Towards pp -> VVjj at NLO QCD: Bosonic contributions to triple vector boson production plus jet

In this work, some of the NLO QCD corrections for pp -> VVjj + X are presented. A program in Mathematica based on the structure of FeynCalc which automatically simplifies a set of amplitudes up to the hexagon level of rank 5 has been created for this purpose. We focus on two different topologies. The first involves all the virtual contributions needed for quadruple electroweak vector boson production, i.e. pp -> VVVV + X. In the second, the remaining "bosonic" corrections to electroweak triple vector boson production with an additional jet (pp -> VVV j + X) are computed. We show the factorization formula of the infrared divergences of the bosonic contributions for VVVV and VVVj production with V=(W,Z,gamma). Stability issues associated with the evaluation of the hexagons up to rank 5 are studied. The CPU time of the FORTRAN subroutines rounds the 2 milliseconds and seems to be competitive with other more sophisticated methods. Additionally, in Appendix A the master equations to obtain the tensor coefficients up to the hexagon level in the external momenta convention are presented including the ones needed for small Gram determinants.Comment: 48 pages,16 figure

The Role of the World Court Today

The International Court of Justice (ICJ, also known as theWorld Court) is the principal judicial organ of the United Nations(UN). I have served as a member of the Court for the past twoyears. During that time, I have had the opportunity to speakabout the Court and about international law to a variety ofaudiences throughout the United States. It is a particularprivilege to deliver the Sibley Lecture here at the University ofGeorgia School of Law, an institution that is known for itscommitment to the study of international law and internationalrelations.The ICJ has its roots in the notion that adjudication in a worldcourt can serve as an alternative to war. In the decades since theCourt was established, there have been enormous changes ininternational law and institutions. In particular, there are nowmany other international courts and tribunals,1 and many otherinstitutions contribute to the peaceful resolution of disputes. 2In view of these developments, what is the role of the WorldCourt? The ICJ is charged with a powerful combination offunctions: the resolution of particular disputes between states; theissuance of advisory opinions requested by the United NationsSecurity Council and General Assembly; and the development ofinternational law. This combination of functions, vested in a courtwhich can hear cases from any region of the world, which has thescope to consider all substantive aspects of international law, andwhich is endowed with the stature of the UN\u27s principal judicialorgan gives the World Court a unique and potent role in thepeaceful resolution of disputes

On the parameterization dependence of the energy momentum tensor and the metric

We use results by Kirilin to show that in general relativity the nonleading terms in the energy-momentum tensor of a particle depends on the parameterization of the gravitational field. While the classical metric that is calculated from this source, used to define the leading long-distance corrections to the metric, also has a parameteriztion dependence, it can be removed by a coordinate change. Thus the classical observables are parameterization independent. The quantum effects that emerge within the same calculation of the metric also depend on the parameterization and a full quantum calculation requires the inclusion of further diagrams. However, within a given parameterization the quantum effects calculated by us in a previous paper are well defined. Flaws of Kirilin's proposed alternate metric definition are described and we explain why the diagrams that we calculated are the appropriate ones.Comment: 8 pages, 2 figure

Effective Gravitational Field of Black Holes

The problem of interpretation of the \hbar^0-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order \hbar^0 to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos correcte

Can one see the number of colors in eta, eta-prime --> pi^+ pi^- gamma?

We investigate the decays eta, eta-prime --> pi^+ pi^- gamma up to next-to-leading order in the framework of the combined 1/N_c and chiral expansions. Counter terms of unnatural parity at next-to-leading order with unknown couplings are important to acommodate the results both to the experimental decay width and the photon spectrum. The presence of these coefficients does not allow for a determination of the number of colors from these decays.Comment: 8 pages, 2 figure

K -> pi pi Electroweak Penguins in the Chiral Limit

We report on dispersive and finite energy sum rule analyses of the electroweak penguin matrix elements in the chiral limit. We accomplish the correct perturbative matching (scale and scheme dependence) at NLO in alpha_s, and we describe two different strategies for numerical evaluation.Comment: 4 pages, 2 figures. Contribution to QCD02, International Conference on Quantum Chromo-Dynamics, Montpellier (France), July 2-9 200