1. Simplified DM models with the full SM
gauge symmetry
Alexander Natale
Korea Institute for Advanced Study
In collaboration with:
Pyungwon Ko, Myeonghun Park, Hiroshi Yokoya
arXiv:1605.07058
Planck 2016
Valencia, Spain
May 23-27th, 2016
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2. Overview
1 EFTs and Simplified Models of DM
2 Our Simplified Model: ’full’ SM gauge
3 Key Results
4 Direct Detection
5 Collider Signatures
6 Summary & Conclusions
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3. EFTs Models of DM
Three major approaches to DM phenomenology:
EFT: non-renomalizable, higher dimension, DM-SM interactions
divided by the mass scale of new physics Λ
Parameters: Λ, mχ
Simplified model: renormalizable, unbroken SM gauge invariant model
with a mediator, DM, and SM interactions.
Parameters: λmed, mmed, mχ
UV-complete models: full, high energy description of BSM physics
Parameters: many
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4. SU(2)L and mono-W
EFTs break down when ECM approaches Λ, however breakdown of EFT
can happen in other situations.
See Bell et al (arXiv:1503.07874):
1
Λ2
(χγµ
χ)(uLγµuL + ξdLγµdL)
W
q
q χ
χ
ξ = −1 leads to mono-W enhancement from inteference between uL and
dL couplings → this violates SU(2)L!
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5. SU(2)L and mono-W
W
q
q χ
χ
→
Comes from enhancement from spurious WL contributions at high E:
ξ − 1 → 0 as E → vEW , so ξ ≈ 1 with ’full’ SM gauge group.
So EFT description with arbitrary ξ can break down on ECM O(v).
Bell, et al: arXiv:1503.07874
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6. SU(2)L and mono-W
Similar problems with EW symmetry can exist in simplified models
Take the following simplified Z model :
L = −Zµχ(gV
DM γµ
+ gA
DM γµ
γ5)χ − Zµf(gV
f γµ
+ gA
f γµ
γ5)f
If gA
u − gA
d − gV
u + gV
d = −2gV
u = 0 spurious contributions to ET
spectrum, enforcing EW symmetry eliminates these.
Tait, et al arXiv:1603.01267
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7. Direct Detection
Running effects form EFT scale to Hadronic scale generically mix
operators. These effects come from EW loops, quark-threshold scales, etc.
Usual method in simplified models of going to EFT to determine direct
detection misses these effects (can be sizable):
Running introduces additional dependence on Λ so cannot re-scale
constraints to eliminate coupling constants
Generally mixes RH and LH couplings, and introduces slight isospin
violation in SI cross section (in addition to the source from
λuR = λdR
)
A practitioner friendly guide for these effects can be found in D’Eramo et
al (arXiv:1411.3342).
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8. The Model
To generate general χqφmed interaction in a simplified model consider
three new scalar types: QLi, uRi,dRi. One Dirac fermion DM particle: χ
χQi†
L (λQL
) j
i QLj + χui†
R (λuR ) j
i uRj + χdi†
R (λdR
) j
i dRj + H.C.
Important quartic term leads to isospin violation (responsible for ξ in EFT
description):
λ4Φ†
QLQ†
LΦ
Recall: mono-W enhancement had arbitrary isospin violation among QL,
but this is actually fixed by λ4, λ4 ≤ 4π has small effect on mono-W
signal (Bell, Cai, Leane arXiv:1512.00476).
