This paper describes the physics case for a new fixed target facility at CERN SPS. The SHiP (search for hidden particles) experiment is intended to hunt for new physics in the largely unexplored domain of very weakly interacting particles with masses below the Fermi scale, inaccessible to the LHC experiments, and to study tau neutrino physics. The same proton beam setup can be used later to look for decays of tau-leptons with lepton flavour number non-conservation, [Formula: see text] and to search for weakly-interacting sub-GeV dark matter candidates. We discuss the evidence for physics beyond the standard model and describe interactions between new particles and four different portals-scalars, vectors, fermions or axion-like particles. We discuss motivations for different models, manifesting themselves via these interactions, and how they can be probed with the SHiP experiment and present several case studies. The prospects to search for relatively light SUSY and composite particles at SHiP are also discussed. We demonstrate that the SHiP experiment has a unique potential to discover new physics and can directly probe a number of solutions of beyond the standard model puzzles, such as neutrino masses, baryon asymmetry of the Universe, dark matter, and inflation.

Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be formulated as algorithms suitable for an implementation on a computer. Examples, such as expansions of generalized hypergeometric functions or Appell functions are discussed. As a further application, we give the general solution of a two-loop integral, the so-called C-topology, in terms of multiple nested sums. In addition, we discuss some important properties of nested sums, in particular we show that they satisfy a Hopf algebra.

12 pages, 1 figure. v2: lapsus corrected in the abstractInternational audienceThe ATLAS and CMS experiments observed a particle at the LHC with a mass $\approx 126$ GeV, which is compatible with the Higgs boson of the Standard Model. A crucial question is, if for such a Higgs mass value, one could extrapolate the model up to high scales while keeping the minimum of the scalar potential that breaks the electroweak symmetry stable. Vacuum stability requires indeed the Higgs boson mass to be $M_H \gsim 129 \pm 1$ GeV, but the precise value depends critically on the input top quark pole mass which is usually taken to be the one measured at the Tevatron, $m_t^{\rm exp}=173.2 \pm 0.9$ GeV. However, for an unambiguous and theoretically well-defined determination of the top quark mass one should rather use the total cross section for top quark pair production at hadron colliders. Confronting the latest predictions of the inclusive $p \bar p \to t\bar t +X$ cross section up to next-to-next-to-leading order in QCD to the experimental measurement at the Tevatron, we determine the running mass in the $\bar{\rm MS}$-scheme to be $m_t^{\bar{\rm MS}}(m_t) = 163.3 \pm 2.7$ GeV which gives a top quark pole mass of $m_t^{\rm pole}= 173.3 \pm 2.8$ GeV. This leads to the vacuum stability constraint $M_H \geq 129.4 \pm 5.6$ GeV to which a $\approx 126$ GeV Higgs boson complies as the uncertainty is large. A very precise assessment of the stability of the electroweak vacuum can only be made at a future high-energy electron-positron collider, where the top quark pole mass could be determined with a few hundred MeV accuracy

We present a determination of parton distribution functions (ABM11) and the strong coupling constant s at next-to-leading order and next-to-next-to-leading order (NNLO) in QCD based on world data for deep-inelastic scattering and fixed-target data for the Drell-Yan process. The analysis is performed in the fixed-flavor number scheme for n f ¼ 3, 4, 5 and uses the MS scheme for s and the heavy-quark masses. At NNLO we obtain the value s ðM Z Þ ¼ 0:1134 AE 0:0011. The fit results are used to compute benchmark cross sections at hadron colliders to NNLO accuracy and to compare to data from the LHC.

We present an update of the theoretical predictions for the cross section of top-quark pair production at Tevatron and LHC. In particular we employ improvements due to soft gluon resummation at next-to-next-to-leading logarithmic accuracy. We expand the resummed results and derive analytical finite-order cross sections through next-to-next-to-leading order which are exact in all logarithmically enhanced terms near threshold. These results are the best present estimates for the top-quark pair production cross section. We investigate the scale dependence as well as the sensitivity on the parton luminosities.