Real Scalars Research Articles

A Real Scalar Field Unifying the Early Inflation and the Late Accelerating Expansion of the Universe through a Quadratic Equation of State: The Vacuumon

In a previous paper we introduced a cosmological model describing the early inflation, the intermediate decelerated expansion, and the late accelerating expansion of the universe in terms of a single barotropic fluid characterized by a quadratic equation of state. We obtained a scalar field representation of this fluid and determined the potential V(ϕ) connecting the inflaton potential in the early universe to the quintessence potential in the late universe. This scalar field has later been called the ‘vacuumon’ by other authors, in the context of the Running Vacuum model. In this paper, we study how the scalar field potential is modified by the presence of other cosmic components such as stiff matter, black-body radiation, baryonic matter, and dark matter. We also determine the mass m and the self-interaction constant λ of the scalar field given by the second and fourth derivatives of the potential at its extrema. We find that its mass is imaginary in the early universe with a modulus of the order of the Planck mass MP=(ℏc/G)1/2=1.22×1019GeV/c2 and real in the late universe with a value of the order of the cosmon mass mΛ=(Λℏ2/c4)1/2=2.08×10−33eV/c2 predicted by string theory. Although our model is able to describe the evolution of the homogeneous background for all times, it cannot account for the spectrum of fluctuations in the early universe. Indeed, by applying the Hamilton–Jacobi formalism to our model of early inflation, we find that the Hubble hierarchy parameters and the spectral indices lead to severe discrepancies with the observations. This suggests that the vacuumon potential is just an effective classical potential that cannot be directly used to compute the fluctuations in the early universe. A fully quantum field theory may be required to achieve that goal. Finally, we discuss the connection between our model based on a quadratic equation of state and the Running Vacuum model which assumes a variation of the cosmological constant with the Hubble parameter.

The FIMP-WIMP dark matter in the extended singlet scalar model

We explore the simplest viable dark matter model with a real singlet scalar, vector-like singlet and doublet fermions. The Yukawa couplings associated with the fermion sector play a crucial role in getting the current relic density through Freeze-in and Freeze-out mechanism. We discuss the constraints from the recent muon anomalous magnetic moment experimental data and relic density. We also perform the collider analysis for the FIMP dark matter in the context of 14 TeV LHC experiments with the MATHUSLA100/200 detector. Our analysis shows that one can get enough events >3 for heavy charged fermion track at 14 TeV LHC with an integrated luminosity L=106fb−1.

Quintic constraints for {{mathcal {N}}}=2 multiplets and complete SUSY breaking

We study real fifth-order superfield constraint for {{mathcal {N}}}=2 vector (and tensor) multiplet and derive most general solution describing complete supersymmetry breaking, and preserving a real scalar, two goldstini, and an abelian gauge field as low-energy degrees of freedom on which both supersymmetries are realized non-linearly. The surviving scalar is identified as an axion of a broken global abelian symmetry, while its scalar partner (saxion) is eliminated in terms of the goldstini. We provide an example of a UV model giving rise to the quintic constraint, and discuss the connection of this constraint and its solution to other known superfield constraints in {{mathcal {N}}}=2 and {{mathcal {N}}}=1 cases.

Dynamic fusion of images from the visible and infrared channels of sightseeing system by complex matrix formalism

The employment of new mathematical and computer approaches for the fusion of target images from the visible and infrared channels of the sightseeing system (SSS) is one of the ways to increase the efficiency of the SSS of armored vehicles. Modern approaches to improving the efficiency of image fusion are aimed to increase the visibility of the target via improving the quality indices of fused images. This paper proposes a fundamentally new approach to image fusion, namely dynamic image fusion, at which the target is observed in the mode of a video clip composed of a sequence of stationary fused images obtained at different parameters of fusion, in contrast to traditional stationary image fusion, at which the decision is made from one fused image. Unlike stationary image fusion, aimed to increase the visibility of the target, the dynamic image fusion allows one to enhance the conspicuity of the target. The principle of dynamic image fusion proposed in this paper is based on matrix formalism, in which the fused image is constructed in the form of a complex vector function, which by its mathematical form is analogous to the Jones vector of elliptically polarized light wave, which in turn opens the possibility of matrix transformation of the complex vector of the fused image and consequently its parameterization by analogy with the Jones matrix formalism for the light wave. The article presents mathematical principles of matrix formalism, which is the basis for dynamic image fusion, gives examples of stationary and dynamic image fusion by the method of complex vector function and compares with the corresponding images, fused by algorithms of weight addition in the field of real and complex scalars. It is shown that by selecting weight coefficients, the general form of a complex amplitude vector image can be reduced to the algorithms of weight and averaged addition in the field of real scalars, weight amplitude and RMS-image in the field of complex scalar numbers, and geometric-mean image in the field of complex vectors, which, thereby, are partial cases of the general form of the complex amplitude image in the field of complex vectors.
 The animated images obtained by the method of complex vector function illustrate the increase of conspicuity of the object of observation due to the dynamic change of the fusion parameters.

