Real Scalars Research Articles

Resonant di-Higgs production at gravitational wave benchmarks: a collider study using machine learning

We perform a complementarity study of gravitational waves and colliders in the context of electroweak phase transitions choosing as our template the xSM model, which consists of the Standard Model augmented by a real scalar. We carefully analyze the gravitational wave signal at benchmark points compatible with a first order phase transition, taking into account subtle issues pertaining to the bubble wall velocity and the hydrodynamics of the plasma. In particular, we comment on the tension between requiring bubble wall velocities small enough to produce a net baryon number through the sphaleron process, and large enough to obtain appreciable gravitational wave production. For the most promising benchmark models, we study resonant di-Higgs production at the high-luminosity LHC using machine learning tools: a Gaussian process algorithm to jointly search for optimum cut thresholds and tuning hyperparameters, and a boosted decision trees algorithm to discriminate signal and background. The multivariate analysis on the collider side is able either to discover or provide strong statistical evidence of the benchmark points, opening the possibility for complementary searches for electroweak phase transitions in collider and gravitational wave experiments.

Effective field theory for dark matter direct detection up to dimension seven

We present the full basis of effective operators relevant for dark matter direct detection, up to and including operators of mass dimension seven. We treat the cases where dark matter is either a Dirac fermion, a Majorana fermion, a complex scalar, or a real scalar, allowing for dark matter to furnish a general representation of the electroweak gauge group. We describe the algorithmic procedure used to obtain the minimal set of effective operators and provide the tree-level matching conditions onto the effective theory valid below the electroweak scale.

Can light dark matter solve the core-cusp problem?

Recently there has been much interest in light dark matter, especially ultra-light axions, as they may provide a solution to the core-cusp problem at the center of galaxies. Since very light bosons can have a de Broglie wavelength that is of astrophysical size, they can smooth out the centers of galaxies to produce a core, as opposed to vanilla dark matter models, and so it has been suggested that this solves the core-cusp problem. In this work, we critically examine this claim. While an ultra-light particle will indeed lead to a core, we examine whether the relationship between the density of the core and its radius matches the data over a range of galaxies. We first review data that shows the core density of a galaxy $\rho_c$ varies as a function of the core radius $R_c$ as $\rho_c\propto1/R_c^\beta$ with $\beta\approx1$. We then compare this to theoretical models. We examine a large class of light scalar dark matter models, governed by some potential $V$. For simplicity, we take the scalar to be complex with a global $U(1)$ symmetry in order to readily organize solutions by a conserved particle number. However, we expect our central conclusions to persist even for a real scalar, and furthermore, a complex scalar matches the behavior of a real scalar in the non-relativistic limit, which is the standard regime of interest. For any potential $V$, we find the relationship between $\rho_c$ and $R_c$ for ground state solutions is always in one of the following regimes: (i) $\beta\gg1$, or (ii) $\beta\ll1$, or (iii) unstable, and so it never matches the data. We also find similar conclusions for virialized dark matter, more general scalar field theories, degenerate fermion dark matter, superfluid dark matter, and general polytropes. We conclude that the solution to the core-cusp problem is more likely due to either complicated baryonic effects or some other type of dark matter interactions.

The Symmetrical Foundation of Measure, Probability, and Quantum Theories

AbstractQuantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are ubiquitous. Specifically, measure theory formalizes addition, and probability theory formalizes inference in terms of proportions. Quantum theory rests on the same simple symmetries, but is formalized in two dimensions, not just one, in order to track an object through its binary interactions with other objects. The symmetries still require sum and product rules (here known as the Feynman rules), but they apply to complex numbers instead of real scalars, with observable probabilities being modulus squared (known as the Born rule). The standard quantum formalism follows. There is no mystery or weirdness, just ordinary probabilistic inference.

A new duality between mathcal{N} = 8 superconformal field theories in three dimensions

We propose a new duality between two 3d mathcal{N} = 8 superconformal Chern-Simons-matter theories: the U(3)1 × U(3)−1 ABJM theory and a theory consisting of the product between the (SU(2)3 × SU(2)− 3)/ℤ2 BLG theory and a free mathcal{N} = 8 theory of eight real scalars and eight Majorana fermions. As evidence supporting this duality, we show that the moduli spaces, superconformal indices, S3 partition functions, and certain OPE coefficients of BPS operators in the two theories agree.