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9. Collider Signatures:mono-X Utility
Contour plots for mono-X when λqi /mqi
are allowed to vary (λdR
= 0):
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV] mono-jet
102
50
10
5
1
0.5
0.1
mono-W
mono-Z
1
1 103
102
5⇥102
0.5
0.1
1
10 2
1
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
10
3
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10. Collider Signatures:mono-X Utility
Diagonal line represents a previously studied simplified model:
A. Natale | Simplified DM models with full SM gauge symmetry
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11. Direct Detection
Models with t-channel colored scalars are highly constrained by direct
detection (10 GeV < mχ < 1 TeV excluded by LUX for Λ ≤ 10 TeV):
2 4 6 8 10
0.01
1
100
104
106
108
mχ [GeV]
σSI
N
[zb]
ΛQL
= 10 TeV
ΛuR
:
1 TeV
2 TeV
3 TeV
5 TeV
10 TeV
Coherent Neutrino Scattering
CDMSlite
LUX
Region where mχ > 1 TeV has significantly reduced mono-X
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12. Direct Detection
Plot (σXe − σGe)/σXe to determine relative difference:
2 4 6 8 10
2
4
6
8
10
ΛuR
[TeV]
ΛdR
[TeV]
ΛQL=3 TeV
-0.02
0
0.02
0.04
2 4 6 8 10
2
4
6
8
10
ΛQL
[TeV]
ΛuR
[TeV]
-0.035
-0.030
-0.025
-0.020
-0.015
-0.010
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13. Collider Signatures:Jet pT
Finite mass effects in kinematic mono-Jet pT :
(J) [GeV]
T
p
200 400 600 800 1000 1200 1400 1600 1800 2000
Normalizeddistribution
4−
10
3−
10
2−
10
1−
10
1
= 1.2 TeV
R
u= m
L
Qm
= 2 TeVR
u= m
L
Qm
= 3 TeVR
u= m
L
Qm
= 5 TeV
R
u= m
L
Qm
= 10 TeV
R
u= m
L
Qm
Mono-J @LHC 13TeV
= 0
R
d
= 1, fR
u= f
L
Qf
= 04
λ= 5 GeV,χm
λdR
= λ4 = 0,λQL
= λuR = 1,muR
= mQL
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14. Collider Signatures:λdR
= 0
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV]
mono-jet
102
50
10
5
1
0.5
0.1
mono-W
mono-Z
1
1
103
102
5⇥102
0.5
0.1
1
10 2
1
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
10
3
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV]
mono-jet
102
50
10
5
1
0.5
mono-W
mono-Z
1
1
103
102
5⇥102
0.5
0.1
1
10 2
1
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
mχ = 5 GeV, λuR = λQL
= 1 and λ4 = 0
LHS: λdR
= 0 → RHS: λdR
= 1, mdR
= 3 TeV
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15. Summary & Conclusions
Summary:
Very important to use the full SM gauge group when investigating
simplified models at colliders (gauge invariance, unitarity, etc.)
’Less simplified’ models: broader range of interesting collider
signatures, with only modest increase in complication (however
tension between thermal relic/direct detection for colored t-channel)
Conclusion:
Loosening constraints from the usual simplified models (ie
ΛQL
= ΛuR = ΛdR
) allows for the clear presentation of mono-X cross
sections.
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16. Thank you!
Thank you!
