Issue with the feynrules model file of V2 Leptoquark

Asked by Arijit Das

I have written a V2 vector Leptoquark model file. The model file is as follows:

(* ************************** *)
(* ***** Information ***** *)
(* ************************** *)

M$ModelName = "V2_Vector_Leptoquark_Model_DA";

M$InteractionOrderHierarchy = {
  {QCD, 1},
  {QED, 2},
  {NP, 3}
};

M$Parameters = {

X2RL == {
     ParameterType -> External,
 ComplexParameter -> True,
     Indices -> {Index[Generation], Index[Generation]},
 BlockName -> YUKV2RL,
     Value -> { X2RL[1,1] -> 0.0, X2RL[1,2] -> 0.0, X2RL[1,3] -> 0.0,
                              X2RL[2,1] -> 0.0, X2RL[2,2] -> 0.0, X2RL[2,3] -> 0.0,
                               X2RL[3,1] -> 0.0, X2RL[3,2] -> 0.0, X2RL[3,3] -> 0.0},
     TeX -> Superscript[Subscript[X, "2"],RL],
 InteractionOrder -> {NP, 1},
     Description -> "V2 leptoquark RL Yukawa coupling matrix"
},

X2LR == {
     ParameterType -> External,
 ComplexParameter -> True,
     Indices -> {Index[Generation], Index[Generation]},
 BlockName -> YUKV2LR,
     Value -> { X2LR[1,1] -> 0.0, X2LR[1,2] -> 0.0, X2LR[1,3] -> 0.0,
                              X2LR[2,1] -> 0.0, X2LR[2,2] -> 0.0, X2LR[2,3] -> 0.0,
                               X2LR[3,1] -> 0.0, X2LR[3,2] -> 0.0, X2LR[3,3] -> 0.0},
     TeX -> Superscript[Subscript[X, "2"],LR],
 InteractionOrder -> {NP, 1},
     Description -> "V2 leptoquark LR Yukawa coupling matrix"
}

};

M$ClassesDescription = {

V[700] == {
    ClassName -> V243,
    SelfConjugate -> False,
    Mass -> {MV243, 1000.0},
    Width -> {WV243, 10.0},
    ParticleName -> "V243",
    AntiParticleName -> "V243~",
    PDG -> 7200014,
    QuantumNumbers -> {Q -> -4/3 , LeptonNumber -> 1},
    Indices -> {Index[Colour]},
    PropagatorLabel -> "V243",
    PropagatorType -> Sine,
    PropagatorArrow -> Forward,
    FullName -> "V243"
},

V[500] == {
    ClassName -> V213,
    SelfConjugate -> False,
    Mass -> {MV213, 1000.0},
    Width -> {WV213, 10.0},
    ParticleName -> "V213",
    AntiParticleName -> "V213~",
    PDG -> 7200012,
    QuantumNumbers -> {Q -> -1/3 , LeptonNumber -> 1},
    Indices -> {Index[Colour]},
    PropagatorLabel -> "V213",
    PropagatorType -> Sine,
    PropagatorArrow -> Forward,
    FullName -> "V213"
},

V[903] == {
    ClassName -> V2,
    Unphysical -> True,
    Indices -> {Index[SU2D], Index[Colour]},
    FlavorIndex -> SU2D,
    SelfConjugate -> False,
    QuantumNumbers -> {Y -> -5/6},
    Definitions -> { V2[mu_,1,cc_] :> V213[mu,cc], V2[mu_,2,cc_] :> V243[mu,cc]}
}

};

LKin := Block[{mu,nu,a,aa},ExpandIndices[-(1/2)(DC[V2bar[nu,a,aa],mu] - DC[V2bar[mu,a,aa],nu]).(DC[V2[nu,a,aa],mu] - DC[V2[mu,a,aa],nu]) + MV243^2 V243bar[mu,aa].V243[mu,aa] + MV213^2 V213bar[mu,aa].V213[mu,aa]]];

LV2RL := -X2RL[a,b] anti[CC[dq]][i,a,ss] Ga[mu,i,j] ProjM[j,k] vl[k,b] V213bar[mu,ss] + X2RL[a,b] anti[CC[dq]][i,a,ss] Ga[mu,i,j] ProjM[j,k] l[k,b] V243bar[mu,ss];

LV2LR := CKM[a,m] X2LR[m,b] anti[CC[uq]][i,a,ss] Ga[mu,i,j] ProjP[j,k] l[k,b] V213bar[mu,ss] - X2LR[a,b] anti[CC[dq]][i,a,ss] Ga[mu,i,j] ProjP[j,k] l[k,b] V243bar[mu,ss];

LBSM := LKin + LV2RL + LV2LR + HC[LV2RL] + HC[LV2LR];

(*****************************************************************************************)

There are a couple of issues that I am facing:

(i) The tchannel lepton exchage contribution to the leptoquark pair production cross-section is not being computed.

(ii) The interference contribution between the indirect production (tchannel leptoquark exchange) and the Standard Model background is not being computed unless both RL and LR sector couplings are turned on.

How can this be rectified ?

Thank you in advance!

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Olivier Mattelaer (olivier-mattelaer) said :
#1

Hi,

I'm sorry but I do not have a mathematica license. So I would not be able to convert your Lagrangian within something usable in our code. So could you send me the model (<email address hidden>)

Additionally, I'm not a leptoquark expert (more a newbie on that type of model).
So could you provide me the syntax of the process that you are looking at.

Finally what do you mean by "not being computed" you mean that the diagram does not exists? or that the cross-section is zero? In both case, this is likely the reason of your second question (if something is zero it will not interfere).

Stating the obvious here, I'm not a FeynRules expert so my help on this is likely going to be something like:
Yes this vertex does not exists in your model. If you need help on the FeynRules side, I can only advise to contact the FR authors (they do have a github now).

Cheers,

Olivier

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