Ben. A. Stefanek

We present a discussion on lattice techniques for the simulation of non-canonical field theory circumstances, complementing our previous monograph [1] on canonical cases. We begin by reviewing basic aspects of lattice field theory, including symplectic and non-symplectic evolution algorithms. We then introduce lattice implementations of non-canonical interactions, considering scalars with a non-minimal coupling to gravity, ϕ ² R , non-minimal scalar kinetic theories, 𝒢 _ab ({ ϕ _c }) ∂ _μ ϕ ^a ∂ ^μ ϕ ^b , and axion-like particle (ALP) interactions with Abelian gauge fields, ϕF _μν F̃ ^μν . Next, we discuss methods to set up special field configurations, including the creation of cosmic defect networks towards scaling (e.g. cosmic strings and domain walls), field configurations based on arbitrary power spectra or spatial profiles, and probabilistic methods as required e.g. for thermal configurations. We further extend the notion of non-canonical theories, discussing the discretization of scalar field dynamics in d + 1 dimensions, with d ≠ 3. Unrelated to non-canonical aspects, we also discuss implementation(s) of gravitational wave (GW) dynamics on the lattice. This document represents the theoretical basis for the non-canonical field theory aspects (interactions, initial conditions, dimensionality) and GW dynamics implemented in 𝒞 osmo ℒ attice v2.0 to be released in 2026.

A bstract: A Tera- Z factory, such as FCC-ee or CEPC, will have indirect sensitivity to heavy new physics up to the tens of TeV scale through higher-order loop contributions to precision measurements at the Z pole. These indirect quantum effects may provide complementary, or even better, sensitivity to potential deviations from the Standard Model that are typically thought to best be constrained at leading order at higher energies above the Z pole. We show in the SMEFT framework how accuracy complements energy for operators that modify the Higgs and gauge boson two- and three-point functions, leading to improved projected sensitivities for models such as the real singlet scalar, weakly interacting massive particles, and a custodial weak quadruplet. A thorough Tera- Z programme may thus anticipate aspects of physics runs at higher energies and provide a wider scope of quantum exploration of the TeV scale than had previously been appreciated.

Single Higgs production at FCC-ee probes the Higgs self-coupling at next-to-leading order (NLO). Extracting a bound requires a global analysis accounting for other possible new physics contributions up to NLO. We determine the FCC-ee sensitivity to Higgs self-coupling modifications δ κ λ within the standard model effective field theory framework, including for the first time flavor, LEP, LHC, and FCC-ee observables in a global analysis with all leading NLO effects via one-loop renormalization group evolution, as well as incorporating finite NLO contributions to electroweak precision and Z H observables. The global sensitivity to δ κ λ is estimated by marginalizing over the effects of all other operators, bringing flavor considerations to the fore. We find that, under reasonable assumptions, FCC-ee sensitivity to δ κ λ can exceed that of the HL-LHC.

We present a comprehensive analysis of electroweak, flavor, and collider bounds on the complete set of dimension-six SMEFT operators in the U(2)⁵-symmetric limit. This operator basis provides a consistent framework to describe a wide class of new physics models and, in particular, the motivated class of models where the new degrees of freedom couple mostly to the third generation. By analyzing observables from all three sectors, and consistently including renormalization group evolution, we provide bounds on the effective scale of all 124 U(2)⁵-invariant operators. The relation between flavor-conserving and flavor-violating observables is analyzed taking into account the leading U(2)⁵ breaking in the Yukawa sector, which is responsible for heavy-light quark mixing. We show that under simple, motivated, and non-tuned hypotheses for the parametric size of the Wilson coefficients at the high scale, all present bounds are consistent with an effective scale as low as 1.5 TeV. We also show that a future circular e ⁺ e ⁻ collider program such as FCC-ee would push most of these bounds by an order of magnitude. This would rule out or provide clear evidence for a wide class of compelling new physics models that are fully compatible with present data.