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17. Backup Slides
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18. Collider Signatures:mono-X
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV]
mono-jet
102
50
10
5
1
0.5
0.1
mono-W
mono-Z
1
1
103
102
5⇥102
0.5
0.1
1
10 2
1
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
10
3
mχ = 5 GeV, λuR = λQL
= 1 and λ4 = 0
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19. Collider Signatures:λdR
= 0 (mχ = 300 GeV)
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV]
mono-jet
102
50
10
5
1
0.5
0.1
mono-W
mono-Z
1
1
103
102
5⇥102
0.5
0.1
10 2
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
10
3
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV]
mono-jet
mono-W
mono-Z
1
1
103
102
5⇥102
0.5
0.1
10 2
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
10
3
102
50
10
5
1
0.5
mχ = 300 GeV, λuR = λQL
= 1 and λ4 = 0
LHS: λdR
= 0 → RHS: λdR
= 1, mdR
= 3 TeV
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20. Collider Signatures:mono-X (mχ = 300 GeV)
2 4 6 8 10
2
4
6
8
10
m˜uR
[TeV]
m ˜QL
[TeV]
mono-jet
102
50
10
5
1
0.5
0.1
mono-W
mono-Z
1
1
103
102
5⇥102
0.5
0.1
10 2
5⇥103
0.1
5 ⇥ 10 2
5 ⇥ 10 3
10
3
mχ = 300 GeV, λuR = λQL
= 1 and λ4 = 0
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21. EFT Approach
Mass scale of new physics (Λ), higher dimensional operator (Dim. > 4),
assume a Lorentz structure (Γi), for instance:
D(6) : 1
Λ2 χΓ1χfΓ2f,
f are SM fermions, χ are DM
Useful tool for understanding direct detection: classify DM-SM operators
by structure of Γi and order of Λ, and measure constraints on operators
Known Issues:
Can break down if mediator mass on order of energy scale (eg 13 TeV
LHC),
More realistic models in general have multiple operators
Running effects generically mix different EFT operators
(arXiv:1411.3342)
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22. Simplified Model Approach
Use (at minimum) unbroken gauge group, minimal set of particles, reduce
to EFT at low energy, respect symmetries like L and B, MFV (see
arXiv:1506.03116).
Simplified models explain finite mediator mass effects and remain useful
even when ECM > Λ.
Known Issues:
Spurious enhancement of mono-W signatures (arXiv:1503.07874)
Spurious enhancement of high ET at colliders(arXiv:1603.01267)
Additional constraints from unitarity in scalar portal
(arXiv:1507.06158, arXiv:1512.00476)
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23. Simplified Model Approach
Use (at minimum) unbroken gauge group, minimal set of particles, reduce
to EFT at low energy, respect symmetries like L and B, MFV (see
arXiv:1506.03116).
Simplified models explain finite mediator mass effects and remain useful
even when ECM > Λ.
Known Issues:
Spurious enhancement of mono-W signatures
(arXiv:1503.07874)
Spurious enhancement of high ET at colliders
(arXiv:1603.01267)
Additional constraints from unitarity in scalar portal
(arXiv:1507.06158, arXiv:1512.00476)
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24. Direct Detection: Running
From a UV or Simplified model it is possible to generate the SM + χ EFT
defined as:
LSMχ = LSM χ(i/∂ − mχ)χ + Σd>4Σα
c
(d)
α
Λd−4 O
(d)
α
Nuclear
Scale
Weak
Mediator Energy
UV Complete Model
Scale
Scale
SM + χ + Mediators
SMχ EFT
SM + χ
EMSMχ EFT
EW broken SM + χ
Running down to the hadronic scale has additional effects:
αs corrections to SMχ and αs running
threshold effects/matching conditions as heavier quarks are integrated
out (ie 5 quark → 4 quark matching conditions for αs RGE/EFT
Wilson coefficients)
D’Eramo et al (arXiv:1411.3342)
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25. Direct Detection: Running
There are several sources of corrections:
SM-level corrections to fermions/Higgs directly and usual RGE effects
EW corrections to SMχ vertices that allow ¯χΓiχ ¯fL,RΓjfL,R terms
even if UV model has specific chirality assumed for SM-χ interaction
For example: ¯χχ ¯ψLψL, H† ¯ψL,RψR,L
χ
χ
H
ψL
ψL
ψR
ψR
D’Eramo et al (arXiv:1411.3342)
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26. Direct Detection: Running
Set of operators at high energy:
CSMχ = (C(u,d)L
), CuR , CdR
, C(ν,e)L
, CeR , . . . , CH)
Nuclear
Scale
Weak
Mediator Energy
UV Complete Model
Scale
Scale
SM + χ + Mediators
SMχ EFT
SM + χ
EMSMχ EFT
EW broken SM + χ
CEMSMχ = (CV u, CV d, . . . , CAu, CAd, . . .)
For Spin Independent direct detection the operators CV u and CV d, a
non-trivial mixing of operators in CSMχ basis.
