We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling all these computations — parton-level fixed order, shower-matched, merged — in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV e + e − collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.

We present NNPDF3.0, the first set of parton distribution functions (PDFs) determined with a methodology validated by a closure test. NNPDF3.0 uses a global dataset including HERA-II deep-inelastic inclusive cross-sections, the combined HERA charm data, jet production from ATLAS and CMS, vector boson rapidity and transverse momentum distributions from ATLAS, CMS and LHCb, W +c data from CMS and top quark pair production total cross sections from ATLAS and CMS. Results are based on LO, NLO and NNLO QCD theory and also include electroweak corrections. To validate our methodology, we show that PDFs determined from pseudo-data generated from a known underlying law correctly reproduce the statistical distributions expected on the basis of the assumed experimental uncertainties. This closure test ensures that our methodological uncertainties are negligible in comparison to the generic theoretical and experimental uncertainties of PDF determination. This enables us to determine with confidence PDFs at different perturbative orders and using a variety of experimental datasets ranging from HERA-only up to a global set including the latest LHC results, all using precisely the same validated methodology. We explore some of the phenomenological implications of our results for the upcoming 13 TeV Run of the LHC, in particular for Higgs production cross-sections.

We perform a combined fit to global neutrino oscillation data available as of fall 2016 in the scenario of three-neutrino oscillations and present updated allowed ranges of the six oscillation parameters. We discuss the differences arising between the consistent combination of the data samples from accelerator and reactor experiments compared to partial combinations. We quantify the confidence in the determination of the less precisely known parameters θ 23, δ CP, and the neutrino mass ordering by performing a Monte Carlo study of the long baseline accelerator and reactor data. We find that the sensitivity to the mass ordering and the θ 23 octant is below 1σ. Maximal θ 23 mixing is allowed at slightly more than 90% CL. The best fit for the CP violating phase is around 270°, CP conservation is allowed at slightly above 1σ, and values of δ CP ≃ 90° are disfavored at around 99% CL for normal ordering and higher CL for inverted ordering.

The version 3.0 of the Delphes fast-simulation is presented. The goal of Delphes is to allow the simulation of a multipurpose detector for phenomenological studies. The simulation includes a track propagation system embedded in a magnetic field, electromagnetic and hadron calorimeters, and a muon identification system. Physics objects that can be used for data analysis are then reconstructed from the simulated detector response. These include tracks and calorimeter deposits and high level objects such as isolated electrons, jets, taus, and missing energy. The new modular approach allows for greater flexibility in the design of the simulation and reconstruction sequence. New features such as the particle-flow reconstruction approach, crucial in the first years of the LHC, and pile-up simulation and mitigation, which is needed for the simulation of the LHC detectors in the near future, have also been implemented. The Delphes framework is not meant to be used for advanced detector studies, for which more accurate tools are needed. Although some aspects of Delphes are hadron collider specific, it is flexible enough to be adapted to the needs of electron-positron collider experiments.

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

We present a global analysis of solar, atmospheric, reactor and accelerator neutrino data in the framework of three-neutrino oscillations based on data available in summer 2014. We provide the allowed ranges of the six oscillation parameters and show that their determination is stable with respect to uncertainties related to reactor neutrino and solar neutrino flux predictions. We find that the maximal possible value of the Jarlskog invariant in the lepton sector is 0.033 ±0.010 (±0.027) at the 1σ (3σ) level and we use leptonic unitarity triangles to illustrate the ability of global oscillation data to obtain information on CP violation. We discuss “tendencies and tensions” of the global fit related to the octant of θ 23 as well as the CP violating phase δ CP. The favored values of δ CP are around 3π/2 while values around π/2 are disfavored at about Δχ2 ≃6. We comment on the non-trivial task to assign a confidence level to this Δχ 2 value by performing a Monte Carlo study of T2K data.

