatron (10 fb, green dotdashed), LEP (10 fb, pinkdotted), LEP2 (10 fb, orange dotted), LHC (1 fb, 10 fb, 100 fb, blue dashed) and the Z0 decaywidth (2.5 ×10−6 GeV, brown dotted) in the (log10 α

′

, log10 MZ′ ) plane. For the relic density, weshow three contours with Ωh2 = 0.106 for MψD = 10 GeV, 100 GeV and 1000 GeV. The blue bandis allowed by ∆aµ = (302 ± 88) × 10−11 within 3 σ.

if the channel Z′

→ ψDψ̄D is open (or closed). Therefore Z′

will decay immediately inside

the detector for a reasonable range of α′

and MZ′ .

Z ′ can be produced at a muon collider as resonances in the µµ or ττ channel [43] via

µ+µ− → Z′∗ → µ+µ−(τ+τ−).

The LHC can also observe the Z ′ which gives the right amount of the relic density as can

be seen in Fig. 1. Its signal is the excess of multi-muon (tau) events without the excess of

multi-e events.

The dominant mechanisms of Z′

productions at available colliders are

qq̄ (or e+e−) → γ∗, Z∗ → µ+µ−Z′

, τ+τ−Z′

→ Z∗ → νµν̄µZ′

, ντντZ′



(or µ+µ−Z′

), etc.


(or µ+µ−Z′

), etc.


(or µ+µ−Z′

), etc.

– 5 –

12년 9월 11일 화

M⇥D�10GeV

M⇥D�100GeV

M⇥D�1000GeV M⇥D�2000GeV

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0

1

2

3

4

log10�M

Z’⇤GeV⇥

log10�S k⇥

Figure: Sommerfeld enhancement factor along the constant relic densitylines. v = 200 km/s.

Dark matter in U(1)Lµ�L⇥ gauge theory and cosmic ray data APCTP, June 18, 2009 43 / 54

12년 9월 11일 화

Lµ � L⇥

E (GeV)1 10

210

))-(e

!)

+

+(e

!)/

(+

(e!

-210

-110

PAMELA (2009)

Background

DM M=2000 (GeV)

PAMELA positron ratio to (electro + positron)

12년 9월 11일 화

E (GeV)10

2103

10

)-1

sr

-1 s

-2 m

2(E

) (G

eV

! 3

E

210

Fermi (2009)

PAMELA (2009)

Background

DM M=2000 (GeV)

PAMELA + FERMI with bkgd x 0.67 and large boost factor ~O(5000)

12년 9월 11일 화

0 5 10 15 20 25 300

5

10

15

20

25

Cone half angle from GC !deg"

Muonflux!10!15cm!2s!1"

Figure 5: Thick solid red curves (thick dashed blue curves) are predictions of the neutrino-inducedup-going muon flux from the annihilation of dark matter with masses 3, 2, 1.5, 1 TeV from above,for the NFW (isothermal) dark matter profile. The thin solid line is the superkamiokande bound.

The lower DMs are allowed with the NFW profile. However, if the isothermal profile isused, all the DM are allowed because this profile is flat near the Galactic center and theneutrinos are not much produced.

Fig. 6 shows the predictions for the gamma-ray flux from the Galactic center (0.1◦

region from the GC) [36] and the Galactic Center ridge (|b| < 0.3◦, |l| < 0.8◦) [37]. We cansee that the constraints on the DM annihilation for the NFW profile become more severethan in the neutrino case. That is the NFW predicts too much gamma-ray, exceedingeven the current data for the massive DM. However, if more flat profile like the isothermalprofile is used, the predictions are below the current data.


New particles in this model are Z ′ , s (the modulus of φ) and ψD. Z′ couples only to muon,

tau or their neutrinos, or the U(1)Lµ−Lτ charged dark matter. The new scalar s can mixwith the SM Higgs boson hSM, affecting the standard Higgs phenomenology.

