High energy resummation of transverse momentum distributions:Higgs in gluon fusion

We derive a general resummation formula for transverse-momentum distributions of hard processes at the leading logarithmic level in the high-energy limit, to all orders in the strong coupling. Our result is based on a suitable generalization of high-energy factorization theorems, whereby all-order resummation is reduced to the determination of the Born-level process but with incoming off-shell gluons. We validate our formula by applying it to Higgs production in gluon fusion in the infinite top mass limit. We check our result up to next-to-leading order by comparison to the high energy limit of the exact expression and to next-to-next-to leading by comparison to NNLL order trasverse momentum (Sudakov) resummation, and we predict the high-energy behaviour at next$^3$-to-leading order. We also show that the structure of the result in the small transverse momentum limit agrees to all orders with general constraints from Sudakov resummation.Comment: 28 pages, 6 figures, Final version published in JHEP: several typos corrected (including in equations

High Energy Resummation of Jet Observables

In this paper we investigate the extension of high energy resummation at LLx accuracy to jet observables. In particular, we present the high energy resummed expression of the transverse momentum distribution of the outgoing parton in the general partonic process $g(q) + g(q) \to g(q) + X$. In order to reach this result, several new ideas are introduced and exploited. First we prove that LLx resummation is achieved by dressing with hard radiation an off-shell gluon initiated LO process even if its on-shell limit is vanishing or trivial. Then we present a gauge-invariant framework where these calculations can be performed by using the modern helicity techniques. Finally, we show a possible way to restore gluon indistinguishability in the final state, which is otherwise lost in the resummation procedure, at all orders in $\alpha_s$ at LLx. All partonic channels are then resummed and cross-checked against fixed-order calculations up to $\mathcal{O}(\alpha_s^3)$Comment: 31 pages, 6 figure

On the Higgs cross section at N3^3LO+N3^3LL and its uncertainty

We consider the inclusive production of a Higgs boson in gluon-fusion and we study the impact of threshold resummation at next-to-next-to-next-to-leading logarithmic accuracy (N$^3$LL) on the recently computed fixed-order prediction at next-to-next-to-next-to-leading order (N$^3$LO). We propose a conservative, yet robust way of estimating the perturbative uncertainty from missing higher (fixed- or logarithmic-) orders. We compare our results with two other different methods of estimating the uncertainty from missing higher orders: the Cacciari-Houdeau Bayesian approach to theory errors, and the use of algorithms to accelerate the convergence of the perturbative series. We confirm that the best convergence happens at $\mu_R=\mu_F=m_H\,/\,2$, and we conclude that a reliable estimate of the uncertainty from missing higher orders on the Higgs cross section at 13 TeV is approximately $\pm4$%.Comment: 27 pages, 6 figures. Version to be published in JHE

Top Quark Pair Production beyond NNLO

We construct an approximate expression for the total cross section for the production of a heavy quark-antiquark pair in hadronic collisions at next-to-next-to-next-to-leading order (N$^3$LO) in $\alpha_s$. We use a technique which exploits the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations, previously introduced and used in the case of Higgs production. We validate our method by comparing to available exact results up to NNLO. We find that N$^3$LO corrections increase the predicted top pair cross section at the LHC by about 4% over the NNLO.Comment: 34 pages, 9 figures; final version, to be published in JHEP; reference added, minor improvement

Meteorological time series forecasting based on MLP modelling using heterogeneous transfer functions

In this paper, we propose to study four meteorological and seasonal time series coupled with a multi-layer perceptron (MLP) modeling. We chose to combine two transfer functions for the nodes of the hidden layer, and to use a temporal indicator (time index as input) in order to take into account the seasonal aspect of the studied time series. The results of the prediction concern two years of measurements and the learning step, eight independent years. We show that this methodology can improve the accuracy of meteorological data estimation compared to a classical MLP modelling with a homogenous transfer function

Bayesian rules and stochastic models for high accuracy prediction of solar radiation

It is essential to find solar predictive methods to massively insert renewable energies on the electrical distribution grid. The goal of this study is to find the best methodology allowing predicting with high accuracy the hourly global radiation. The knowledge of this quantity is essential for the grid manager or the private PV producer in order to anticipate fluctuations related to clouds occurrences and to stabilize the injected PV power. In this paper, we test both methodologies: single and hybrid predictors. In the first class, we include the multi-layer perceptron (MLP), auto-regressive and moving average (ARMA), and persistence models. In the second class, we mix these predictors with Bayesian rules to obtain ad-hoc models selections, and Bayesian averages of outputs related to single models. If MLP and ARMA are equivalent (nRMSE close to 40.5% for the both), this hybridization allows a nRMSE gain upper than 14 percentage points compared to the persistence estimation (nRMSE=37% versus 51%).Comment: Applied Energy (2013