Hunting for WIMPs: how low should we go?

Aaron Pierce Michigan Center for Theoretical Physics

TevPA 2017 August 10, 2017

with J. Kearney and N. Orlofsky 1611.05048 and N. Shah and S. Vogl 1706.01911

WIMP with a capital W

• Cosmology and direct detection are really controlled by interactions with gauge/ SM Higgs boson

• e.g. Singlet-doublet model, split SUSY…

https://arxiv.org/pdf/1109.2604.pdf

h

⌫1

⌫1

q

q

! h

q

⌫1

q

⌫1

(�SI)

Z

⌫1

⌫1

q

q

! Z

q

⌫1

q

⌫1

(�SD)

E

⌫1

⌫1

W

W

! No tree-level direct detection analog

⌫1

E

W ! No tree-level direct detection analog

FIG. 1: Relevant diagrams for annihilation and corresponding direct detection diagrams, where

applicable. Achieving su�cient dark matter annihilation in the early universe in order to obtain

the measured relic density requires at least one of these diagrams to be significant. In the case of

s-channel Higgs or Z boson exchange, this may imply correspondingly large �SI or �SD respectively.

In the case of t-channel annihilation or co-annihilation, there is not a clear direct detection analog,

but the processes will be related through couplings and mixing angles.

6

Pressure on !SI

✤ Xenon-based experiments place severe constraints on spin-independent (coherent) scattering.

✤ PandaX, LUX (current)

✤ Xenon1T, LZ (future)

✤ So, e.g., “higgs-mediated” DM largely disfavored.

LUX [arXiv: 1608.07648]

Escudero et al [arXiv: 1609.09079]

Spin Independent Scattering

y��h = .1

Dirac DM coupling to Z ~ 10 � ⇡ few ⇥ 10�40Zµ�̄�µ�

Z-mediated Dark MatterZ-mediated DM

✤ Simplest, gauge-invariant realization

✤ Contains axial coupling to Z

as well as !!Zh, !!Zhh contact interactions.

✤ Simple “benchmark” for spin-dependent DM.

L � c

2⇤2(iH†DµH + h.c.)�̄�µ�5�

L � � g24cW

cv2

⇤2Zµ�̄�

µ�5�

Z-mediated DM

✤ Simplest, gauge-invariant realization

✤ Contains axial coupling to Z

as well as !!Zh, !!Zhh contact interactions.

✤ Simple “benchmark” for spin-dependent DM.

L � c

2⇤2(iH†DµH + h.c.)�̄�µ�5�

L � � g24cW

cv2

⇤2Zµ�̄�

µ�5�

Also 𝝌-𝝌-Z-h and 𝝌-𝝌-Z-h-h contact interactions(!)Also:

de Simone et al, arXiv:1402.6287; Arcadi, Mambrini and Richard, arXiv:1411.2985,

Berlin, Escudero, Hooper and Lin, arXiv 1609.09079;

Thermal relic

No Zh, Zhh No Zhh

10 50 100 500 1000

0.001

0.005

0.010

0.050

0.100

0.500

mχ (GeV)

g A

J. Kearney and N. Orlofsky, AP 1611.05048

IC

PandaX

LZ

Thermal relic

No Zh, Zhh No Zhh

ΓZ

10 50 100 500 1000

0.001

0.005

0.010

0.050

0.100

0.500

mχ (GeV)

g A

J. Kearney and N. Orlofsky, AP 1611.05048

Contribution to T parameter

IC

PandaX

LZ

T<-.01 T<-.09

Thermal relic

No Zh, Zhh No Zhh

ΓZ

10 50 100 500 1000

0.001

0.005

0.010

0.050

0.100

0.500

mχ (GeV)

g A

Large contributions to ΔT

In allowed region, sizable contributions to EW precision observable !.

Indicates presence of additional electroweak states.

�L �c2m2

�

⇡2⇤

4log

✓⇤

m�

◆ ��H†DµH��2

2/22/2017 15ec0eb753e9537c18fcee8b1f211687da53b54f.svg

file:///Users/atpierce/Desktop/For%20Cornell/15ec0eb753e9537c18fcee8b1f211687da53b54f.svg 1/1

Z-mediated DM

✤ Simplest, gauge-invariant realization

✤ Contains axial coupling to Z

as well as !!Zh, !!Zhh contact interactions.

✤ Simple “benchmark” for spin-dependent DM.

