The theory of leptoquarks used by this generator starts from
an effective lagrangian with the most general dimensionless
invariant couplings of scalar
and vector leptoquarks satisfying baryon and lepton number
conservation [2].
From the effective lagrangian one obtains the various
partial leptoquark decay widths,
.
For the scalar (S) and vector (V) leptoquarks we have
where denote the leptoquark couplings
to a particular final state and
is the
leptoquark mass.
The total widths are obtained by summing over all possible
final states.
In the limit of very narrow width ( )
leptoquarks, the cross-section can be approximated (narrow
width approximation) by
where the parton density q is evaluated at the resonance
peak and QCD scale
.
For some leptoquarks the parton density is for anti-quarks,
.
In addition to integrating the full cross-section, LQUARK\
calculates the cross-section using two different narrow width
approximations for comparison.
The above formula is obtained by using a delta-function approximation
to the Briet-Wigner resonance.
The total cross-section is also estimated by assuming the parton
densities change very little within the resonance region.
Adapting the notation of reference 9 and using the calculated amplitudes in
reference 2, the possible leptoquark reactions proceeding
from an electron beam are as follows.
where q is either a u- or d-type quark.
An equivalent set of processes have also been coded for a
positron beam.
Whereas processes 1-5 and 11-12 are mainly produced in
collisions, processes 6-10 and 13-14 are
primarily created in the
reactions.
Table 1 gives the quantum numbers, couplings, production and
decay channels for all leptoquarks.
Table 1: Quantum numbers (Q is electric
charge, T is weak isospin and is third component of
isospin), coupling constants, and production and decay
channels for leptoquarks.