UCI Seminar

43
Dark Matter and the Higgs in Natural SUSY Sebastian Macaluso NHETC, Rutgers University UC Irvine November 16, 2016 Aria Basirnia, SM & David Shih arXiv:1605.08442

Transcript of UCI Seminar

Dark Matter and the Higgs in Natural SUSY

Sebastian MacalusoNHETC, Rutgers University

UC IrvineNovember 16, 2016

Aria Basirnia, SM & David Shih arXiv:1605.08442

Introduction: Big Questions

Why is the Higgs at 125 GeV?

Is it compatible with naturalness?

What is the dark matter?

Does it realize the WIMP miracle?

Higgs @ 125 GeV in the MSSM

V (H) = m2H |H|2 + 1

2�|H|4

At tree-level in the MSSM...

...need loop corrections to lift mh to 125 GeV

� 1

4(g2 + g02)c22� ) m2

h m2Zc

22�

hh

h

h

Att̃L t̃R

h

hh

h

t̃ t̃y2t

�� =

3y4t4⇡2

log

m2t̃

m2t

+

X2t

m2t̃

✓1� X2

t

12m2t̃

◆�

Xt = At � µ cot�

m2h = �2m2

H = 2�v2 = (125GeV)2

Simple test-point:MS = 10 TeV,

Xt = 0, tanß = 20

Draper et al : Mh = 123.2 GeV

Bagnaschi et al : Mh = 123.6 GeV

SusyHD: Mh = 123.6 GeV

1 103 30115

120

125

130

135

Degenerate SUSY scale in TeV

HiggsmassinGeV

Quasi�natural SUSY, tan⇤ ⇥ 20

SUSY thresholds at 2 QCD loops

SUSY thresholds at 1 loop Maximal stop

mixing

Minimal sto

p mixing

exp

Bagnaschi et al., 1407.4081

Hahn et al. (FeynHiggs), 1312.4937; Draper et al., 1312.5743; Bagnaschi et al., 1407.4081; PardoVega+Villadoro (SusyHD) 1504.05200 Recent incarnations of the decades-old EFT approach:

FeynHiggs: Mh = 126.5 GeV

mh=125 GeV in the MSSM requires either ≳10 TeV stops or multi-TeV A-terms

Higgs @ 125 GeV in the MSSM

Higgs @ 125 GeV in the MSSM

Fine-tuning of the electroweak scale is percent level or worse in the MSSM!

m2Z ⇡ �2(|µ|2 +m2

Hu)

�m2Hu

⇠ � 3y2t8⇡2

(m2t̃L

+m2t̃R

+A2t ) log

mt̃

� ⇠ 104

� ⇠ 102

for 10 TeV stops

for multi-TeV A-terms

Hall, Pinner & Ruderman ‘12

tan� = 20, mQ3 = mu3 = mt̃,

mh = (124� 126)GeV

� =2�m2

Hu

m2h

Neutralino DM in the MSSM

WIMP miracle: DM relic abundance via thermal freeze-out suggests ~ TeV scale DM.

G. Jungman et al. JPhysics Reports 267 (1996) 195-373 221

Using the above relations (H = 1.66g$‘2 T 2/mpl and the freezeout condition r = Y~~(G~z~) = H), we find

(n&)0 = (n&f = 1001(m,m~~g~‘2 +JA+)

N 10-S/[(m,/GeV)((~A~)/10-27 cm3 s-‘)I, (3.3)

where the subscript f denotes the value at freezeout and the subscript 0 denotes the value today. The current entropy density is so N 4000 cmm3, and the critical density today is pC II 10-5h2 GeVcmp3, where h is the Hubble constant in units of 100 km s-l Mpc-‘, so the present mass density in units of the critical density is given by

0,h2 = mxn,/p, N (3 x 1O-27 cm3 C1/(oAv)) . (3.4)

The result is independent of the mass of the WIMP (except for logarithmic corrections), and is inversely proportional to its annihilation cross section.

Fig. 4 shows numerical solutions to the Boltzmann equation. The equilibrium (solid line) and actual (dashed lines) abundances per comoving volume are plotted as a function of x = m,/T

0 .01

0 .001

0.0001

10-b

,h 10-s

-; 10-7 c aJ 10-a a 2

10-Q

p lo-‘9

$ lo-”

z 10-m

F! lo-‘3

10 100

x=m/T (time +)

Fig. 4. Comoving number density of a WIMP in the early Universe. The dashed curves are the actual abundance, and the solid curve is the equilibrium abundance. From [31].

