A complex singlet with dark matter

Constraining phase diagrams with
A complex singlet with dark matter
Rita Coimbra
Marco Sampaio
:
Rui Santos
gravitation.web.ua.pt
15 september 2013
Based on: Eur. Phys. J. C (2013) 73 [arXiv:1301.2599]
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Constraining phase diagrams with
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Outline
1
Motivation
2
Review of the Complex Singlet Model
3
Constraints: theoretical & experimental
4
Results
5
Conclusions
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Motivation
Besides the success of SM, SM does not explain, for instances,
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the existence of dark matter
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the measured baryon asymetry of the universe
Why complex singlet to test Scanners program?
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it’s the simplest extension to SM but
can provide a viable dark matter candidate
can achieve electroweak baryogenesis through a strong first-order
phase transition during the era of EWSB
it has some structure to test ScannerS
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Constraining phase diagrams with
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Complex scalar singlet extension of SM
Add a complex scalar field S = S + i A to the scalar sector of the
SM
The most general renormalizable potential with Z2 (S ! S) and
U(1) (S ! ei↵ S) symmetries
(Barger et al., arXiv:0811.0393)
VcxSM =
m2 †
b2
d2
2
H H + (H † H)2 + H † H|S|2 + |S|2 + |S|4
2
4
2
2
4
✓
◆
b1 2
+
S + a1 S + c.c.
4
Depending on the potential parameters we can have
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particle spectra with or without DM candidates and
scalar particles that may mixture with SM Higgs boson.
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Constraining phase diagrams with
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Classification of indepedent models and their phases
Expand around
1
hHi = p
2
✓
0
v
◆
,
1
hSi = p (vS + ivA ),
2
(v = 246)
Imposing local minimum conditions with EWSB we obtain the
following classification for different models and phases:
Model
U(1) symmetry
(a1 = b1 = 0)
Z2 ⇥ Z02
(a1 = 0)
Z02
(a1 2 R)
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Phase
1 Higgs + 2 degenerate DM
2 mixed Higgs + 1 Goldstone
1 Higgs + 2 DM
2 mixed Higgs + 1 DM
2 mixed Higgs + 1 DM
3 mixed
Constraining phase diagrams with
VEV’s at minimum
hS = 0i
hA = 0i
hS = 0i
hA = 0i
hA = 0i
hS 6= 0i
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Example: Z02 model
Symmetric phase: 2 mixed Higgs + 1 DM
0
1 0
higgs with125 GeV !
H1
cos
sin
@ H2 A = @ sin
cos
A0
0
0
10
1
0
h
0 A@ S A
1
A
Broken phase: 3 mixed higgs
0
1 0
10
1
higgs with125 GeV !
H1
M1h M1S M1A
h
@ H2 A = @ M2h M2S M2A A @ S A
H3
M3h M3S M3A
A
with
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MT M = 1
Constraining phase diagrams with
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Theoretical constraints
Stability conditions on i (routine CheckStability in ScannerS):
the scalar potential is bounded from below only if
>0
^
d2 > 0
^
(
2
2
>
d2 if
2
< 0)
Global minimum (routine CheckGlobal in ScannerS):
closed expressions for stationary points that can be below the
local minimum we selected
Imposing tree level unitarity in 2 ! 2 high energy scattering
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SM: mH . 700 GeV
CxSM: (making d2 =
I
This is done automatically with generic routine in ScannerS.
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= 0 we reproduce SM)
q
3
| |  16⇡, |d2 |  16⇡, | 2 |  16⇡,
+ d2 ± (3/2 + d2 )2 + d22  16⇡
2
2
Electroweak Precision Observables: we calculate the variation of
the S, T and U and check whether they fall into the 95% ellipsoid.
