Direct  ditection  of  wino  Dark  Matter  in  the  High-­‐scale  SUSY

Natsumi  Nagata    

Based  on  J.  Hisano,  K.  Ishiwata,  Natsumi  Nagata,  Phys.  Lett.  B690,  311  (2010)  and  1210.5985  .  

2  November,  2012  Na.onal  Tsing  Hua  University  

Nagoya  University  

Outline

1.  Introduction  

2.  Direct  detection  of  Majorana  dark  matter  

3.  Calculation  &  Results  

4.  Summary  

1.  Introduc,on

Introduction Observational  evidence  for  dark  matter  (DM)

Galactic  scale

Cosmological  scale

Scale  of  galaxy  clusters

About  80%  of  the  matter  in  the  Universe  is  nonbaryonic  dark  matter.

Begeman  et.  al.  (1991).

Komatsu  et.  al.  (2010).

hAp://map.gsfc.nasa.gov/

Clowe  et.  al.  (2006).

Introduction Weakly  Interacting  Massive  Particles  (WIMPs)

One  of  the  most  promising  candidates  for  dark  matter  is

Weakly  Interacting  Massive  Particles  (WIMPs)

•  have  masses  roughly  between  10  GeV  ~  a  few  TeV.  

•  interact  only  through  weak  and  gravita.onal  interac.ons.  

•  Their  thermal  relic  abundance  is  naturally  consistent  with  the  cosmological  observa.ons  [thermal  relic  scenario].  

•  appear  in  models  beyond  the  Standard  Model.    

SUSY  SM

Supersymmetric  (SUSY)  Standard  Model  (SM)  

One  of  the  promising  candidates  for  physics  beyond  the  SM.  

LHC  results •  Stringent  limits  are  imposed  on  the  masses  of  

SUSY  par.cles  

•  125  GeV  Higgs  boson  requires  sufficient  radia.ve  correc.ons  in  the  Minimal  Supersymmetric  Standard  Model  (MSSM)  

High-­‐scale  SUSY  ??  

High-­‐scale  SUSY

High-­‐scale  SUSY  scenario  has  a  lot  of  fascina.ng  aspects  from  a  phenomenological  point  of  view.  

  125  GeV  Higgs  boson  can  be  achieved  

  SUSY  CP/flavor  problems  are  relaxed  

  Gravi.no  problem  is  avoided  

  Gauge  coupling  unifica.on  

This  scenario  also  accommodates  the  existence  of  Dark  Matter  (DM)  .

(sufficient  radia.ve  correc.ons)    

(suppressed  by  sfermion  masses)    

(heavy  gravi.no)    

(sfermions  form  SU(5)  mul.plets)    

Assump.on

A  chiral  supermul.plet  X  responsible  for  SUSY  is  charged    under  some  symmetry.

SUSY  is  transferred  via  operators  involving  X†  X

Sob  masses  of  the  scalar  par.cles  arise  from

(MPl:  the  reduced  Planck  scale)

VEV  of  X  field Scalar/gravi.no  mass

Gaugino  mass

Anomaly  media.on   L. Randall and R. Sundrum (1998) G.F. Giudice, M.A. Luty, H. Murayama, R. Rattazzi (1998)

Wino  is  the  lightest  in  the  gaugino  sector  

Since  the  field  X  is  charged  under  some  symmetry,  the  gaugino  mass  terms  are  not  given  by  the  X  field  linear  terms.  

In  this  case,  the  gaugino  masses  are  generated  by    

Higgsinos

We  regard  the  higgsino  mass  as  a  free  parameter  in  the  following  discussion.

(e.g.,  Peccei-­‐Quinn  symmetry)    

Origin  of  Higgsino  mass  is  somewhat  model-­‐dependent.  

  On  the  assump.on  of  a  generic  Kahler  poten.al  

  It  can  be  suppressed  by  some  symmetry.  

Higgsinos  can  be  much  lighter  than  the  gravi.no.  

