Abstract
We verify to order alpha_s^4 two previously conjectured relations, valid in four dimensions, between constant terms in threshold resummation (for Deep Inelastic Scattering and the Drell-Yan process) and the second logarithmic derivative of the massless quark form factor. The same relations are checked to all orders in the large beta_0 limit; as a byproduct a dispersive representation of the form factor is obtained. These relations allow to compute in a symmetrical way the three-loop resummation coefficients B_3 and D_3 in terms of the three-loop contributions to the virtual diagonal splitting function and to the quark form factor, confirming results obtained in the literature.
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