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Motivation Coannihilation Codex Using the Codex

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

UC Davis - 29 February 2016

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Motivation Coannihilation Codex Using the Codex

Outline

1 Motivation

2 Coannihilation Codex

3 Using the Codex

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Motivation Coannihilation Codex Using the Codex

Outline

1 Motivation

2 Coannihilation Codex

3 Using the Codex

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Motivation Coannihilation Codex Using the Codex

Dark Matter

Begeman, Broeils & Sanders, 1991

Planck, 2013

Viel, Becker, Bolton & Haehnelt, 2013

Ωnbmh2 = 0.1198± 0.0026

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Motivation Coannihilation Codex Using the Codex

Dark Matter

Begeman, Broeils & Sanders, 1991 Planck, 2013

Viel, Becker, Bolton & Haehnelt, 2013

Ωnbmh2 = 0.1198± 0.0026

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Motivation Coannihilation Codex Using the Codex

Dark Matter

Begeman, Broeils & Sanders, 1991 Planck, 2013

Viel, Becker, Bolton & Haehnelt, 2013

Ωnbmh2 = 0.1198± 0.0026

4/51

Motivation Coannihilation Codex Using the Codex

Dark Matter

Begeman, Broeils & Sanders, 1991 Planck, 2013

Viel, Becker, Bolton & Haehnelt, 2013

Ωnbmh2 = 0.1198± 0.0026

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Motivation Coannihilation Codex Using the Codex

Relic Density from Thermal Freeze-out

DM DM↔ SM SM

H(T) vs. Γ(T)

Γ(T) = n(T)σ(T)v(T)

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Motivation Coannihilation Codex Using the Codex

Relic Density from Thermal Freeze-out

DM DM↔ SM SM

H(T) vs. Γ(T)

Γ(T) = n(T)σ(T)v(T)

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Motivation Coannihilation Codex Using the Codex

Relic Density from Thermal Freeze-out

DM DM↔ SM SM

H(T) vs. Γ(T)

Γ(T) = n(T)σ(T)v(T)

5/51

Motivation Coannihilation Codex Using the Codex

Relic Density from Thermal Freeze-out

DM DM↔ SM SM

H(T) vs. Γ(T)

Γ(T) = n(T)σ(T)v(T)

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Motivation Coannihilation Codex Using the Codex

Relic Density from Thermal Freeze-out

dndt

= −〈σv〉(n(t)2 − neq(t)2)− 3H(t)n(t)

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Motivation Coannihilation Codex Using the Codex

Relic Density from Thermal Freeze-out

dndt

= −〈σv〉(n(t)2 − neq(t)2)− 3H(t)n(t)

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Motivation Coannihilation Codex Using the Codex

The WIMP Miracle

ΩDMh2

0.12∼ O(1)

T30

M3PlH

20〈σannv〉

∼ 1

〈σann1pb

v/c0.1 〉

σann ∝g4

m2DM

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Motivation Coannihilation Codex Using the Codex

The WIMP Miracle

ΩDMh2

0.12∼ O(1)

T30

M3PlH

20〈σannv〉

∼ 1

〈σann1pb

v/c0.1 〉

σann ∝g4

m2DM

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Motivation Coannihilation Codex Using the Codex

The WIMP Miracle in SUGRA

Baer, Box and Summy: 1005.2215

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Motivation Coannihilation Codex Using the Codex

The WIMP Miracle in SUGRA

Baer, Box and Summy: 1005.2215

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Motivation Coannihilation Codex Using the Codex

Three Exceptions

PHYSICAL REVIEW 0 VOLUME 43, NUMBER 10 15 MAY 1991

Three exceptions in the calculation of relic abundances

Kim GriestCenter for Particle Astrophysics and Astronomy Department, University of California, Berkeley, California 94720

David SeckelBartol Research Institute, University ofDelaware, Newark, Delaware 19716

(Received 15 November 1990)

The calculation of relic abundances of elementary particles by following their annihilation andfreeze-out in the early Universe has become an important and standard tool in discussing particledark-rnatter candidates. We find three situations, all occurring in the literature, in which the stan-dard methods of calculating relic abundances fail. The first situation occurs when another particlelies near in mass to the relic particle and shares a quantum number with it. An example is a lightsquark with neutralino dark matter. The additional particle must be included in the reaction net-work, since its annihilation can control the relic abundance. The second situation occurs when therelic particle lies near a mass threshold. Previously, annihilation into particles heavier than the rel-ic particle was considered kinematically forbidden, but we show that if the mass diA'erence is—5 —15%%uo, these "forbidden" channels can dominate the cross section and determine the relic abun-dance. The third situation occurs when the annihilation takes place near a pole in the cross section.Proper treatment of the thermal averaging and the annihilation after freeze-out shows that the dipin relic abundance caused by a pole is not nearly as sharp or deep as previously thought.

I. INTRODUCTION

The calculation of the present-day density of elementa-ry particles which were in thermal equilibrium in the ear-ly Universe has become quite commonplace. ' Of particu-lar interest is the so-called Lee-Weinberg ' calculation inwhich annihilation after a particle species has becomenonrelativistic determines the present-day abundance ofthat species. Standard approximate solutions to theBoltzmann equation exist for this calculation and havebeen tested numerically. In this paper we wish to pointout three cases where naive application of the standardmethods fails to give correct results and a modified treat-ment is required. All three cases exist in the literature,and in all three cases erroneous conclusions have beendrawn. For each case we present appropriate approxi-mate solutions to the Boltzmann equation(s) and describethe values of the parameters for which they apply.

The first case occurs when the relic particle is the light-est of a set of similar particles whose masses are nearlydegenerate. In this case the relic abundance of the light-est particle is determined not only by its annihilationcross section, but also by the annihilation of the heavierparticles, which will later decay into the lightest. We callthis the case of "coannihilation. " As an example, consid-er a supersymmetric theory in which the scalar quarks orscalar electrons are only slightly more massive than thelightest supersymmetric particle (LSP), usually taken tobe a neutralino. Previous calculations of the relic abun-dance which consider only the LSP annihilation can be inerror by more than two orders of magnitude.

