The lowest order Feynman diagrams for leptoquark production in
electron-positron annihilation ( 
) are
straightforward to evaluate using the general couplings from the
effective Lagrangian[1].
In general, the pair production amplitudes for the s-channel and
t-channel processes can interfere and the differential cross-section
for the production of scalar leptoquarks is given by three terms.
where 
and 
denote the photon and Z-boson
s-channel exchange terms, and 
is the t-channel exchange
term.
The sum is over electron polarizations and 
are the
generalized couplings.
is the polar angle and 
is
a kinematic threshold factor.
Similarly the differential cross-section for the production of vector leptoquarks is
From the effective lagrangian one can obtain 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.
Table 1 gives the quantum numbers, couplings and decay channels for
all leptoquarks.
We have adapted the notation of reference 4 
.
The states in table 1 are the charge conjugate states of those in
reference 1.
Table 1: Quantum numbers (Q is the electric charge, T
is the weak isospin and 
is the third component of isospin),
coupling constants and decay channels for leptoquarks.