Effective four-fermion operators in top physics: A roadmap

We write down a minimal basis for dimension-six gauge-invariant four-fermion operators, with some operator replacements with respect to previous ones which make it simpler for calculations. Using this basis we classify all four-fermion operator contributions involving one or two top quarks. Taking into account the different fermion chiralities, possible colour contractions and independent flavour combinations, a total number of 572 gauge-invariant operators are involved. We apply this to calculate all three-body top decay widths t→dkuid¯j, t→dkei+νj, t→ukuiu¯j, t→ukej+ei−, t→ukν¯jνi (with i,j,k generation indices) mediated by dimension-six four-fermion operators, including the interference with the Standard Model amplitudes when present. All single top production cross sections in pp, pp¯ and e+e− collisions are calculated as well, namely uidk→djt, d¯jdk→u¯it, uid¯j→d¯kt, uiuk→ujt, uiu¯j→u¯kt, e+e−→u¯kt and the charge conjugate processes. We also compute all top pair production cross sections, u¯iuj→tt¯, d¯idj→tt¯, uiuj→tt and e+e−→tt¯. Our results are completely general, without assuming any particular relation among effective operator coefficients.