�v ⇠ g4

16⇡m2

⌦DMh2 ⇠ 0.1⇣ m

1 TeV

⌘2

⌦DMh2 ⇡ 3⇥ 10�27cm3s�1

h�vi

Neutralino DM in the MSSM• TeV scale a bit heavy for the LSP, rest of the superpartners even heavier, fine

tuning...

• Pure bino: too small annihilation xsec, overcloses universe

Cheung, Hall, Pinner & Ruderman ‘12

• Pure wino and Higgsino: too large annihilation xsec, require ~2-3 TeV and ~1 TeV respectively to raise abundance.

• Going to mixed neutralinos (“well-tempering”) introduces further contrivances -- additional tuning, numerical coincidences (e.g. co-annihilation, blind spots).

We need Higgsinos ~ 1TeV to have and satisfy experimental constraints.

Neutralino DM in the MSSM

Cheung, Hall, Pinner & Ruderman ‘12

⌦DM = 0.12

Higgs at 125 GeV in the MSSM requires multi-TeV A-terms or 10 TeV stops. Either way it is fine tuned at the sub-percent level or worse.

WIMP dark matter in the MSSM requires either a heavy SUSY scale or contrived numerical coincidences (blind spots, co-annihilation).

So if SUSY solves the hierarchy problem in a fully natural way, the source of both DM and the Higgs mass likely lies beyond the MSSM.

mh and DM in Natural SUSY

Introduction: Big Questions

Why is the Higgs at 125 GeV?

Is it compatible with naturalness?

What is the dark matter?

Does it realize the WIMP miracle?

Singlet-doublet DM extension of SM

[Mahbubani & Senatore ’05, Cohen et al ’11, Cheung & Sanford ’13, Abe et al ’14, Calibbi et al ’15, Freitas et al ’15]

Lifting the Higgs mass with vector-like extensions of the MSSM

[Moroi & Okada ’92...Martin ’09 ’10, Graham et al ’09...Evans et al ’11, Li et al ’11, Moroi et al ’11, Martin & Wells ’12, Endo et al ’11 ’12, Ishikawa et al ’12,...]

But as far as we know, nobody has combined the two ideas before. Similar idea: [Abdullah, Feng ’15, Abdullah, Feng, Iwamoto & Lillard ‘16]

This talk

In this talk, we will study a simple, economical extension of the MSSM that includes both DM and the source of the Higgs mass. We will get

• 125 GeV Higgs mass with ~10% fine-tuning

• Natural thermal WIMP DM consistent with existing limits

S

L, L̄, superpartners

h, t,Higgsinos

by adding a singlet and pair of vector-like doublets to the MSSM.

Outline

1. The Model

2. Direct detection

3. Higgs mass and fine tuning

4. Need for mostly-singlet DM

5. DM annihilation in the mostly-singlet regime

6. Putting it all together

7. Outlook

The Model

SU(3)c

SU(2)L

U(1)Y

ZDM

2

L 1 2 �12 �1

L̃ 1 2 12 �1

S 1 1 0 �1

3 Direct Detection

3.1 Experimental limits

• Here we show the experimental results, ch��

, cz��

plots

• Spin Independent

• Spin Dependent

3.2 Discussion of impact of limits on model parameter space

• Blind spot – 1D plots vs kd

• Argument for mostly singlet case:

– Mostly doublet not promising because of fine-tuning, ⌦DM

for Higgsinos,

blind spot, and direct-detection bounds.

– Well-tempered not promising because of DD bounds.

• Show plot of DD bounds in ML

, MS

plane for various ku

?

4 DM annihilation

• Analytic formulas for every annihilation channel in mostly singlet case (large ML

limit)

– Only leading-order in ML

s-wave is tt̄. Every other channel suppressed by v

and/or 1/ML

.

2

Z2 symmetry keeps lightest state stable -- WIMP DM candidate!

• Majorana mass term for S, otherwise immediately killed by Z-mediated SI DD. (Key diff with previous works on vector-like MSSM extensions!)

• Take ku > 1 to help lift the Higgs mass and improve fine tuning.

• One physical CPV phase. Assume real couplings for simplicity.