L � c

2⇤2(iH†DµH + h.c.)�̄�µ�5�

L � � g24cW

cv2

⇤2Zµ�̄�

µ�5�

IC

PandaX

LZ

T<-.01 T<-.09

Thermal relic

No Zh, Zhh No Zhh

ΓZ

10 50 100 500 1000

0.001

0.005

0.010

0.050

0.100

0.500

mχ (GeV)

g A

Precision Electroweak Constraints

J. Kearney and N. Orlofsky, AP 1611.05048

Motivates inclusion of new EW states

What do these states have to do with DM?

✤ Could be other sector that happens to compensate.

✤ But more minimal (and perhaps more realistic): ∃ additional dark sector states whose contributions are related to those of DM…could affect the DM pheno!

✤ e.g., “Cutting the self-energy diagram” argument

Scissors credit: J. Kearney

Singlet-Doublet Dark Matter

• Dirac doublet, D/Dc and Majorana N.

• Similar to Higgsino/Bino sector of the MSSM, but without all the pesky symmetry.

• Gives couplings to h and Z

• Ensures approximate unification (cf. split SUSY)Arkani-Hamed, Dimopoulos, and Kachru hep-th/0501082;

Mahbubani, Senatore [hep-ph/0510064] D’Eramo [arXiv:0705.4493]

Enberg et al. [arXiv:0706.0918] Cohen, Kearney, AP, Tucker-Smith [arXiv:1109.2604]

A simple embedding: Singlet-Doublet Dark Matter (SDDM)

✤ Dirac doublet D, DC, Majorana singlet N coupled via

✤ Lightest (neutral) state is DM candidate.

✤ New states in complete EW representations contribute to ΔT, and allow new annihilation channels.

L � �yDHN � ycDcH̃N �MDDDc � MN

2N2 + h.c.

Mahbubani, Senatore [hep-ph/0510064]D’Eramo [arXiv:0705.4493]

Enberg et al. [arXiv:0706.0918]Cohen, JK, Pierce, Tucker-Smith [arXiv:1109.2604]

Spin-Independent Coupling?

• There is a direct detection “blind spot” Cohen, Kearney, AP, Tucker-Smith [arXiv:1109.2604] Cheung, Hall, Pinner, Ruderman [arXiv:1211.4873]

The “Higgs Blindspot”

✤ Generically, DM has diagonal couplings to Higgs, but these vanish for specific choice of Yukawas

✤ Large MD, in blindspot ⇒ Z-mediated DM

✤ But, ∃ other interesting parameter space…to which we are (or are rapidly becoming) sensitive!

Cohen, JK, Pierce, Tucker-Smith [arXiv:1109.2604]Cheung, Hall, Pinner, Ruderman [arXiv:1211.4873]

ycBS = �yMN

MD

0

@1±

s

1�✓MN

MD

◆21

A�1

Can be found by “low energy theorem”

m� condition signs

M1

M1

+ µ sin 2� = 0 sign(M1

/µ) = �1M

2

M2

+ µ sin 2� = 0 sign(M2

/µ) = �1�µ tan � = 1 sign(M

1,2/µ) = �1⇤

M2

M1

= M2

sign(M1,2/µ) = �1

Table 1: Table of SI blind spots, which occur when the DM coupling to the Higgs vanishesat tree-level. The first and second columns indicate the DM mass and blind spot condition,respectively. All blind spots require relative signs among parameters, as emphasized in thethird column. ⇤For the third row, the blind spot requires that µ and M

1

(M2

) have oppositesigns when M

2

(M1

) is heavy.

of any of neutralino to the Higgs boson can then be obtained by replacing v ! v+h, as dictatedby low-energy Higgs theorems [45, 46]:

Lh�� =1

2m�i(v + h)�i�i (13)

=1

2m�i(v)�i�i +

1

2

@m�i(v)

@vh�i�i +O(h2), (14)

which implies that @m�i(v)/@v = ch�i�i [47, 48].Consider the characteristic equation satisfied by one of the eigenvalues m�i(v),

det(M� � 1m�i(v)) = 0. (15)

Di↵erentiating the left-hand side with respect to v and setting @m�i(v)/@v = ch�i�i = 0, onethen obtains a new equation which defines when the neutralino of mass m�i(v) has a vanishingcoupling to the Higgs boson1:

(m�i(v) + µ sin 2�)

✓m�i(v)�

1

2(M

1

+M2

+ cos 2✓W (M1

�M2

))

◆= 0. (16)

The above equation implies that for regions in which ch�i�i = 0, m�i(v) is entirely independentof v. At such cancellation points, m�i(v) = m�i(0), so the neutralino mass is equal to the massof a pure gaugino or Higgsino state and m�i(v) = M

1

,M2

,�µ. As long as Eq. (16) holds for theLSP mass, m�1(v), then the DM will have a vanishing coupling to the Higgs boson, yielding aSI scattering blind spot. It is a nontrivial condition that Eq. (16) holds for the LSP, rather thana heavier neutralino, because for some choices of parameters the DM retains a coupling to theHiggs but one of the heavier neutralinos does not. We have identified these physically irrelevantpoints and eliminated them from consideration. The remaining points are the SI scattering

1We have checked that Eq. 16 can also be derived using analytical expressions for bilinears of the neutralino

diagonalization matrix from Ref. [49].

