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1/27
Motivation Classification of Simplified Models LHC Phenomenology
The Coannihilation Codex
Michael J. Baker
with
Joachim Brod, Sonia El Hedri, Anna Kaminska, Joachim Kopp, Jia Liu,Andrea Thamm, Maikel de Vries, Xiao-Ping Wang, Felix Yu, José Zurita
arXiv:1510.03434
JGU Mainz
Dark Matter 2016 - UCLA - 18 February 2016
2/27
Motivation Classification of Simplified Models LHC Phenomenology
Outline
1 Motivation
2 Classification of Simplified Models
3 LHC Phenomenology
3/27
Motivation Classification of Simplified Models LHC Phenomenology
Outline
1 Motivation
2 Classification of Simplified Models
3 LHC Phenomenology
4/27
Motivation Classification of Simplified Models LHC Phenomenology
Dark Matter
Begeman, Broeils & Sanders, 1991
Planck, 2013
Viel, Becker, Bolton & Haehnelt, 2013
Ωnbmh2 = 0.1198± 0.0026
4/27
Motivation Classification of Simplified Models LHC Phenomenology
Dark Matter
Begeman, Broeils & Sanders, 1991 Planck, 2013
Viel, Becker, Bolton & Haehnelt, 2013
Ωnbmh2 = 0.1198± 0.0026
4/27
Motivation Classification of Simplified Models LHC Phenomenology
Dark Matter
Begeman, Broeils & Sanders, 1991 Planck, 2013
Viel, Becker, Bolton & Haehnelt, 2013
Ωnbmh2 = 0.1198± 0.0026
4/27
Motivation Classification of Simplified Models LHC Phenomenology
Dark Matter
Begeman, Broeils & Sanders, 1991 Planck, 2013
Viel, Becker, Bolton & Haehnelt, 2013
Ωnbmh2 = 0.1198± 0.0026
5/27
Motivation Classification of Simplified Models LHC Phenomenology
Theoretical Framework
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
Abdallah et al., 1506.03116
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
5/27
Motivation Classification of Simplified Models LHC Phenomenology
Theoretical Framework
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
Abdallah et al., 1506.03116
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
5/27
Motivation Classification of Simplified Models LHC Phenomenology
Theoretical Framework
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
Abdallah et al., 1506.03116
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
More complete
Complete Dark Matter
Models
Dark Matter Effective Field Theories
Minimal Supersymmetric Standard Model
Universal Extra
DimensionsLittleHiggs
ContactInteractions
“Sketches of models”
Z′ bosonSimplified
Dark MatterModels
HiggsPortal “Squarks”
DarkPhoton
DipoleInteractions
Less complete
FIG. 1. Artistic view of the DM theory space. See text for detailed explanations.
us to describe the DM-SM interactions mediated by all kinematically inaccessible
particles in an universal way. The DM-EFT approach [3–9] has proven to be very
useful in the analysis of LHC Run I data, because it allows to derive stringent bounds
on the “new-physics” scale Λ that suppresses the higher-dimensional operators. Since
for each operator a single parameter encodes the information on all the heavy states
of the dark sector, comparing LHC bounds to the limits following from direct and
indirect DM searches is straightforward in the context of DM-EFTs.
(II) The large energies accessible at the LHC call into question the momentum expansion
underlying the EFT approximation [6, 9–16], and we can expand our level of detail
toward simplified DM models (for early proposals see for example [17–22]). Such
models are characterized by the most important state mediating the DM particle
interactions with the SM, as well as the DM particle itself. Unlike the DM-EFTs,
simplified models are able to describe correctly the full kinematics of DM production
at the LHC, because they resolve the EFT contact interactions into single-particle s-
channel or t-channel exchanges. This comes with the price that they typically involve
not just one, but a handful of parameters that characterize the dark sector and its
6
6/27
Motivation Classification of Simplified Models LHC Phenomenology
Simplified Models
Much recent work on simplified models of DM, e.g.,Abdallah et al. 1506.03116,Abercrombie et al. 1507.00966,. . .
Simple one particle freeze-out often leads to tensions, e.g.,between relic density and direct/indirect constraintsFor some models this is not a good approximationCoannihilating models can relieve these tensions and/orgive a better approximation
6/27
Motivation Classification of Simplified Models LHC Phenomenology
Simplified Models
Much recent work on simplified models of DM, e.g.,Abdallah et al. 1506.03116,Abercrombie et al. 1507.00966,. . .
Simple one particle freeze-out often leads to tensions, e.g.,between relic density and direct/indirect constraintsFor some models this is not a good approximationCoannihilating models can relieve these tensions and/orgive a better approximation
6/27
Motivation Classification of Simplified Models LHC Phenomenology
Simplified Models
Much recent work on simplified models of DM, e.g.,Abdallah et al. 1506.03116,Abercrombie et al. 1507.00966,. . .
