Gauge-invariant top quark form factors frome+e−experiments

Motivated by the possibility of experimental determination of top quark form factors in upcoming ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ experiments, as recently discussed by Atwood and Soni, we show at the one loop level that the conventionally defined magnetic dipole moment (MDM) form factor of the top quark is gauge dependent, in the class of renormalizable (${\mathit{R}}_{\xi }$) gauges. We explicitly calculate its gauge dependence, which, due to the massiveness of the top quark, turns out to be numerically very sizable. We show how to use the S-matrix pinch technique in order to define gauge-independent form factors. The form factors so obtained coincide with those conventionally defined defined only if the latter are calculated in the Feynman gauge (ξ=1). The real and imaginary parts of the gauge-independent MDM form factor are calculated and their depenence on the top quark and Higgs boson masses is discussed. Most noticeably, the dependence on the Higgs boson mass turns out to be stronger than that of the cross section as a whole.