Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.Comment: 12 page

Dual parametrization of GPDs versus the double distribution Ansatz

We establish a link between the dual parametrization of GPDs and a popular parametrization based on the double distribution Ansatz, which is in prevalent use in phenomenological applications. We compute several first forward-like functions that express the double distribution Ansatz for GPDs in the framework of the dual parametrization and show that these forward-like functions make the dominant contribution into the GPD quintessence function. We also argue that the forward-like functions $Q_{2 \nu}(x)$ with $\nu \ge 1$ contribute to the leading singular small-$x_{Bj}$ behavior of the imaginary part of DVCS amplitude. This makes the small-$x_{Bj}$ behavior of \im A^{DVCS} independent of the asymptotic behavior of PDFs. Assuming analyticity of Mellin moments of GPDs in the Mellin space we are able to fix the value of the $D$-form factor in terms of the GPD quintessence function $N(x,t)$ and the forward-like function $Q_0(x,t)$.Comment: 18 pages, 5 figures. A version that appeared in Eur. Phys. J. A. Some of the statements were refined and misprints in the formulas were correcte