The second case concerns annihilation into particleswhich are more massive than the relic particle. Previous

treatments regarded this as kinematically forbidden, butwe show that if the heavier particles are on1y 5 —1S%more massive, these channels can dominate the annihila-tion cross section and determine the relic abundance. Wecall this the "forbidden" channel annihilation case. Ex-amples include annihilation into bb, tt, W+ W, or Higgsbosons, when the annihilating particle is lighter than thefinal-state particle.

The third case occurs when the annihilation takesplace near a pole in the cross section. This happens, forexample, in Z -exchange annihilation when the mass ofthe relic particle is near mz/2. Previous treatments haveincorrectly handled the thermal averages and the integra-tion of the Boltzmann equation in these situations. Thedip in relic abundance caused by a pole is broader andnot nearly as deep as previous treatments imply.

For all three cases we present simple formulas whichallow for a more correct treatment. We also present ex-amples for each case and describe the precise conditionsunder which the modified treatment is necessary. In Sec.II we review the standard method for performing theLee-Weinberg calculation and describe the approxima-tions within which we will work. In Sec. III we discussthe coannihilation case, in Sec. IV we discuss the forbid-den channel case, and in Sec. V we discuss annihilationnear a pole.

II. STANDARD CALCULATIONOF RELIC ABUNDANCE

Here we summarize the standard technique for calcu-lating the relic abundance of a particle species y in theLee-Weinberg scenario. First, a note about the philoso-

43 3191 1991 The American Physical Society

Forbidden annihilationResonant annihilation

Coannihilation

10/51

Motivation Coannihilation Codex Using the Codex

Three Exceptions

PHYSICAL REVIEW 0 VOLUME 43, NUMBER 10 15 MAY 1991

Three exceptions in the calculation of relic abundances

Kim GriestCenter for Particle Astrophysics and Astronomy Department, University of California, Berkeley, California 94720

David SeckelBartol Research Institute, University ofDelaware, Newark, Delaware 19716

(Received 15 November 1990)

The calculation of relic abundances of elementary particles by following their annihilation andfreeze-out in the early Universe has become an important and standard tool in discussing particledark-rnatter candidates. We find three situations, all occurring in the literature, in which the stan-dard methods of calculating relic abundances fail. The first situation occurs when another particlelies near in mass to the relic particle and shares a quantum number with it. An example is a lightsquark with neutralino dark matter. The additional particle must be included in the reaction net-work, since its annihilation can control the relic abundance. The second situation occurs when therelic particle lies near a mass threshold. Previously, annihilation into particles heavier than the rel-ic particle was considered kinematically forbidden, but we show that if the mass diA'erence is—5 —15%%uo, these "forbidden" channels can dominate the cross section and determine the relic abun-dance. The third situation occurs when the annihilation takes place near a pole in the cross section.Proper treatment of the thermal averaging and the annihilation after freeze-out shows that the dipin relic abundance caused by a pole is not nearly as sharp or deep as previously thought.

I. INTRODUCTION

The calculation of the present-day density of elementa-ry particles which were in thermal equilibrium in the ear-ly Universe has become quite commonplace. ' Of particu-lar interest is the so-called Lee-Weinberg ' calculation inwhich annihilation after a particle species has becomenonrelativistic determines the present-day abundance ofthat species. Standard approximate solutions to theBoltzmann equation exist for this calculation and havebeen tested numerically. In this paper we wish to pointout three cases where naive application of the standardmethods fails to give correct results and a modified treat-ment is required. All three cases exist in the literature,and in all three cases erroneous conclusions have beendrawn. For each case we present appropriate approxi-mate solutions to the Boltzmann equation(s) and describethe values of the parameters for which they apply.

The first case occurs when the relic particle is the light-est of a set of similar particles whose masses are nearlydegenerate. In this case the relic abundance of the light-est particle is determined not only by its annihilationcross section, but also by the annihilation of the heavierparticles, which will later decay into the lightest. We callthis the case of "coannihilation. " As an example, consid-er a supersymmetric theory in which the scalar quarks orscalar electrons are only slightly more massive than thelightest supersymmetric particle (LSP), usually taken tobe a neutralino. Previous calculations of the relic abun-dance which consider only the LSP annihilation can be inerror by more than two orders of magnitude.

The second case concerns annihilation into particleswhich are more massive than the relic particle. Previous

treatments regarded this as kinematically forbidden, butwe show that if the heavier particles are on1y 5 —1S%more massive, these channels can dominate the annihila-tion cross section and determine the relic abundance. Wecall this the "forbidden" channel annihilation case. Ex-amples include annihilation into bb, tt, W+ W, or Higgsbosons, when the annihilating particle is lighter than thefinal-state particle.

The third case occurs when the annihilation takesplace near a pole in the cross section. This happens, forexample, in Z -exchange annihilation when the mass ofthe relic particle is near mz/2. Previous treatments haveincorrectly handled the thermal averages and the integra-tion of the Boltzmann equation in these situations. Thedip in relic abundance caused by a pole is broader andnot nearly as deep as previous treatments imply.

For all three cases we present simple formulas whichallow for a more correct treatment. We also present ex-amples for each case and describe the precise conditionsunder which the modified treatment is necessary. In Sec.II we review the standard method for performing theLee-Weinberg calculation and describe the approxima-tions within which we will work. In Sec. III we discussthe coannihilation case, in Sec. IV we discuss the forbid-den channel case, and in Sec. V we discuss annihilationnear a pole.

II. STANDARD CALCULATIONOF RELIC ABUNDANCE

Here we summarize the standard technique for calcu-lating the relic abundance of a particle species y in theLee-Weinberg scenario. First, a note about the philoso-

43 3191 1991 The American Physical Society

Forbidden annihilationResonant annihilation

Coannihilation

10/51

Motivation Coannihilation Codex Using the Codex

Three Exceptions

PHYSICAL REVIEW 0 VOLUME 43, NUMBER 10 15 MAY 1991

Three exceptions in the calculation of relic abundances

Kim GriestCenter for Particle Astrophysics and Astronomy Department, University of California, Berkeley, California 94720

David SeckelBartol Research Institute, University ofDelaware, Newark, Delaware 19716

(Received 15 November 1990)

The calculation of relic abundances of elementary particles by following their annihilation andfreeze-out in the early Universe has become an important and standard tool in discussing particledark-rnatter candidates. We find three situations, all occurring in the literature, in which the stan-dard methods of calculating relic abundances fail. The first situation occurs when another particlelies near in mass to the relic particle and shares a quantum number with it. An example is a lightsquark with neutralino dark matter. The additional particle must be included in the reaction net-work, since its annihilation can control the relic abundance. The second situation occurs when therelic particle lies near a mass threshold. Previously, annihilation into particles heavier than the rel-ic particle was considered kinematically forbidden, but we show that if the mass diA'erence is—5 —15%%uo, these "forbidden" channels can dominate the cross section and determine the relic abun-dance. The third situation occurs when the annihilation takes place near a pole in the cross section.Proper treatment of the thermal averaging and the annihilation after freeze-out shows that the dipin relic abundance caused by a pole is not nearly as sharp or deep as previously thought.