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Experimental constraints: Dark Matter Relic Density
Dark Matter Relic Density from WMAP
⌦cdm h2 = 0.112 ± 0.006
(h is the Hubble constant)
Thermal relic density: ⌦A h2 ⇠ 1/ h ann vrel i
Annihilation processes that contribute to the thermally averaged
cross section (2Higgs+1DM phase), mediated by the two Higgs
eigenstates (fig from Barger et al. [arXiv:0811.0393])
The relic density for DM candidate is calculated with
micrOMEGAS and is excluded if it is above the limit for relic
density ⌦h2 > 0.112 (we can have another DM contributor)
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Constraining phase diagrams with
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Result on spin-independent WIMP-nucleon scattering
from XENON100 (arXiv:1207.5988)
WIMP-Nucleon Cross Section [cm2]
10-39
XENON100 (2012)
DAMA/Na
10-40
observed limit (90% CL)
Expected limit of this run:
± 1 σ expected
± 2 σ expected
CoGeNT
DAMA/I
10-41
SIMPLE
XENON10 (2011)
(2012)
CRESST-II (2012)
10-42
ZEP
-43
II (2
LIN-I
EDELWEISS (2011/12)
10
CDMS
012)
PP (2
COU
ON1
)
(2010/11 XEN
012)
011)
00 (2
10-44
10-45
6 7 8 910
20
30 40 50
200
100
300 400
1000
WIMP Mass [GeV/c2]
We exclude a point in parameter space if, for a given DM mass,
the scaled cross section scaled > XENON100
scaled
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=
A
Constraining phase diagrams with
⌦A h 2
0.112
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Experimental constraints: Collider searches for the SM
Higgs boson
Predicted signal strength µ for each search channel
µi =
⇥ BrNew (Hi ! XSM )
BrNew (Hi ! XSM )
= Mih2
BrSM (hSM ! XSM )
SM (hSM ) ⇥ BrSM (hSM ! XSM )
New (Hi )
where Mih = (cos , sin ) or (M1h , M2h , M3h ) and
Mih2 (hSM ! XSM )
BrNew (Hi ! XSM )
= 2
BrSM (hSM ! XSM )
Mih (hSM ! XSM ) + (Hi ! newscalars)
For example, the decay width for a process Hi ! Hj Hj
(if MHi > 2MHj )
(Hi ! Hj Hj ) =
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gijj2
32⇡mi
Constraining phase diagrams with
v
u
u
t1
4mj2
mi2
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+ -
95% CL limit on ξ B(H→τ τ )
1
LEP
(b)
√s = 91-210
GeV
–
H→bb
1
LEP
(c)
√s = 91-210
GeV
H→τ+τ-
2
2
–
95% CL limit on ξ B(H→bb)
Experimental constraints: Collider searches
-1
10
-2
10
20
2
=
40
60
80
100
120
-1
10
-2
10
20
40
60
80
100
120
2
!2m (GeV/c2)
mH(GeV/c )
H
gHi ZZ
⇥ BrNew (Hi ! SM) = µi ⇥ BrSM (hSM ! SM)
SM
gHZZ
We applied limits from bb̄ and ⌧ + ⌧
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Constraining phase diagrams with
channel.
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Experimental constraints: Collider searches
Combined 95% CL exclusion limits on LHC signal normalized to SM
prediction µi as a function of mH (arXiv:1207.7214)
For mh = 125 GeV we exclude points outside the range
µi = 1.1 ± 0.4
For the other scalar particle we apply the 95% CL combined
ATLAS upper limits on µi as a function of mi
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Constraining phase diagrams with
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Scan over the phase space
Scan with 106 points uniformly generated in phase space
mh = 125 GeV
Other scalar masses: 0 < m < 300(500) GeV in standard (wide)
run
v = 246 GeV
Other vev’s: 0 < vS , vA < 500 (1000) GeV in standard (wide) run
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Constraining phase diagrams with
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Phase Diagram for Model 2 cSM2
|M1h |
cSM2 (mix & all bounds)
cSM2 (1DM & all bounds)
mlight (GeV)
|M1h |
cSM2 (mix & all bounds)
cSM2 (1DM & all bounds)
mheavy (GeV)
We can say if we are observing the lighter or the heavier scalar
given a measurement of M1h and the mass of a new scalar in a
region exclusively of the "mix" phase (in pink), excluding the DM
phase.
p
M1h ⇡ µ if 125 GeV is not allowed to decay to any of the other
p
scalars (M1h & 0.84 1 LHC bound for µ)
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Phase Diagram for Model 2 cSM2
|Mih |
cSM2 (mix & all bounds)
cSM2 (1DM & all bounds)
|Mih |
mlight (GeV)
cSM2 (mix & all bounds)
cSM2 (1DM & all bounds)
mheavy (GeV)
We can say if we are observing the lighter or the heavier scalar
given a measurement on LHC of Mih and the mass of a new scalar
in a region exclusively of the "mix" phase (in pink), excluding the
DM phase.
From experimental bounds: |Mih | . 0.55.
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Conclusions
We applied ScannerS to the complex singlet model using
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theoretical constraints,
updated LHC and LEP data,
dark matter data.
By measuring physical particle masses and mixing angles we
found that
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identification of the phase that is realized in Nature is possible in
some cases,
we can exclude the dark matter phase with a simultaneous
measurement of the mass of a non-dark matter scalar together with
its mixing angle
we can say whether the new scalar is the lightest or the heaviest.
