Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry

We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a $P_\infty$-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an $L_\infty$-algebra which is not a $P_\infty$-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a $P_\infty$-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on $A_\infty$-algebras.

A window on infrared QCD with small expansion parameters

Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector — defined, e.g., in the Taylor scheme— remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with ab-initio lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.

Polarized Z bosons from the decay of a Higgs boson produced in association with two jets at the LHC

Investigating the polarization of weak bosons provides an important probe of the scalar and gauge sector of the Standard Model. This can be done in the Higgs decay to four leptons, whose Standard-Model leading-order amplitude enables to generate polarized observables from unpolarized ones via a fully-differential reweighting method. We study the $$\text {Z} $$ Z -boson polarization from the decay of a Higgs boson produced in association with two jets, both in the gluon-fusion and in the vector-boson fusion channel. We also address the possibility of extending the results of this work to higher orders in perturbation theory.

New heavy gauge bosons decaying to pair of electroweak bosons: prospect studies at Run 3 and HL-LHC with ATLAS

The expected ATLAS Run 3 data set with time-integrated luminosity of 300 fb-1 and HL-LHC option of the LHC with L = 3000 fb-1 in the diboson channels in semileptonic final states are used to probe a simple benchmark model with an extended gauge sector, proposed by Altarelli et al. This model accommodates new charged W' and neutral Z' vector bosons with modified trilinear Standard Model gauge couplings, decaying into electroweak gauge boson pairs WZ or WW , where W / Z decay semileptonically. We present upper limits on the mixing parameters, W - W' and Z- Z ' , by using the expected Run 3 data and HL-LHC options of the LHC.

Higher-dimensional invariants in 6D super Yang-Mills theory

We exploit the 6D,$$ \mathcal{N} $$ N = (1, 0) and $$ \mathcal{N} $$ N = (1, 1) harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension d = 12 in 6D,$$ \mathcal{N} $$ N = (1, 1) supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace invariants are derived. Only four single-trace and two double-trace invariants prove to be independent. The invariants constructed can provide the possible counterterms of $$ \mathcal{N} $$ N = (1, 1) SYM theory at four-loop order, where the first double-trace divergences are expected to appear. We explicitly exhibit the gauge sector of all invariants in terms of $$ \mathcal{N} $$ N = (1, 0) gauge superfields and find the absence of $$ \mathcal{N} $$ N = (1, 1) supercompletion of the F6 term in the abelian limit.

Vector-Boson scattering at the LHC: Unraveling the electroweak sector

Vector-boson scattering (VBS) processes probe the innermost structure of electroweak (EW) interactions in the Standard Model (SM), and provide a unique sensitivity for new physics phenomena affecting the gauge sector. In this review, we report on the salient aspects of this class of processes, both from the theory and experimental point of view. We start by discussing recent achievements relevant for their theoretical description, some of which have set important milestones in improving the precision and accuracy of the corresponding simulations. We continue by covering the development of experimental techniques aimed at detecting these rare processes and improving the signal sensitivity over large backgrounds. We then summarize the details of the most relevant VBS signatures and review the related measurements available to date, along with their comparison with SM predictions. We conclude by discussing the perspective at the upcoming Large Hadron Collider runs and at future hadron facilities.

Seiberg-Witten map for D-branes in large R-R field background

We obtain a Seiberg-Witten map for the gauge sector of multiple Dp-branes in a large R-R (p − 1)-form field background up to the first-order in the inverse R-R field background. By applying the Seiberg-Witten map and then electromagnetic duality on the non-commutative D3-brane theory in the large R-R 2-form background, we find the expected commutative diagram of the Seiberg-Witten map and electromagnetic duality. Extending the U(1) gauge group to the U(N) gauge group, we obtain a commutative description of the D-branes in the large R-R field background. This construction is different from the known result.

Covariant phase space and soft factorization in non-Abelian gauge theories

We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

Cosmic inflation in minimal $$U(1)_{B-L}$$ model: implications for (non) thermal dark matter and leptogenesis

We study the possibility of realising cosmic inflation, dark matter (DM), baryon asymmetry of the universe (BAU) and light neutrino masses in non-supersymmetric minimal gauged $$B-L$$ B - L extension of the standard model with three right handed neutrinos. The singlet scalar field responsible for spontaneous breaking of $$B-L$$ B - L gauge symmetry also plays the role of inflaton by virtue of its non-minimal coupling to gravity. While the lightest right handed neutrino is the DM candidate, being stabilised by an additional $$Z_2$$ Z 2 symmetry, we show by performing a detailed renormalisation group evolution (RGE) improved study of inflationary dynamics that thermal DM is generally overproduced due to insufficient annihilations through gauge and scalar portals. This happens due to strict upper limits obtained on gauge and other dimensionless couplings responsible for DM annihilation while assuming the non-minimal coupling to gravity to be at most of order unity. The non-thermal DM scenario is viable, with or without $$Z_2$$ Z 2 symmetry, although in such a case the $$B-L$$ B - L gauge sector remains decoupled from the inflationary dynamics due to tiny couplings. We also show that the reheat temperature predicted by the model prefers non-thermal leptogenesis with hierarchical right handed neutrinos while being consistent with other requirements.