Abstract: There exists a vast literature examining the electroweak (EW) fine-tuning problem in supersymmetric scenarios, but little concerned with the dark matter (DM) one, which should be combined with the former. In this paper, we study this problem in an, as much as possible, exhaustive and rigorous way. We have considered the MSSM framework, assuming that the LSP is the lightest neutralino, chi(0)(1), and exploring the various possibilities for the mass and composition of chi(0)(1), as well as different mechanisms for annihilation of the DM particles in the early Universe (well-tempered neutralinos, funnels and co-annihilation scenarios). We also present a discussion about the statistical meaning of the fine-tuning and how it should be computed for the DM abundance, and combined with the EW fine-tuning. The results are very robust and model-independent and favour some scenarios (like the h-funnel when M-chi 10 is not too close to m(h)/2) with respect to others (such as the pure wino case). These features should be taken into account when one explores “natural SUSY” scenarios and their possible signatures at the LHC and in DM detection experiments.

Abstract: We present a comprehensive study of the determination of the strong coupling from tau decay, using the most recent release of the experimental ALEPH data. We critically review all theoretical strategies used in previous works and put forward various novel approaches which allow one to study complementary aspects of the problem. We investigate the advantages and disadvantages of the different methods, trying to uncover their potential hidden weaknesses and test the stability of the obtained results under slight variations of the assumed inputs. We perform several determinations, using different methodologies, and find a very consistent set of results. All determinations are in excellent agreement, and allow us to extract a very reliable value for alpha(s)(m(tau)(2)). The main uncertainty originates in the pure perturbative error from unknown higher orders. Taking into account the systematic differences between the results obtained with the contour-improved perturbation theory and fixed-order perturbation theory prescriptions, we find alpha((nf=3))(s) (m(tau)(2)) = 0.328 +/- 0.013 which implies alpha((nf=5))(s) (M-Z(2)) = 0.1197 +/- 0.0015.

Abstract: We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes, and the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for gamma* -> q (q) over bar (g), and its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.