Simple one particle freeze-out often leads to tensions, e.g.,between relic density and direct/indirect constraintsFor some models this is not a good approximationCoannihilating models can relieve these tensions and/orgive a better approximation
6/27
Motivation Classification of Simplified Models LHC Phenomenology
Simplified Models
Much recent work on simplified models of DM, e.g.,Abdallah et al. 1506.03116,Abercrombie et al. 1507.00966,. . .
Simple one particle freeze-out often leads to tensions, e.g.,between relic density and direct/indirect constraintsFor some models this is not a good approximationCoannihilating models can relieve these tensions and/orgive a better approximation
7/27
Motivation Classification of Simplified Models LHC Phenomenology
Our Goal
A complete classification of simplified coannihilation models
The Coannihilation Codex
A bottom-up framework for discovering dark matter at theLHCLHC phenomenology testing DM freeze-outIdentify lesser studied models & searchesIn the event of a signal, gives a framework for the inverseproblem
7/27
Motivation Classification of Simplified Models LHC Phenomenology
Our Goal
A complete classification of simplified coannihilation models
The Coannihilation Codex
A bottom-up framework for discovering dark matter at theLHCLHC phenomenology testing DM freeze-outIdentify lesser studied models & searchesIn the event of a signal, gives a framework for the inverseproblem
7/27
Motivation Classification of Simplified Models LHC Phenomenology
Our Goal
A complete classification of simplified coannihilation models
The Coannihilation Codex
A bottom-up framework for discovering dark matter at theLHCLHC phenomenology testing DM freeze-outIdentify lesser studied models & searchesIn the event of a signal, gives a framework for the inverseproblem
8/27
Motivation Classification of Simplified Models LHC Phenomenology
Outline
1 Motivation
2 Classification of Simplified Models
3 LHC Phenomenology
9/27
Motivation Classification of Simplified Models LHC Phenomenology
Assumptions
To complete a classification we need to make someassumptions
DM is a thermal relicDM is a colourless, electrically neutral particle in (1,N, β)
Coannihilation diagram is 2-to-2 via dimension four,tree-level couplingsNew particles have spin 0, 1/2 or 1
9/27
Motivation Classification of Simplified Models LHC Phenomenology
Assumptions
To complete a classification we need to make someassumptions
DM is a thermal relicDM is a colourless, electrically neutral particle in (1,N, β)
Coannihilation diagram is 2-to-2 via dimension four,tree-level couplingsNew particles have spin 0, 1/2 or 1
9/27
Motivation Classification of Simplified Models LHC Phenomenology
Assumptions
To complete a classification we need to make someassumptions
DM is a thermal relicDM is a colourless, electrically neutral particle in (1,N, β)
Coannihilation diagram is 2-to-2 via dimension four,tree-level couplingsNew particles have spin 0, 1/2 or 1
9/27
Motivation Classification of Simplified Models LHC Phenomenology
Assumptions
