Leptoquarks

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.

1. ,
2. ,
3. ,
4. ,
5. ,
6. ,
7. ,
8. ,
9. ,
10. ,
11. ,
12. ,
13. or
14. ,

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.