Two component Feebly Interacting Massive Particle (FIMP) dark matter

We explore the idea of an alternative candidate for particle dark matter namely Feebly Interacting Massive Particle (FIMP) in the framework of a two component singlet scalar model. Singlet scalar dark matter has already been demonstrated to be a viable candidate for WIMP (Weakly Interacting Massive Particle) dark matter in literature. In the FIMP scenario, dark matter particles are slowly produced via “thermal freeze-in” mechanism in the early Universe and are never abundant enough to reach thermal equilibrium or to undergo pair annihilation inside the Universe's plasma due to their extremely small couplings. We demonstrate that for smaller couplings too, required for freeze-in process, a two component scalar dark matter model considered here could well be a viable candidate for FIMP . In this scenario, the Standard Model of particle physics is extended by two gauge singlet real scalars whose stability is protected by an unbroken Z2× Z′2 symmetry and they are assumed to acquire no VEV after Spontaneous Symmetry Breaking. We explore the viable mass regions in the present two scalar DM model that is in accordance with the FIMP scenario. We also explore the upper limits of masses of the two components from the consideration of their self interactions.

Singlet fermionic dark matter with Veltman conditions

We reexamine a renormalizable model of a fermionic dark matter with a gauge singlet Dirac fermion and a real singlet scalar which can ameliorate the scalar mass hierarchy problem of the Standard Model (SM). Our model setup is the minimal extension of the SM for which a realistic dark matter (DM) candidate is provided and the cancellation of one-loop quadratic divergence to the scalar masses can be achieved by the Veltman condition (VC) simultaneously. This model extension, although renormalizable, can be considered as an effective low-energy theory valid up to cut-off energies about 10 TeV. We calculate the one-loop quadratic divergence contributions of the new scalar and fermionic DM singlets, and constrain the model parameters using the VC and the perturbative unitarity conditions. Taking into account the invisible Higgs decay measurement, we show the allowed region of new physics parameters satisfying the recent measurement of relic abundance. With the obtained parameter set, we predict the elastic scattering cross section of the new singlet fermion into target nuclei for a direct detection of the dark matter. We also perform the full analysis with arbitrary set of parameters without the VC as a comparison, and discuss the implication of the constraints by the VC in detail.

Towards sharp Bohnenblust–Hille constants

We investigate the optimality problem associated with the best constants in a class of Bohnenblust–Hille-type inequalities for [Formula: see text]-linear forms. While germinal estimates indicated an exponential growth, in this work we provide strong evidences to the conjecture that the sharp constants in the classical Bohnenblust–Hille inequality are universally bounded, irrespectively of the value of [Formula: see text]; hereafter referred as the Universality Conjecture. In our approach, we introduce the notions of entropy and complexity, designed to measure, to some extent, the complexity of such optimization problems. We show that the notion of entropy is critically connected to the Universality Conjecture; for instance, that if the entropy grows at most exponentially with respect to [Formula: see text], then the optimal constants of the [Formula: see text]-linear Bohnenblust–Hille inequality for real scalars are indeed bounded universally with respect to [Formula: see text]. It is likely that indeed the entropy grows as [Formula: see text], and in this scenario, we show that the optimal constants are precisely [Formula: see text]. In the bilinear case, [Formula: see text], we show that any extremum of the Littlewood’s [Formula: see text] inequality has entropy [Formula: see text] and complexity [Formula: see text], and thus we are able to classify all extrema of the problem. We also prove that, for any mixed [Formula: see text]-Littlewood inequality, the entropy do grow exponentially and the sharp constants for such a class of inequalities are precisely [Formula: see text]. In addition to the notions of entropy and complexity, the approach we develop in this work makes decisive use of a family of strongly non-symmetric [Formula: see text]-linear forms, which has further consequences to the theory, as we explain herein.