To complete a classification we need to make someassumptions
DM is a thermal relicDM is a colourless, electrically neutral particle in (1,N, β)
Coannihilation diagram is 2-to-2 via dimension four,tree-level couplingsNew particles have spin 0, 1/2 or 1
9/27
Motivation Classification of Simplified Models LHC Phenomenology
Assumptions
To complete a classification we need to make someassumptions
DM is a thermal relicDM is a colourless, electrically neutral particle in (1,N, β)
Coannihilation diagram is 2-to-2 via dimension four,tree-level couplingsNew particles have spin 0, 1/2 or 1
10/27
Motivation Classification of Simplified Models LHC Phenomenology
Coannihilation Diagrams
X
DM
SM2
SM1
⇓X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Mt
X
DM
SM2
SM1
11/27
Motivation Classification of Simplified Models LHC Phenomenology
Classification Procedure
Work in unbroken SU(2)L × U(1)Y
Given SM field content, iterate over SM1 and SM2 to find allpossible X using
Gauge invarianceLorentz invarianceZ2 parity (to prevent DM decay)
Then find all s-channel and t-channel mediators, usingsame restrictions and
Dimension four, tree-level couplingsGauge bosons only couple through kinetic terms
11/27
Motivation Classification of Simplified Models LHC Phenomenology
Classification Procedure
Work in unbroken SU(2)L × U(1)Y
Given SM field content, iterate over SM1 and SM2 to find allpossible X using
Gauge invarianceLorentz invarianceZ2 parity (to prevent DM decay)
Then find all s-channel and t-channel mediators, usingsame restrictions and
Dimension four, tree-level couplingsGauge bosons only couple through kinetic terms
11/27
Motivation Classification of Simplified Models LHC Phenomenology
Classification Procedure
Work in unbroken SU(2)L × U(1)Y
Given SM field content, iterate over SM1 and SM2 to find allpossible X using
Gauge invarianceLorentz invarianceZ2 parity (to prevent DM decay)
Then find all s-channel and t-channel mediators, usingsame restrictions and
Dimension four, tree-level couplingsGauge bosons only couple through kinetic terms
12/27
Motivation Classification of Simplified Models LHC Phenomenology
s-channel classification - sample
DM in (1,N, β)ID X α + β Ms Spin (SM1 SM2) SM3 M-X-X
ST11
(3, N ± 1, α)
73
(3, 2, 73)
B (QL`R), (uRLL)
ST12 F (uRH)
ST13 13
(3, 2, 13)
B (dRLL), (QLdR), (uRLL)
ST14 F (uRH†), (dRH) QL
ST15− 5
3(3, 2,− 5
3)
B (QLuR), (QL`R), (dRLL)
ST16 F (dRH†)
ST17
(3, N ± 2, α)
43
(3, 3, 43)
B (QLLR) Xα = − 23
ST18 F (QLH)
ST19− 2
3(3, 3,− 2
3)
B (QLQL), (QLLL) Xα = 13
ST20 F (QLH†)
B:
X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Ms
F:
X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Ms
X
DM
SM2
SM1
Ms
13/27
Motivation Classification of Simplified Models LHC Phenomenology
t-channel classification - sample
DM in (1,N, β)
ID X α + β Mt Spin (SM1 SM2) SM3
TU26
(1, N ± 2, α)
0
(1, N ± 1, β − 1) I (HH†)
TU27 (1, N ± 1, β + 1) II (LLH)
TU28 (1, N ± 1, β − 1) III (HLL)
TU29 (3, N ± 1, β − 13
) IV (QLQL)
TU30 (1, N ± 1, β + 1) IV (LLLL)
TU31
−2
(1, N ± 1, β + 1) I (H†H†)
