Two-Loop g -> gg Splitting Amplitudes in QCD

Splitting amplitudes are universal functions governing the collinear behavior of scattering amplitudes for massless particles. We compute the two-loop g -> gg splitting amplitudes in QCD, N=1, and N=4 super-Yang-Mills theories, which describe the limits of two-loop n-point amplitudes where two gluon momenta become parallel. They also represent an ingredient in a direct x-space computation of DGLAP evolution kernels at next-to-next-to-leading order. To obtain the splitting amplitudes, we use the unitarity sewing method. In contrast to the usual light-cone gauge treatment, our calculation does not rely on the principal-value or Mandelstam-Leibbrandt prescriptions, even though the loop integrals contain some of the denominators typically encountered in light-cone gauge. We reduce the integrals to a set of 13 master integrals using integration-by-parts and Lorentz invariance identities. The master integrals are computed with the aid of differential equations in the splitting momentum fraction z. The epsilon-poles of the splitting amplitudes are consistent with a formula due to Catani for the infrared singularities of two-loop scattering amplitudes. This consistency essentially provides an inductive proof of Catani's formula, as well as an ansatz for previously-unknown 1/epsilon pole terms having non-trivial color structure. Finite terms in the splitting amplitudes determine the collinear behavior of finite remainders in this formula.Comment: 100 pages, 33 figures. Added remarks about leading-transcendentality argument of hep-th/0404092, and additional explanation of cut-reconstruction uniquenes

Review: intellectual property aspects of plant transformation

One of the recurring themes of the debates concerning the application of genetic transformation technology has been the role of Intellectual Property Rights (IPR). This term covers both the content of patents and the confidential expertise usually related to methodology and referred to as 'Trade Secrets'. This review explains the concepts behind patent protection, and discusses the wide-ranging scope of existing patents that cover all aspects of transgenic technology, from selectable markers and novel promoters to methods of gene introduction. Although few of the patents in this area have any real commercial value, there are a small number of key patents that restrict the 'freedom to operate' of new companies seeking to exploit the methods. Over the last 20 years, these restrictions have forced extensive cross-licensing between ag-biotech companies and have been one of the driving forces behind the consolidation of these companies. Although such issues are often considered of little interest to the academic scientist working in the public sector, they are of great importance in any discussion of the role of 'public-good breeding' and of the relationship between the public and private sectors