A saddle-point expansion around the true, interacting-theory saddle point gives an analytic inverse transform of the QCD resummed form factor that matches exact numerical inversion, unlike the standard Taylor expansion around the free saddle point.
A model for next-to-leading order threshold resummed form factors
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We present a model for next-to-leading order resummed threshold form factors based on a time-like coupling recently introduced in the framework of small x physics. Improved expressions for the form factors in N-space are obtained which are not plagued by Landau-pole singularities, as the included absorptive effects -- usually neglected -- act as regulators. The physical reason is that, because of faster decay of gluon jets, there is not enough resolution time to observe the Landau pole. Our form factors reduce to the standard ones when the absorptive parts related to the coupling are neglected. The inverse transform from N-space to x-space can be done directly without any prescription and we obtain analytical expressions for the form factors, which are well defined in all x-space.
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Saddle-point method for resummed form factors in QCD
A saddle-point expansion around the true, interacting-theory saddle point gives an analytic inverse transform of the QCD resummed form factor that matches exact numerical inversion, unlike the standard Taylor expansion around the free saddle point.