12

m� condition signs

M1

M1

+ µ sin 2� = 0 sign(M1

/µ) = �1M

2

M2

+ µ sin 2� = 0 sign(M2

/µ) = �1�µ tan � = 1 sign(M

1,2/µ) = �1⇤

M2

M1

= M2

sign(M1,2/µ) = �1

Table 1: Table of SI blind spots, which occur when the DM coupling to the Higgs vanishesat tree-level. The first and second columns indicate the DM mass and blind spot condition,respectively. All blind spots require relative signs among parameters, as emphasized in thethird column. ⇤For the third row, the blind spot requires that µ and M

1

(M2

) have oppositesigns when M

2

(M1

) is heavy.

of any of neutralino to the Higgs boson can then be obtained by replacing v ! v+h, as dictatedby low-energy Higgs theorems [45, 46]:

Lh�� =1

2m�i(v + h)�i�i (13)

=1

2m�i(v)�i�i +

1

2

@m�i(v)

@vh�i�i +O(h2), (14)

which implies that @m�i(v)/@v = ch�i�i [47, 48].Consider the characteristic equation satisfied by one of the eigenvalues m�i(v),

det(M� � 1m�i(v)) = 0. (15)

Di↵erentiating the left-hand side with respect to v and setting @m�i(v)/@v = ch�i�i = 0, onethen obtains a new equation which defines when the neutralino of mass m�i(v) has a vanishingcoupling to the Higgs boson1:

(m�i(v) + µ sin 2�)

✓m�i(v)�

1

2(M

1

+M2

+ cos 2✓W (M1

�M2

))

◆= 0. (16)

The above equation implies that for regions in which ch�i�i = 0, m�i(v) is entirely independentof v. At such cancellation points, m�i(v) = m�i(0), so the neutralino mass is equal to the massof a pure gaugino or Higgsino state and m�i(v) = M

1

,M2

,�µ. As long as Eq. (16) holds for theLSP mass, m�1(v), then the DM will have a vanishing coupling to the Higgs boson, yielding aSI scattering blind spot. It is a nontrivial condition that Eq. (16) holds for the LSP, rather thana heavier neutralino, because for some choices of parameters the DM retains a coupling to theHiggs but one of the heavier neutralinos does not. We have identified these physically irrelevantpoints and eliminated them from consideration. The remaining points are the SI scattering

1We have checked that Eq. 16 can also be derived using analytical expressions for bilinears of the neutralino

diagonalization matrix from Ref. [49].

12

h

⌫1

⌫1

q

q

! h

q

⌫1

q

⌫1

(�SI)

Z

⌫1

⌫1

q

q

! Z

q

⌫1

q

⌫1

(�SD)

E

⌫1

⌫1

W

W

! No tree-level direct detection analog

⌫1

E

W ! No tree-level direct detection analog

FIG. 1: Relevant diagrams for annihilation and corresponding direct detection diagrams, where

applicable. Achieving su�cient dark matter annihilation in the early universe in order to obtain

the measured relic density requires at least one of these diagrams to be significant. In the case of

s-channel Higgs or Z boson exchange, this may imply correspondingly large �SI or �SD respectively.

In the case of t-channel annihilation or co-annihilation, there is not a clear direct detection analog,

but the processes will be related through couplings and mixing angles.

6

h

⌫1

⌫1

q

q

! h

q

⌫1

q

⌫1

(�SI)

Z

⌫1

⌫1

q

q

! Z

q

⌫1

q

⌫1

(�SD)

E

⌫1

⌫1

W

W

! No tree-level direct detection analog

⌫1

E

W ! No tree-level direct detection analog

FIG. 1: Relevant diagrams for annihilation and corresponding direct detection diagrams, where

applicable. Achieving su�cient dark matter annihilation in the early universe in order to obtain

the measured relic density requires at least one of these diagrams to be significant. In the case of

s-channel Higgs or Z boson exchange, this may imply correspondingly large �SI or �SD respectively.

In the case of t-channel annihilation or co-annihilation, there is not a clear direct detection analog,

but the processes will be related through couplings and mixing angles.