I. INTRODUCTION

The calculation of the present-day density of elementa-ry particles which were in thermal equilibrium in the ear-ly Universe has become quite commonplace. ' Of particu-lar interest is the so-called Lee-Weinberg ' calculation inwhich annihilation after a particle species has becomenonrelativistic determines the present-day abundance ofthat species. Standard approximate solutions to theBoltzmann equation exist for this calculation and havebeen tested numerically. In this paper we wish to pointout three cases where naive application of the standardmethods fails to give correct results and a modified treat-ment is required. All three cases exist in the literature,and in all three cases erroneous conclusions have beendrawn. For each case we present appropriate approxi-mate solutions to the Boltzmann equation(s) and describethe values of the parameters for which they apply.

The first case occurs when the relic particle is the light-est of a set of similar particles whose masses are nearlydegenerate. In this case the relic abundance of the light-est particle is determined not only by its annihilationcross section, but also by the annihilation of the heavierparticles, which will later decay into the lightest. We callthis the case of "coannihilation. " As an example, consid-er a supersymmetric theory in which the scalar quarks orscalar electrons are only slightly more massive than thelightest supersymmetric particle (LSP), usually taken tobe a neutralino. Previous calculations of the relic abun-dance which consider only the LSP annihilation can be inerror by more than two orders of magnitude.

The second case concerns annihilation into particleswhich are more massive than the relic particle. Previous

treatments regarded this as kinematically forbidden, butwe show that if the heavier particles are on1y 5 —1S%more massive, these channels can dominate the annihila-tion cross section and determine the relic abundance. Wecall this the "forbidden" channel annihilation case. Ex-amples include annihilation into bb, tt, W+ W, or Higgsbosons, when the annihilating particle is lighter than thefinal-state particle.

The third case occurs when the annihilation takesplace near a pole in the cross section. This happens, forexample, in Z -exchange annihilation when the mass ofthe relic particle is near mz/2. Previous treatments haveincorrectly handled the thermal averages and the integra-tion of the Boltzmann equation in these situations. Thedip in relic abundance caused by a pole is broader andnot nearly as deep as previous treatments imply.

For all three cases we present simple formulas whichallow for a more correct treatment. We also present ex-amples for each case and describe the precise conditionsunder which the modified treatment is necessary. In Sec.II we review the standard method for performing theLee-Weinberg calculation and describe the approxima-tions within which we will work. In Sec. III we discussthe coannihilation case, in Sec. IV we discuss the forbid-den channel case, and in Sec. V we discuss annihilationnear a pole.

II. STANDARD CALCULATIONOF RELIC ABUNDANCE

Here we summarize the standard technique for calcu-lating the relic abundance of a particle species y in theLee-Weinberg scenario. First, a note about the philoso-

43 3191 1991 The American Physical Society

Forbidden annihilationResonant annihilation

Coannihilation

10/51

Motivation Coannihilation Codex Using the Codex

Three Exceptions

PHYSICAL REVIEW 0 VOLUME 43, NUMBER 10 15 MAY 1991

Three exceptions in the calculation of relic abundances

Kim GriestCenter for Particle Astrophysics and Astronomy Department, University of California, Berkeley, California 94720

David SeckelBartol Research Institute, University ofDelaware, Newark, Delaware 19716

(Received 15 November 1990)

The calculation of relic abundances of elementary particles by following their annihilation andfreeze-out in the early Universe has become an important and standard tool in discussing particledark-rnatter candidates. We find three situations, all occurring in the literature, in which the stan-dard methods of calculating relic abundances fail. The first situation occurs when another particlelies near in mass to the relic particle and shares a quantum number with it. An example is a lightsquark with neutralino dark matter. The additional particle must be included in the reaction net-work, since its annihilation can control the relic abundance. The second situation occurs when therelic particle lies near a mass threshold. Previously, annihilation into particles heavier than the rel-ic particle was considered kinematically forbidden, but we show that if the mass diA'erence is—5 —15%%uo, these "forbidden" channels can dominate the cross section and determine the relic abun-dance. The third situation occurs when the annihilation takes place near a pole in the cross section.Proper treatment of the thermal averaging and the annihilation after freeze-out shows that the dipin relic abundance caused by a pole is not nearly as sharp or deep as previously thought.

I. INTRODUCTION

The calculation of the present-day density of elementa-ry particles which were in thermal equilibrium in the ear-ly Universe has become quite commonplace. ' Of particu-lar interest is the so-called Lee-Weinberg ' calculation inwhich annihilation after a particle species has becomenonrelativistic determines the present-day abundance ofthat species. Standard approximate solutions to theBoltzmann equation exist for this calculation and havebeen tested numerically. In this paper we wish to pointout three cases where naive application of the standardmethods fails to give correct results and a modified treat-ment is required. All three cases exist in the literature,and in all three cases erroneous conclusions have beendrawn. For each case we present appropriate approxi-mate solutions to the Boltzmann equation(s) and describethe values of the parameters for which they apply.

The first case occurs when the relic particle is the light-est of a set of similar particles whose masses are nearlydegenerate. In this case the relic abundance of the light-est particle is determined not only by its annihilationcross section, but also by the annihilation of the heavierparticles, which will later decay into the lightest. We callthis the case of "coannihilation. " As an example, consid-er a supersymmetric theory in which the scalar quarks orscalar electrons are only slightly more massive than thelightest supersymmetric particle (LSP), usually taken tobe a neutralino. Previous calculations of the relic abun-dance which consider only the LSP annihilation can be inerror by more than two orders of magnitude.

