Fakeons, quantum gravity and the correspondence principle

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity.Comment: Proceedings of the conference "Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics", Max Planck Institute for Mathematics in the Sciences, Leipzig, October 2018 - to appear in a book with the same title edited by F. Finster, D. Giulini, J. Kleiner and J. Tolksdorf - 21 page

On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions

We study the low-momentum behaviour of Yang-Mills propagators obtained from Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare the ghost propagator numerical results with the analytical ones obtained by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge, assuming for the truncation a constant ghost-gluon vertex and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order ${\cal O}(q^2)$ is proven to fit pretty well the numerical PT-BFM results. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the numerical PT-BFM propagators tend to behave as the scaling ones. We also show that the scaling solution, implying a diverging ghost dressing function, cannot be a DSE solution in the PT-BFM scheme but an unattainable limiting case.Comment: 16 pages, 2 figs., 2 tabs (updated version to be published in JHEP

Comment on Higgs Inflation and Naturalness

We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.Comment: 5 pages, 1 figure V3: Journal Versio

Strong Double Higgs Production at the LHC

The hierarchy problem and the electroweak data, together, provide a plausible motivation for considering a light Higgs emerging as a pseudo-Goldstone boson from a strongly-coupled sector. In that scenario, the rates for Higgs production and decay differ significantly from those in the Standard Model. However, one genuine strong coupling signature is the growth with energy of the scattering amplitudes among the Goldstone bosons, the longitudinally polarized vector bosons as well as the Higgs boson itself. The rate for double Higgs production in vector boson fusion is thus enhanced with respect to its negligible rate in the SM. We study that reaction in pp collisions, where the production of two Higgs bosons at high pT is associated with the emission of two forward jets. We concentrate on the decay mode hh -> WW^(*)WW^(*) and study the semi-leptonic decay chains of the W's with 2, 3 or 4 leptons in the final states. While the 3 lepton final states are the most relevant and can lead to a 3 sigma signal significance with 300 fb^{-1} collected at a 14 TeV LHC, the two same-sign lepton final states provide complementary information. We also comment on the prospects for improving the detectability of double Higgs production at the foreseen LHC energy and luminosity upgrades.Comment: 54 pages, 26 figures. v2: typos corrected, a few comments and one table added. Version published in JHE

Gauge-independent MS‾\overline{MS} renormalization in the 2HDM

We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on $\overline{MS}$ renormalization of the mixing angles and the soft-$Z_2$-symmetry-breaking scale $M_{sb}$ in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent $S$-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general $R_{\xi}$-gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the $\overline{MS}$ renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.Comment: 52 pages, PDFLaTeX, PDF figures, JHEP version with Eq. (5.23) correcte

Locality in Theory Space

Locality is a guiding principle for constructing realistic quantum field theories. Compactified theories offer an interesting context in which to think about locality, since interactions can be nonlocal in the compact directions while still being local in the extended ones. In this paper, we study locality in "theory space", four-dimensional Lagrangians which are dimensional deconstructions of five-dimensional Yang-Mills. In explicit ultraviolet (UV) completions, one can understand the origin of theory space locality by the irrelevance of nonlocal operators. From an infrared (IR) point of view, though, theory space locality does not appear to be a special property, since the lowest-lying Kaluza-Klein (KK) modes are simply described by a gauged nonlinear sigma model, and locality imposes seemingly arbitrary constraints on the KK spectrum and interactions. We argue that these constraints are nevertheless important from an IR perspective, since they affect the four-dimensional cutoff of the theory where high energy scattering hits strong coupling. Intriguingly, we find that maximizing this cutoff scale implies five-dimensional locality. In this way, theory space locality is correlated with weak coupling in the IR, independent of UV considerations. We briefly comment on other scenarios where maximizing the cutoff scale yields interesting physics, including theory space descriptions of QCD and deconstructions of anti-de Sitter space.Comment: 40 pages, 11 figures; v2: references and clarifications added; v3: version accepted by JHE

The Standard Model of Electroweak Interactions

In this chapter, we summarize the structure of the standard EW theory and specify the couplings of the intermediate vector bosons W\ub1, Z and of the Higgs particle with the fermions and among themselves, as dictated by the gauge symmetry plus the observed matter content and the requirement of renormalizability

Flavour-coherent propagators and Feynman rules: Covariant cQPA formulation

We present a simplified and generalized derivation of the flavour-coherent propagators and Feynman rules for the fermionic kinetic theory based on coherent quasiparticle approximation (cQPA). The new formulation immediately reveals the composite nature of the cQPA Wightman function as a product of two spectral functions and an effective two-point interaction vertex, which contains all quantum statistical and coherence information. We extend our previous work to the case of nonzero dispersive self-energy, which leads to a broader range of applications. By this scheme, we derive flavoured kinetic equations for local 2-point functions $S^{}_\mathbf{k}(t,t)$, which are reminiscent of the equations of motion for the density matrix. We emphasize that in our approach all the interaction terms are derived from first principles of nonequilibrium quantum field theory.Comment: 20 pages, 3 figures. Minor modifications, version published in JHE

Inorganic carbon physiology underpins macroalgal responses to elevated CO2

Beneficial effects of CO2 on photosynthetic organisms will be a key driver of ecosystem change under ocean acidification. Predicting the responses of macroalgal species to ocean acidification is complex, but we demonstrate that the response of assemblages to elevated CO2 are correlated with inorganic carbon physiology. We assessed abundance patterns and a proxy for CO2:HCO3- use (\u3b413C values) of macroalgae along a gradient of CO2 at a volcanic seep, and examined how shifts in species abundance at other Mediterranean seeps are related to macroalgal inorganic carbon physiology. Five macroalgal species capable of using both HCO3- and CO2 had greater CO2 use as concentrations increased. These species (and one unable to use HCO3-) increased in abundance with elevated CO2 whereas obligate calcifying species, and non-calcareous macroalgae whose CO2 use did not increase consistently with concentration, declined in abundance. Physiological groupings provide a mechanistic understanding that will aid us in determining which species will benefit from ocean acidification and why