Gravi!noScalar Par!cles Higgsinos

Gauginos

Gluino

BinoWino

Mass  spectrum

3  TeV

103  TeV

30  TeV 10  TeV

Thermal relic

J. Hisano, S. Matsumoto, M. Nagai, O. Saito, M. Senami (2006).

Higgsinos  can  be  light

Higgs  mass

The  125  GeV  Higgs  boson  mass  is  easily  accounted.  

mt= 173.2 ± 0.9 GeV M. Ibe, T.T. Yanagida (2012).

tan�50

tan�5

tan�2

tanΒ�1 ΜH � MSUSY

10 100 1000 104110

115

120

125

130

135

140

MSUSY�TeV

mh�GeV

Small tanβ is favored

125 GeV

Mo.va.on

•  Although  sfermions  may  be  beyond  the  reach  of  the  LHC,  wino  DM  can  be  searched  in  the  DM  detection  experiments.  Especially,  

•  The  discovery  of  125  GeV  Higgs  boson  allows  us  to  make  a  robust  prediction  for  the  detection  rate.  

•  It  is  found  that  both  the  tree-­‐level  and  the  loop-­‐level  processes  give  rise  to  sizable  contributions.  

Direct  detec.on  experiments  are  promising  

•  Xenon100  collabora.on  gives  a  stringent  constraint  on  spin-­‐independent  elas.c  WIMP-­‐nucleon  scaAering  cross  sec.on.  

•   Ton-­‐scale  detectors  for  direct  detec.on  experiments  are  expected  to  yield  significantly  improved  sensi.vi.es.  

Introduction Direct  Detection  Experiments

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP-

Nuc

leon

Cro

ss S

ectio

n [c

m

-4510

-4410

-4310

-4210

-4110

-4010

-3910

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP-

Nuc

leon

Cro

ss S

ectio

n [c

m

-4510

-4410

-4310

-4210

-4110

-4010

-3910

DAMA/I

DAMA/Na

CoGeNT

CDMS

EDELWEISS

XENON100 (2010)

XENON100 (2011) Buchmueller et al.

(for  WIMPs  of  mass  50  GeV)

[XENON100  collabora.on,  arXiv:  1104.  2549]

WIMP DM

Nucleus

Recoil energy

2.  Direct  detec,on  of  Majorana  DM

Effective  Lagrangian  for  Majorana  Dark  Matter

χ̃0 : DM mq : quark mass M : DM mass

€

LG = fG ¯̃χ0χ̃0GaµνG

aµν

+fqmq¯̃χ0χ̃0q̄q

Spin-­‐dependent  interac.on

Spin-­‐independent  interac.on

Twist-­‐2  operator Scalar-­‐type  interaction

• Couplings  of  DM  with  “nucleon  mass”  

• Nucleon  matrix  element  is  evaluated  with  lattice  simulations

• Couplings  of  DM  with  “quark  momentum”  

• Parton  Distribution  Functions  (PDF)

Twist-­‐2-­‐type  interac.on

Gluon  contribution

The  gluon  contribu.on  turns  out  to  be  comparable  to  the  quark  contribu.on  even  if  the  DM-­‐gluon  interac.on  is  induced  by  higher  loop  diagrams.

Scalar-­‐type  interac.ons,                                                                                                                                                ,  induce     fqmqχ̄χq̄q fGχ̄χGaµνG

aµν

The  couplings  of  DM  with  “nucleon  mass”

Nucleon  matrix  elements:

mN : nucleon mass

1−�

q=u,d,s

fTq ≡ fTG

By  using  the  trace  anomaly  of  the  energy  momentum  tensor  in  QCD,  

This  enhancement  originates  from  the  large  gluon  contribu.on  to  the  nucleon  mass.

gluon

u sd

Mass  frac.ons  for  proton

3.  Calcula,on  &  Results

Diagrams   Tree-­‐level

!̃0 q

q!̃0

h

!̃0

!̃0

g

g

! Higgsh

Q

!̃0 q

q!̃0

Z

! axial-tree``Higgs”  contribu.on

Effec.ve  coupling

(Zij:  Neutralino  mixing  matrix)

The  SI  effective  interaction  is  not  suppressed  even  if  the  Wino  mass  is  much  larger  than  the  W  boson  mass.  