�W =1

2MSS

2 +MLLL̄+ kuHuLS � kdHdL̄S

The Model

�Lsoft

= m2S

|S|2 +m2L

|L|2 +m2L̃

|L̃|2 + (A� terms) + (B � terms)

Assume m2S = m2

L = m2L̃= m2, A = B = 0 for simplicity

• Take m2 > 0 to lift the Higgs mass => DM is fermionic

Fermion mass matrix:

• Assume large tanβ otherwise MSSM contribution to Higgs mass too small

M =

0

@MS kuvs� kdvc�

kuvs� 0 ML

kdvc� ML 0

1

A = U†MdiagU

The Model

In our model, these are given by:

Part of a broader framework of Higgs and Z-portal dark matter (cf e.g. Giudice, de Simone and Strumia ’14)

σSI

σSD <σv>

�L � m��̄�+ chh�̄�+ cZZµ�̄�µ�5�

After diagonalizing, get couplings of mass eigenstates to h and Z :

Then much of the physics (thermal relic density, direct detection, LHC signatures, ...) controlled by DM-DM-Higgs and DM-DM-Z couplings. (Cheung & Sanford ’13; Calibbi et al ’15)

ch =1p2Re(k̂uU

⇤11U

⇤12 + k̂dU

⇤11U

⇤13)

cZ =g24cW

�|U12|2 � |U13|2

Perhaps it didn’t look promising, because direct-detection bounds on the Higgs portal are quite stringent?

Key points:

• Blind spot: since it’s a 2HDM, effective DM-DM-Higgs coupling ch can be reduced by balancing up-type and down-type couplings against each other in a particular way.

• DM is lightest mass eigenstate out of a singlet+doublet+anti-doublet, so there is more than one ch coupling. DD only probes ch for DM, while Higgs mass is sensitive to all of them.

ch

h

q

qh

hch ch

The Model

Direct detection

Direct Detection

DM direct detection experiments are probing couplings of DM to nucleons

SI controlled by ch and SD controlled by cZ.

Nχ1

χ̄1 N̄

h

Nχ1

χ̄1 N̄

Z

⇠SIq = yq

chm2

h⇠SDq =

g⌘q4cW

cZm2

Z

�L �X

q

⇠SIq ( ̄� �)(q̄q) + ⇠SD

q ( ̄��µ�5 �)(q̄�µ�5q)

!

⌘q = 1 (�1)down-type (up-type) quarks

Direct detection: SI

LUX currently sets strongest SI constraints.

LUX 1608.07648

Direct Detection: SD

101 102 103 104

Dark matter mass m� (GeV)

10�42

10�41

10�40

10�39

10�38

10�37

10�36

10�35

10�34

10�33

Darkmatter-protoncross-section�SD,p(cm

2)

IceCube Collaboration 2016

IC79

gg

bb̄

hh

tt̄

W+W�

ZZ

⌧+⌧�

⌫⌫̄

Figure 7: Limits on the spin-dependent WIMP-proton cross-section from IC79, for a rangeof di↵erent annihilation final states. The canonical hard (W+

W

� and ⌧

+⌧

�) and soft (bb̄)channels bracket the possible limits for di↵erent models reasonably well. More extremechannels (hardest: ⌫⌫̄, softest: gg) less often found in SUSY can lead to even strongeror weaker constraints. For the ⌫⌫̄ channel we have assumed equal branching fractions forall three neutrino flavours. The ability to easily and quickly compute full limits for anycombination of final states is a particular feature of the method and tools we present in thispaper.

are up to a factor of 4 stronger than the previous analysis at multi-TeV masses. The latestupdate of WIMPSim fixes an issue with propagation of neutrinos in the Sun that a↵ectedthe version used to derive the original IC79 limits [1]. This resulted in conservative limitsfor WIMP masses above ⇠500GeV, ranging from a factor of 1.05 at 500GeV to 1.2 at 1TeVand up to 1.5 at 5TeV for the W

+W

� and ⌧

+⌧

� final states. Improvements beyond thosefactors are due to the improved analysis method in this paper.