The second case concerns annihilation into particleswhich are more massive than the relic particle. Previous

treatments regarded this as kinematically forbidden, butwe show that if the heavier particles are on1y 5 —1S%more massive, these channels can dominate the annihila-tion cross section and determine the relic abundance. Wecall this the "forbidden" channel annihilation case. Ex-amples include annihilation into bb, tt, W+ W, or Higgsbosons, when the annihilating particle is lighter than thefinal-state particle.

The third case occurs when the annihilation takesplace near a pole in the cross section. This happens, forexample, in Z -exchange annihilation when the mass ofthe relic particle is near mz/2. Previous treatments haveincorrectly handled the thermal averages and the integra-tion of the Boltzmann equation in these situations. Thedip in relic abundance caused by a pole is broader andnot nearly as deep as previous treatments imply.

For all three cases we present simple formulas whichallow for a more correct treatment. We also present ex-amples for each case and describe the precise conditionsunder which the modified treatment is necessary. In Sec.II we review the standard method for performing theLee-Weinberg calculation and describe the approxima-tions within which we will work. In Sec. III we discussthe coannihilation case, in Sec. IV we discuss the forbid-den channel case, and in Sec. V we discuss annihilationnear a pole.

II. STANDARD CALCULATIONOF RELIC ABUNDANCE

Here we summarize the standard technique for calcu-lating the relic abundance of a particle species y in theLee-Weinberg scenario. First, a note about the philoso-

43 3191 1991 The American Physical Society

Forbidden annihilationResonant annihilation

Coannihilation

11/51

Motivation Coannihilation Codex Using the Codex

Coannihilation

DM DM ↔ SM1 SM2

DM X ↔ SM1 SM2

X X ↔ SM1 SM2

DM SM1 ↔ X SM2

dndt

=− 〈σeffv〉(n(t)2 − neq(t)2)− 3Hn

σeff ∼σDMDM + 2σDMX(1 + ∆)3/2e−xf ∆ + σXX(1 + ∆)e−2xf ∆

∆ =mDM − mX

mDM, xf =

mDM

Tf

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Motivation Coannihilation Codex Using the Codex

Coannihilation

DM DM ↔ SM1 SM2

DM X ↔ SM1 SM2

X X ↔ SM1 SM2

DM SM1 ↔ X SM2

dndt

=− 〈σeffv〉(n(t)2 − neq(t)2)− 3Hn

σeff ∼σDMDM + 2σDMX(1 + ∆)3/2e−xf ∆ + σXX(1 + ∆)e−2xf ∆

∆ =mDM − mX

mDM, xf =

mDM

Tf

11/51

Motivation Coannihilation Codex Using the Codex

Coannihilation

DM DM ↔ SM1 SM2

DM X ↔ SM1 SM2

X X ↔ SM1 SM2

DM SM1 ↔ X SM2

dndt

=− 〈σeffv〉(n(t)2 − neq(t)2)− 3Hn

σeff ∼σDMDM + 2σDMX(1 + ∆)3/2e−xf ∆ + σXX(1 + ∆)e−2xf ∆

∆ =mDM − mX

mDM, xf =

mDM

Tf

11/51

Motivation Coannihilation Codex Using the Codex

Coannihilation

DM DM ↔ SM1 SM2

DM X ↔ SM1 SM2

X X ↔ SM1 SM2

DM SM1 ↔ X SM2

dndt

=− 〈σeffv〉(n(t)2 − neq(t)2)− 3Hn

σeff ∼σDMDM + 2σDMX(1 + ∆)3/2e−xf ∆ + σXX(1 + ∆)e−2xf ∆

∆ =mDM − mX

mDM, xf =

mDM

Tf

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Motivation Coannihilation Codex Using the Codex

Coannihilation in the literature

Bino-Higgsino: 1601.01569, 1510.06151, 1510.02760, 1509.08838Bino-gluino: 1509.03613, 1508.04811Bino-wino: 1509.03613, 1506.08206Bino-stau: 1509.08838, 1509.07152Bino-sleptons: 1506.08202Bino-stop: 1509.08838Neutralino-chargino: 1509.08485, 1507.02288, 1506.08202Neutralino-sbottom: 1507.01001Neutralino-gluino: 1510.03498Radiative Neutrino Mass Models: 1512.07961, 1509.04068, 1507.06782Scalar DM & vector-like quark mediator: 1511.04452Triplet-Quadruplet DM: 1601.01354Lepton-flavored DM: 1510.00100Kaluza-Klein DM: 1601.00081Inert Zee model: 1511.01873Flavoured DM: 1510.04694

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Motivation Coannihilation Codex Using the Codex

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

13/51

Motivation Coannihilation Codex Using the Codex

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

13/51

Motivation Coannihilation Codex Using the Codex

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

14/51

Motivation Coannihilation Codex Using the Codex

Simplified Models of DM at the LHC

Simplified Models for Dark Matter Searches at the LHCAbdallah et al. 1506.03116

. . . outlines a set of simplified models of DM for searches at theLHC

Dark Matter Benchmark Models for Early LHC Run-2 Searches:Report of the ATLAS/CMS Dark Matter Forum

Abercrombie et al. 1507.00966

. . . a minimal basis of dark matter models that should influencethe design of the early Run-2 searches. At the same time, athorough survey of realistic collider signals of Dark Matter

15/51

Motivation Coannihilation Codex Using the Codex

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

15/51

Motivation Coannihilation Codex Using the Codex

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

15/51

Motivation Coannihilation Codex Using the Codex

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

16/51

Motivation Coannihilation Codex Using the Codex

Outline

1 Motivation

2 Coannihilation Codex

3 Using the Codex

17/51

Motivation Coannihilation Codex Using the Codex

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

17/51

Motivation Coannihilation Codex Using the Codex

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

17/51

Motivation Coannihilation Codex Using the Codex

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

17/51

Motivation Coannihilation Codex Using the Codex

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

17/51

Motivation Coannihilation Codex Using the Codex

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

18/51

Motivation Coannihilation Codex Using the Codex

Coannihilation Diagrams

X

DM

SM2

SM1

⇓X

DM

SM2

SM1

Ms

X

DM

SM2

SM1

Mt

X

DM

SM2

SM1

19/51

Motivation Coannihilation Codex Using the Codex

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

19/51

Motivation Coannihilation Codex Using the Codex

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

19/51

Motivation Coannihilation Codex Using the Codex

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

20/51

Motivation Coannihilation Codex Using the Codex

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

21/51

Motivation Coannihilation Codex Using the Codex

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

22/51

Motivation Coannihilation Codex Using the Codex

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

23/51

Motivation Coannihilation Codex Using the Codex

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

24/51

Motivation Coannihilation Codex Using the Codex

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

25/51

Motivation Coannihilation Codex Using the Codex

Complete Classification

We have written down all possible simplified models of 2-to-2coannihilating dark matter!