Neutrino Mass and the Higgs Portal Dark Matter in the ESSFSM

We extend the standard model with three right-handed singlet neutrinos and a real singlet scalar. We impose two Z2 and Z2′ symmetries. We explain the tiny neutrino mass-squared differences with two Z2- and Z2′-even right-handed neutrinos using type I seesaw mechanism. The Z2-odd fermion and the Z2′-odd scalar can both serve as viable dark matter candidates. We identify new regions in the parameter space which are consistent with relic density of the dark matter from recent direct search experiments LUX-2016 and XENON1T-2017 and LHC data.

The variational problem in lagrange spaces endowed with a special type of (α,β)-metrics

In this paper, we will continue our investigation on the new recently introduced (?,?)-metric F = ? + a?2+?2/? in [12]; where ? is a Riemannian metric; ? is an 1-form and a ? (1/4,+?) is a real positive scalar. We will investigate the variational problem in Lagrange spaces endowed with this type of metrics. Also, we will study the dually local flatness for this type of metric and we will proof that this kind of metric can be reduced to a locally Minkowskian metric. Finally, we will introduce the 2-Killing equation in Finsler spaces.

On max-k-sums

The max-k-sum of a set of real scalars is the maximum sum of a subset of size k, or alternatively the sum of the k largest elements. We study two extensions: first, we show how to obtain smooth approximations to functions that are pointwise max-k-sums of smooth functions. Second, we discuss how the max-k-sum can be defined on vectors in a finite-dimensional real vector space ordered by a closed convex cone.

A bounded real lemma type-result with respect to the anisotropic norm setup for stochastic systems with multiplicative noise

The anisotropic norm of discrete-time linear stochastic systems with state dependent noise is considered. Using first principles analysis applying completing the square arguments, it is proved that the anisotropic norm of such systems is upper bounded by a given positive real scalar, if a specific Riccati equation has a stabilizing positive semidefinite solution satisfying two additional conditions. It is shown that these conditions are sufficient and necessary for the boundedness of the anisotropic norm. Numerical algorithms to determine the stabilizing solution of this Riccati equation allowing thus to compute the anisotropic norm of stochastic systems with multiplicative noise are also presented. The theoretical results are illustrated by numerical examples.

High-scale baryogenesis with testable neutron-antineutron oscillation and dark matter

We propose a new scenario for predicting a one-loop neutron-antineutron oscillation at a testable level, meanwhile, realizing a thermal or inflationary baryogenesis at a very high scale. Besides the standard model content, this scenario involves two real singlet scalars with very heavy masses, two color-triplet and iso-singlet scalars at the TeV scale, as well as a Majorana singlet fermion for a dark matter candidate.

Simply split strongly interacting massive particles

Dark Matter which interacts strongly with itself, but only feebly with the Standard Model is a possibility that has been entertained to solve apparent small-scale structure problems that are pertinent to the non-interacting cold Dark Matter paradigm. In this paper, we study the simple case in which the self-scattering rate today is regulated by kinematics and/or the abundance ratio, through the mass-splitting of nearly degenerate pseudo-Dirac fermions $\chi_1$ and $\chi_2$ or real scalars $\phi_1$ and $\phi_2$. We calculate the relic density of these states in a scenario where self-scattering proceeds through off-diagonal couplings with a vector particle $V$ (Dark Photon) and where the abundance is set through number-depleting 4-to-2 reactions in the hidden sector, or, alternatively, via freeze-in. We study the implications of the considered models and their prospect of solving astrophysical small-scale structure problems. We also show how the introduction of the (meta-)stable heavier state may be probed in future dark matter searches.

Reopening the Higgs portal for single scalar dark matter

A real singlet scalar, connected to the Standard Model sector through a portal with the Higgs boson, is one of the simplest and most popular models for dark matter (DM). However, the experimental advances in direct and indirect DM searches, together with the latest results from the LHC, have ruled out vast areas of the parameter space of this scenario; and are expected to probe it completely within the next years, ruling it out if no signal is found. Motivated by the simplicity of this model, in this article we address a minimal, renormalizable extension that could evade detection, consisting of the addition of an extra real singlet scalar field in the dark sector. We analyze the physical constraints on the model and show that the new annihilation and/or coannihilation channels involving the extra singlet allow to reproduce the correct DM relic abundance while avoiding the bounds from direct and indirect searches for any DM mass above 50 GeV. We also show that, in some interesting regions of the parameter space, the extra particle can be integrated-out, leaving a “clever” effective theory (just involving the DM particle and the Higgs), that essentially reproduces the results.