TU32 (1, N ± 1, β + 1) II (LLH†)
TU33 (1, N ± 1, β + 1) III (H†LL)
I
X
DM
SM2
SM1
Mt
X
DM
SM2
SM1
Mt II
X
DM
SM2
SM1
Mt
X
DM
SM2
SM1
Mt
III
X
DM
SM2
SM1
Mt
X
DM
SM2
SM1
Mt IV
X
DM
SM2
SM1
Mt
X
DM
SM2
SM1
Mt
X
DM
SM2
SM1
Mt
14/27
Motivation Classification of Simplified Models LHC Phenomenology
Classification: hybrid models
ID X α + β SM partner Extensions
H1(1, N, α)
0 B,WN≥2i SU1, SU3, TU1, TU4–TU8
H2 −2 `R SU6, SU8, TU10, TU11
H3(1, N ± 1, α) −1
H† SU10, TU18–TU23
H4 LL SU11, TU16, TU17
H5(3, N, α)
43
uR ST3, ST5, TT3, TT4
H6 − 23
dR ST7, ST9, TT10, TT11
H7 (3, N ± 1, α) 13
QL ST14, TT28–TT31
7 models
15/27
Motivation Classification of Simplified Models LHC Phenomenology
Classification: s-channel
ID X α + β Ms Spin (SM1 SM2) SM3 M-X-X
SU1
(1, N, α)
0
(1, 1, 0)B
(uRuR), (dRdR), (QLQL)B,W
N≥2i
X(`R`R), (LLLL), (HH†)
SU2 F (LLH)
SU3(1, 3, 0)N≥2
B (QLQL), (LLLL), (HH†) B, Wi X
SU4 F (LLH)
SU5
−2
(1, 1,−2)B (dRuR), (H†H†) X
SU6 F (LLH†) `R
SU7(1, 3,−2)N≥2
B (H†H†), (LLLL) X(α = ±1)
SU8 F (LLH†) `R
SU9 −4 (1, 1,−4) B (`R`R) X(α = ±2)
SU10
(1, N ± 1, α)
−1 (1, 2,−1)B (dRQL), (uRQL), (LL`R) H†
SU11 F (`RH) LL
SU12−3 (1, 2,−3)
B (LL`R)
SU13 F (`RH†)
SU14
(1, N ± 2, α)
0 (1, 3, 0)B (LLLL), (QLQL), (HH†) X(α = 0)
SU15 F (LLH)
SU16−2 (1, 3,−2)
B (H†H†), (LLLL) X(α = ±1)
SU17 F (LLH†)
SU type - 17 models
ID X α + β Ms Spin (SM1 SM2) SM3 M-X-X
ST1
(3, N, α)
103
(3, 1, 103
) B (uRlR) Xα = − 53
ST2
43
(3, 1, 43)
B (dR`R), (QLLL), (dRdR) Xα = − 23
ST3 F (QLH) uR
ST4(3, 3, 4
3)N≥2 B (QLLL) Xα = − 2
3
ST5 F (QLH) uR
ST6
− 23
(3, 1,− 23)
B (QLQL), (uRdR), (uR, `R), (QLLL) Xα = 13
ST7 F (QLH†) dR
ST8(3, 3,− 2
3)N≥2 B (QLQL), (QLLL) Xα = 1
3
ST9 F (QLH†) dR
ST10 − 83
(3, 1,− 83) B (uRuR), (dR`R) Xα = 4
3
ST11
(3, N ± 1, α)
73
(3, 2, 73)
B (QL`R), (uRLL)
ST12 F (uRH)
ST13 13
(3, 2, 13)
B (dRLL), (QLdR), (uRLL)
ST14 F (uRH†), (dRH) QL
ST15− 5
3(3, 2,− 5
3)
B (QLuR), (QL`R), (dRLL)
ST16 F (dRH†)
ST17
(3, N ± 2, α)
43
(3, 3, 43)
B (QLLR) Xα = − 23
ST18 F (QLH)
ST19− 2
3(3, 3,− 2
3)
B (QLQL), (QLLL) Xα = 13
ST20 F (QLH†)
ST type - 20 models
U: X uncoloured
T: X SU(3) triplet
O: X SU(3) octet
E: X SU(3) exotic
ID X α + β Ms Spin (SM1 SM2) SM3 M-X-X
SO1
(8, N, α)0
(8, 1, 0)6=g[s2] B (dRdR), (uRuR), (QLQL) Xα = 0
SO2 (8, 3, 0)N≥2 B (QLQL) Xα = 0
SO3 −2 (8, 1,−2) B (dRuR) Xα = ±1
SO4 (8, N ± 1, α) −1 (8, 2,−1) B (dRQL), (QLuR)
SO5 (8, N ± 2, α) 0 (8, 3, 0) B (QLQL) Xα = 0
SE1
(6, N, α)
83
(6, 1, 83) B (uRuR) Xα = − 4
3
SE2 23
(6, 1, 23) B (QLQL), (uRdR) X(α = − 1
3)
SE3 (6, 3, 23)N≥2 B (QLQL) Xα = − 1
3
SE4 − 43
(6, 1,− 43) B (dRdR) Xα = 2
3
SE5(6, N ± 1, α)
53
(6, 2, 53) B (QLuR)
SE6 − 13
(6, 2,− 13) B (QLdR)
SE7 (6, N ± 2, α) 23
(6, 3, 23) B (QLQL) Xα = − 1
3
SO and SE type - 5 and 7 models
16/27
Motivation Classification of Simplified Models LHC Phenomenology
Classification: t-channel
ID X α + β Mt Spin (SM1 SM2) SM3
TU1
(1, N, α)
0
(1, N ± 1, β − 1) I (HH†) B, WN≥2i
TU2 (1, N ± 1, β + 1) II (LLH)
TU3 (1, N ± 1, β − 1) III (HLL)
TU4 (3, N ± 1, β − 13
) IV (QLQL) B, WN≥2i
TU5 (3, N, β − 43
) IV (uRuR) B, WN≥2i
