## Dark Matter Processes

This page contains the production of Dirac fermion Dark Matter via new s-channel mediators. A summary of the physics scenarios and parameters involved can be found in [Des18]. Examples how these processes can be run are found in `main507.cc` and `main508.cc`.

The particles in the scenarios considered here are a mix of established PDG ones (51 - 55) and extensions thereof ( 56 - 59), as follows:

51 | Scalar DM (currently unused);
52 | Fermionic DM (chi_1);
53 | Vector DM (currently unused);
54 | Scalar (or pseudoscalar) mediator (S);
55 | Vector (or axial vector) mediator (Z');
56 | Charged scalar partner (l^~);
57 | Singly charged partner (chi^+);
58 | Neutral partner (chi_2);
59 | Doubly charged partner (chi^++).

### Scalar Mediator

`flag` DM:gg2S2XX (`default = off`)
Scattering g g → S → X Xbar. Code 6011. S is assumed to be on-shell.

`flag` DM:gg2S2XXj (`default = off`)
Scattering g g →S → X Xbar j. Code 6012. S is assumed to be on-shell. (Not yet available.)

Fermion couplings to scalar S are assumed to be proportional to mass of the fermion and couplings are the factor multiplying SM Higgs coupling (i.e. sin(mixing) in case of portal models).

`parm` Sdm:vf (`default = 0.1`)
Scalar coupling of SM fermions.

`parm` Sdm:af (`default = 0`)
Pseudo-scalar coupling of SM fermions.

`parm` Sdm:vX (`default = 1.0`)
Scalar coupling of DM fermion.

`parm` Sdm:aX (`default = 0`)
Pseudo-scalar coupling of DM fermion.

### Vector Mediator Z'

The Vector mediator model assumes a simplified U(1) model with couplings to fermionic Dark Matter. Both vector and axial couplings are possible. Interference with gamma/Z is currently not implemented, therefore this should mainly be used when Z' → X Xbar. However, a quick check of dijet or dilepton cross sections can be made by setting the mode `Zp:decayMode`.

`mode` Zp:decayMode (`default = 0`; `minimum = 0`; `maximum = 3`)
Switch to change decay of the Z'.
`option` 0 : X Xbar
`option` 1 : q qbar (dijets)
`option` 2 : l lbar (charged dileptons)
`option` 3 : nu nubar + X Xbar (invisible)

`flag` DM:ffbar2Zp2XX (`default = off`)
Scattering f fbar →Z'^0 → X Xbar. Code 6001. Z' is assumed to be on-shell.

`flag` DM:ffbar2ZpH (`default = off`)
Scattering f fbar →Z'^0 H . Code 6004. Z' is assumed to be on-shell. The coupling of the Z' to the SM Higgs is given by the parameter `Zp:coupH`. Interference with gamma/Z currently not implemented therefore this is only suitable when Z' → X Xbar. This can be ensured using
`55:onMode = off`
`55:onIfAny = 52`

`flag` DM:ffbar2Zp2XXj (`default = off`)
Scattering f fbar →Z'^0 j → X Xbar j. Code 6002. Z' is assumed to be on-shell. (Not yet available.)

`flag` DM:qg2Zp2XXj (`default = off`)
Scattering q g →Z'^0 j → X Xbar j. Code 6003. Z' is assumed to be on-shell. (Not yet available.)

The vector and axial couplings of fermionic DM to the Z'^0 can be set freely. The couplings of quarks and leptons can either be chosen freely for a new U(1) or be given by kinetic mixing with the SM U(1)_Y. The SM fermion couplings are assumed to be universal, i.e. generation-independent. The choice of fixed axial and vector couplings implies a resonance width that increases linearly with the Z' mass. Also some overall coupling strengths can be chosen freely.

`parm` Zp:vX (`default = 1.`)
Vector coupling of DM fermion.

`parm` Zp:aX (`default = 0.`)
Axial coupling of DM fermion.

