Form factor effects in a Higgs portal pionic dark matter model

Shohei Okawa (Nagoya U.)

in collaboration with　Masaharu Tanabashi (Nagoya U.)

March 16-20, 2015 Exploring the Dark Sector @ KIAS

Outline!

Introduction

Model

What are form factor effects ?

Our strategy

Results

Summary and Outlook

Higgs portal DM＝DM which interacts the SM particles only through the Higgs The nature of the DM is mainly determined by DM mass and the portal interactions to the Higgs !

The simplest case : mDM , λhXX predictive ⇔ severe constrained

λhXX is determined as a function of DM mass

mDM is constrained

Thermal relic density

hSM

SM

DM

DM s = 4m2DM

Direct detection

h

NN

DM DM

s = 0

Collider search

h

SM

SM

DM

DMs = E2

cm

Higgs portal dark matter

h

DM

DM

However, each process occurs at different energies and/or channels !!!!!

It’s significant to consider a case that the portal interactions to the Higgs depend on the energy and/or channels, not just constant

!!!!

Possibilities : Radiative corrections Extra mediator Composite DM … etc.

Motivation

Thermal relic density

hSM

SM

DM

DM s = 4m2DM

Direct detection

h

NN

DM DM

s = 0

Collider search

h

SM

SM

DM

DMs = E2cm

�hXX(s) = h

DM

DMs

Klasen, Yaguna, Ruiz-Alvarez (2013) ; T. Abe and R. Sato (2015) ; Tsai’s talk on Wed.

P. Ko et al. (2007) ; Y. G. Kim et al. (2008), etc.

Jung, et al. (2011) ; Wudka et al. (2013) ; Tuominen et al. (2013) ; J. Kubo et al. (2013), etc.

MotivationComposite DM

MotivationComposite DM

Strong interactions behind the SM

MotivationComposite DM

Strong interactions behind the SM

Scale invariant extension of the Standard Model

Dong-Won Jung’s talk

EW scale can be originated from the strong dynamics

MotivationComposite DM

Strong interactions behind the SM

Scale invariant extension of the Standard Model

EW scale can be originated from the strong dynamics

Form factor effects characteristic of composite particles

Dong-Won Jung’s talk

MotivationComposite DM

Strong interactions behind the SM

EW scale can be originated from the strong dynamics

Form factor effects characteristic of composite particles

Scale invariant extension of the Standard Model

Our work

Dong-Won Jung’s talk

Outline!

Introduction

Model

What are form factor effects ?

Our strategy

Results

Summary and Outlook

Model

A QCD-like SU(3) gauge interaction w/ 2-flavor fermions in the fundamental rep. Q’s are invariant under the SM gauge transf.

Dark pions = DM candidates

Dark-QCD

L = LSM +X

Q=U,D

✓Q̄(i /D �MQ)Q� 1

⇤(H†H)Q̄Q

◆

Higgs portal int.

Dim. 5 op. → EFT Λ : Cut-off scale

Dynamical chiral symmetry breaking (DχSB) ＋

Dark color confinement

&　　　Higgs portal

Outline!

Introduction

Model

What are form factor effects ?

Our strategy

Results

Summary and Outlook

!!!!!

!For illustration, let us consider a specific case

h⇧a(p0)| Q̄Q |⇧b(p)i = FS(s)�ab, s = (p� p0)2

scalar form factor of the dark pion�h⇧⇧(s) = h

p� p0

⇧a

⇧a

=v

⇤FS(s)

What are form factor effects ?Higgs portal interaction

Decay constant Mass

F⇧ = 103f⇡

M⇧ = 103m⇡

Dark pion’s properties

Typical scale

Dark quark mass MU = 103mu, MD = 103md

⇤dark = 103⇤QCD ⇠ 1 TeV

In this case,

What are form factor effects ?

In this case,

Collider search

s = E2cm

h

SM

SM

⇧a

⇧a

Thermal relic density

hSM

SM

⇧a

⇧a s = 4M2⇧

Direct detection

h

NN

s = 0

⇧a ⇧a

Form factor effects

�h⇧⇧(s = M2⇧) 6= �h⇧⇧(s = 0) 6= �h⇧⇧(s = E2

cm)

What are form factor effects ?

Outline!

Introduction

Model

What are form factor effects ?

Our strategy

Results

Summary and Outlook

!!!!!!!!!!!!!Then, how do we calculate the scalar form factor of the dark pions ?