A test of lepton universality, performed by measuring the ratio of the branching fractions of the B 0 → K *0 μ + μ − and B 0 → K *0 e + e − decays, R K * 0 $$ {R}_{K^{*0}} $$ , is presented. The K *0 meson is reconstructed in the final state K + π −, which is required to have an invariant mass within 100 MeV/c 2 of the known K *(892)0 mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of about 3 fb−1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The ratio is measured in two regions of the dilepton invariant mass squared, q 2, to be R K * 0 = 0.66 − + 0.07 0.11 stat ± 0.03 syst f o r 0.045 < q 2 < 1.1 GeV 2 / c 4 , 0.69 − + 0.07 0.11 stat ± 0.05 syst f o r 1.1 < q 2 < 6.0 GeV 2 / c 4 . $$ {R}_{K^{*0}}=\left\{\begin{array}{l}{0.66_{-}^{+}}_{0.07}^{0.11}\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right)\kern1em \mathrm{f}\mathrm{o}\mathrm{r}\kern1em 0.045<{q}^2<1.1\kern0.5em {\mathrm{GeV}}^2/{c}^4,\hfill \\ {}{0.69_{-}^{+}}_{0.07}^{0.11}\left(\mathrm{stat}\right)\pm 0.05\left(\mathrm{syst}\right)\kern1em \mathrm{f}\mathrm{o}\mathrm{r}\kern1em 1.1<{q}^2<6.0\kern0.5em {\mathrm{GeV}}^2/{c}^4.\hfill \end{array}\right. $$ The corresponding 95.4% confidence level intervals are [0.52, 0.89] and [0.53, 0.94]. The results, which represent the most precise measurements of R K * 0 $$ {R}_{K^{*0}} $$ to date, are compatible with the Standard Model expectations at the level of 2.1–2.3 and 2.4–2.5 standard deviations in the two q 2 regions, respectively.

We extract from data the parameters of the Higgs potential, the top Yukawa coupling and the electroweak gauge couplings with full 2-loop NNLO precision, and we extrapolate the SM parameters up to large energies with full 3-loop NNLO RGE precision. Then we study the phase diagram of the Standard Model in terms of high-energy parameters, finding that the measured Higgs mass roughly corresponds to the minimum values of the Higgs quartic and top Yukawa and the maximum value of the gauge couplings allowed by vacuum metastability. We discuss various theoretical interpretations of the near-criticality of the Higgs mass.

An angular analysis of the B 0 → K *0(→ K + π −)μ + μ − decay is presented. The dataset corresponds to an integrated luminosity of 3.0 fb−1 of pp collision data collected at the LHCb experiment. The complete angular information from the decay is used to determine CP-averaged observables and CP asymmetries, taking account of possible contamination from decays with the K + π − system in an S-wave configuration. The angular observables and their correlations are reported in bins of q 2, the invariant mass squared of the dimuon system. The observables are determined both from an unbinned maximum likelihood fit and by using the principal moments of the angular distribution. In addition, by fitting for q 2-dependent decay amplitudes in the region 1.1 < q 2 < 6.0 GeV2/c 4, the zero-crossing points of several angular observables are computed. A global fit is performed to the complete set of CP-averaged observables obtained from the maximum likelihood fit. This fit indicates differences with predictions based on the Standard Model at the level of 3.4 standard deviations. These differences could be explained by contributions from physics beyond the Standard Model, or by an unexpectedly large hadronic effect that is not accounted for in the Standard Model predictions.

MadGraph 5 is the new version of the MadGraph matrix element generator, written in the Python programming language. It implements a number of new, efficient algorithms that provide improved performance and functionality in all aspects of the program. It features a new user interface, several new output formats including C++ process libraries for Pythia 8, and full compatibility with FeynRules for new physics models implementation, allowing for event generation for any model that can be written in the form of a Lagrangian. MadGraph 5 builds on the same philosophy as the previous versions, and its design allows it to be used as a collaborative platform where theoretical, phenomenological and simulation projects can be developed and then distributed to the high-energy community. We describe the ideas and the most important developments of the code and illustrate its capabilities through a few simple phenomenological examples.

Relative entropy between two states in the same Hilbert space is a fundamental statistical measure of the distance between these states. Relative entropy is always positive and increasing with the system size. Interestingly, for two states which are infinitesimally different to each other, vanishing of relative entropy gives a powerful equation ΔS = ΔH for the first order variation of the entanglement entropy ΔS and the expectation value of the modular Hamiltonian ΔH. We evaluate relative entropy between the vacuum and other states for spherical regions in the AdS/CFT framework. We check that the relevant equations and inequalities hold for a large class of states, giving a strong support to the holographic entropy formula. We elaborate on potential uses of the equation ΔS = ΔH for vacuum state tomography and obtain modified versions of the Bekenstein bound.

We present the first complete next-to-next-to-leading order analysis of the Standard Model Higgs potential. We computed the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling (λ) and the Higgs mass (M h ), reducing the theoretical uncertainty in the determination of the critical value of M h for vacuum stability to 1 GeV. While λ at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98 % C.L. for M h < 126 GeV. Possible consequences of the near vanishing of λ at the Planck scale, including speculations about the role of the Higgs field during inflation, are discussed.

We argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, and (iii) the infalling observer encounters nothing unusual at the horizon. Perhaps the most conservative resolution is that the infalling observer burns up at the horizon. Alternatives would seem to require novel dynamics that nevertheless cause notable violations of semiclassical physics at macroscopic distances from the horizon.