χ̃− : charged winoWµ : W boson

g2 : weak coupling constant

Pure  Wino  DM   Quark  contribution  |    1-­‐loop

h0

!" 0 !" 0 !" 0 !" 0!"# !"#

W- W- W-

q q’ q

(a) (b)

q q

J.  Hisano,  S.  Matsumoto,  M.  Nojiri,  O.  Saito,  Phys.  Rev.  D  71  (2005)  015007.

Lint = −g2( ¯̃χ0γµχ̃−W †

µ + h.c.)

The  gauge  interaction:

χ̃0 : DM

1-­‐loop  diagrams:

Remark:

(a)  ``Scalar”  (b)   ``twist-­‐2”

!" 0 !" 0!"#

Q/q

Q’/q’W- W -

g g

!" 0 !" 0!"#

W- W-

QQ’

g g

(b) (c)

h0

!" 0 !" 0!"#

W-

(a)

Qg g

Pure  Wino  DM   Gluon  contribution  |    2-­‐loop

J.  Hisano,  K.  Ishiwata,  and  N.  Nagata,  Phys.  LeA.  B  690  (2010)  311.

2-­‐loop  diagrams:

``Gluon”  contribu.on

Results  

-2

-1.5

-1

-0.5

0

0.5

1

1 10 100 1000

f p (1

0-9 G

eV-2

)

| | - M2 (TeV)

Wino-like DM (M2 = 3 TeV, lattice)

1 10 100 1000| | - M2 (TeV)

scalartwist-2gluonHiggs

! !

< 0! > 0!

　tanβ = 1, 2, 5, 50 tanβ = 1, 2, 5, 50 (from  top  to  boAom) (from  boAom  to  top)

There  is  a  cancellation  among  these  contributions  

Effec.ve  coupling  with  a  proton  

Results  

10-48

10-47

10-46

10-45

1 10 100 1000

SI cr

oss s

ectio

n (cm

2 )

|!| - M2 (TeV)

Wino-like DM (M2 = 3 TeV, !>0, lattice)

tan"=1.1

1 10 100 1000|!| - M2 (TeV)

tan"=2

1 10 100 1000|!| - M2 (TeV)

tan"=50TotalTree

ScaAering  cross  sec.ons  with  a  proton  

•  Cancellations  between  tree-­‐  and  loop-­‐level  contributions  occur  at  a  certain  value  of  μ  

•  Loop  contribution  is  dominant  in  a  wide  range  of  parameter  region  

Results  

10-48

10-47

10-46

10-45

1 10 100 1000

SI cr

oss s

ectio

n (cm

2 )

|!| - M2 (TeV)

Wino-like DM (M2 = 3 TeV, !<0, lattice)

tan"=1.1

1 10 100 1000|!| - M2 (TeV)

tan"=2

1 10 100 1000|!| - M2 (TeV)

tan"=50TotalTree

ScaAering  cross  sec.ons  with  a  proton  

Tree-­‐level  contribution  interferes  constructively  to  the  loop  contribution  in  the  case  of  low  tanβ  

J.  Hisano,  K.  Ishiwata,  and  N.  Nagata,  arXiv:1210.5985.

4.  Summary

Summary

•  We  evaluate  the  wino-­‐DM  elastic  scattering  cross  sections  in  the  High-­‐scale  SUSY  scenario.  

•  Electroweak  loop  contribu.on  is  dominant  in  a  wide  range  of  parameter  region.  