D’Eramo et al (arXiv:1411.3342)
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27. The Philosophy
Our model building guidelines:
Respect the full EW symmetry, not just the unbroken SM gauge
SU(3)C × U(1)EM
The dark sector can be more complicated (self-interaction,
multipartite, etc.), for DM at LHC we assume that χ is stable at least
lifetime of detector (ET )
work with a more ’UV-complete’ model than usual Simplified models
take into account flavor constraints, but loosen assumptions on
couplings to mediators & masses
Try to consider direct detection (+ running), thermal relic, but goal is
ultimately looking at collider signatures
The ultimate goal: try to find optimal balance between simplicity, and
UV-complete, that allows us to elucidate DM properties at colliders for
broadest possible set of models
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28. Less Simplified Model
Consider SM-DM quark operator:
1
Λ2 χγµχqγµq = 1
Λ2 χγµχ(qLγµqL + qRγµqR)
SU(2)L fixes coupling between u and d, but to have both χqR, χqL
interactions require a doublet and a singlet (χγµχqγ5γµq).
Earlier simplified models previously assumed only doublet
(arXiv:1512.00476, arXiv:1503.07864), only singlet
(arXiv:1506.03116), or universal mass/coupling (arXiv:1507.00966).
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29. Flavor Constraints
Cannot simultaneously diagonalize λ and m for scalars and q†qH†H terms
yield:
Rare Higgs decays: H → q∗
i q∗
j → qiqjχχ
Modified Higgs branching ratios to gg, γγ, Z γ, etc.
FCNC
χ is Dirac (no helicity flip in loop), and only one species (reduces FCNC as
compared to MSSM)
Assume: md
≈ ms, allows reduced K0 − K
0
mixing constraints
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30. Direct Detection
Relaxing the assumptions about coupling constants significantly
complicates the direct detection, as there are generic material dependence
effects in the spin independent cross section:
1
64π
m2
N m2
χ
(mχ+mN )2
3|λQL
|2
m2
QL
+
|λuR
|2
m2
uR
+
|λdR
|2
m2
dR
+ 1
2
Z
A
|λuR
|2
m2
uR
−
|λdR
|2
m2
dR
Without considering running effects, the direct detection probes λ/mmed,
but there are isospin violating effects from λuR = λdR
.
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31. Thermal Relic
Known tension between thermal relic and direct detection for t-channel,
colored, scalar mediators and from existing LHC constraints
(mmed > 1.2 TeV).
mχ ≈ 5 GeV → generically over-produced
if χ couples to Leptons, this can be alleviated
mχ ≈ 1 TeV → generically under-produced
if χ is not the only thermal relic this can be accommodated
For the LHC phenomenology we assume mχ = 5 GeV, but mχO(100) GeV
can be accommodated if there are additional thermal relics (reduced direct
detection constraints via t-channel mediator).
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32. Collider Signatures
Collider signatures: mono-Jet, mono-W, mono-Z, two jets + ET, etc.
q χ
¯χ¯q
g
u χ
¯χ¯d
W
¯χ
χ
q
q
g ¯χ χ
qq
g
Mono-W signature depends on ΛQL
=
λQL
mQL
Mono-jet/mono-Z depends on all mediators
Complementary information from each mono-X when RH/LH quarks
reduces complexity
At 13 TeV: No significant difference from σEFT for mqR,L
O(10) TeV.
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33. Collider Signatures
0 1 2 3 4 5 6 7 8 9 10
mQL
[TeV]
10
-2
10
-1
10
0
10
1
10
2
σtot
[fb]
10 TeV
3 TeV
Mono-J @ LHC 13 TeV ΛuR
= 10 TeV, mχ
= 5 GeV
fuR
= 1, fdR
= 0, λ4
= 0
5 TeV
ΛQL
= 2 TeV
pT
(J) > 100 GeV, |η(J)| < 5
0 1 2 3 4 5 6 7 8 9 10
mQL
[TeV]
10
-3
10
-2
10
-1
10
0
σtot
[fb]
10 TeV
3 TeV
Mono-W
+
@ LHC 13 TeV mχ
= 5 GeV, λ4
= 0
5 TeV
ΛQL
= 2 TeV
Mono-jet and mono-w+ cross sections for λQL
= λuR = 1,
muR
= 10 TeV, mono-W− will be 1/2 mono-W+ due to PDFs. For
mono-jet: | η |< 5, pT > 100 GeV.