Let us discuss first the decay of Z ′ gauge boson and its productions at various colliders.In the broken phase with MZ′ != 0, Z

′ can decay through the following channels:

Z′ → µ+µ−, τ+τ−, ναν̄α (with α = µ or τ), ψDψD ,

if they are kinematically allowed. Since these decays occur through U(1)Lµ−Lτ gaugeinteraction, the branching ratios are completely fixed once particle masses are specified. In

– 11 –

SK Constraint on upgoing muon flux

12년 9월 11일 화

200 500 1000 2000 500010!12

10!11

10!10

10!9

10!8

10!7

E !GeV"

E2dNΓ#dE!GeVcm!2s!1"

Galactic Center

1!104200 500 1000 2000 500010"9

10"8

10"7

10"6

10"5

10"4

0.001

E !GeV"

E2dNΓ#dE!GeVcm"2s"1sr"1"

Galactic Ridge $b$$0.3%, $l$$0.8%

Figure 6: The gamma ray flux from the GC (left panel) and GC ridge (right panel). Thick solidred curves (thick dashed blue curves) are predictions of the gamma ray flux from the annihilationof dark matter with masses 3, 2, 1.5, 1 TeV from above, for the NFW (isothermal) dark matterprofile.

particular,

Γ(Z′ → µ+µ−) = Γ(Z ′ → τ+τ−) = 2Γ(Z ′ → νµν̄µ) = 2Γ(Z

′ → ντ ν̄τ ) = Γ(Z′ → ψDψ̄D)

if MZ′ " mµ, mτ ,MDM. The total decay rate of Z′ is approximately given by

Γtot(Z′) =

α′

3MZ′ × 4(3) ≈

4(or 3)3

GeV

(α

′

10−2

) (MZ′

100GeV

)

if the channel Z ′ → ψDψ̄D is open (or closed). Therefore Z′ will decay immediately inside

the detector for a reasonable range of α′ and MZ′ .Z ′ can be produced at a muon collider as resonances in the µµ or ττ channel [18] via

µ+µ− → Z ′∗ → µ+µ−(τ+τ−).

The LHC can also observe the Z ′ which gives the right amount of the relic density as canbe seen in Fig. 1. Its signal is the excess of multi-muon (tau) events without the excess ofmulti-e events.

The dominant mechanisms of Z ′ productions at available colliders are

qq̄ (or e+e−) → γ∗, Z∗ → µ+µ−Z ′ , τ+τ−Z ′

→ Z∗ → νµν̄µZ′, ντ ν̄τZ

′



(or µ+µ−Z′), etc.





and the channels with µ → τ . We will ignore the vector boson fusion channels in this paper,since their contributions are expected to be subdominant to the qq̄ or e+e− annihilations.

– 12 –

텍스트

Gamma ray flux constraint (HESS)

Indirect DD exp’s favor isothermal profile

12년 9월 11일 화

Conclusions

DM from leptophilic U(1)Lµ�L⇥ model can be an explanation ofpositron/electron excess in PAMELA, Fermi LAT and HESS CRexperiments.

� the fit to the data is excellent when MDM = 2000 GeV� the required BF can be obtained from the Sommerfeld

enhancement� MDM = 2000 GeV is only marginally allowed. MDM > 2000 GeV is

ruled out by SK muon flux.� NFW density profile is disfavored by the HESS gamma-ray data.

The isothermal profile is consistent with the data.

LHC can cover the large parameter space of U(1)Lµ�L⇥ modelthrough multi muon/tau events.

The Higgs searches can be non-standard.

Dark matter in U(1)Lµ�L⇥ gauge theory and cosmic ray data APCTP, June 18, 2009 54 / 5412년 9월 11일 화

(1) arXiv:1112.1847, JHEP 1202 (2012) 047, with Seungwon Baek, Wan-Il Park, and(2) work in preparation including Eibun Senaha

Talk by Wan-Il Park (Mon)

61

Singlet Fermion DM with 125 GeV Higgs Boson

12년 9월 11일 화

• VL VL scattering amp violates perturbative unitarity

• New strongly interacting EWSB sector below ~1 TeV, and there appear new resonances in the VV channels (B.W.Lee, C. Quigg, Thacker, 1977)