•  There  is  a  cancella.on  between  tree-­‐  and  loop-­‐level  contribu.ons  and  it  significantly  reduces  the  scaAering  cross  sec.ons.  

•  The  resultant  cross  sec.ons  might  be  within  a  reach  of  future  experiments.  

Backup

Split  SUSY

N. Arkani-Hamed, S. Dimopoulos (2004).

The  SUSY  scale  is  much  higher  than  the  EW  scale.  The  spectrum  below  the  SUSY  scale  contains  

  The  SM  par.cles  (1  Higgs  douplet)  

  Bino    Wino    Gluino    Higgsino  

  Gauge  coupling  unifica.on    Existence  of  DM  

  SUSY  Flavor/CP  problem  

OK  !!

Gauge  coupling  unifica.on

6 8 10 12 14 16

20

30

40

50

Good  enough  !!

N. Arkani-Hamed, S. Dimopoulos (2004).

α-­‐1

sfermions   ・・・   SU(5)  mul.plets  

do  not  affect  unifica.on  @  1-­‐loop  

(The  other  Higgs  doublet  makes  a  small  contribu.on)  

Wino  dark  maAer

Then,  what  determines  the  SUSY  scale  ??      

(Naturalness  for  the  EW  scale  is  not  in  our  hand,  any  more)  

The  amount  of  dark  maAer  abundance  !!  

0

0.1

0.2

0.3

1 2 3m (TeV)

Non perturbativePerturbative

WMAP

J. Hisano, S. Matsumoto, M. Nagai, O. Saito, M. Senami (2006).

 The  second  moments  of  the  parton  distribu.on  func.ons  (PDFs)

mN : nucleon mass

Nucleon  matrix  elements

�N |mq q̄q|N�/mN ≡ fTq ,

• The  mass  frac.ons  (  for  the  scalar-­‐type  quark  operators)    

1−�

q=u,d,s

fTq ≡ fTG

• For  the  twist-­‐2  operators    

Trace  anomaly  of  energy-­‐momentum  tensor  in  QCD

mQQ̄Q

g g

Q

M.  A.  Shifman,  A.  I.  Vainshtein  and  V.  I.  Zakharov,  Phys.  LeA.  B  78  (1978)  443.

The  matrix  element  of  gluon  field  strength  tensor  can  be  evaluated  by  using the  trace  anomaly  of  the  energy-­‐momentum  tensor  in  QCD

Θµµ =

β(αs)

4αsGa

µνGaµν +

�

q=u,d,s

mq q̄q +�

Q=c,b,t

mQQ̄Q

 The  trace  anomaly  of  the  energy-­‐momentum  tensor  in  QCD  (Nf=3)

mN

�

q=u,d,s

mNfTq

mNfTG = −9αs

8π�N |Ga

µνGaµν |N�

Heavy  quark  contribution

Gluon  contribution

SI  coupling  of  Majorana  DM  with  nucleon

The  effective  coupling  of  DM  with  nucleon  is  given  as  follows:

Leff = fN ¯̃χχ̃N̄N

The  gluon  contribu.on  can  be  comparable  to  the  quark  contribu.on  even  if  the  DM-­‐gluon  interac.on  is  induced  by  higher  loop  diagrams.

Suppressed by αs

gluon

u sd

Mass  frac.ons  for  proton

Elastic  scattering  cross  section

mT : the mass of the target nucleusnp : the number of protonnn : the number of neutron

From  now  on,  we  just  show  the  results  for  the  SI  cross  sec.on  of  WIMP  DM  with  a  proton  as  a  reference  value.

One  can  derive  the  SI  cross  section  by  using  the  SI  effective  couplings  as  follows  :

Loop  contribu.ons  only  

10-48

10-47

10-46

10-45

100 1000

SI cr

oss s

ectio

n (cm

2 )

Wino mass (GeV)

Wino DM

130GeV

115GeV

J.  Hisano,  K.  Ishiwata,  and  N.  Nagata,  Phys.  LeA.  B  690  (2010)  311.

The  SI  cross  section  is  almost  independent  of  the  wino  mass.  

