Jiayin Gu

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.

A bstract: Understanding the implication of positivity bounds on loop-generated dim-8 operator coefficients is a nontrivial task, as these bounds only strictly hold when all the contributions are included in the dispersion relation up to a certain loop order in the UV theory. As a step towards more realistic gauge theories such as the Standard Model, in this paper we study the positivity bounds in the Scalar QED Effective Field Theory (EFT) from the scalar-photon scattering ( γϕ → γϕ ) and the photon-photon scattering ( γγ → γγ ), derived from the dispersion relation of the full one-loop EFT amplitudes. Assuming the UV theory is weakly coupled and all heavy particles have spin ≤ 1, the leading dim-8 interaction for both amplitudes are generated at the one-loop level in the UV theory. Gauge invariance imposes strong constraints on the loop structures, while potential IR divergences also require careful treatments. Our findings reveal that, for γϕ → γϕ , while the tree-level bound does not necessarily hold, the one-loop β -function of the corresponding coefficient always tends to restore the tree-level bound in the IR, unless its actual loop order in the UV theory is further suppressed. For γγ → γγ , on the other hand, the tree-level positivity bound is still robust at the one-loop level in the UV theory. These findings are verified in two example UV models with a heavy scalar extension. Importantly, the bounds on the β -functions that we obtain should be considered as an accidental feature at one loop, rather than a fundamental property of the theory.

A bstract: Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree level, but would become more obscure when loop effects are important. Using scalar theories as examples, we carefully exam the positivity bounds in a case where the leading contribution to a forward elastic amplitude arises at the one-loop level, and point out certain subtleties in terms of the implications of positivity bounds on the theory parameter space. In particular, the one-loop generated dimension-8 operator coefficients (that would be positive if generated at the tree level), as well as their β -functions are generally not subject to positivity bounds as they might correspond to interference terms of the cross sections under the optical theorem, which could have either sign. A strict positivity bound can only be implied when all contributions at the same loop order are considered, including the ones from dim-4 and dim-6 operator coefficients, which have important effects at the one-loop level. Our results may have important implications on the robustness of experimental tests of positivity bounds.

By tagging one or two intact protons in the forward direction, it is possible to select and measure exclusive photon-fusion processes at the LHC. The same processes can also be measured in heavy ion collisions, and are often denoted as ultraperipheral collisions (UPC) processes. Such measurements open up the possibility of probing certain dimension-8 operators and their positivity bounds at the LHC. As a demonstration, we perform a phenomenological study on the γγ → ℓ ⁺ ℓ ⁻ processes, and find out that the measurements of this process at the HL-LHC provide reaches on a set of dimension-8 operator coefficients that are comparable to the ones at future lepton colliders. We also point out that the γq → γq process could potentially have better reaches on similar types of operators due to its larger cross section, but a more detailed experimental study is need to estimate the signal and background rates of this process. The validity of effective field theory (EFT) and the robustness of the positivity interpretation are also discussed.