High-scale leptogenesis with three-loop neutrino mass generation and dark matter

We demonstrate a common origin for high-scale leptogenesis and three-loop neutrino mass generation. Specifically we extend the standard model by two real singlet scalars, two singly charged scalars carrying different quantum numbers under certain global symmetry and two or more singlet fermions with Majorana masses. This global symmetry is only allowed to be softly or spontaneously broken. Our model also respects an exactly conserved Z2 discrete symmetry. Through the real scalar decays and then the charged scalar decays, we can obtain a lepton asymmetry stored in the standard model leptons. This lepton asymmetry can be partially converted to a baryon asymmetry by the sphaleron processes. The interactions for this leptogenesis can also result in a three-loop diagram to generate the neutrino masses. The lightest singlet fermion can keep stable to serve as a dark matter particle.

Dimensional reduction of the Standard Model coupled to a new singlet scalar field

We derive an effective dimensionally reduced theory for the Standard Model augmented by a real singlet scalar. We treat the singlet as a superheavy field and integrate it out, leaving an effective theory involving only the Higgs and SU(2)L × U(1)Y gauge fields, identical to the one studied previously for the Standard Model. This opens up the possibility of efficiently computing the order and strength of the electroweak phase transition, numerically and nonperturbatively, in this extension of the Standard Model. Understanding the phase diagram is crucial for models of electroweak baryogenesis and for studying the production of gravitational waves at thermal phase transitions.

On the generalized Bohnenblust–Hille inequality for real scalars

In this paper we obtain new lower and upper estimates for the sharp constants in the generalized Bohnenblust–Hille inequality introduced in Albuquerque et al. (J Funct Anal 266:3726–3740, 2014). We apply these results to find optimal constants in the generalized Bohnenblust–Hille inequality and also to recover the optimal constants of the mixed $$\left( \ell _{1},\ell _{2}\right) $$ -Littlewood inequalities recently obtained in Pellegrino (J Number Theory 160:11–18, 2016) and Pellegrino and Teixeira (Commun Contemp Math, to appear).

Clues on the Majorana scale from scalar resonances at the LHC

In order to address the observation of the neutrino oscillations and the metastability of the Standard Model (SM), we extend the fermion sector with two right-handed (i.e. sterile) neutrinos, and the scalar sector of the SM with a real scalar, the Hill field. The latter takes the role of a Majoron and generates the Majorana masses for the neutrino sector, such that the particle spectrum features two CP-even scalars h1and h2, and also two heavy, mass degenerate neutrinos. When the h1is identified with the scalar resonance at [Formula: see text] 125 GeV and the condition is imposed that the h1self-coupling and its running vanish at the Planck scale, the scalar mixing and the vacuum expectation value of the Hill field are fixed by the h2mass.The h2can be searched for at the LHC, and it has prospects of being discovered for the target integrated luminosities of the HL-LHC and the Future Circular hadron Collider (FCC-hh) when its mass is on the weak scale. The knowledge of the h2mass and its decay properties can yield an insight into its coupling to the heavy neutrinos, and thus also on the heavy neutrino mass scale. This yields an interesting connection between potentially detectable heavy scalars in high-energy proton collisions and the mass scale of the heavy neutrinos that is testable at the LHC and at future colliders.

Chern-Simons-matter dualities with SO and USp gauge groups

In the last few years several dualities were found between the low-energy behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to scalars, and similar theories coupled to fermions. In this paper we generalize those dualities to orthogonal and symplectic gauge groups. In particular, we conjecture dualities between SO(N)k Chern-Simons theories coupled to Nf real scalars in the fundamental representation, and SO(k)–N + N f / 2 theories coupled to Nf real (Majorana) fermions in the fundamental. For Nf = 0 these are just level-rank dualities of pure Chern-Simons theories, whose precise form we clarify. They lead us to propose new gapped boundary states of topological insulators and superconductors. For k = 1 we get an interesting low-energy duality between Nf free Majorana fermions and an SO(N)1 Chern-Simons theory coupled to Nf scalar fields (with Nf ≤ N − 2).