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Constraining phase diagrams with
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BACKUP SLIDES
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Constraining phase diagrams with
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Example: 2 mixed Higgs + 1 DM phase
Minimum conditions:
m2 =
b2 =
2
v2
b1
2
v2
2 S
p a1
2 2
vS
d2 2
v
2 S
2
2
v2
At the minimum the mass matrix (second derivative) is
1
0
2
2
mh2 mh,S
mh,A
B 2
C
2
@ mh,S mS2 mS,A
A=
2
2
mh,A
mS,A
mA2
0
v 2 /2
2 v vp
S /2
2
@
=
2a1/vS
2 v vS /2 d2 vS /2
0
0
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Constraining phase diagrams with
b1
0
0
p
2a1 vS
(1)
1
A
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Electroweak Precision Observables
The effects of new physics on EWPO appear only through vacuum
polarisation and can be parametrized by three gauge self-energy
parameters S, T , U (Peskin & Takeuchi)
The constraints on the S, T and U parameters are derived from a
fit to the electroweak precision data (Gfitter collaboration):
S = 0.02 ± 0.11, T = 0.05 ± 0.12, U = 0.07 ± 0.12
with the correlation matrix
0
1
@
0.879
⇢=
0.469
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0.879
1
0.716
Constraining phase diagrams with
1
0.469
0.716 A
1
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Electroweak Precision Observables
T
We calculate the variation of the S, T and U and check whether
they fall into the 95% ellipse.
0.5
0.4
68%, 95%, 99% CL fit contours, U free
(SM : MH=126 GeV, m t =173 GeV)
ref
0.3
0.2
0.1
0
SM Prediction
MH = 125.7 ± 0.4 GeV
mt = 173.18 ± 0.94 GeV
-0.1
MH
-0.2
SM Prediction
with MH ∈ [100,1000] GeV
-0.3
-0.5
-0.5
G fitter
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
B
SM
Sep 12
-0.4
0.5
S
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Constraining phase diagrams with
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Decay Widths Expressions
Decay width for a process of the type Hi ! Hj Hj (if kinematically
allowed)
v
u
2
2
gijj u
t1 4mj
(Hi ! Hj Hj ) =
32⇡mi
mi2
Decay width for a process of the type Hi ! Hj Hk (if kinematically
allowed)
s
s
2
gijk
(mj + mk )2
(mj mk )2
(Hi ! Hj Hj ) =
1
1
16⇡mi
mi2
mi2
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Constraining phase diagrams with
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Scan over the phase space
106 points uniformely generated in phase space
Parameter ranges
standard run
coupling
min
max
m2 (GeV2 )
2
b2 (GeV2 )
d2
b1 (GeV2 )
a1 (GeV2 )
106
0
4
106
0
106
106
106
4
4
106
4
106
106
wide run
min
max
2 ⇥ 106
0
50
2 ⇥ 106
0
2 ⇥ 106
108
2 ⇥ 106
50
50
2 ⇥ 106
50
2 ⇥ 106
108
mh = 125 GeV, other scalar masses: 0 < m < 300(500) GeV in
standard (wide) run
v = 246 GeV, 0 < vS , vA < 500 (1000) GeV in standard (wide) run
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Constraining phase diagrams with
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Experimental constraints: Dark Matter Direct Detection
Scattering cross section of the DM candidate with a proton target
(Barger et al., arXiv:1005.3328)
A
A
A
A
H1,2
H1,2
q
q
SI
q
mp4
1
=
2
2⇡v (mp + mA )2
I
g
2
2
M1h
gAAH1
M2h
gAAH2
+
2
MH1
MH2 2
!✓
g
fpu + fpd + fps +
2
3fG
27
◆2
fpi are the proton matrix elements
fpu = 0.020, fpd = 0.026, fps = 0.118, fG = 0.836
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Mjh = (cos , sin ) or (M1h , M2h , M3h )
We have done some checks with micrOmegas
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Phase Diagram for Model 2 cSM2
cSM2 (mix & all bounds)
cSM2 (1DM & all bounds wider)
cSM2 (1DM & all bounds)
|Mih |
cSM2 (1DM & no exp. bounds)
cSM2 (1DM & EWPO only)
cSM2 (1DM & all bounds)
|M2h |
For small values of |Mih | we can identify two pink regions
exclusively of the "mix phase" above and below SM & 0.5
EWPO constraints are responsible for the upper right boundary
Theoretical constraints are responsible for the bottom boundary
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