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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
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: 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
• 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
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
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
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
d̄
W+
χ+
χ1
χ2,3
χ1
h
g
g
h
h
χ1
χ2,3
χ1
q̄
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!