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34. Collider Signatures: Methods
Lt−channel = χQi†
L (λQL
) j
i QLj+χui†
R (λuR ) j
i uRj+χdi†
R (λdR
) j
i dRj+H.C.
Implement L in Feynrules (scalar widths implemented as internal
parameter, function of λq(L,R)
, mq(L,R)
)
Generate events with Madgraph 5 (| η |< 5, pT > 100 GeV for
mono-jet)
For kinematic distributions analyze with Delphes/Root
Make assumptions about coupling constants, masses, to simplify
parameter space but look at parameter choices different from previous
simplified models
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35. Collider Signatures: mono-W
(l) [GeV]
T
p
100 200 300 400 500 600 700 800 900 1000
Normalizeddistribution
3−
10
2−
10
1−
10
= 04λ= 5 GeV,χ
LHC 13TeV, m
= 1.2 TeV
L
Qm
= 2 TeV
L
Qm
= 3 TeV
L
Qm
= 5 TeV
L
Qm
= 10 TeV
L
Qm
MET [GeV]
100 200 300 400 500 600 700 800 900 1000
Normalizeddistribution
3−
10
2−
10
1−
10
= 04λ= 5 GeV,χ
LHC 13TeV, m
= 1.2 TeV
L
Qm
= 2 TeV
L
Qm
= 3 TeV
L
Qm
= 5 TeV
L
Qm
= 10 TeV
L
Qm
0
Normalizeddistribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
(l) [GeV]
T
p
100 200 300 400 500 600 700 800 900 1000
Normalizeddistribution
3−
10
2−
10
1−
10
= 04λ= 5 GeV,χ
LHC 13TeV, m
= 1.2 TeV
L
Qm
= 2 TeV
L
Qm
= 3 TeV
L
Qm
= 5 TeV
L
Qm
= 10 TeV
L
Qm
MET [GeV]
100 200 300 400 500 600 700 800 900 1000
Normalizeddistribution
3−
10
2−
10
1−
10
= 04λ= 5 GeV,χ
LHC 13TeV, m
= 1.2 TeV
L
Qm
= 2 TeV
L
Qm
= 3 TeV
L
Qm
= 5 TeV
L
Qm
= 10 TeV
L
Qm
0
Normalizeddistribution
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Lepton mono-W kinematics produced in Delphes for λ4 = 0, mχ = 5 GeV
Simplified models with lighter scalar mass has broader pT and ET
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36. Collider Signatures:mono-X
0 1 2 3 4 5 6 7 8 9 10
mQL
[TeV]
10
-3
10
-2
10
-1
10
0
σtot
[fb]
10 TeV
3 TeV
Mono-W
+
@ LHC 13 TeV mχ
= 5 GeV / 300 GeV, λ4
= 0
5 TeV
ΛQL
= 2 TeV
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37. Collider Signatures:mono-X
0 1 2 3 4 5 6 7 8 9 10
mQL
[TeV]
10
-3
10
-2
10
-1
10
0
σtot
[fb]
10 TeV
3 TeV
Mono-Z @ LHC 13 TeV mχ
= 5 GeV / 300 GeV, fuR
= 1
fdR
= 0, ΛuR
= 10 TeV, λ4
= 0
5 TeV
ΛQL
= 2 TeV
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38. Collider Signatures:mono-X
Diagonal line represents a previously studied simplified model:
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39. Collider Signatures:mono-X
Diagonal line represents a previously studied simplified model:
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