Higgs and Z boson associated production via gluon fusion in the SM and the 2HDM

We analyse the associated production of Higgs and $Z$ boson via heavy-quark loops at the LHC in the Standard Model and beyond. We first review the main features of the Born $2\to 2$ production, and in particular discuss the high-energy behaviour, angular distributions and $Z$ boson polarisation. We then consider the effects of extra QCD radiation as described by the $2 \to 3$ loop matrix elements, and find that they dominate at high Higgs transverse momentum. We show how merged samples of 0-- and 1--jet multiplicities, matched to a parton shower can provide a reliable description of differential distributions in $ZH$ production. In addition to the Standard Model study, results in a generic two-Higgs-doublet-model are obtained and presented for a set of representative and experimentally viable benchmarks for $Zh^0$, $ZH^0$ and $ZA^0$ production. We observe that various interesting features appear either due to the resonant enhancement of the cross-section or to interference patterns between resonant and non-resonant contributions.Comment: 29 pages, 12 figure

Higgs pair production via gluon fusion in the Two-Higgs-Doublet Model

We study the production of Higgs boson pairs via gluon fusion at the LHC in the Two-Higgs-Doublet Model. We present predictions at NLO accuracy in QCD, matched to parton showers through the MC@NLO method. A dedicated reweighting technique is used to improve the NLO calculation upon the infinite top-mass limit. We perform our calculation within the MadGraph5_aMC@NLO framework, along with the 2HDM implementation based on the NLOCT package. The inclusion of the NLO corrections leads to large K-factors and significantly reduced theoretical uncertainties. We examine the seven 2HDM Higgs pair combinations using a number of representative 2HDM scenarios. We show how the model-specific features modify the Higgs pair total rates and distribution shapes, leading to trademark signatures of an extended Higgs sector.Comment: 39 pages, 10 figures, 11 tables, matching published versio

From contradiction to conciliation:a way to "dualize" sheaves

Our aim is to give some insights about how to approach the formal description of situations where one has to conciliate several contradictory statements, rules, laws or ideas. We show that such a conciliation structure can be naturally defined on a topological space endowed with the set of its closed sets and that this specific structure is a kind of "dualization" of the sheaf concept where "global" and "local" levels are reversed

On algebraic identification of causal functionals

AbstractWe present here a second step in solving the Algebraic Identification Problem for the causal analytic functionals in the sense of Fliess. These functionals are symbolically represented by noncommutative formal power series G=∑w∈Z★〈G|w〉w, where w is a word on a finite-encoding alphabet Z. The problem consists in computing the coefficients 〈G|w〉 from the choice of a finite set of informations on the input/output behaviour of the functional. In a previous work, we already presented a first step: we showed that one can compute the contributions of G relative to a family of noncommutative polynomials gμ with integer coefficients, indexed by the set of partitions. Hence it remains to inverse these relations by computing the words w as linear combinations of the gμ. An answer could be found in two ways: firstly by providing an identification computation tool, secondly by solving the ‘Identifiability Problem’: is the previous identification effectively computable at any order? A computational tool is here presented, in the form of a concise Maple package IDENTALG that computes the polynomials gμ by a block recursive matrix implementation, and allows then to test the identification (when possible) at any order by matrix inversion. It requires a combinatorial study of the differential monomials on the inputs. The computation of a test set covering the identification of 2048 words is presented. This package is given in the widely significant case of functionals depending on ‘a single input with drift part’. It can be used without change in case of ‘two inputs without drift’. It could be extended very easily to the case of ‘several inputs with drift part’. Finally, we discuss the Identifiability Problem: we summarize the current state of our results, and we conclude with a conjecture in a weak form and in a strong form

Approximation of nonlinear dynamic systems by rational series

AbstractGiven an analytic system, we compute a bilinear system of minimal dimension which approximates it up to order k (i.e. the outputs of these two systems have the same Taylor expansion up to order k). The algorithm is based on noncommutative series computation: let s be the generating series of the analytic system; then a rational series g is constructed, whose coefficients are equal to those of s, for all words of length smaller than or equal to k. These words are digitally encoded, in order to simplify the computations of the Hankel matrices of s and g. We then associate with g, a bilinear system, which is a solution to our problem. Another method may be used for computing a bilinear system which approximates a given analytic system (S). We associate with (S) an R-automaton of vector fields and build the truncated automaton by cancelling all the states which have the following property: the length of the shortest successful path labelled by a word that gets through this state is strictly greater than k. Then, the number of states of this truncated automaton yields the dimension (not necessarily minimal) of the state-space