LHC Phenomenology

25/51

Motivation Coannihilation Codex Using the Codex

Complete Classification

We have written down all possible simplified models of 2-to-2coannihilating dark matter!

LHC Phenomenology

26/51

Motivation Coannihilation Codex Using the Codex

LHC Production: Common

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

if (SM1SM2) ∈ p

SM2

SM1

X

DM

27/51

Motivation Coannihilation Codex Using the Codex

Decays: Common

X

DM

SM1

SM2

/ET+

soft

28/51

Motivation Coannihilation Codex Using the Codex

Signature Table: Common

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]

29/51

Motivation Coannihilation Codex Using the Codex

LHC Production: s-channel

Gauge boson production +

if (SM1SM2) ∈ p

SM2

SM1

X

DM

⇒q

q′

M

if SM1/SM2 ∈ p

q

gq∗

SM

M

29/51

Motivation Coannihilation Codex Using the Codex

LHC Production: s-channel

Gauge boson production +

if (SM1SM2) ∈ p

SM2

SM1

X

DM

⇒q

q′

M

if SM1/SM2 ∈ p

q

gq∗

SM

M

30/51

Motivation Coannihilation Codex Using the Codex

Decays: s-channel

X

DM

Ms

SM1

SM2

/ET+

soft

Ms

SM1

SM2

Resonance

Ms

DM

XDM

M∗s

SM1

SM2

/ET

+soft

30/51

Motivation Coannihilation Codex Using the Codex

Decays: s-channel

X

DM

Ms

SM1

SM2

/ET+

soft

Ms

SM1

SM2

Resonance

Ms

DM

XDM

M∗s

SM1

SM2

/ET

+soft

30/51

Motivation Coannihilation Codex Using the Codex

Decays: s-channel

X

DM

Ms

SM1

SM2

/ET+

soft

Ms

SM1

SM2

Resonance

Ms

DM

XDM

M∗s

SM1

SM2

/ET

+soft

31/51

Motivation Coannihilation Codex Using the Codex

Signature Table: s-channel

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]

32/51

Motivation Coannihilation Codex Using the Codex

LHC Production: t-channel

Gauge boson production +Coannihilation diagram +

if SM1 ∈ p

q

gq∗

DM

M

if SM2 ∈ p

q

gq∗

X

M

32/51

Motivation Coannihilation Codex Using the Codex

LHC Production: t-channel

Gauge boson production +Coannihilation diagram +

if SM1 ∈ p

q

gq∗

DM

M

if SM2 ∈ p

q

gq∗

X

M

33/51

Motivation Coannihilation Codex Using the Codex

Decays: t-channel

X

SM2

Mt

SM1

DM /ET

+

soft

Mt

SM1

DM

hard+

/ET

Mt

SM2

XSM2

M∗t

SM1

DM

hard+

soft

+

/ET

33/51

Motivation Coannihilation Codex Using the Codex

Decays: t-channel

X

SM2

Mt

SM1

DM /ET

+

soft

Mt

SM1

DM

hard+

/ET

Mt

SM2

XSM2

M∗t

SM1

DM

hard+

soft

+

/ET

33/51

Motivation Coannihilation Codex Using the Codex

Decays: t-channel

X

SM2

Mt

SM1

DM /ET

+

soft

Mt

SM1

DM

hard+

/ET

Mt

SM2

XSM2

M∗t

SM1

DM

hard+

soft

+

/ET

34/51

Motivation Coannihilation Codex Using the Codex

Signature Table: t-channel

pp→ . . . Prod. via Signatures Search

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 SM[114,120-124]

[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]

35/51

Motivation Coannihilation Codex Using the Codex

LHC Production: hybrid models

Gauge boson production +

if SM ∈ p

q

gq∗

X

DM

35/51

Motivation Coannihilation Codex Using the Codex

LHC Production: hybrid models

Gauge boson production +

if SM ∈ p

q

gq∗

X

DM

36/51

Motivation Coannihilation Codex Using the Codex

Decays: hybrid models

X

SM

DM

soft+

/ET

37/51

Motivation Coannihilation Codex Using the Codex

Signature Table: hybrid models

pp→ . . . Prod. via Signatures Search

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]

38/51

Motivation Coannihilation Codex Using the Codex

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]

39/51

Motivation Coannihilation Codex Using the Codex

Outline

1 Motivation

2 Coannihilation Codex

3 Using the Codex

40/51

Motivation Coannihilation Codex Using the Codex

Bino-gluino Coannihilation

Label Field Rep. Spin assignment

DM Bino (1,1,0) Fermion

X Gluino (8,1,0) Fermion

M Squark (3,1,4/3) Scalar

DM ∼ (1,N, β)X ∼ (8,N, α)α+ β = 0

M ∼ (3,N, β + 4/3)

t-channel: IV

X

DM

SM2

SM1

Mt

41/51

Motivation Coannihilation Codex Using the Codex

Bino-gluino Coannihilation

X ∼ (8,N, α) α+ β = 0

M ∼ (3,N, β + 4/3) Spin: IV

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)

42/51

Motivation Coannihilation Codex Using the Codex

Bino-gluino Coannihilation

DM ∼ (1, 1, 0)F X ∼ (8, 1, 0)F

M ∼ (3, 1, 4/3)B (SM1SM2) = (uRuR)

g

B

uR

uR

uRg2

g1

pp→ . . . Prod. via Signatures Search Strength

com

mon

DM + DM + ISR

gauge int.

mono-Y + /ET [55,56,62,63,104] g41αior 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]

α2sαi, g4

2αior 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]

g21g2

2αimono-Y + /ET+ ≤ 2 SM Partial coverage [105]

pp→ . . . Prod. via Signatures Search Strength

t-ch

anne

l

Mt (→ SM1 DM)Mt (→ SM1 DM)

gauge int.