Chiral Perturbation Theory (χPT)

M⇧, F⇧ : Free parameters

Specific case → General case

Decay constant Mass

F⇧ = 103f⇡

M⇧ = 103m⇡

Specific case General case

？

In the SM QCD, χPT is successful calculation method in describing the mesonic interactions at low energy !!!!!!!!!!!!!O(p2) χPT corresponds to the simplest case → No form factor effect O(p6) χPT can explain the experimental behavior quite well up to ~400 MeV

O(p2)

O(p4)

O(p6)

Experiment

Bijnens et al. , JHEP 9805 (1998)

χPT estimate of form factor

Outline!

Introduction

Model

What are form factor effects ?

Our strategy

Results

Summary and Outlook

Thermal relic density

hSM

SM

⇧a

⇧a s = 4M2⇧

h

NN

s = 0

⇧a ⇧a

Direct detection

h

s = m2h

⇧a

⇧a

Higgs invisible decay

Measurements we use

(PDG 2014)

LUXXENON100

Spin-independent (SI) cross section

Br(h ! inv) = 0.51

(arXiv:1404.1344 CMS)

(2014)

(2012)

⌦CDMh2 = 0.1198± 0.0026

O(p2) χPT (no form factor effect)

2M⇧ ⇠ mh, 200 GeV . M⇧Kanemura et al. (2010) ; CMS collaboration (2014), etc.

DM thermal relic

Higgs invisible decay

XENON100

LUX

Resonance region

O(p6) χPT (FΠ = 50 GeV)

2M⇧ ⇠ mh, 100 GeV . M⇧2M⇧ ⇠ mh, 200 GeV . M⇧

O(p2) χPT O(p6) χPT (FΠ = 50 GeV)

DM thermal relic

Higgs invisible decay

XENON100

LUX

Varying FΠ continuously, we can obtain the figure below

+ Resonance regionF⇧ [GeV]

M⇧[G

eV]

Excluded region

Lower bound in O(p2) χPT

non-reliable region of the calculation in χPT

O(p2) χPT O(p6) χPT

200 GeV . M⇧ 80 GeV . M⇧

Results

Outline!

Introduction

Model

What are form factor effects ?

Our strategy

Results

Summary and Outlook

Summary and OutlookSummary When we consider a QCD-like strong interaction in the hidden sector, the pNGBs resulting from DχSB, which we call the dark pions, can be Higgs portal dark matters !Form factor effects on the portal interaction between the Higgs and the dark pions tend to relax the constraint on the dark pion mass !

Outlook Since the non-reliable region of the calculation in χPT isn’t equal to the excluded region, thus we want to reduce that region

Modified Omnès representation

Back UP

O(p4) chiral Lagrangian !!!!!!!We determined the LECs as follows,

Low energy constants (LECs) in Dark-QCD

LO(p4)chiral = L1

�tr[(@µU)(@µU†)]

�2+ L2 tr[(@µU)(@⌫U

†)(@µU)(@⌫U †)]

+ L3 tr[(@µU)(@µU†)(@⌫U)(@⌫U †)]

+ L4 tr[(@µU)(@µU†)] tr[�U† + U�†] + L5 tr[(@µU)(@µU†)(�U† + U�†)]

+ L6

�tr[�U† + U�†]

�2+ L7

�tr[�U† � U�†]

�2

+ L8 tr[�U†�U† + U�†U�†]

Lr5(µ = 770 MeV)⇥ 103 = 1.21± 0.08

Lr5(µ = 770 GeV)⇥ 103 = 1.21± 0.08

SM QCD

Dark-QCD

( f⇡ = 93 MeV )

( F⇧ = 93 GeV )

!!!!!!Generally, scalar form factor in χPT can be divided into two parts

Explicit expression of scalar form factor

N = 16⇡2

PS(s) 3s

M2⇧

,

✓s

M2⇧

◆2

US(s) 3 lns

M2⇧

,s

M2⇧

lns

M2⇧

,

✓s

M2⇧

◆2

lns

M2⇧

, · · ·

Polynomial term

Dispersive term

FS(s) = FS(0)

⇢1 +

M2⇧

F 2⇧

✓s

M2⇧

� 1

2

◆J(s) +

s

M2⇧

✓lr4 � L� 1

N

◆�+

M4⇧

F 4⇧

(PS(s) + US(s))

�

L =1

Nln

M2⇧

µ2

s

M2⇧

✓lr4 � L� 1

N

◆

J(s) ⇠ lns

M2⇧

!!! is necessary ? → Yes !

�h⇧⇧(s = 0)

v=

2M2⇧

v2F(M⇧/F⇧)

⇠ 2M2⇧

v2(M⇧/F⇧ . 3)

F⇧ = 50 GeV

Necessity of dark quark mass

L = LSM +X

Q=U,D

✓Q̄(i /D �MQ)Q� 1

⇤(H†H)Q̄Q

◆