With the BackgroundField option, the user may set a field to be non-propagating, i.e., it is treated as a background field. A scalar field background field can be defined with

Background fields are treated as Light fields with a vanishing mass (trying to associate a mass with a background field results in a failure). It does not have a kinetic term associated, and it cannot be passed to FreeLag:

The Charges option is used to specify that the field is charged under one or more U(1) gauge groups. Having defined a U(1) group with DefineGaugeGroup,

it becomes possible to specify the charge of a field under that group. The charge under the group is specified in the format groupName[charge]. Thus to specify a scalar with charge 2, use the option

Charges can also take a list of charges as a value.

The chiral option is used exclusively for fermions. Matchete employs Dirac spinor notation, and the chirality option lets the user specify if the spinor is left- or right-handed or if it is vector-like.

The default option sets the field to be vector-like, which appears from the associated free Lagrangian

Option values LeftHanded or RightHanded designates that the field is chiral, such as

By default such fields are assumed to have a Majorana mass.

A common use case, known from the SM, is to have massless chiral fermions. In that case, one can also invoke the mass option to obtain

The index option specifies all the indices of a field associated with non-Abelian gauged or global groups or simple flavor (generation). Thus, indices are implicitly used to specify the transformation of the field under the non-Abelian gauge groups. First Matchete needs to recognize the index type we wish to specify. For instance defining a gauge group with DefineGaugeGroup automatically defines some common representations, e.g.,

Then we may make a new field with a fundamental representation (fund) of the SU3 group

which now needs to be specified with one index. For instance

Flavor indices for a field are specified in a similar way. Defining a generation index counting 2 generations with DefineFlavorIndex

lets us define a field with that generation index:

We see that the index is of the appropriate type

When more indices are specified for the same field, for instance and SU(3) triplet with 2 generations, the ordering in which the indices are specified informs the ordering of the labels in the field short cut.

We may specify an instance of this field with triplet index a and generation index p by

The mass option is used to specify the label for the default mass of the field (used in FreeLag) and to inform the program whether the field is considered heavy or light for the purposes of matching.

Specifying a heavy mass (the default), produces a generic mass label for the field and sets it as heavy:

In the associated field information, the field now appears with designation heavy:

Specifying a light mass (the default), produces a generic mass label for the field and sets it as light:

In the associated field information, the field now appears with designation light:

Setting the mass to zero also defines it as light, as would be expected. It ensures that no mass term is included in the free Lagrangian:

To use a custom mass label rather than the generic one, one has to specify the label in addition to Light or Heavy. For instance,

When the field has a flavor index, it will default to the assumption of a flavor universal mass:

If the mass of the heavy field is non-universal, it can be defined with a third entry to the list of mass arguments {<Heavy>,<label>,<List of flavor indices>}. Note, that the heavy mass matrix is assumed to be diagonal; hence, it receives just a single diagonal index.

The NiceForm option provides the possibility of defining how the field is displayed in NiceForm. The Default choice uses the label for the field in NiceForm, but this can be changed

This does not change the internal representation of the field f, but we see the difference in the NiceForm display

We can control also the display of the mass, by giving a list of two strings to the option:

The Default value can be used in place of either string to use the default NiceForm that would be associated to the field label.

Self-conjugate allows specifying if a scalar is real, e.g.,

This is reflected both in the generic free Lagrangian

and in complex conjugation (Bar)

Fermions can also be self conjugate

In this case charge conjugation (CConj) returns the original field

The free Lagrangian in this case provides a Majorana mass for the fermion