Fig. 6 compares these limits to other searches for spin-dependent DM-proton scattering,both from the Sun and direct detection experiments. The 79-string IceCube data provide thestrongest limits of any search for all masses above ⇠100–200GeV (the exact value dependson the annihilation channel). Super-Kamiokande [2] is the most sensitive experiment at alllower masses. Limits from direct detection [33, 34] are weaker, except in the case of DMwith soft or suppressed annihilation spectra, in which case the PICO experiment [33, 34]is the most constraining. Indirect DM searches by Antares [36] and Baksan [37] have setless stringent limits on the spin-dependent DM-proton scattering and are consequently notincluded in Fig. 6.

Figure 7 shows new limits for all major two-body annihilation final states. Annihilation

– 17 –

Official ttbar limit is new; previously had to be recasted (see e.g. Cheung, Hall & Ruderman ’12).

Factor of a few weaker ttbar vs WW makes a big difference for our model!

LUX neutron (IceCube proton) strongest below (above) ~500 GeV.

LUX 1608.07648

IceCube 1601.00653

We translated the SI limits from LUX into SD ones (Buckley & Lippincott ‘13)

Indirect detection

Dark Matter Searches with the Fermi-LAT in the Direction of Dwarf Spheroidals Matthew Wood

realizations of the two data sets. Because the Pass8 six-year and Pass7 Reprocessed four-year event samples have a shared fraction of only 20–40%, the two analyses are nearly statisticallyindependent. For masses below 100GeV, the upper limits of [1] were near the 95% upper boundof the expected sensitivity band while the limits in the present analysis are within one standarddeviation of the median expectation value.

101 102 103 104

DM Mass (GeV/c2)

10�27

10�26

10�25

10�24

10�23

10�22

10�21

h�vi

(cm

3s�

1)

bb̄

4-year Pass 7 Limit

6-year Pass 8 Limit

Median Expected

68% Containment

95% Containment

Thermal Relic Cross Section(Steigman et al. 2012)

101 102 103 104

DM Mass (GeV/c2)

10�27

10�26

10�25

10�24

10�23

10�22

10�21

h�vi

(cm

3s�

1)

�+��

4-year Pass 7 Limit

6-year Pass 8 Limit

Median Expected

68% Containment

95% Containment

Thermal Relic Cross Section(Steigman et al. 2012)

Figure 1: Constraints on the DM annihilation cross section at 95% CL for the bb̄ (left) and t+t� (right)channels derived from a combined analysis of 15 dSphs. Bands for the expected sensitivity are calculated byrepeating the same analysis on 300 randomly selected sets of high-Galactic-latitude blank fields in the LATdata. The dashed line shows the median expected sensitivity while the bands represent the 68% and 95%quantiles. For each set of random locations, nominal J-factors are randomized in accord with their measure-ment uncertainties. The solid blue curve shows the limits derived from a previous analysis of four years ofPass7 Reprocessed data and the same sample of 15 dSphs [1]. The dashed gray curve corresponds tothe thermal relic cross section from [12].

Figure 2: Constraints on the DM annihilation cross at 95% CL section for the bb̄ (left) and t+t� (right)channels derived from the combined analysis of 15 dSphs with 6 years of Pass 8 data. For comparison limitsfrom previously published searches are shown from LAT analysis of the Milky Way halo (3s limit) [13], 112hours of observations of the Galactic Center with H.E.S.S. [14], and 157.9 hours of observations of Segue 1with MAGIC [15]. Pure annihilation channel limits for the Galactic Center H.E.S.S. observations are takenfrom [16] and assume an Einasto Milky Way density profile with r� = 0.389GeVcm�3. Closed contoursand the marker with error bars show the best-fit cross section and mass from several interpretations of theGalactic center excess [17, 18, 19, 20].

Figure 2 shows the comparison of the limits from this work with other published limits onthe DM annihilation cross section. The Pass8 combined dSph limits are currently among the

5

Fermi 1503.02641

No official ttbar limits, but probably ineffective above 100 GeV...

Direct Detection Reinterpretation in terms of ch and cZ

Note: although SD bounds are 5 orders of magnitude weaker than SI bounds in terms of cross section, SD is slightly stronger than SI in terms of cZ and ch!

0 200 400 600 800 1000 12000.00

0.01

0.02

0.03

0.04

mDM [GeV]

LUX SI ch

IceCube SD (tt) cZ

LUX SD cZ

Higgs mass and fine tuning

Higgs mass and fine-tuning

• One-loop Higgs mass ( ) (cf Martin ’09)

where and

Assume MSSM stops get you to mh ~ 110 GeV (~10% FT). Need δmh2 ~ 3500 GeV2 .