`flag` Zp:kineticMixing (`default = off`)
Flag for the two main options to set the couplings of the Z' to SM quarks and leptons. In the default off option the overall coupling strength of the new U(1) gauge group is given by `Zp:gZp` and the separate fermion couplings by `Zp:vu` through `Zp:av`. In the alternative, with kinetic mixing on, the coupling to the DM is still given by `Zp:gZp`, but the mixing parameter `Zp:epsilon` now specifies how the separate fermion couplings are related to their U(1)_Y values.

`parm` Zp:gZp (`default = 0.1`)
Gauge coupling of a new U(1). This parameter also sets the coupling of the DM to the Z', whether kinetic mixing is on or not.

`parm` Zp:vu (`default = 1.`)
Vector coupling of up-type quarks.

`parm` Zp:au (`default = 0.`)
Axial coupling of up-type quarks.

`parm` Zp:vd (`default = 1.`)
Vector coupling of down-type quarks.

`parm` Zp:ad (`default = 0.`)
Axial coupling of down-type quarks.

`parm` Zp:vl (`default = 1.`)
Vector coupling of charged leptons.

`parm` Zp:al (`default = 0.`)
Axial coupling of charged leptons.

`parm` Zp:vv (`default = 1.`)
Vector coupling of neutrinos.

`parm` Zp:av (`default = 0.`)
Axial coupling of neutrinos.

`parm` Zp:epsilon (`default = 0.1`)
Kinetic mixing parameter between the dark U(1) and the SM hypercharge U(1). In the implemented case the Z'^0 mass is larger than the SM Z^0 one. The fermionic current for Z'^0 is described in [Cli184].

`parm` Zp:coupH (`default = 0.1`)
Coupling to the SM higgs when kinetic mixing is off. When on the coupling is instead set by `Zp:epsilon`.

### Drell-Yan production of charged co-annihilation partners

We implement two models of co-annihilating Dark Matter where the co-annihilation partner carries EW charge and therefore can be produced via Drell-Yan production. The underlying model and production process can be selected by choosing the parameter `DM:DYtype`.

The first model consists of co-annihilation with a scalar with leptonic quantum numbers and which couples to a right-handed SM lepton and a Dirac fermion Dark Matter via Yukawa couplings. It is possible to choose lepton flavour violating couplings.

The next model is a generalisation of the mixed gaugino sector of Supersymmetry parametrised by one SM singlet and one SU(2) N-plet which mix to form Dark matter. N = 2, 3 and 5 are supported by the code. The main motivation for this choice is to provide a fully flexible implementation to calculate production of long-lived particles at the LHC. The resultant spectrum consists of one neutral partner, one singly charged partner, and one doubly charged partner (in the case of the 5-plet). The only free parameters are masses of the singlet and N-plet and the mixing suppression scale. This determines both production and decay of the particles and can cover a range of signatures including displaced leptons and vertices, long-lived, kinked or disappearing tracks.

`flag` DM:qqbar2DY (`default = off`)
Scattering q qbar → X_i Xbar_i . Code 6020.

`mode` DM:DYtype (`default = 1`; `minimum = 1`; `maximum = 4`)
Select the co-annihilation partner to produce via Drell-Yan production.
`option` 1 : Scalar lepton production. Coupling to electrons, muons and taus can be fixed by `DM:yuk1`, `DM:yuk2`, and `DM:yuk3` respectively.
`option` 2 : Production of charged partners (i.e. "charginos").
`option` 3 : Production of doubly charged partners.
`option` 4 : Production of neutral and singly-charged partners.

The Yukawa couplings can be set using

`parm` DM:yuk1
Electron-DM Yukawa.

`parm` DM:yuk2
Muon-DM Yukawa.

`parm` DM:yuk3
Tau-DM Yukawa.

The parameters for the singlet-N-plet model can be set via the following:

`mode` DM:Nplet (`default = 2`; `minimum = 1`; `maximum = 3`)
`option` 1 : Doublet
`option` 2 : Triplet
`option` 3 : Quintuplet

`parm` DM:M1
Mass of the DM singlet state.

`parm` DM:M2
Mass of the DM N-plet state.

`parm` DM:Lambda
The suppression scale of the mixing. The Wilson co-efficient is absorbed into the suppression scale as there is no independent measurement to disentangle it from the scale.