/ET+ ≤ 2 SM[120-122,124]

α2s

[104,147-153]Mt (→ SM1 DM)Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 4 SM[106-112]

α2s

[114,119-124]Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

Mt (→ SM2 + X (→ SMsoft1 SMsoft

2 DM))/ET+ ≤ 6 SM

[113,114,120-124]α2

s[116-118,159-163]

DM + Mt (→ SM1 DM)

SM1 ∈ p

/ET+ ≤ 1 SM[55,56,62,63]

αsg21

[104,149]DMMt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 3 SM[114,120-124]

αsg21

[152,153,156-158]Mt (→ SM1 DM)X (→ SMsoft

1 SMsoft2 DM)

SM2 ∈ p

/ET+ ≤ 3 SM[114,120-124]

αsg22

[152,153,156-158]Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

X (→ SMsoft1 SMsoft

2 DM)/ET+ ≤ 5 SM

[113,114,116-124]αsg2

2[159-161,164]

42/51

Motivation Coannihilation Codex Using the Codex

Bino-gluino Coannihilation

DM ∼ (1, 1, 0)F X ∼ (8, 1, 0)F

M ∼ (3, 1, 4/3)B (SM1SM2) = (uRuR)

g

B

uR

uR

uRg2

g1

pp→ . . . Prod. via Signatures Search Strength

com

mon

DM + DM + ISR

gauge int.

mono-Y + /ET [55,56,62,63,104] g41αior 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]

α2sαi, g4

2αior 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]

g21g2

2αimono-Y + /ET+ ≤ 2 SM Partial coverage [105]

pp→ . . . Prod. via Signatures Search Strength

t-ch

anne

l

Mt (→ SM1 DM)Mt (→ SM1 DM)

gauge int.

/ET+ ≤ 2 SM[120-122,124]

α2s

[104,147-153]Mt (→ SM1 DM)Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 4 SM[106-112]

α2s

[114,119-124]Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

Mt (→ SM2 + X (→ SMsoft1 SMsoft

2 DM))/ET+ ≤ 6 SM

[113,114,120-124]α2

s[116-118,159-163]

DM + Mt (→ SM1 DM)

SM1 ∈ p

/ET+ ≤ 1 SM[55,56,62,63]

αsg21

[104,149]DMMt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 3 SM[114,120-124]

αsg21

[152,153,156-158]Mt (→ SM1 DM)X (→ SMsoft

1 SMsoft2 DM)

SM2 ∈ p

/ET+ ≤ 3 SM[114,120-124]

αsg22

[152,153,156-158]Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

X (→ SMsoft1 SMsoft

2 DM)/ET+ ≤ 5 SM

[113,114,116-124]αsg2

2[159-161,164]

42/51

Motivation Coannihilation Codex Using the Codex

Bino-gluino Coannihilation

DM ∼ (1, 1, 0)F X ∼ (8, 1, 0)F

M ∼ (3, 1, 4/3)B (SM1SM2) = (uRuR)

g

B

uR

uR

uRg2

g1

pp→ . . . Prod. via Signatures Search Strength

com

mon

DM + DM + ISR

gauge int.

mono-Y + /ET [55,56,62,63,104] g41αior 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]

α2sαi, g4

2αior 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]

g21g2

2αimono-Y + /ET+ ≤ 2 SM Partial coverage [105]

pp→ . . . Prod. via Signatures Search Strength

t-ch

anne

l

Mt (→ SM1 DM)Mt (→ SM1 DM)

gauge int.

/ET+ ≤ 2 SM[120-122,124]

α2s

[104,147-153]Mt (→ SM1 DM)Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 4 SM[106-112]

α2s

[114,119-124]Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

Mt (→ SM2 + X (→ SMsoft1 SMsoft

2 DM))/ET+ ≤ 6 SM

[113,114,120-124]α2

s[116-118,159-163]

DM + Mt (→ SM1 DM)

SM1 ∈ p

/ET+ ≤ 1 SM[55,56,62,63]

αsg21

[104,149]DMMt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 3 SM[114,120-124]

αsg21

[152,153,156-158]Mt (→ SM1 DM)X (→ SMsoft

1 SMsoft2 DM)

SM2 ∈ p

/ET+ ≤ 3 SM[114,120-124]

αsg22

[152,153,156-158]Mt (→ SM2 + X (→ SMsoft

1 SMsoft2 DM))

X (→ SMsoft1 SMsoft

2 DM)/ET+ ≤ 5 SM

[113,114,116-124]αsg2

2[159-161,164]

43/51

Motivation Coannihilation Codex Using the Codex

Using the Codex II

Underexplored DM Models

44/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - 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

44/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - 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

45/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - 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.

∆ =mX − mDM

mDMyij

Q` = yLu = 0 yD = y11Q`

45/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - 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.

∆ =mX − mDM

mDMyij

Q` = yLu = 0 yD = y11Q`

45/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - 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.

∆ =mX − mDM

mDMyij

Q` = yLu = 0 yD = y11Q`

45/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - 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.

∆ =mX − mDM

mDMyij

Q` = yLu = 0 yD = y11Q`

46/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Relic Density

mLQ=400, Δ=0.1, y=0.5

mLQ=1000, Δ=0.1, y=0.5

mLQ=1000, Δ=0.15, y=0.5

mLQ=1500, Δ=0.1, y=0.1

mLQ=1500, Δ=0.1, y=0.5

Relic Density (3σ)

yD=yQl, yLu=0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.001

0.01

0.1

1.0

10.0

mDM [GeV]

Ωh2

σann ∝ 1m2

e.g.,X

X

g

gX

X

DMM

`+

q

DM

DM

M

M†X

46/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Relic Density

mLQ=400, Δ=0.1, y=0.5

mLQ=1000, Δ=0.1, y=0.5

mLQ=1000, Δ=0.15, y=0.5

mLQ=1500, Δ=0.1, y=0.1

mLQ=1500, Δ=0.1, y=0.5

Relic Density (3σ)

yD=yQl, yLu=0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.001

0.01

0.1

1.0

10.0

mDM [GeV]

