Z3 symmetry violated in Lagrangian terms

[JamesM]

Hello,

I am trying to implement a Z3 scalar singlet extension of the SM in SARAH. I give the scalar field a charge Exp[2*Pi*\[ImaginaryI]/3], however I get a warning that the Z3 symmetry is violated,

Lagrange::ViolationGlobal: Warning! Global symmetry Z3 not conserved.

The cause of this is terms of the form S.conj[S] in the Lagrangian. The term S.S.S is okay. Now I would expect that S.conj[S] would work okay too, but perhaps this isn't supported or I am using the wrong notation for SARAH.

The relevant part of my model file is (I have attached the file as well):

(* Global Symmetries *)

Global[[1]] = {Z[3], Z3};


(* Gauge Groups *)

Gauge[[1]]={B, U[1], hypercharge, g1,False,1};
Gauge[[2]]={WB, SU[2], left, g2,True,1};
Gauge[[3]]={G, SU[3], color, g3,False,1};



(* Matter Fields *)

FermionFields[[1]] = {q, 3, {uL, dL}, 1/6, 2, 3,1};
FermionFields[[2]] = {l, 3, {vL, eL}, -1/2, 2, 1,1};
FermionFields[[3]] = {d, 3, conj[dR], 1/3, 1, -3,1};
FermionFields[[4]] = {u, 3, conj[uR], -2/3, 1, -3,1};
FermionFields[[5]] = {e, 3, conj[eR], 1, 1, 1,1};

ScalarFields[[1]] = {H, 1, {Hp, H0}, 1/2, 2, 1,1};
ScalarFields[[2]] = {S, 1, ss, 0, 1, 1, Exp[2*Pi*\[ImaginaryI]/3]};




(*----------------------------------------------*)
(* DEFINITION *)
(*----------------------------------------------*)

NameOfStates={GaugeES, EWSB};

(* ----- Before EWSB ----- *)

DEFINITION[GaugeES][LagrangianInput]= {
{LagHC, {AddHC->True}},
{LagNoHC,{AddHC->False}}
};


LagNoHC = -(muH conj[H].H + LamH/2 conj[H].H.conj[H].H+ 1/2 muS S.conj[S] + 1/2 LamSH S.conj[S].conj[H].H + 1/4 LamS S.conj[S].S.conj[S]);
LagHC = -(Yd conj[H].d.q + Ye conj[H].e.l + Yu H.u.q)-mu3/2 (S.S.S);


Any advice on implementing this would be greatly appreciated. Also if it is okay to ignore this warning without any consequences to the validity of the result, then that would be good to know.

Cheers,
James

[FStaub]

Hi,

the assumption in SARAH is that fields and anti-fields transform the same under global Z-symmetries (as for instance SUSY particles do under RpV). That's the origin of the warning. Since it is just a warning, you can ignore it.

Cheers
Florian

[JamesM]

Okay that is good to know!

Thanks for confirming this so quickly.

Cheers,
James