A Model for Next-to-leading Order Threshold Resummed Form Factors

We present a model for next-to-leading order resummed threshold form factors based on a time-like coupling. Since the latter acts as a regulator for Landau-pole singularities, our form factors are regular for any value of the Mellin variable N ; they reduce to the standard ones when absorptive parts related to the coupling are neglected. e-mail address: [email protected] e-mail address: [email protected] Resummation of large infrared logarithms in form factors and shape variables is essential in order to predict accurate cross sections [1, 2, 3, 4, 5]. In this note we present a model for next-to-leading order resummed form factors based on the time-like coupling considered in [6] (see also [7]). The usual expression for resummed threshold form factors in N -space is [3, 4, 5]: fN(αS) = exp ∫ 1 0 dz z − 1 1− z { ∫ Q(1−z) Q(1−z) dk t k2 t [ A1 αS(k 2 t ) +A2 αS(k 2 t ) 2 + · · · ] + + B1 αS(Q (1− z)) + · · · + D1 αS(Q (1− z)) + · · · } . (1) Q is the hard scale of the process. A1, A2, · · ·B1, · · ·D1, · · · are the first coefficients of the functions A (αS), B (αS) and D (αS): A (αS) = A1αS +A2α 2 S + · · · , B (αS) = B1αS +B2α 2 S + · · · , D (αS) = D1αS +D2α 2 S + · · · . (2) A (αS) describes the emission of partons which are both soft and collinear, B (αS) describes hard and collinear partons while D (αS) describe partons which are soft and at large angles. The knowledge of the quantities A1, A2, B1 and D1 is needed for next-to-leading order resummation. For instance, in the case of the thrust distribution we have [8]: A1 = 2CF π , A2 = 2CF π2 [