Ωh2

σann ∝ 1m2

e.g.,X

X

g

gX

X

DMM

`+

q

DM

DM

M

M†X

46/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Relic Density

mLQ=400, Δ=0.1, y=0.5

mLQ=1000, Δ=0.1, y=0.5

mLQ=1000, Δ=0.15, y=0.5

mLQ=1500, Δ=0.1, y=0.1

mLQ=1500, Δ=0.1, y=0.5

Relic Density (3σ)

yD=yQl, yLu=0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.001

0.01

0.1

1.0

10.0

mDM [GeV]

Ωh2

σann ∝ 1m2

e.g.,X

X

g

gX

X

DMM

`+

q

DM

DM

M

M†X

46/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Relic Density

mLQ=400, Δ=0.1, y=0.5

mLQ=1000, Δ=0.1, y=0.5

mLQ=1000, Δ=0.15, y=0.5

mLQ=1500, Δ=0.1, y=0.1

mLQ=1500, Δ=0.1, y=0.5

Relic Density (3σ)

yD=yQl, yLu=0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.001

0.01

0.1

1.0

10.0

mDM [GeV]

Ωh2

σann ∝ 1m2

e.g.,X

X

g

gX

X

DMM

`+

q

DM

DM

M

M†X

47/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Signatures

DM ∼ (1, 1, 0)F X ∼ (3, 2, 7/3)F M ∼ (3, 2, 7/3)B (SM1SM2) = (QLeR)

pp→ . . . Prod. via Signatures Search Strength

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]

α2sαior 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]

pp→ . . . Prod. via Signatures Search Strength

s-ch

anne

l

Ms (→ [SM1 SM2]res)Ms (→ [SM1 SM2]res)

gauge int.

2 resonances [106-112] α2s

Ms (→ [SM1 SM2]res)Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

resonance + /ET No searchα2

sresonance + /ET+ ≤ 2 SM No search

Ms (→ DM + X (→ SMsoft1 SMsoft

2 DM))Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 4 SM [113-124] α2s

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] αs(y11Q`)

2SM1,2Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

/ET + 1 ≤ 3 SM[114,120-124]

αs(y11Q`)

2

[147-153,156-158]

47/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Signatures

DM ∼ (1, 1, 0)F X ∼ (3, 2, 7/3)F M ∼ (3, 2, 7/3)B (SM1SM2) = (QLeR)

pp→ . . . Prod. via Signatures Search Strength

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]

α2sαior 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]

pp→ . . . Prod. via Signatures Search Strength

s-ch

anne

l

Ms (→ [SM1 SM2]res)Ms (→ [SM1 SM2]res)

gauge int.

2 resonances [106-112] α2s

Ms (→ [SM1 SM2]res)Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

resonance + /ET No searchα2

sresonance + /ET+ ≤ 2 SM No search

Ms (→ DM + X (→ SMsoft1 SMsoft

2 DM))Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

/ET+ ≤ 4 SM [113-124] α2s

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] αs(y11Q`)

2SM1,2Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

/ET + 1 ≤ 3 SM[114,120-124]

αs(y11Q`)

2

[147-153,156-158]

48/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Signatures

DM ∼ (1, 1, 0)F X ∼ (3, 2, 7/3)F M ∼ (3, 2, 7/3)B (SM1SM2) = (QLeR)

pp→ . . . Signatures Existing Searches Strength Search

com

mon

DM + DM + ISR mono-Y + /ET [ 55,56,62,63,104] – –

X (→ SMsoft1 SMsoft

2 DM)X (→ SMsoft

1 SMsoft2 DM)

ISR

mono-Y + /ET [55,56,62,63,104]

α2sαi

(I) monojet + /ET

mono-Y + /ET+ ≤ 4 SM Partial coverage [105] (II) monojet + /ET + soft e

DM + X (→ SMsoft1 SMsoft

2 DM) + ISRmono-Y + /ET [55,56,62,63,104]

– –mono-Y + /ET+ ≤ 2 SM Partial coverage [105]

s-ch

anne

l

Ms (→ [SM1 SM2]res)Ms (→ [SM1 SM2]res)

2 resonances [106-111,112] α2s (III) Leptoquark pair

Ms (→ [SM1 SM2]res)Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

resonance + /ET No searchα2

s(IV) Leptoquark + /ET

resonance + /ET+ ≤ 2 SM No search (V) Leptoquark + /ET + j + eMs (→ DM + X (→ SMsoft

1 SMsoft2 DM))

Ms (→ DM + X (→ SMsoft1 SMsoft

2 DM))/ET+ ≤ 4 SM

[113,114-124]α2

s(VI) 2e+2j + /ET

(I) monojet + /ET

Ms (→ [SM1 SM2]res) 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) 1 resonance + 1 SM Partial coverage [154,155] αs(y11Q`)

2 (VII) Leptoquark + eSM1,2Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

/ET + 1 ≤ 3 SM[114,120-124]

αs(y11Q`)

2 (VI) 2e + j + /ET

[128,129,147-153,156-158] (VIII) e + /ET

←←

←←

←

48/51

Motivation Coannihilation Codex Using the Codex

Leptoquark Mediated DM - ST11 - Signatures

DM ∼ (1, 1, 0)F X ∼ (3, 2, 7/3)F M ∼ (3, 2, 7/3)B (SM1SM2) = (QLeR)

pp→ . . . Signatures Existing Searches Strength Search

com

mon

DM + DM + ISR mono-Y + /ET [ 55,56,62,63,104] – –

X (→ SMsoft1 SMsoft

2 DM)X (→ SMsoft

1 SMsoft2 DM)

ISR

mono-Y + /ET [55,56,62,63,104]

α2sαi

(I) monojet + /ET

mono-Y + /ET+ ≤ 4 SM Partial coverage [105] (II) monojet + /ET + soft e

DM + X (→ SMsoft1 SMsoft

2 DM) + ISRmono-Y + /ET [55,56,62,63,104]

– –mono-Y + /ET+ ≤ 2 SM Partial coverage [105]

s-ch

anne

l

Ms (→ [SM1 SM2]res)Ms (→ [SM1 SM2]res)

2 resonances [106-111,112] α2s (III) Leptoquark pair

Ms (→ [SM1 SM2]res)Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

resonance + /ET No searchα2

s(IV) Leptoquark + /ET

resonance + /ET+ ≤ 2 SM No search (V) Leptoquark + /ET + j + eMs (→ DM + X (→ SMsoft