6

Question:

• Suppose Higgs coupling is small (near the blindspot), can we expect to see the Dark Matter through its spin-dependent scattering?

Singlet DoubletIn blind spot (fixes yc)

Relic density thermal (fixes MD)

������(�������)

�������(�����)

��(�����)

������� ������� = ����

��� ���

��� ���

��� ���

��� ���

��� ��� ��� ��� ��� ������

���

���

���

���

���

���

���

�

�χ(���

)

Well modeled

by Z

mD

A simple embedding: Singlet-Doublet Dark Matter (SDDM)

✤ Dirac doublet D, DC, Majorana singlet N coupled via

✤ Lightest (neutral) state is DM candidate.

✤ New states in complete EW representations contribute to ΔT, and allow new annihilation channels.

L � �yDHN � ycDcH̃N �MDDDc � MN

2N2 + h.c.

Mahbubani, Senatore [hep-ph/0510064]D’Eramo [arXiv:0705.4493]

Enberg et al. [arXiv:0706.0918]Cohen, JK, Pierce, Tucker-Smith [arXiv:1109.2604]

J. Kearney and N. Orlofsky, AP 1611.05048

Breaking the Crossing Symmetry: Co-annihilation

If 𝝌 and Y simultaneously inhabit the thermal bath at freeze-

out (Boltzman suppression not too large)

e��m/TFO ⇡ e�20�mm

Griest and Seckel, Phys.Rev. D43 (1991) 3191-3203

μ

SMDM + stop

stop+sbottom

Rest of MSSM

Loop Induced Dark Matter Couplings

Xt

10 Direct Detection Program Roadmap 39

1 10 100 1000 10410!5010!4910!4810!4710!4610!4510!4410!4310!4210!4110!4010!39

10!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

WIMP Mass !GeV"c2#

WIMP!nucleoncrosssection!cm2 #

WIMP!nucleoncrosssection!pb#

7BeNeutrinos

NEUTRINO C OHER ENT SCATTERING

NEUTRINO COHERENT SCATTERING(Green&ovals)&Asymmetric&DM&&(Violet&oval)&Magne7c&DM&(Blue&oval)&Extra&dimensions&&(Red&circle)&SUSY&MSSM&&&&&&MSSM:&Pure&Higgsino&&&&&&&MSSM:&A&funnel&&&&&&MSSM:&BinoEstop&coannihila7on&&&&&&MSSM:&BinoEsquark&coannihila7on&&

8BNeutrinos

Atmospheric and DSNB Neutrinos

CDMS II Ge (2009)

Xenon100 (2012)

CRESST

CoGeNT(2012)

CDMS Si(2013)

EDELWEISS (2011)

DAMA SIMPLE (2012)

ZEPLIN-III (2012)COUPP (2012)

SuperCDMS Soudan Low ThresholdSuperCDMS Soudan CDMS-lite

XENON 10 S2 (2013)CDMS-II Ge Low Threshold (2011)

SuperCDMS Soudan

Xenon1T

LZ

LUX

DarkSide G2

DarkSide 50

DEAP3600

PICO250-CF3I

PICO250-C3F8

SNOLAB

SuperCDMS

Figure 26. A compilation of WIMP-nucleon spin-independent cross section limits (solid curves), hintsfor WIMP signals (shaded closed contours) and projections (dot and dot-dashed curves) for US-led directdetection experiments that are expected to operate over the next decade. Also shown is an approximateband where coherent scattering of 8B solar neutrinos, atmospheric neutrinos and di↵use supernova neutrinoswith nuclei will begin to limit the sensitivity of direct detection experiments to WIMPs. Finally, a suite oftheoretical model predictions is indicated by the shaded regions, with model references included.

We believe that any proposed new direct detection experiment must demonstrate that it meets at least oneof the following two criteria:

• Provide at least an order of magnitude improvement in cross section sensitivity for some range ofWIMP masses and interaction types.

• Demonstrate the capability to confirm or deny an indication of a WIMP signal from another experiment.

The US has a clear leadership role in the field of direct dark matter detection experiments, with mostmajor collaborations having major involvement of US groups. In order to maintain this leadership role, andto reduce the risk inherent in pushing novel technologies to their limits, a variety of US-led direct search

Community Planning Study: Snowmass 2013

Snowmass 1310.8327

Mass Splitting

Imposing Higgs Mass

Mass Splittings

Higgs OK

But…• It is always possible that there could be “some

Higgsino” in the dark matter, in which case, direct detection may have nothing to do with the cosmology.

stop can impact both of these processes. The measurement of the Higgs boson mass of 125

GeV suggests that there indeed is a large mixing in the stop sector. In this case, it makes

sense to include the full stop sector in the simplified model.

