Riccardo Torre

Volume 1 of the FCC Feasibility Report presents an overview of the physics case, experimental programme, and detector concepts for the Future Circular Collider (FCC). This volume outlines how FCC would address some of the most profound open questions in particle physics, from precision studies of the Higgs and EW bosons and of the top quark, to the exploration of physics beyond the Standard Model. The report reviews the experimental opportunities offered by the staged implementation of FCC, beginning with an electron-positron collider (FCC-ee), operating at several centre-of-mass energies, followed by a hadron collider (FCC-hh). Benchmark examples are given of the expected physics performance, in terms of precision and sensitivity to new phenomena, of each collider stage. Detector requirements and conceptual designs for FCC-ee experiments are discussed, as are the specific demands that the physics programme imposes on the accelerator in the domains of the calibration of the collision energy, and the interface region between the accelerator and the detector. The report also highlights advances in detector, software and computing technologies, as well as the theoretical tools/reconstruction techniques that will enable the precision measurements and discovery potential of the FCC experimental programme. The content and structure of this report are guided by the scope and priorities defined in the mandate of the FCC Feasibility Study. It is therefore not intended to serve as an exhaustive review of the full physics potential of FCC. Several topics, already covered in earlier reports such as the FCC CDR, are not reiterated here or are addressed only briefly, in alignment with the study’s focus. This volume reflects the outcome of a global collaborative effort involving hundreds of scientists and institutions, aided by a dedicated community-building coordination, and provides a targeted assessment of the scientific opportunities and experimental foundations of the FCC programme.

We study a simplified model of two colourless heavy vector resonances in the singlet representation of SU(2) _L , with zero and unit hypercharge. We discuss mixing with the Standard Model gauge bosons due to electroweak symmetry breaking, semi-analytic formulae for production at proton colliders, requirements to obey the narrow width approximation and selected low energy constraints. We show current LHC constraints and sensitivity projections for the HL-LHC, HE-LHC, SPPC and FCC-hh on the charged and neutral heavy vectors. The utility of the simplified model Lagrangian is demonstrated by matching these results onto three explicit models: a weakly coupled abelian extension of the Standard Model gauge group, a weakly coupled non-abelian extension and a strongly coupled minimal composite Higgs model. All our results are presented in terms of physical resonance masses, using expressions which are accurate even at vector masses near the electroweak scale due to a parameter inversion we derive. We discuss the importance of this inversion and point out that its effect, and the effects of electroweak symmetry breaking, can remain important up to resonance masses of several TeV. Finally, we clarify the relation between this simplified model and the Heavy Vector Triplet (HVT) model, a simplified model for heavy SU(2) _L triplets with zero hypercharge, and provide exact and approximate matching relations.

We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle physics. The study focuses on tests built from univariate integral probability measures: the sliced Wasserstein distance and the mean of the Kolmogorov–Smirnov (KS) statistics, already discussed in the literature, and the novel sliced KS statistic. These metrics can be evaluated in parallel, allowing for fast and reliable estimates of their distribution under the null hypothesis. We also compare these metrics with the recently proposed unbiased Fréchet Gaussian distance and the unbiased quadratic Maximum Mean Discrepancy, computed with a quartic polynomial kernel. We evaluate the proposed tests on various distributions, focusing on their sensitivity to deformations parameterized by a single parameter ε. Our experiments include correlated Gaussians and mixtures of Gaussians in 5, 20, and 100 dimensions, and a particle physics dataset of gluon jets from the JetNet dataset, considering both jet- and particle-level features. Our results demonstrate that one-dimensional-based tests provide a level of sensitivity comparable to other multivariate metrics, but with significantly lower computational cost, making them ideal for evaluating generative models in high-dimensional settings. This methodology offers an efficient, standardized tool for model comparison and can serve as a benchmark for more advanced tests, including machine-learning-based approaches.

We propose the NFLikelihood, an unsupervised version, based on Normalizing Flows, of the DNNLikelihood proposed in [Eur. Phys. J. C 80, 664 (2020)]. We show, through realistic examples, how Autoregressive Flows, based on affine and rational quadratic spline bijectors, are able to learn complicated high-dimensional Likelihoods arising in High Energy Physics (HEP) analyses. We focus on a toy LHC analysis example already considered in the literature and on two Effective Field Theory fits of flavor and electroweak observables, whose samples have been obtained through the HEPFit code. We discuss advantages and disadvantages of the unsupervised approach with respect to the supervised one and discuss a possible interplay between the two.

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth comparison of coupling and autoregressive flows, both based on symmetric (affine) and non-symmetric (rational quadratic spline) bijectors, considering four different architectures: real-valued non-Volume preserving (RealNVP), masked autoregressive flow (MAF), coupling rational quadratic spline (C-RQS), and autoregressive rational quadratic spline (A-RQS). We focus on a set of multimodal target distributions of increasing dimensionality ranging from 4 to 400. The performances were compared by means of different test statistics for two-sample tests, built from known distance measures: the sliced Wasserstein distance, the dimension-averaged one-dimensional Kolmogorov–Smirnov test, and the Frobenius norm of the difference between correlation matrices. Furthermore, we included estimations of the variance of both the metrics and the trained models. Our results indicate that the A-RQS algorithm stands out both in terms of accuracy and training speed. Nonetheless, all the algorithms are generally able, without too much fine-tuning, to learn complicated distributions with limited training data and in a reasonable time of the order of hours on a Tesla A40 GPU. The only exception is the C-RQS, which takes significantly longer to train, does not always provide good accuracy, and becomes unstable for large dimensionalities. All algorithms were implemented using TensorFlow2 and TensorFlow Probability and have been made available on GitHub.

We generalize previous studies on constraining operators of the Standard Model Effective Field Theory using Drell-Yan (DY) measurements to include at the same time all relevant operators and uncertainties. It has been shown that fully differential measurements (triple differential for neutral and double differential for charged) are more sensitive to EFT effects. Nevertheless, due to the finite statistics, the fully differential measurements sacrifice some statistical power on the shape (less invariant mass or transverse momentum bins) in favour of more kinematic variables. We show that when the observables are particularly sensitive to the shape of the distributions, such as the invariant mass of the two leptons in neutral DY, the single differential measurement with more bins, may be as sensitive as the fully differential one, at least for specific EFT operators. This suggests to always supplement fully differential analyses with projections into the relevant distributions evaluated with finer bins.