Results   Wino  LSP

10-48

10-47

10-46

10-45

1 10 100 1000

SI cr

oss s

ectio

n (cm

2 )

|!| - M2 (TeV)

Wino-like DM (M2 = 200 GeV, !<0, lattice)

tan"=1.1

1 10 100 1000|!| - M2 (TeV)

tan"=2

1 10 100 1000|!| - M2 (TeV)

tan"=50TotalTree

10-48

10-47

10-46

10-45

1 10 100 1000

SI cr

oss s

ectio

n (cm

2 )

|!| - M2 (TeV)

Wino-like DM (M2 = 200 GeV, !>0, lattice)

tan"=1.1

1 10 100 1000|!| - M2 (TeV)

tan"=2

1 10 100 1000|!| - M2 (TeV)

tan"=50TotalTree

Results   Higgsino  LSP

-2

-1.5

-1

-0.5

0

0.5

1

1 10 100 1000

f p (1

0-9 G

eV-2

)

M2 - | | (TeV)

Higgsino-like DM (| | = 1 TeV, lattice)

1 10 100 1000M2 - | | (TeV)

scalartwist-2gluonHiggs

! !

< 0! > 0!

!

　tanβ = 1, 2, 5, 50 tanβ = 1, 2, 5, 50 (from  top  to  boAom) (from  boAom  to  top)

Results   Higgsino  LSP

10-50

10-49

10-48

10-47

10-46

10-45

1 10 100 1000

SI cr

oss s

ectio

n (cm

2 )

M2 - |!| (TeV)

Higgsino-like DM (|!| = 1 TeV, !<0, lattice)

tan"=1.1

1 10 100 1000M2 - |!| (TeV)

tan"=2

1 10 100 1000M2 - |!| (TeV)

tan"=50TotalTree

10-50

10-49

10-48

10-47

10-46

10-45

1 10 100 1000

SI cr

oss s

ectio

n (cm

2 )

M2 - |!| (TeV)

Higgsino-like DM (|!| = 1 TeV, !>0, lattice)

tan"=1.1

1 10 100 1000M2 - |!| (TeV)

!

tan"=2

1 10 100 1000M2 - |!| (TeV)

!

tan"=50TotalTree

Results  

1

10

100

1 10 100

M2 (

TeV)

|!| (TeV)

!<0, lattice tan"=1.1

1 10 100|!| (TeV)

tan"=2

1 10 100|!| (TeV)

tan"=50!

10 44-10 45-

10 47-

10 47-10 44- 10 46-10 45-10 47-

10 48-

10 46-

10 48-

10 48-10 45-

10 46-

10 45-

10 46-

10 48-

10 47-

10 46-10 45-

10 47-

10 47-

10 48-

10 46- 10 48-

10 46-10 47- 10 48-

10 46-10 47- 10 48-

10 48-

10 47-

XENON10010 47-@60GeV

10 48- @60GeV

1

10

100

1 10 100

M2 (

TeV)

|!| (TeV)

!>0, lattice tan"=1.1

1 10 100|!| (TeV)

tan"=2

1 10 100|!| (TeV)

tan"=50!

10 44-10 45-

10 47-

10 47-10 48-10 44- 10 46-10 45- 10 47-10 48-

10 46-

10 48-

10 44-10 45-

10 47-

10 47-10 48-10 44- 10 46-10 45- 10 47-10 48-

10 46-

10 48-

10 44-10 45-

10 47-

10 47-10 44- 10 46-10 45-10 47-

10 48-

10 46-

10 48-

10 48-

10 47-

10 47-

10 48-

10 46- 10 48- 10 47-

10 47-

10 48-

10 46- 10 48-10 47-

10 47-

10 48-

10 46- 10 48-

XENON100

10 47- @60GeV

10 48- @60GeV