This article is organized as follows. In Sec. II we explore the basics of the parameter

space, and discuss constraints unrelated to the Dark Matter story. We then analyze the

cosmology in Sec. III. We then turn to implications for direct detection. Finally, in Sec. V,

we conclude.

II. ORIENTATION

We are interested in the case of a nearly pure Bino. The dominant co-annihilations will

result from the presence of one or more colored states, X with masses not dissimilar to

that of the neutralino. If equilibrium between the the neutralino, � and the color state is

maintained (as is typically the case, due to scatterings o↵ the standard model bath), then

processes of the form �X ! SM or XX ! SM will be relevant for setting the dark matter

abundance.

A small admixture of Higgsino or Wino will not e↵ect the cosmological history in any

detail. However, even a small admixture can impact direct detection. The Higgsino fraction

is largely controlled by mixing that goes like MZ/µ, the result is a cross section that goes

like:

�SI ⇡ 3⇥ 10�47cm2

✓1 TeV

µ

◆4 ⇣ m�

500 GeV

⌘2✓1 +

µ s2�m�

◆2 ✓1�

m2�

µ2

◆�2

. (1)

Here, we will be interested in the case where this contribution to direct detection is subdom-

inant. That is, we are considering the case where µ is large, and we are asking the question:

what is the direct detection cross section induced by the presence of a stop co-annihilation

cosmology? For concreteness we will take µ = XX TeV and M2 = unless otherwise

specified. For these values, the Higgsino and wino content is irrelevant both for

cosmology and for direct detection.

Because we will be interested in discussing the e↵ects of reproducing the required Higgs

boson mass, we will include the full stop sector, both t̃R and t̃L. This means that the left-

handed sbottom, b̃L is necessarily in the spectrum as well. For simplicity, we assume that

3

Conclusion WIMPs: a Status Report

• Higgs-centric cosmology getting squeezed

• Z-centric cosmology is exciting now

• Symmetry reason for blind spot?

• Co-annihilation-centric cosmology (stop or otherwise) will be very hard for the foreseeable future, but we could get lucky.

• Why co-annihilation? (AP, Kearney, Phys.Rev. D88 (2013) no.9, 095009)

Extra Slides

FIG. 4: Scatter plots of �(p)SD against �SI depicting points with the correct relic density. Shown are

m⌫1 70 GeV [top] and m

⌫1 � 85 GeV [bottom]. At bottom, the blue/light gray points represent

85 GeV m⌫1 160 GeV and green/darker gray represent 175 GeV m

⌫1 500 GeV; these

mass ranges are chosen to avoid regions where WW ⇤ and tt⇤ final states are expected to become

important (see text for discussion). In both plots, gray indicates points excluded by current direct

detection limits.

14

Cohen, Kearney, AP, Tucker-Smith 1109.2604

85<m<160

175<m<500

Cohen, Kearney, AP, Tucker-Smith 1109.2604FIG. 2: An example of the suppression of �SI and �SD as a function of �0 for M

S

= 200 GeV,

MD

= 300 GeV and � = 0.36. The critical value for ⌫1⌫1h cancellation is �0 = �0.138, and for

⌫1⌫1Z cancellation is �0 = ±0.36. The lines shown are �(p)SD [green], �SI [red] and ⌦h2 [blue].

For the alternative case where MD

< MS

, the analogous analysis reveals the condition for⌫1⌫1h cancellation to be �0

crit = �� ) �+ = 0 (m⌫1 = M

D

). The resultant WIMP is⌫1 =

1p2(⌫c + ⌫), and has suppressed coupling to both the Higgs and Z boson. However, the

dark matter particle retains a full-strength coupling to the charged dark sector fermion andthe W boson. Because the E fermion also has mass M

D

, there is significant contributionto dark matter annihilation from co-annihilation with the charged state.4 As this couplingstrength is fixed, to achieve the correct relic density the value of M

D

is constrained toM

D

& 1 TeV. This situation is similar to the case of “pure” Higgsino dark matter inthe MSSM, for which M

D

⇠ 1.1 TeV yields the correct value of ⌦h2. So, there is thepossibility that m

⌫1 & 1 TeV with heavily suppressed spin-independent and spin-dependentcross sections. For instance, we find that for M

S

= 2 TeV and � = ��0 = 0.2, the correctrelic density is achieved forM

D

= 1.1 TeV. For this point, �SI and �SD are heavily suppressedas the ⌫1⌫1h and ⌫1⌫1Z couplings are small, and m