TU6 (3, N, β + 23
) IV (dRdR) B, WN≥2i
TU7 (1, N ± 1, β + 1) IV (LLLL) B, WN≥2i
TU8 (1, N, β + 2) IV (`R`R) B, WN≥2i
TU9
−2
(1, N ± 1, β + 1) I (H†H†)
TU10 (1, N ± 1, β + 1) II (LLH†) `R
TU11 (1, N ± 1, β + 1) III (H†LL) `R
TU12 (1, N ± 1, β + 1) IV (LLLL)
TU13 (3, N, β + 43
) IV (uRdR)
TU14 (3, N, β + 23
) IV (dRuR)
TU15 −4 (1, N, β + 2) IV (`R`R)
TU16
(1, N ± 1, α)
−1
(1, N, β + 2) II (`RH) LL
TU17 (1, N ± 1, β − 1) III (H`R) LL
TU18 (1, N, β + 2) IV (`RLL) H†
TU19 (1, N ± 1, β − 1) IV (LL`R) H†
TU20 (3, N, β + 23
) IV (dRQL) H†
TU21 (3, N ± 1, β + 13
) IV (QLdR) H†
TU22 (3, N ± 1, β − 13
) IV (QLuR) H†
TU23 (3, N, β + 43
) IV (uRQL) H†
TU24−3
(1, N ± 1, β + 1) IV (LL`R)
TU25 (1, N, β + 2) IV (`RLL)
TU26
(1, N ± 2, α)
0
(1, N ± 1, β − 1) I (HH†)
TU27 (1, N ± 1, β + 1) II (LLH)
TU28 (1, N ± 1, β − 1) III (HLL)
TU29 (3, N ± 1, β − 13
) IV (QLQL)
TU30 (1, N ± 1, β + 1) IV (LLLL)
TU31
−2
(1, N ± 1, β + 1) I (H†H†)
TU32 (1, N ± 1, β + 1) II (LLH†)
TU33 (1, N ± 1, β + 1) III (H†LL)
TU type - 33 models
IDX
α+β
Mt
Spin
(SM
1SM
2)
SM
3
TT
1
(3,N,α
)
10 3
(3,N,β
−4 3
)IV
(uR`R
)
TT
2(1,N,β
−2)
IV(`
RuR
)
TT
3
4 3
(3,N
±1,β
−1 3
)II
(QLH
)uR
TT
4(1,N
±1,β
−1)
III
(HQ
L)
uR
TT
5(1,N,β
−2)
IV(`
RdR
)
TT
6(3,N
±1,β
−1 3
)IV
(QLL
L)
TT
7(1,N
±1,β
−1)
IV(L
LQ
L)
TT
8(3,N,β
+2 3
)IV
(dR`R
)
TT
9(3,N,β
−2 3
)IV
(dRdR
)
TT
10
−2 3
(3,N
±1,β
−1 3
)II
(QLH
†)
dR
TT
11
(1,N
±1,β
+1)
III
(H†Q
L)
dR
TT
12
(3,N,β
+4 3
)IV
(uRdR
)
TT
13
(3,N
±1,β
+1 3
)IV
(QLQ
L)
TT
14
(3,N,β
−4 3
)IV
(uR`R
)
TT
15
(1,N,β
+2)
IV(`
RuR
)
TT
16
(3,N
±1,β
−1 3
)IV
(QLL
L)
TT
17
(1,N
±1,β
+1)
IV(L
LQ
L)
TT
18
(3,N,β
−2 3
)IV
(dRuR
)
TT
19
−8 3
(3,N,β
+4 3
)IV
(uRuR
)
TT
20
(3,N,β
+2 3
)IV
(dR`R
)
TT
21
(1,N,β
+2)
IV(`
RdR
)
TT
22
(3,N
±1,α
)
7 3
(3,N,β
−4 3
)II
(uRH
)
TT
23
(1,N
±1,β
−1)
III
(HuR
)
TT
24
(3,N,β
−4 3
)IV
(uRL
L)
TT
25
(1,N
±1,β
−1)
IV(L
LuR
)
TT
26
(3,N
±1,β
−1 3
)IV
(QL`R
)
TT
27
(1,N,β
−2)
IV(`
RQ
L)
TT
28
1 3
(3,N,β
−4 3
)II
(uRH
†)
QL
TT
29
(3,N,β
+2 3
)II
(dRH
)Q
L
TT
30
(1,N
±1,β
+1)
III
(H†uR
)Q
L
TT
31
(1,N
±1,β
−1)
III
(HdR
)Q
L
TT
32
(3,N,β
−4 3
)IV
(uRL
L)
TT
33
(1,N
±1,β
+1)
IV(L
LuR
)
TT
34
3,N,β
−2 3
)IV
(dRQ
L)
TT
35
(3,N
±1,β
+1 3
)IV
(QLdR
)
TT
36
−5 3
(3,N,β
+2 3
)II
(dRH
†)
TT
37
(1,N
±1,β
+1)
III
(H†dR
)
TT
38
(3,N,β
+2 3
)IV
(dRL
L)
TT
39
(1,N
±1,β
+1)
IV(L
LdR
)
TT
40
(3,N
±1,β
−1 3
)IV
(QL`R
)
TT
41
(1,N,β
+2)
IV(`
RQ
L)
TT
42
(3,N,β
+4 3
)IV
(uRQ
L)
TT
43
(3,N
±1,β
+1 3
)IV
(QLuR
)
TT
44
(3,N
±2,α
)
4 3
(3,N
±1,β
−1 3
)II
(QLH
)
TT
45
(1,N
±1,β
−1)
III
(HQ
L)
TT
46
(3,N
±1,β
−1 3
)IV
(QLL
L)
TT
47
−2 3
(1,N
±1,β
−1)
IV(L
LQ
L)
TT
48
(3,N
±1,β
−1 3
)II
(QLH
†)
TT
49
(1,N
±1,β
+1)
III
(H†Q
L)
TT
50
(3,N
±1,β
−1 3
)IV
(QLL
L)
TT
51
(1,N
±1,β
+1)
IV(L
LQ
L)
TT
52
(3,N
±1,β
+1 3
)IV
(QLQ
L)
TT type - 52 models
ID X α + β Mt Spin (SM1 SM2) SM3
TO1
(8, N, α)
0
(3, N ± 1, β − 13
) IV (QLQL)
TO2 (3, N, β − 43
) IV (uRuR)
TO3 (3, N, β + 23
) IV (dRdR)
TO4−2
(3, N, β + 23
) IV (dRuR)
TO5 (3, N, β + 43
) IV (uRdR)
TO6
(8, N ± 1, α) −1
(3, N, β + 23
) IV (dRQL)
TO7 (3, N ± 1, β + 13
) IV (QLdR)