• Fine tuning measure:

tan� ! 1

� =

2�m2Hu

m2h

=

k2um

2

4⇡2 log

⇤UV⇤IR

(125GeV)

2

�m

2h =

1

4⇡

2k

4uv

2

✓f1 log(1 + x

2L) + f2 log(1 + x

2S) + f3 log

x

2S

x

2L

xL = m/MLxS = m/MS

500

1500

2500

3500

0 5 10 15 200

5

10

15

20

xL

x S

0 500 1000 15000

500

1000

1500

ML [GeV]

MS[GeV

]

ku=1

ku=1.2

ku=1.5

ku=2

k�4u �m2

h in GeV2

Higgs mass and fine-tuning

� = 20, mh = 125GeV

Need for mostly singlet DM

Need for mostly singlet DM

Focus on mostly singlet DM: mχ ~ MS < ML and v << ML , ML-MS

• Mostly doublet regime is not promising for fine-tuning (cf pure Higgsino DM), direct detection

• Well-tempered regime ruled out by DD

One-loop Higgs mass in the mostly singlet DM regime:

ch = �m� + 2kdML

ku tan �p2v

k2uv2

M2L

+ . . . cZ =g

4cW

k2uv2

M2L

+ . . .

�m2h =

k4uv2

4⇡2log

✓1 +

m2

M2L

◆+O(M2

S/M2L)

Need for mostly singlet DM

ch =

MS � 2kdML

ku tan �p2v

!k2uv

2

M2L

+ . . .

To satisfy LUX SI bounds, need a mild blind spot cancellation

-1.8 -1.6 -1.4 -1.2 -1.00.000

0.005

0.010

0.015

kd

|ch|

mχ=200 GeV, ML=1200 GeV, ku=1.6, tanβ=10

LUX SI ch

Thermal relic density

Thermal relic density

DM slowly moving at freeze out (v2~0.1), so all else being equal, annihilation rate dominated by s-wave.

Initial state (pair of identical Majorana fermions) is CP odd, so no s-wave through s-channel Higgs. This leaves s-channel Z and t-channel.

Additional simplifications in large ML limit...

rxy

⌘q

1� (mx

+my

)2/4m2�

�xy

v�

= rxy

(axy

+ bxy

v2�

+O(v4�

))

⌦DM

h

2 ⇡ 9.2⇥ 10�12 GeV�2 ⇥ Z 1

xf

dx

h�v�

ix

2

!�1

Thermal relic density

Comments:

• s-wave annihilation is to tt and Higgsinos to leading order in v2/ML2.

• Dependence on DM mass drops out at leading order -- WIMP miracle in terms of mediator scale!

• Annihilation to dibosons is always subdominant for the parameter space that we study.

• cZ controls both the SD DD cross section and the annihilation to tt.

a H H=

(k2d + k2u)2

16⇡M2L

µ2

M2L(1 + (MS/ML)2 + (m/ML)2)2

aff̄ =3k4u

32⇡M2L

m2f

M2L(1� (MS/ML)2)2

s-channel Z

t-channel

Putting it all together

Putting it all together

Numerical pipeline: SARAH-SPheno-Micromegas. Confirmed using analytics.

800 1000 1200 1400 1600 1800

200

300

400

500

600

ML [GeV]

MS[GeV

]

ku=1.6, kd=-1.5ΩDM=0.12

IceCube SD (tt)LUX SDLUX SI

Δ=10

Δ=20

Δ=40

m=1TeV

m=1.5

TeV

m=2TeV

μ=300

μ=100

800 1000 1200 1400 1600 1800

200

300

400

500

600

ML [GeV]

MS[GeV

]

ku=1.2, kd=-1ΩDM=0.12

IceCube SD (tt)LUX SDLUX SI

Δ=40

Δ=80

Δ=160

m=2.7

TeV

m=3.8

TeV

m=5.4

TeV

μ=300

μ=100

Confirms that relic density only cares about ML to first approx.

Confirms estimates of FT via one-loop Higgs mass.

Confirms analytics of DD bounds.

250 300 350 400

20

25

30

mDM [GeV]

Δ

ku=1.6, kd=-1.5

Thermal relic contour plots

Regions of the allowed parameter space with � ' 20

Thermal relic contour plots

We can move toward the blind spot by varying kd.

