Much ado about leptoquarks: A comprehensive analysis

We examine the phenomenological implications of a $\sim 200\mathrm{GeV}$ leptoquark in light of the recent excess of events at DESY HERA. Given the relative predictions of events rates in $e^{+}p$ versus $e^{-}p,$ we demonstrate that classes of leptoquarks may be excluded, including those contained in ${\mathrm{E}}_6$ grand unified theory (GUT) models. It is shown that future studies with polarized beams at HERA could reveal the chirality of the leptoquark fermionic coupling and that given sufficient luminosity in each $e_{L,R}^{\pm }$ channel the leptoquark quantum numbers could be determined. The implications of 200–220 GeV leptoquarks at the Fermilab Tevatron are examined. While present Tevatron data most likely exclude vector leptoquarks and leptogluons in this mass region, it does allow for scalar leptoquarks. We find that while leptoquarks have little influence on Drell-Yan production, further studies at the Main Injector may be possible in the single production channel provided the Yukawa couplings are sufficiently large. We investigate precision electroweak measurements as well as the process $e^{+}{e}^{-}\to q\overline{q}$ at CERN LEP II and find they provide no further restrictions on these leptoquark models. We then ascertain that cross section and polarization asymmetry measurements at the Next Linear Collider (NLC) provide the only direct mechanism to determine the leptoquark’s electroweak quantum numbers. The single production of leptoquarks in $\gamma e$ collisions by both the back-scattered laser and Weisacker-Williams techniques at the NLC is also discussed. Finally, we demonstrate that we can obtain successful coupling constant unification in models with leptoquarks, both with or without supersymmetry. The supersymmetric case requires the GUT group to be larger than SU(5) such as flipped ${\mathrm{SU}\left(5\right)\mathrm{}\times \mathrm{U}\left(1\right)\mathrm{}}_X.$