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We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed graphs (digraphs). FOPT is a coordinate space analogue of time-ordered perturbation theory and loop-tree duality, but it has the advantage of having combinatorial and canonical Feynman rules, combined with a simplified iε dependence of the resulting integrals. Moreover, we introduce a novel digraph-based representation for the S-matrix. The associated integrals involve the Fourier transform of the flow polytope. Due to this polytope’s properties, our S-matrix representation exhibits manifest infrared singularity factorization on a per-diagram level. Our findings reveal an interesting interplay between spurious singularities and Fourier transforms of polytopes., Journal of High Energy Physics, 2023 (1), ISSN:1126-6708, ISSN:1029-8479

The Standard Model Effective Field Theory (SMEFT) is the parametrization chosen to interpret many modern measurements. We have recently discussed, building on the work of other groups, that its overall framework can be experimentally tested, beyond simply constraining its parameters. This is because the Higgs Effective Field Theory (HEFT) is somewhat more general, as it does not assume that the Higgs boson $h$ needs to be embedded in a complex doublet $H$ on which the Standard Model (SM) and SMEFT are built. As a result, the HEFT parameter spaces for the various relevant channels contains hypersurfaces over which one may use SMEFT to describe data. If experimental measurements of HEFT's parameters in any of those various channels yield a point outside of any of the hypersurfaces, SMEFT is falsified; meanwhile, its framework remains appropriate (in particular, as long as the SM remains compatible with data). A common necessity of the various possible tests is that processes involving different number of Higgs bosons (maintaining the number and nature of other particles unchanged) need to be contrasted., Comment: 8 pages, 5 plots, intended for the proceedings of the XVth International Conference on Quark Confinement and the Hadron Spectrum, August 2022, Stavanger; submitted to EPJ Web of Conferences

Effective Field Theories (EFTs) for Goldstone Boson scattering at a low order allow the computation of near--threshold observables in terms of a few coefficients arranged by a counting. As a matter of principle they should make sense up to an energy scale $E\sim 4\pi F$ but the expansion in powers of momentum violates exact elastic unitarity and renders the derivative expansion unreliable at much lower energies. If new--physics deviations from the Standard Model are found and encoded in low-energy coefficients, perhaps at the LHC, it will be profitable to extend the reach of the EFT to regimes where partial waves are saturating unitarity. The methods known in hadron physics as "Unitarized Chiral Perturbation Theory" extend the EFT up to its nominal reach or up to the first new physics resonance or structure (if found below that energy reach) in the partial wave amplitude, but they usually have unknown uncertainties. We recapitulate our analysis of the systematic theory uncertainties of the well known Inverse Amplitude Method (IAM)., Comment: 5 page letter for the proceedings of QCD20, 23TH International Conference in Quantum Chromodynamics (27-20 October 2020, Montpellier)

Effective Field Theories (EFTs) constructed as derivative expansions in powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a controllable approximation to strong dynamics as long as the energy of the interacting particles remains small, as they do not respect exact elastic unitarity. This limits their predictive power towards new physics at a higher scale if small separations from the Standard Model are found at the LHC or elsewhere. Unitarized chiral perturbation theory techniques have been devised to extend the reach of the EFT to regimes where partial waves are saturating unitarity, but their uncertainties have hitherto not been addressed thoroughly. Here we take one of the best known of them, the Inverse Amplitude Method (IAM), and carefully following its derivation, we quantify the uncertainty introduced at each step. We compare its hadron ChPT and its electroweak sector Higgs EFT applications. We find that the relative theoretical uncertainty of the IAM at the mass of the first resonance encountered in a partial-wave is of the same order in the counting as the starting uncertainty of the EFT at near-threshold energies, so that its unitarized extension should \textit{a priori} be expected to be reasonably successful. This is so provided a check for zeroes of the partial wave amplitude is carried out and, if they appear near the resonance region, we show how to modify adequately the IAM to take them into account., Revised version, 47 pages in SciPost format, with 13 captioned figures

Higgs Effective Field Theory (HEFT) is deployed to study elastic vector-boson scattering at the high LHC energies. The interaction is strong over most of the parameter space, with the minimal Standard Model being a remarkable exception. One-loop HEFT complemented with dispersion relations and the Equivalence Theorem leads to two different unitarization methods which produce analytical amplitudes corresponding to different approximate solutions to the dispersion relations: the Inverse Amplitude method (IAM) and the N/D method. The partial waves obtained can show poles in the second Riemann sheet whose natural interpretation is that of dynamical resonances with masses and widths depending on the starting HEFT parameters. Different unitarizations yield qualitatively, and in many cases quantitatively, very similar results. The amplitudes obtained provide realistic resonant and nonresonant cross sections to be compared with and to be used for a proper interpretation of the LHC data., Comment: 4 pages, 3 plots, for the proceedings of the EPS-HEP2019 Conference- 10-17 July, 2019 Ghent, Belgium

We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Unification scale, extending the Renormalization Group Equations in the perturbative regime to two-loops and matching to the Dyson-Schwinger Equations in the strong coupling regime., Comment: 8 pages, 12 plots