⌫2 � m⌫1 ⇠ 1 GeV, su�ciently large to

4 Note that, in fact, the E will be slightly heavier than the WIMP due to Coulombic radiative corrections.

9

yc

IC

PandaX

LZ

T<-.01 T<-.09 EFT c>1 EFT c>4π

Thermal relic

No Zh, Zhh No Zhh

ΓZ

10 50 100 500 1000

0.001

0.005

0.010

0.050

0.100

0.500

mχ (GeV)

g A

Effective Field Theory Validity

Both gluino mass signs

Preliminary, AP, N

.Shah, S. Vogl

Higgs Mass Calculations

• Longlistof2-loop(andmore!)computations:

– Carena,Degrassi,Ellis,Espinoza,Haber,Harlander,Heinemeyer,Hempfling,Hoang,Hollik,Hahn,Martin,Pilaftsis,Quiros,Ridolfi,Rzehak,Slavich,Wagner,Weiglein,Zhang,Zwirner.

• mh ~125GeV:LargeXt andModerate/Largetanb

Carena andHaber,hep-ph/0208209

NAUSHEEN R. SHAH // 2nd PIKIO Meeting 2016 – Dark Matter Sep 24, 2016 // Slide 10

Stops.&

-��� -��� ��� ��� ���

���

����

����

����

����

����

����

��� θ

��~�(���

)

� �~�= ��� ���

��� ��� < �� < ��� ���

δρ ��� �������+γγ �������������� ��������

Approximate Empirical Vacuum Stability limit from D. Morrissey and N. Blinov arXiv:1310.4174

Approximate Higgs mass 1-loop formula

Preliminary&A.&Pierce,&NRS&&&S.&Vogl&

NAUSHEEN R. SHAH // LBNL Seminar Nov 16, 2016 // Slide 16

INDIRECTColor/Charge Breaking Vacuum

V=V2+V3+V4

LargeXt

Colored:123GeV <mh <127GeV

LightstopsOK!LargeXt (At)canbe

problematic

D.MorrisseyandN.Blinov arXiv:1310.4174

Charge Color-Breaking Vacuua

Morrissey and Blinov 1310.4174

Singlet Doublet Away from Blind Spot

7

For instance, the small mass splittings make this

region of parameter space susceptible to searches

such as [38] based on soft leptons.

So, while the pure Z-mediated model is a good proxy

for the singlet-doublet model in the blind spot at

large y (where direct detection constraints may be

directly translated), the reach of future experiments

extends well beyond this regime to smaller y. Even

if the Z-mediated model of the preceding section is

excluded up to a given m�, this model presents a

minimal variation in which that DM mass remains

viable, and yet meaningful constraints can still be

achieved. As such, the singlet-doublet model in

the Higgs blind spot represents a worthy target for

future WIMP searches, and it would be valuable for

experiments to quote constraints in terms of this

parameter space.

Finally, we comment on the e↵ect of tuning away

from the exact blind spot. This will result in a non-

zero DM-h coupling that, as mentioned previously,

can result in strong constraints from SI scattering—

in fact, this is the case even if the DM-h coupling is

su�ciently small to have a negligible impact on the

DM thermal history. Parameterizing the deviation

from the blind spot as

�yc =yc

ycBS

� 1, (12)

we show in Fig. 3 the parameter space for �yc =

�0.3. Note that, for yc 6= ycBS

, m� 6= MN , so here

we plot with respect to {y,MN}—however, for the

values of y and �yc considered, m� ' MN .

To the left, where t-channel and co-annihilation play

a significant role in determining the relic density,

changing yc simply changes the DM-Z and DM-

h couplings, altering the exact values of �SD,SI

(and hence the future experimental reach) relative

to Fig. 2 in this region of parameter space. To

FIG. 3: Similar to Fig. 2, but with yc deviating from theHiggs blind spot by �yc = �0.3, see Eq. (12). Mirroringthe previous figure, contours of MD are shown in blue.Current and projected limits on �

SD

(�SI

) are shown inred (orange).

the right however, where the relic density is pre-

dominantly determined by s-channel Z-exchange,

MD changes to compensate the change in yc and

maintain approximately the same DM-Z coupling as

in Fig. 2. As a result, the current SD exclusions (and

the region well-described by the pure Z-mediated

model) do not change significantly. While it is not

plotted, we note that the parameter space is not

symmetric about ycBS

.