1 SMsoft2 DM))

Ms (→ DM + X (→ SMsoft1 SMsoft

2 DM))/ET+ ≤ 4 SM

[113,114-124]α2

s(VI) 2e+2j + /ET

(I) monojet + /ET

Ms (→ [SM1 SM2]res) 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) 1 resonance + 1 SM Partial coverage [154,155] αs(y11Q`)

2 (VII) Leptoquark + eSM1,2Ms (→ DM + X (→ SMsoft

1 SMsoft2 DM))

/ET + 1 ≤ 3 SM[114,120-124]

αs(y11Q`)

2 (VI) 2e + j + /ET

[128,129,147-153,156-158] (VIII) e + /ET

←←

←←

←

49/51

Motivation Coannihilation Codex Using the Codex

ST11 - Existing Collider Constraints

LQPair(Visible)[8TeV]

SingleLQ

(Visible)[8TeV](yQl=0.4)

XX+j (Monojet) [8 TeV]

LQPair(Visible)[13TeV

]

XX+j (Monojet) [13 TeV]

(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

M

M†

q

e+

e−

q

g

qq∗

e−

Mq

e+

g g

g

X

X

DMDM

q

e+

e−

q

49/51

Motivation Coannihilation Codex Using the Codex

ST11 - Existing Collider Constraints

LQPair(Visible)[8TeV]

SingleLQ

(Visible)[8TeV](yQl=0.4)

XX+j (Monojet) [8 TeV]

LQPair(Visible)[13TeV

]

XX+j (Monojet) [13 TeV]

(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

M

M†

q

e+

e−

q

g

qq∗

e−

Mq

e+

g g

g

X

X

DMDM

q

e+

e−

q

49/51

Motivation Coannihilation Codex Using the Codex

ST11 - Existing Collider Constraints

LQPair(Visible)[8TeV]

SingleLQ

(Visible)[8TeV](yQl=0.4)

XX+j (Monojet) [8 TeV]

LQPair(Visible)[13TeV

]

XX+j (Monojet) [13 TeV]

(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

M

M†

q

e+

e−

q

g

qq∗

e−

Mq

e+

g g

g

X

X

DMDM

q

e+

e−

q

49/51

Motivation Coannihilation Codex Using the Codex

ST11 - Existing Collider Constraints

LQPair(Visible)[8TeV]

SingleLQ

(Visible)[8TeV](yQl=0.4)

XX+j (Monojet) [8 TeV]

LQPair(Visible)[13TeV

]

XX+j (Monojet) [13 TeV]

(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

M

M†

q

e+

e−

q

g

qq∗

e−

Mq

e+

g g

g

X

X

DMDM

q

e+

e−

q

50/51

Motivation Coannihilation Codex Using the Codex

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+

50/51

Motivation Coannihilation Codex Using the Codex

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+

51/51

Motivation Coannihilation Codex Using the Codex

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 coannihilating models of DMwith interesting collider signatures to studyat the LHC and future colliders

51/51

Motivation Coannihilation Codex Using the Codex

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 coannihilating models of DMwith interesting collider signatures to studyat the LHC and future colliders

51/51

Motivation Coannihilation Codex Using the Codex

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 coannihilating models of DMwith interesting collider signatures to studyat the LHC and future colliders

51/51

Motivation Coannihilation Codex Using the Codex

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 coannihilating models of DMwith interesting collider signatures to studyat the LHC and future colliders

51/51

Motivation Coannihilation Codex Using the Codex

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 coannihilating models of DMwith interesting collider signatures to studyat the LHC and future colliders

52/51

EWSB I

The main effect of EWSB on our models is from mixing:Due to Z2 symmetry, in t-channel models the effects of themixing will be entirely in the dark sectorMediators in s-channel models may mix with SM particles,giving hybrid model like signatures

53/51

EWSB II

It is also possible to construct new 2-to-2 diagrams exist thanksto EWSB

E.g.: mixing between Wi(1, 3, 0) and Vi(1, 5, 0) in the 3–3–1model

However, all diagrams are built from verticies present in ourtables and LHC signatures (almost always) differ only by mixingangles and group theory factors

54/51

Cut-flow table - Mixed decay

QCD W + 1, 2j tt Zνν + j Zττ + j W+W− WZνν + j WZjj signal

pT(j1) > 50 GeV 2.1×1012 4.4×108 1.3×108 7.0×107 1.3×107 1.2×106 1.3×105 3.1×105 600

Nhe = 1, Ne ≤ 2 4.8×109 8.8×107 1.2×107 8.6×104 4.8×105 2.4×105 1.9×104 6.1×104 415

b-jet veto 4.0×109 8.2×107 5.0×106 8.2×104 4.6×105 2.2×105 1.9×104 5.4×104 395

Nhard jets ≤ 3 3.9×109 8.2×107 4.3×106 8.2×104 4.6×105 2.2×105 1.9×104 5.4×104 335

Z veto 3.9×109 8.2×107 1.7×106 8.2×104 4.6×105 2.2×105 1.9×104 5.4×104 326

/ET > 700 GeV 133 1738 15 19 9 10 27 2 75

mT > 150 GeV 132 16 10−3 18 0.005 0.01 10 0.001 67

mass window 3 0.2 0 0.3 10−5 10−5 0.1 10−5 24

55/51

Cut-flow table - XXj

tt Z`` + j Diboson W`ν + j t + j Signal

/ET > 50 GeV 1.9× 107 7.9× 106 1.1× 106 1.9× 108 5.6× 105 8.5× 104

pleadT > 50 GeV 1.8× 107 6.1× 106 5.9× 105 1.5× 108 4.6× 105 7.1× 104

∆φj1j2 < 2.5 1.2× 107 4.2× 106 5.0× 105 1.1× 108 2.9× 105 5.4× 104

Z and µ veto 8.5× 106 2.7× 106 4.0× 105 8.6× 107 1.9× 105 5.2× 104

b veto 3.6× 106 2.6× 106 3.7× 105 8.2× 107 1.1× 105 2.0× 104

Nl ≥ 2 2.5× 104 4371 1076 9.8× 104 382 1748

/ET > 400 GeV 12 11 0.07 780 2 118∣∣∣∣pT j1/ET− 1∣∣∣∣ < 0.2 1 11 0.07 148 0.2 85