TO8 (3, N ± 1, β − 13
) IV (QLuR)
TO9 (3, N, β + 43
) IV (uRQL)
TO10 (8, N ± 2, α) 0 (3, N ± 1, β − 13
) IV (QLQL)
TE1
(6, N, α)
83
(3, N, β − 43
) IV (uRuR)
TE2
23
(3, N ± 1, β − 13
) IV (QLQL)
TE3 (3, N, β − 43
) IV (uRdR)
TE4 (3, N, β + 23
) IV (dRuR)
TE5 − 43
(3, N, β + 23
) IV (dRdR)
TE6
(6, N ± 1, α)
53
(3, N, β − 43
) IV (uRQL)
TE7 (3, N ± 1, β − 13
) IV (QLuR)
TE8- 13
(3, N, β + 23
) IV (dRQL)
TE9 (3, N ± 1, β − 13
) IV (QLdR)
TE10 (6, N ± 2, α) 23
(3, N ± 1, β − 13
) IV (QLQL)
TO and TE type - 10 and 10 models
17/27
Motivation Classification of Simplified Models LHC Phenomenology
Complete Classification
We have written down all possible simplified models of 2-to-2coannihilating dark matter!
LHC Phenomenology
17/27
Motivation Classification of Simplified Models LHC Phenomenology
Complete Classification
We have written down all possible simplified models of 2-to-2coannihilating dark matter!
LHC Phenomenology
18/27
Motivation Classification of Simplified Models LHC Phenomenology
Outline
1 Motivation
2 Classification of Simplified Models
3 LHC Phenomenology
19/27
Motivation Classification of Simplified Models LHC Phenomenology
Production: s-channel
q
q
X, M
X, M
q
qγ/Z
X, M, DM
X, M, DM
q
q
FJ
FJ
X, M, DM
X, M, DM
q
q′
M
q
gq∗
SM
M
19/27
Motivation Classification of Simplified Models LHC Phenomenology
Production: s-channel
q
q
X, M
X, M
q
qγ/Z
X, M, DM
X, M, DM
q
q
FJ
FJ
X, M, DM
X, M, DM
q
q′
M
q
gq∗
SM
M
20/27
Motivation Classification of Simplified Models LHC Phenomenology
Decay: s-channel
Xs
DM
Ms
SM1
SM2
/ET+
soft
Ms
SM1
SM2
Resonance
Ms
DM
Xs
DM
Ms
SM1
SM2
/ET
+soft
20/27
Motivation Classification of Simplified Models LHC Phenomenology
Decay: s-channel
Xs
DM
Ms
SM1
SM2
/ET+
soft
Ms
SM1
SM2
Resonance
Ms
DM
Xs
DM
Ms
SM1
SM2
/ET
+soft
20/27
Motivation Classification of Simplified Models LHC Phenomenology
Decay: s-channel
Xs
DM
Ms
SM1
SM2
/ET+
soft
Ms
SM1
SM2
Resonance
Ms
DM
Xs
DM
Ms
SM1
SM2
/ET
+soft
21/27
Motivation Classification of Simplified Models LHC Phenomenology
Generic Signatures: s-channel
Mono-Y (Y=jet, photon, Z,. . . ) + /ET from DM DM, XX,. . .classic signature
Single and Double Resonances from M and MMATLAS/CMS Exotics
Mono-Y + /ET + soft from XX,MM,. . .has been motivated, no searches yet
Resonance + /ET + soft from MMnew signature to explore!
21/27
Motivation Classification of Simplified Models LHC Phenomenology
Generic Signatures: s-channel
Mono-Y (Y=jet, photon, Z,. . . ) + /ET from DM DM, XX,. . .classic signature
Single and Double Resonances from M and MMATLAS/CMS Exotics
Mono-Y + /ET + soft from XX,MM,. . .has been motivated, no searches yet
Resonance + /ET + soft from MMnew signature to explore!
21/27
Motivation Classification of Simplified Models LHC Phenomenology
Generic Signatures: s-channel
Mono-Y (Y=jet, photon, Z,. . . ) + /ET from DM DM, XX,. . .classic signature
Single and Double Resonances from M and MMATLAS/CMS Exotics
Mono-Y + /ET + soft from XX,MM,. . .has been motivated, no searches yet
Resonance + /ET + soft from MMnew signature to explore!