We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.

The SYK model consists of N ≫ 1 fermions in 0 + 1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the SchwingerDyson equation and compute the spectrum of two-particle states in SYK, finding both a continuous and discrete tower. The four-point function is expressed as a sum over the spectrum. The sum over the discrete tower is evaluated.

The discovery by the ATLAS and CMS experiments of a new boson with mass around 125 GeV and with measured properties compatible with those of a Standard-Model Higgs boson, coupled with the absence of discoveries of phenomena beyond the Standard Model at the TeV scale, has triggered interest in ideas for future Higgs factories. A new circular e+e− collider hosted in a 80 to 100 km tunnel, TLEP, is among the most attractive solutions proposed so far. It has a clean experimental environment, produces high luminosity for top-quark, Higgs boson, W and Z studies, accommodates multiple detectors, and can reach energies up to the $$ \mathrm{t}\overline{\mathrm{t}} $$ threshold and beyond. It will enable measurements of the Higgs boson properties and of Electroweak Symmetry-Breaking (EWSB) parameters with unequalled precision, offering exploration of physics beyond the Standard Model in the multi-TeV range. Moreover, being the natural precursor of the VHE-LHC, a 100 TeV hadron machine in the same tunnel, it builds up a long-term vision for particle physics. Altogether, the combination of TLEP and the VHE-LHC offers, for a great cost effectiveness, the best precision and the best search reach of all options presently on the market. This paper presents a first appraisal of the salient features of the TLEP physics potential, to serve as a baseline for a more extensive design study.

We present an up-to-date global analysis of solar, atmospheric, reactor, and accelerator neutrino data in the framework of three-neutrino oscillations. We provide results on the determination of θ 13 from global data and discuss the dependence on the choice of reactor fluxes. We study in detail the statistical significance of a possible deviation of θ 23 from maximal mixing, the determination of its octant, the ordering of the mass states, and the sensitivity to the CP violating phase, and discuss the role of various complementary data sets in those respects.

BMS+ transformations act nontrivially on outgoing gravitational scattering data while preserving intrinsic structure at future null infinity ( ℐ $$ \mathrm{\mathcal{I}} $$ +). BMS− transformations similarly act on ingoing data at past null infinity ( ℐ $$ \mathrm{\mathcal{I}} $$ −). In this paper we apply — within a suitable finite neighborhood of the Minkowski vacuum — results of Christodoulou and Klainerman to link ℐ $$ \mathrm{\mathcal{I}} $$ + to ℐ $$ \mathrm{\mathcal{I}} $$ − and thereby identify “diagonal” elements BMS0 of BMS+ × BMS−. We argue that BMS0 is a nontrivial infinite-dimensional symmetry of both classical gravitational scattering and the quantum gravity S $$ \mathcal{S} $$ -matrix. It implies the conservation of net accumulated energy flux at every angle on the conformal S 2 at ℐ $$ \mathrm{\mathcal{I}} $$ . The associated Ward identity is shown to relate S-matrix elements with and without soft gravitons. Finally, BMS0 is recast as a U(1) Kac-Moody symmetry and an expression for the Kac-Moody current is given in terms of a certain soft graviton operator on the boundary of ℐ $$ \mathrm{\mathcal{I}} $$ .

We present a detailed discussion of the current theoretical and experimental situation of the anomaly in the angular distribution of B → K * (→ Kπ)μ + μ −, observed at LHCb in the 1 fb−1 dataset and recently confirmed by the 3 fb−1 dataset. The impact of this data and other recent measurements on b → sℓ + ℓ − transitions (ℓ = e, μ) is considered. We review the observables of interest, focusing on their theoretical uncertainties and their sensitivity to New Physics, based on an analysis employing the QCD factorisation approach including several sources of hadronic uncertainties (form factors, power corrections, charm-loop effects). We perform fits to New Physics contributions including experimental and theoretical correlations. The solution that we proposed in 2013 to solve the B → K * μ + μ − anomaly, with a contribution C 9 N P ≃ − 1 $$ {\mathcal{C}}_9^{\mathrm{NP}}\simeq -1 $$ , is confirmed and reinforced. A wider range of New-Physics scenarios with high significances (between 4 and 5 σ) emerges from the fit, some of them being particularly relevant for model building. More data is needed to discriminate among them conclusively. The inclusion of b → se + e − observables increases the significance of the favoured scenarios under the hypothesis of New Physics breaking lepton flavour universality. Several tests illustrate the robustness of our conclusions.