Efficient Color-Dressed Calculation of Virtual Corrections

With the advent of generalized unitarity and parametric integration techniques, the construction of a generic Next-to-Leading Order Monte Carlo becomes feasible. Such a generator will entail the treatment of QCD color in the amplitudes. We extend the concept of color dressing to one-loop amplitudes, resulting in the formulation of an explicit algorithmic solution for the calculation of arbitrary scattering processes at Next-to-Leading order. The resulting algorithm is of exponential complexity, that is the numerical evaluation time of the virtual corrections grows by a constant multiplicative factor as the number of external partons is increased. To study the properties of the method, we calculate the virtual corrections to $n$-gluon scattering.Comment: 48 pages, 23 figure

Indirect (source-free) integration method. II. Self-force consistent radial fall

We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force. The Mode-Sum regularisation is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the self-force through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in Int. J. Geom. Meth. Mod. Phys., 11, 1450090 (2014).Comment: To appear in Int. J. Geom. Meth. Mod. Phy

Azimuthal asymmetries in QCD hard scattering: infrared safe but divergent

We consider high-mass systems of two or more particles that are produced by QCD hard scattering in hadronic collisions. We examine the azimuthal correlations between the system and one of its particles. We point out that the perturbative QCD computation of such azimuthal correlations and asymmetries can lead to divergent results at fixed perturbative orders. The fixed-order divergences affect basic (and infrared safe) quantities such as the total cross section at fixed (and arbitrary) values of the azimuthal-correlation angle $\varphi$. Examples of processes with fixed-order divergences are heavy-quark pair production, associated production of vector bosons and jets, dijet and diboson production. A noticeable exception is the production of high-mass lepton pairs through the Drell--Yan mechanism of quark-antiquark annihilation. However, even in the Drell--Yan process, fixed-order divergences arise in the computation of QED radiative corrections. We specify general conditions that produce the divergences by discussing their physical origin in fixed-order computations. We show lowest-order illustrative results for $\cos(n\varphi)$ asymmetries (with $n=1,2,4,6$) in top-quark pair production and associated production of a vector boson and a jet at the LHC. The divergences are removed by a proper all-order resummation procedure of the perturbative contributions. Resummation leads to azimuthal asymmetries that are finite and computable. We present first quantitative results of such a resummed computation for the $\cos(2\varphi)$ asymmetry in top-quark pair production at the LHC.Comment: 43 pages, 5 eps figure