21/27
Motivation Classification of Simplified Models LHC Phenomenology
Generic Signatures: s-channel
Mono-Y (Y=jet, photon, Z,. . . ) + /ET from DM DM, XX,. . .classic signature
Single and Double Resonances from M and MMATLAS/CMS Exotics
Mono-Y + /ET + soft from XX,MM,. . .has been motivated, no searches yet
Resonance + /ET + soft from MMnew signature to explore!
22/27
Motivation Classification of Simplified Models LHC Phenomenology
Signature Table
pp→ . . . Prod. via Signatures Search
com
mon
DM + DM + ISR
gauge int.
mono-Y + /ET [55,56,62,63,104]or SM1 ∈ p
for t-channelX (→ SMsoft1 SMsoft
2 DM)X (→ SMsoft
1 SMsoft2 DM)
ISR
gauge int. mono-Y + /ET [55,56,62,63,104]
or SM2 ∈ p mono-Y + /ET+ ≤ 4 SM Partial coverage [105]
for t-channel
DM + X (→ SMsoft1 SMsoft
2 DM) + ISR (SM1 SM2) ∈ pmono-Y + /ET [55,56,62,63,104]
mono-Y + /ET+ ≤ 2 SM Partial coverage [105]s-
chan
nel
Ms (→ [SM1 SM2]res)Ms (→ [SM1 SM2]res)
gauge int.
2 resonances [106-112]
Ms (→ [SM1 SM2]res)Ms (→ DM + X (→ SMsoft
1 SMsoft2 DM))
resonance + /ET No search
resonance + /ET+ ≤ 2 SM No searchMs (→ DM + X (→ SMsoft
1 SMsoft2 DM))
Ms (→ DM + X (→ SMsoft1 SMsoft
2 DM))/ET+ ≤ 4 SM [113-124]
Ms (→ [SM1 SM2]res)
(SM1 SM2) ∈ p
1 resonance [125-146]
Ms (→ DM + X (→ SMsoft1 SMsoft
2 DM)) /ET+ ≤ 2 SM[120-122,124]
[104,147-153]
SM1,2 + Ms (→ [SM1 SM2]res)
SM2,1 ∈ p
1 resonance + 1 SM Partial coverage [154,155]SM1,2Ms (→ DM + X (→ SMsoft
1 SMsoft2 DM))
/ET + 1 ≤ 3 SM[114,120-124]
[147-153,156-158]
t-ch
anne
l
Mt (→ SM1 DM)Mt (→ SM1 DM)
gauge int.
/ET+ ≤ 2 SM[120-122,124]
[104,147-153]Mt (→ SM1 DM)Mt (→ SM2 + X (→ SMsoft
1 SMsoft2 DM))
/ET+ ≤ 4 SM[106-112]
[114,119-124]Mt (→ SM2 + X (→ SMsoft
1 SMsoft2 DM))
Mt (→ SM2 + X (→ SMsoft1 SMsoft
2 DM))/ET+ ≤ 6 SM
[113,114,120-124]
[116-118,159-163]
DM + Mt (→ SM1 DM)
SM1 ∈ p
/ET+ ≤ 1 SM[55,56,62,63]
[104,149]DMMt (→ SM2 + X (→ SMsoft
1 SMsoft2 DM))
/ET+ ≤ 3 SM114,120-124]
[152,153,156-158]Mt (→ SM1 DM)X (→ SMsoft
1 SMsoft2 DM)
SM2 ∈ p
/ET+ ≤ 3 SM[114,120-124]
[152,153,156-158]Mt (→ SM2 + X (→ SMsoft
1 SMsoft2 DM))
X (→ SMsoft1 SMsoft
2 DM)/ET+ ≤ 5 SM
[113,114,116-124]
[159-161,164]
hybr
id
X (→ DM + SMsoft
3 )X (→ DM + SMsoft
3 )gauge int.
/ET+ ≤ 2 SM[120-122,124]
or SM3 ∈ p [104,147-153]
DM + X (→ DM + SMsoft3 ) SM3 ∈ p /ET+ ≤ 1 SM
[128,129,149]
[55,56,62,63,104]
23/27
Motivation Classification of Simplified Models LHC Phenomenology
Signature Table: Excerpt
pp→ . . . Prod. via Signatures Search
s-ch
anne
l
Ms (→ [SM1 SM2]res)Ms (→ [SM1 SM2]res)
gauge int.