The two disjoint regions at larger y ⇠> 0.35 are

related to the top quark threshold. For m� ⇠>

mt, the observed relic abundance is achieved for a

smaller DM-Z coupling, which is accompanied by

a similar suppression of the DM-h coupling. This

allows the model to evade present SI limits near

threshold (m�⇠> 190 GeV). However, while the relic

density constraint largely fixes the DM-Z coupling

at larger MN , the DM-h coupling exhibits di↵erent

parametric dependence and modestly increases with

� = -���

�� ���������

�� ���������

�� ���������

�������

��

��� ��� ��� ��� ��� ������

���

���

���

���

���

���

���

�

��(���

)

Double Blind spot

• There is a spot where both the SI and SD vanish.

• Requiring these two couplings to vanishes, along with reproducing the thermal abundance, sets MN =MD=850 GeV. (model building?)

“Pure” Higgsino

0.60.8

11.21.4

103 104 105 106

resu

m/t

ree

|M2| [GeV]

10�49

10�48

10�47

10�46

10�45

10�44SI

cros

sse

ctio

n�p SI

[cm

2] �2 = 0�

90�180�

LUX exclusionNeutrino BG

Figure 8: SI scattering cross sections of the Higgsino DM with a proton as functions of |M2| in solidlines. Here we take tan � = 2, µ = 500 GeV, M1 = M2 and em = |M2|. Red-solid, green-dashed, andblue short-dashed lines correspond to �2 = arg(M2) = 0, ⇡/2 and ⇡, respectively. Upper blue-shadedregion is excluded by the LUX experiment [61]. Lower gray-shaded region represents the limitationof the direct detection experiments due to the neutrino background [69]. Lower panel represents thee↵ects of the resummation on the calculation.

5 Electric Dipole Moments

Generally, the MSSM induces new sources of CP violations, which may lead to large electric dipole

moments (EDMs) of the SM fermions. One of the important contributions comes from one-loop

diagrams which includes SUSY scalar particles. Another significant contribution is two-loop dia-

grams without the SUSY scalar particles. In the present “lonely Higgsino” scenario (typically when

em � 10 TeV), the latter contribution is dominant.

As we noted above, the mass di↵erence between the neutral components depends on the new

CP phases in the e↵ective interactions in Eqs. (4) and (8), and their e↵ects can be probed with the

EDMs. The dominant contribution to the EDMs comes from the two-loop Barr-Zee diagrams [70]

shown in Fig. 9 [71–73]. To evaluate the contribution, let us first show the Higgs-charged Higgsino

vertex:

Lint = �Re(d2)vh eH+ eH+ + Im(d2)vh eH+i�5 eH+ , (52)

and the CP-odd part (the second term) is relevant to our calculation.

The definition of the EDMs of fermion f is

LEDM = � i

2dff�

µ⌫�5Fµ⌫f . (53)

15

Nagata and Shirai arXiv:1410.4549

Another caveat• If willing to tune to the Higgs blindspot, there is one

more out (not requiring SD): CP Violation

CP ! ��5�h ! (q̄q)(��5�)X 1.µ 10-30

1.µ 10-30

1.µ 10-29

1.µ 10-29

2.µ 10-29

2.µ 10-29

3.µ 10-29

200 400 600 800 10000.5

0.6

0.7

0.8

0.9

1.0

mDM@GeVDfêp

current bound Hblind spot, r=0.9L

Figure 3: The current constraints and prospects in blind spot. The red regions are excluded by the bound

on the �SI from LUX experiment [1]. The orange regions are excluded by the bound on �SD from PandaX-II

experiment [2]. The contour lines show the absolute value of the electron EDM. In the gray regions, we

cannot obtain the DM thermal relic abundance that matched the measured value of DM density.

viable even if direct detection experiments do not find any signal. We also show the absolute value

of the electron EDM in the figure. The value is within the reach of the future experiments in most

of the parameter space, and thus we can confirm the validity of this model by the observation of

the electron EDM.

4 Conclusion

The recent progress of the dark matter direct detection experiments gives stringent constraint

on the scattering cross section of dark matter with nucleon. Dark matter models in the thermal

relic scenario have to evade this constraint. One simple way to evade the constraint is to rely on

pseudoscalar interactions of a fermionic dark matter candidate.

