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The Table Vertices contains interaction vertices.
The first four fields
, , , include the names of the interacting particles.
These fields
must contain particle names in CompHEP notation. may be
empty. The last two fields 'Factor' and 'LorentzPart' define a
vertex itself. Let be the action, then a functional derivative of
over fields is represented as
Here and denote 4-momenta and Lorentz indices. The brackets
[ ] are used to mark the optional parts of expression. Thus,
, , and appear only in the case of four particle
vertex. In the case of anti-commuting fields the right-side
derivatives are assumed. The Fourier transformation is defined by
'LorentzPart' must be a tensor or Dirac -matrix expression. Coefficients of this expression are polynomials of the model identifiers and scalar products of momenta. The division '/' operator is forbidden in 'LorentzPart'. It must be transferred to the 'Factor' field.
Similar to the Reduce notation, in order to construct scalar products of momenta, momentum components, and metric tensors we use the dot symbol, for example,
To implement the Dirac -matrix with index we
use a symbol , whereas denotes
. Anti-commutation
relations for matrices should be written as
The matrix is denoted by . It is defined by equation
The number of fermion fields in one vertex must be two or zero. If you would like to implement a four-fermion interaction, use an auxiliary unphysical field which may be constructed by means of the '*' symbol in the 'Aux' column of the particle table (see Section ).
CompHEP interprets the anti-particle spinor field as the Hermitian
conjugated particle field, rather than the Dirac conjugated one. Also it is
assumed that all spinor fields are written in the
Majorana basis and the matrix of C-conjugation is equal to
1. After substitution
all possible vertices could be
written as
Note that structures like and are forbidden for the vertex with fermions. In order to implement these structures use the equation (10).
Let us note that by definition (8) the LorentzPart
has the corresponding symmetry property in the case when
identical particles appear in one vertex. This symmetry is not checked by
CompHEP, but its absence will lead to wrong results. The following
equation may be used to check the symmetry in the case of fermion vertex:
ColorStructure is substituted by CompHEP automatically. For a
colorless particle vertex it is equal to 1. For
and for
vertices the unity tensor is substituted. If CompHEP meets
a vertex
with three particles in the adjoint representation
,
it substitutes