Model definitions in Matchete

Defining a model is the starting point of any Matchete workflow. A model specifies the gauge symmetry structure, all fields (together with their representations and mass assignments), all coupling constants, and the interaction Lagrangian.

---

Gauge groups

Gauge groups are defined with DefineGaugeGroup. Both Abelian $U(1)$ and non-Abelian groups are supported. For example, the Standard Model gauge group $SU(3)_c \times SU(2)_L \times U(1)_Y$ is defined as:

DefineGaugeGroup[SU3c, SU3, gs, G, Abelian -> False];
DefineGaugeGroup[SU2L, SU2, gw, W, Abelian -> False];
DefineGaugeGroup[U1Y,  U1,  g1, B, Abelian -> True ];

For most applications the SM gauge group is already available through predefined modelfiles that cna be loaded using LoadModel (see below).

---

Fields

Fields are introduced with DefineField. Each field requires a spin specification (Scalar, Fermion, or Vector), and may carry gauge or flavor indices. The Mass option distinguishes heavy fields (to be integrated out) from light ones:

(* A heavy real scalar singlet *)
DefineField[S, Scalar, SelfConjugate -> True, Mass -> {Heavy, M}];

(* A heavy Dirac fermion in the fundamental of SU(3)c *)
DefineField[Psi, Fermion, SelfConjugate -> False,
  Mass    -> {Heavy, MPsi},
  Indices -> {SU3c[fund]}
];

Fields charged under multiple gauge groups or carrying flavor indices can be defined by supplying a list to the Indices option.

---

Couplings

All free parameters beyond the masses set in DefineField are introduced with DefineCoupling:

DefineCoupling[lam, SelfConjugate -> True];   (* real *)
DefineCoupling[yuk, SelfConjugate -> False];  (* complex *)

---

Writing the Lagrangian

Once all building blocks are in place, the Lagrangian can be written in a notation close to the pen-and-paper form. The kinetic and mass terms are generated automatically by FreeLag:

Lkin = FreeLag[S] + FreeLag[Psi];
Lint = -lam[]/2 (Bar@H[i] H[i]) S[]^2;
L    = Lkin + Lint //RelabelIndices;

RelabelIndices assigns canonical dummy indices and should be applied after assembling the Lagrangian. Bar denotes Hermitian conjugation for complex scalars and the Dirac bar for fermions.

---

Loading a predefined model

For common theories, Matchete ships a library of model files that can be loaded directly with LoadModel:

LSM = LoadModel["SM"];

A catalogue of available models is maintained in the model database. For a full worked example of a model definition see the Quickstart.