• EWSB w/o Higgs boson is possible in extra dim, with suitable bc : infinitely many KK modes appear (Csaki, Grojean, Murayama, Pilo, Terning, 2003)

• I propose a new paradigm in this talk : this motivation is now obsolete, but still makes an interesting case

• Only a part of Higgs bosons may be found

Folklore on “ What if no SM Higgs boson at the LHC ? ”

12년 9월 11일 화

• Higgs in standard model• Current status of Higgs search• Ratiocination • Constraints• Discovery possibility• Vaccum Stability• Conclusions

63

Outlines

12년 9월 11일 화

Brief Article

The Author

November 14, 2011

1 Standard model

LSM = LG,K + LM,K + LYukawa + LH (1)

where LG,K, LM,K and LH are gauge-kinetic, matter-kinetic and Higgs La-grangian, respectively. The Lagrangian for Higgs field is

LH = (DµH)† (DµH)� ⇥�|H|2 � v2

⇥2+ LYukawa (2)

where LYukawa is the Yukawa interactions of Higgs to matter fields.SM Higgs potential is

VH =1

4⇥�|H0|2 � v2

⇥⇤ mH = 2

⌅⇥ v (3)

where H0 is the neutral component of SM Higgs doublet, and v = 246GeVis the VEV of the canonically normalized real component of H0. The massof SM Higgs is

mH = 2⌅⇥ v (4)

Linde-Weinberg lower bound and the unitarity restricts the mass of SM Higgsto be

4.5GeV ⇥ mH ⇥⇤4⇤

⌅2

3GF

⌅1/2= 713GeV (5)

In the more recent analysis, vacuum stability provides a lower-bound andunitarity, perturbativity and triviality (and fine tuning problem) provide aupper-bound so that

50GeV � mH � 700GeV (6)In our case, it becomes

m21 cos2 � +m22 sin

2 � ⇥ (713GeV)2 (7)

1

• Lagrangian in SM

64

Brief Article

The Author

November 9, 2011

1 Standard model



LH = (DµH)† (DµH)� ⇥�|H|2 � v2

⇥2+ LYukawa (2)


VH =1

4⇥�|H0|2 � v2

⇥⇤ mH = 2

⌅⇥ v (3)


mH = 2⌅⇥ v (4)


4.5GeV ⇥ mH ⇥⇤4⇤

⌅2

3GF

⌅1/2= 713GeV (5)

In our case, it becomes


2 � ⇥ (713GeV)2 (6)

Field contents⌅ , ⌅̄ (7)

1

λ: unknown

Theoretical constraint on the Higgs mass

Vacuum stability

Brief Article

The Author

November 9, 2011

1 Standard model



LH = (DµH)† (DµH)� ⇥�|H|2 � v2

⇥2+ LYukawa (2)


VH =1

4⇥�|H0|2 � v2

⇥⇤ mH = 2

⌅⇥ v (3)


mH = 2⌅⇥ v (4)


4.5GeV ⇥ mH ⇥⇤4⇤

⌅2

3GF

⌅1/2= 713GeV (5)

In our case, it becomes


2 � ⇥ (713GeV)2 (6)

Field contents⌅ , ⌅̄ (7)

1

unitarity, perturbativity,triviality

Higgs in Standard Model

Djouadi, Phys.Rept.457,1 (2008)

12년 9월 11일 화

• Theoretical band of Higgs mass vs. UV-cutoff

triviality

vacuum stability

Higgs in standard model

12년 9월 11일 화

2011 March(Tevatron) [157,183]

2011 Aug(LHC) [141,476]

2011 Dec(LHC) [127,600]

If Higgs exists, its mass should be between 114 and 127 GeV.