200 250 300 350 400 4500.000

0.005

0.010

0.015

0.020

0.025

mDM [GeV]

ch

ku=1.6, ΩDM=0.12LUX SI c h

kd=-1.5kd=-1

μ=300

μ=100

μ=300

μ=100

200 250 300 350 400 4500.000

0.005

0.010

0.015

0.020

0.025

mDM [GeV]

ch

ku=1.2, ΩDM=0.12LUX SI c h

kd=-1.5kd=-1

μ=300

μ=100

μ=300

μ=100

Thermal relic contour plots

200 400 600 800 10000.005

0.010

0.015

0.020

0.025

mDM [GeV]

c Z

ku=1.6, kd=-1.5ΩDM= 0.12

IceCube SD (tt) c ZLUX SD c Z

200 400 600 800 10000.005

0.010

0.015

0.020

0.025

mDM [GeV]

c Z

ku=1.2, kd=-1ΩDM= 0.12

IceCube SD (tt) c ZLUX SD c Z

Within a factor of a few of being ruled out by SD DD!

Confirms the direct relation between ΩDM and cZ!

LHC prospectsOur model could be probed by LHC from mono(H,Z,W) + MET searches

W+

χ1

χ1u

W+

χ+

χ1

χ2,3

χ1

h

g

g

h

h

χ1

χ2,3

χ1

q

Z

LHC prospects

200 300 400 500 600 700 800 900

0.001

0.005

0.010

0.050

0.100

0.500

mDM @GeVD

s@fbD

ku=1.6, kd=-1.5, m=300 GeV

c2,3Æ c1 h c2,3Æ c1 Z c±Æ c1W±

50 events

10 events

{= 300 fb-1

c1c1h c1c1Z c1c1W± c1 c1 Hh+Z+W±L

200 300 400 500 600 700 800 900

0.001

0.005

0.010

0.050

0.100

0.500

mDM @GeVD

s@fbD

ku=1.6, kd=-1.5, m=100 GeV

c2,3Æ c1 h c2,3Æ c1 Z c±Æ c1W±

50 events

10 events

{= 300 fb-1

c1c1h c1c1Z c1c1W± c1 c1 Hh+Z+W±L

Numerical pipeline: SARAH-SPheno-MadGraph5. Confirmed using analytics.

LHC Run II will probe the small mass region

Landau Pole Problem

Generally there is a Landau pole well before the GUT scale. Theory needs to be UV completed -- or extended with gauge interactions to deflect the Yukawas...

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.5

1.0

1.5

2.0

2.5

3.0

ku

k d

10

103

106

1013

Landau Pole Scale [TeV]

�gi =bi

16⇡2g3i (b1, b2, b3) = (

36

5, 2,�2)

�ku =ku

16⇡2(2k2d + 4k2u + 3y2t �

3

5g21 � 3g22)

�kd =kd

16⇡2(4k2d + 2k2u � 3

5g21 � 3g22)

�yt =yt

16⇡2(6y2t + k2u � 16g23

3� 13

15g21 � 3g22)

Outlook

Xenon1T and LZ should probe the entire parameter space of this model in a few years. And more generally for Higgs and Z-portal DM!

Other models for Higgs and DM beyond the MSSM:

• Other SU(2) representations ?

• NMSSM?

• Non-decoupling D-terms ?

• ...

Landau pole problem? Add non-Abelian gauge interactions to postpone the Landau pole.

Outlook

Adding A-terms could allow for smaller and open more parameter space.

Phenomenology of lighter DM masses (Higgs and Z resonances)

Model has one physical CP phase. Constrained by EDMs; can qualitatively change the DM phenomenology.

• Turns on a pseudoscalar coupling to the Higgs ⇠1

2(ch � c⇤h)h ̄��

5 �

ku, kd

Summary

We studied an economic extension of the MSSM that gives a 125 GeV Higgs mass with a fine-tuning as low as ~10% and provides a natural thermal WIMP DM candidate.

The main annihilation channels in our model are s-wave annihilation to tt and Higgsinos.

Imposing the relic density constraint immediately implies a particular value for the SD cross-section. This value is not ruled out yet, but the next generation of DM experiments (e.g.\ Xenon1T , LZ) should completely rule out or discover this model.

Thanks for your attention!