2 resonances [106-112]
Ms (→ [SM1 SM2]res)Ms (→ DM + X (→ SMsoft
1 SMsoft2 DM))
resonance + /ET No search
resonance + /ET+ ≤ 2 SM No searchMs (→ DM + X (→ SMsoft
1 SMsoft2 DM))
Ms (→ DM + X (→ SMsoft1 SMsoft
2 DM))/ET+ ≤ 4 SM [113-124]
Ms (→ [SM1 SM2]res)
(SM1 SM2) ∈ p
1 resonance [125-146]
Ms (→ DM + X (→ SMsoft1 SMsoft
2 DM)) /ET+ ≤ 2 SM[120-122,124]
[104,147-153]
SM1,2 + Ms (→ [SM1 SM2]res)
SM2,1 ∈ p
1 resonance + 1 SM Partial coverage [154,155]SM1,2Ms (→ DM + X (→ SMsoft
1 SMsoft2 DM))
/ET + 1 ≤ 3 SM[114,120-124]
[147-153,156-158]
24/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
ID X α + β Ms Spin (SM1 SM2) SM3 M-X-X
ST11 (3, N ± 1, α) 73
(3, 2, 73) B (QL`R), (uRLL)
DM in (1,N, β)
Field Rep. Spin and mass assignment
DM (1,1,0) Majorana fermion
X (3,2,7/3) Dirac fermion
M (3,2,7/3) Scalar
24/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
ID X α + β Ms Spin (SM1 SM2) SM3 M-X-X
ST11 (3, N ± 1, α) 73
(3, 2, 73) B (QL`R), (uRLL)
DM in (1,N, β)
Field Rep. Spin and mass assignment
DM (1,1,0) Majorana fermion
X (3,2,7/3) Dirac fermion
M (3,2,7/3) Scalar
25/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
Field Rep. Spin and mass assignment
DM (1,1,0) Majorana fermion
X (3,2,7/3) Dirac fermion
M (3,2,7/3) Scalar
X
DMM
`+
q
L ⊃ Lkin + yDX M DM + yQ`QLM`R + yLuLLMcuR + h.c.
25/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
Field Rep. Spin and mass assignment
DM (1,1,0) Majorana fermion
X (3,2,7/3) Dirac fermion
M (3,2,7/3) Scalar
X
DMM
`+
q
L ⊃ Lkin + yDX M DM + yQ`QLM`R + yLuLLMcuR + h.c.
25/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
Field Rep. Spin and mass assignment
DM (1,1,0) Majorana fermion
X (3,2,7/3) Dirac fermion
M (3,2,7/3) Scalar
X
DMM
`+
q
L ⊃ Lkin + yDX M DM + yQ`QLM`R + yLuLLMcuR + h.c.
26/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
X
DMM
`+
q
L ⊃Lkin + yDX M DM+ yQ`QLM`R + yLuLLMcuR + h.c.
g
gMs
M†s`−
q
DM
XDM
Ms
q
`+
Resonance
+/ET
+soft
Strong productionLepton-jet resonance + /ET + soft lepton & jetNo dedicated LHC search
26/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
X
DMM
`+
q
L ⊃Lkin + yDX M DM+ yQ`QLM`R + yLuLLMcuR + h.c.
g
gMs
M†s`−
q
DM
XDM
Ms
q
`+
Resonance
+/ET
+soft
Strong productionLepton-jet resonance + /ET + soft lepton & jetNo dedicated LHC search
26/27
Motivation Classification of Simplified Models LHC Phenomenology
Example - ST11
X
DMM
`+
q
L ⊃Lkin + yDX M DM+ yQ`QLM`R + yLuLLMcuR + h.c.
g
gMs
M†s`−
q
DM
XDM
Ms
q
`+
Resonance
+/ET
+soft
Strong productionLepton-jet resonance + /ET + soft lepton & jetNo dedicated LHC search
27/27
Motivation Classification of Simplified Models LHC Phenomenology
Summary
Coannihilation Codex gives a complete list of simplifiedmodels of coannihilationGuaranteed kinetic & coannihilation vertices→ signaturesClassify signatures of a wide range of models
Identify new signaturesIdentify interesting models, e.g., leptoquarks and DM
Huge number of DM modelscollider signaturesdirect and indirect detectionprecision testsflavour boundscosmology. . .
28/27
ST11 - Constraints from New Searches
LQPair(Visible)[8TeV]
XX+j (Monojet) [8 TeV]
LQPair(Visible)[13TeV
]
LQPair(M
ixed)
[13TeV
]
XX+j (Monojet) [13 TeV]
XX+j (Leptons) [13 TeV] (pT(l) > 10 GeV)
XX+j (Leptons) [13 TeV] (pT(l) > 25 GeV)
Relic Density + APV (3σ allowed)
(2+Δ)mD
M=m
LQ
Δ = 0.1, Br(LQ→lq)|mDM=0 = 0.5
400 600 800 1000 1200 1400 1600 1800 2000
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
mLQ [GeV]
mDM[GeV
]
g g
g
X
X
DMDM
q
e+
e−
q
g
g M
M† e−
qDM
XDM
M∗q
e+