We modified the tauola-pythia interface so that it finds and assigns polarisation to $\tau$’s from leptoquark decay.

The various scalar leptoquarks of Eq. (1) have recently been included in herwig [26], which would avoid this limitation that pythia only knows one chiral structure for leptoquark interactions.

We checked that changing the $\tau$ polarisation makes a relatively insignificant change to the bounds.

The numbers are extracted from a histogram.

This means, for instance, that our simulation now includes events with two leptonic $W$’s, which could pass cuts if there are additional QCD jets (this accounts for $\sim 10\%$ of our events at $m_S=200\mathrm{GeV}$).

This factor $\sim 10$ arises from kinematics and counting degrees of freedom. At Tevatron energies, $gg\to S\overline{S}$ and $gg\to t\overline{t}$ are subdominant, so can be neglected in the following. It is simple to show, at leading order, that $4\widehat{\sigma }(q\overline{q}\to S\overline{S})={\beta }^2\widehat{\sigma }(q\overline{q}\to t\overline{t})$. The 4 may be understood from the cancellation of quadratic divergences in the gluon propagator in supersymmetry models, where the top bubble compensates the two scalar bubbles (in and on the gluon line) of two complex scalars ${\tilde{t}}_L$ and ${\tilde{t}}_R$. Whereas the $S\overline{S}$ production cross section corresponds to a scalar bubble in the gluon line for a single complex scalar, there is a relative factor of 4. The ${\beta }^2$ accounts for the remaining factor of $\sim 1/2$ suppressing leptoquark production relative to $t\overline{t}$ for masses $\sim m_t$ at Tevatron energies.