Color-dressed recursive relations for multi-parton amplitudes

Remarkable progress inspired by twistors has lead to very simple analytic expressions and to new recursive relations for multi-parton color-ordered amplitudes. We show how such relations can be extended to include color and present the corresponding color-dressed formulation for the Berends-Giele, BCF and a new kind of CSW recursive relations. A detailed comparison of the numerical efficiency of the different approaches to the calculation of multi-parton cross sections is performed.Comment: 31 pages, 4 figures, 6 table

Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems

Two-loop corrections for the correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein and Knecht et.al. We find that as in the one-loop case also at the two loops the correlator has only 3 independent form-factors instead of 4. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C_2(R) alpha_s/pi in the MSbar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non- anomalous thansversal amplitudes. The finite overall alpha_s dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity. Our observations, together with known facts, suggest that in perturbation theory the correlator is proportional to the one-loop term to all orders and that the non- renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator.Comment: 10 pages, 2 Postscript figures, uses axodraw.st

Space-like (vs. time-like) collinear limits in QCD: is factorization violated?

We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of square amplitudes and, more generally, cross sections in hadron--hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-to-next-to-next-to-leading order).Comment: 81 pages, 5 figures, typos corrected in the text, few comments added and inclusion of NOTE ADDED on recent development

Triple collinear splitting functions at NLO for scattering processes with photons

We present splitting functions in the triple collinear limit at next-to-leading order. The computation was performed in the context of massless QCD+QED, considering only processes which include at least one photon. Through the comparison of the IR divergent structure of splitting amplitudes with the expected known behavior, we were able to check our results. Besides that we implemented some consistency checks based on symmetry arguments and cross-checked the results among them. Studying photon-started processes, we obtained very compact results

Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations

The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required in unintegrated and integrated forms. In view of extending the antenna subtraction method to next-to-next-to-leading order (NNLO) calculations at hadron colliders, we derive the full set of initial-initial double real radiation antenna functions in integrated form.Comment: 38 pages; a FORM file with the integrated antennae is included with this submission. arXiv admin note: text overlap with arXiv:1011.6631, arXiv:1107.403

Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations

The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required. In view of extending the antenna subtraction method to next-to-next-to-leading order (NNLO) calculations at hadron colliders, we derive the one-loop initial-initial antenna functions in unintegrated and integrated form.Comment: 24 page