We have studied the singlet-doublet dark matter model with a special emphasis on the CP vio-

9

r= ratio of yukawas

E↵ectofCP

violationinthesinglet-doubletdarkmattermodel

Tom

ohiro

Abe

Institu

teforAdvanced

Resea

rch,Nagoya

University,

Furo-ch

oChiku

sa-ku

,Nagoya,Aich

i,464-8602Japan

and

Kobayashi-M

aska

waInstitu

tefortheOrigin

ofParticles

andtheUniverse,

Nagoya

University,

Furo-ch

oChiku

sa-ku

,Nagoya,Aich

i,464-8602Japan

Werevisit

thesin

glet-dou

blet

dark

matter

mod

elwith

aspecial

emphasis

ontheCPviola-

tione↵

ecton

thedark

matter

phen

omen

ology.TheCP

violationin

thedark

sectorinduces

apseu

doscalar

interactionof

aferm

ionic

dark

matter

candidate

with

theSM

Higgs

boson

.

Thepseu

doscalar

interactionhelp

sthedark

matter

candidate

evadethestron

gcon

straints

fromthedark

matter

direct

detection

experim

ents.Weshow

that

themod

elcan

explain

the

measu

redvalu

eof

thedark

matter

den

sityeven

ifdark

matter

direct

detection

experim

ents

donot

observe

anysign

al.Wealso

show

that

theelectron

electricdipole

mom

entis

an

important

complem

entto

thedirect

detection

fortestin

gthis

mod

el.Its

valueis

smaller

than

thecu

rrentupper

bou

ndbutwith

inthereach

offuture

experim

ents.

1Introduction

Dark

matter

(DM)is

alead

ingcan

didate

forphysics

beyon

dthestan

dard

mod

elof

particle

physics.

Mod

elsbased

ontheW

IMPparad

igmare

pop

ular

andhave

been

widely

studied

.Onthe

other

han

d,therecent

dark

matter

direct

detection

experim

ents[1,

2]give

severecon

straintson

themod

els.

Itispossib

leto

evadethecon

straintsfrom

thedirect

detection

experim

entsifaDM

candidate

is

aferm

ionan

dinteracts

with

thestan

dard

mod

el(SM)sector

throu

ghpseu

doscalar

interactions[3,

4].In

that

case,thecross

sectionfor

thedirect

detection

issuppressed

bythevelocity

oftheDM

andthu

sis

negligib

le.Ontheoth

erhan

d,thesam

einteraction

sare

relevantto

DM

annihilation

processes

andwecan

obtain

theDM

therm

alrelic

abundan

cethat

match

esthemeasu

redvalu

eof

theDM

density.

There

aretw

osim

ple

ways

tointrod

uce

thepseu

doscalar

interactions.

Oneway

isto

addCP-

oddscalar

med

iatorsthat

couple

both

toaDM

candidate

andtheSM

particles

[5–13].Theoth

er

way

isto

introduce

CP-violation

intothedark

sector.In

thelatter

case,theSM

Higgs

boson

can

beamed

iator,an

dwedonot

need

CP-od

dscalar

med

iators.Wefocu

son

thelatter

possib

ility.

Wecon

sider

thesin

glet-dou

blet

mod

el[14–16].

This

mod

elis

oneof

theminim

alsetu

psin

arXiv:1702.07236v1 [hep-ph] 23 Feb 2017T. Abe

Figure 1: Barr-Zee type contributions to the EDM. The Z2-odd charged and neutral fermions run in the

triangle part.

where tan ✓ = y/y0 = r. By di↵erentiate this equation with respect to v and setting @mDM/@v = 0,

we find

0 =m4DM �m2

DM

✓M2

2 +v2�2

2�M1M2 sin 2✓ cos�

◆�M2

2 sin 2✓

✓M1M2 cos�� v2

2�2 sin 2✓

◆.

(2.16)

Using Eqs. (2.15) and (2.16), we can obtain two relations. For example, we can solve for mDM and

�,

mDM =

0

B@M2

1M22 sin

2 2✓ sin2 �

M21 +M2

2 sin2 2✓ + 2M1M2 sin 2✓ cos�

1

CA

1/2

, (2.17)

� =

s2(M2

2 �m2DM)(m2

DM +M1M2 sin 2✓ cos�)

v2(M22 sin

2 2✓ �m2DM)

. (2.18)

This is the blind spot condition where ch�1�1 = 0.

For � = 0, there is no blind spot because it requires mDM = 0. For � = ⇡, mDM is non-zero if

the denominator of Eq. (2.17) is zero and we find the following blind spot condition for � = ⇡,

mDM =M1 = M2 sin 2✓. (2.19)

2.3 EDM

This model predicts a new contribution to the EDM because of the new CP violation source �.

The electron EDM is an important complement to direct detection experiments as we will see in

Sec. 3. We summarize the formulae here. The leading contribution comes from the Barr-Zee type

diagram shown in Fig. 1. The electron EDM is defined through

Heff =ide2 ̄e�µ⌫�5 eF

µ⌫ . (2.20)

6