12년 9월 11일 화

12년 9월 11일 화

• A scenario of a singlet fermion dark matter with global U(1) for dark matter

Brief Article

The Author

November 7, 2011

The model Lagrangian has extended structure with the hidden sector andHiggs portal terms in addition to the SM Lagrangian

L = LSM � µHSSH†H ��HS2

S2H†H

+1

2(⇤µS⇤

µS �m2SS2)� µ3SS �µ�S3S3 � �S

4S4

+⇥(i ⇥ ⇤ �m�0)⇥ � �S⇥⇥

where

Lportal = �µHSSH†H ��HS2

S2H†H,

Lhidden = LS + L� � �S⇥⇥, (1)

with

LS =1

2(⇤µS⇤

µS �m2SS2)� µ3SS �µ�S3S3 � �S

4S4,

L� = ⇥(i/⇤ �m�0)⇥ (2)

Except the dark sector, this model was quite well studied in detail in [?, ?].The Higgs potential has three parts: the SM, the hidden sector and the

portal parts

VHiggs = VSM + Vhidden + Vportal, (3)

where Vhidden, Vportal can be read from (1), (2) and

VSM = �µ2HH†H + �H(H†H)2. (4)

In general the Higgs potential develops nontrivial vacuum expectation values(vev)

⇤H⌅ = 1⇧2

�0vH

⇥, ⇤S⌅ = vS. (5)

1

ΨSM H S

mixing

invisibledecay

Production and decay rates are suppressed relative to SM.

70

Ratiocination

This simple model has not been studied !!

12년 9월 11일 화

• Mixing and Eigenstates of Higgs-like bosons

Ratiocination

at vacuum

Mixing of Higgs and singlet

12년 9월 11일 화

• Signal strength (reduction factor)

0< α < π/2 ⇒ r₁(r₂) < 1Invisible decay mode is not necessary!

72

Ratiocination

If r_i > 1 for any single channel, this model will be excluded !!

12년 9월 11일 화

• Unitarity• LEP bound• Electroweak precision observables• DM-nucleon cross-section • CDM relic density

73

Constraints

12년 9월 11일 화

• LEP bound on r_i for m_i < 120 GeV

Perturbative Unitarityri =

⇥i Br(Hi � SM)⇥h Br(h � SM)

(6)


2 � � (700GeV)2 (7)

2

74

Constraints

12년 9월 11일 화

Constraints

!

!!!

""""

! ! !!!

" """"

! 0.2 ! 0.1 0.0 0.1 0.2 0.3

! 0.2

! 0.1

0.0

0.1

0.2

0.3

0.4

S

T

EW precision observables

75

α=π/9, π/4m_h(ref)=120 GeV115< m_h < 750 GeV 30.< m₁ < 150 GeV150< m₂< 750 GeV

Same for T and U

2 Dark matter to nucleon cross section

In the model we are considering,

⌅p ⌅1

⇤m2pf

2p (14)

⇧ 1⇤m2p

⇤0.164

mpv⇥ sin� cos�

�1

m21� 1

m22

⇥⌅2(15)

⇧ 5⇥ 10�9pb�⇥ sin� cos�

0.1

⇥2 �143GeVm1

⇥4 �1� m

21

m22

⇥2(16)

⌅p ⌅1

⇤m2pf

2p ⇧

1

⇤m2p

⇤0.164

mpv⇥ sin� cos�

�1

m21� 1

m22

⇥⌅2(17)

3 Electroweak precision observables

STU-parameters [1]

�emS = 4s2W c

2W

⇤�ZZ(M2Z)� �ZZ(0)

M2Z

⌅(18)

�emT =�WW (0)

M2W� �ZZ(0)

M2Z(19)

�emU = 4s2W

⇤�WW (M2W )� �WW (0)

M2W

⌅(20)

VWX-parameters

�emV = �⇥ZZ(M

2Z)�

�S

4s2W c2W

(21)

�emW = �⇥WW (M

2W )�

�U

4s2W(22)

In case of a singlet mixed with Higgs,

�emS = cos2 � �emS(m1) + sin

2 � �emS(m2) (23)

4 Dark matter relic density

⇥CDM ⇤ 0.11�10�36cm2

⌃⌅v⌥fz

⇥(24)

3

Peskin & Takeuchi, Phys.Rev.Lett.65,964(1990)

U=0

12년 9월 11일 화

• Dark matter to nucleo

kiasworkshop.kias.re.kr/pheno2/downloads/2012_kias_pheno_pko.pdf · 2012-09-14 · hidden sector ?...

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