Ultralight bosons for strong gravity applications from simple Standard Model extensions

We construct families, and concrete examples, of simple extensions of the Standard Model that can yield ultralight real or complex vectors or scalars with potential astrophysical relevance. Specifically, the mass range for these putative fundamental bosons (∼ 10-10-10-20 eV) would lead dynamically to both new non-black hole compact objects (bosonic stars) and new non-Kerr black holes, with masses of ∼ M⊙ to ∼ 1010 M⊙, corresponding to the mass range of astrophysical black hole candidates (from stellar mass to supermassive). For each model, we study the properties of the mass spectrum and interactions after spontaneous symmetry breaking, discuss its theoretical viability and caveats, as well as some of its potential and most relevant phenomenological implications linking them to the physics of compact objects.

Dynamical friction from scalar dark matter in the relativistic regime

Light bosonic scalars (e.g. axions) may form clouds around black holes via superradiant instabilities, or via accretion if they form some component of the dark matter. It has been suggested that their presence may lead to a distinctive dephasing of the gravitational wave signal when a small compact object spirals into a larger black hole. Motivated by this, we study numerically the dynamical friction force on a black hole moving at relativistic velocities in a background scalar field with an asymptotically homogeneous energy density. We show that the relativistic scaling is analogous to that found for supersonic collisional fluids, assuming an approximate expression for the pressure correction which depends on the velocity and scalar mass. While we focus on a complex scalar field, our results confirm the expectation that real scalars would exert a force which oscillates between positive and negative values in time with a frequency set by the scalar mass. The complex field describes the time averaged value of this force, but in a real scalar the rapid force oscillations could in principle leave an imprint on the trajectory. The approximation we obtain can be used to inform estimates of dephasing in the final stages of an extreme mass ratio inspiral.

Two real scalar WIMP model in the assisted freeze-out scenario

We study a simple dark matter model given by two interacting real singlet scalars,with only one of them coupled to the Higgs. The model therefore presents a minimal assisted-freeze-outframework: both scalars contribute to the dark matter relic density, but only one ofthem takes part in the elastic scattering with nuclei.This reduces the expected interaction rate in direct detection experiments in such a way that the model in some regions of the parameter space may evade XENON1T constraints. We explore the model under theoretical (perturbativity, stability potential and unitarity) and experimental constraints (Higgs to invisible, relic density, direct detection), with the use of the narrow-width-approximation near the Higgs resonance to calculate the averaged annihilation cross section. We show that the model is viable in the Higgs resonance region and for scalar singlets masses of hundreds of GeV, although the model becomes highly constrained at high energies.

Two-component scalar dark matter in Z2n scenarios

In multi-component scalar dark matter scenarios, a single ZN (N ≥ 4) symmetry may account for the stability of different dark matter particles. Here we study the case where N is even (N = 2n) and two species, a complex scalar and a real scalar, contribute to the observed dark matter density. We perform a phenomenological analysis of three scenarios based on the Z4 and Z6 symmetries, characterizing their viable parameter spaces and analyzing their detection prospects. Our results show that, thanks to the new interactions allowed by the Z2n symmetry, current experimental constraints can be satisfied over a wider range of dark matter masses, and that these scenarios may lead to observable signals in direct detection experiments. Finally, we argue that these three scenarios serve as prototypes for other two-component Z2n models with one complex and one real dark matter particle.

Gravitational positivity bounds on scalar potentials

We derive constraints on scalar field theories coupled to gravity by using recently developed positivity bounds in the presence of gravity. It is found that a canonically-normalized real scalar cannot have an arbitrarily flat potential unless some new physics enters well below the Planck scale. An upper bound on the scale of new physics is determined by loop corrections to the self-energy. Our result provides a swampland condition for scalar potentials.

Renormalization and non-renormalization of scalar EFTs at higher orders

We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using Hilbert series and related ideas in commutative algebra and conformal representation theory, including their novel application to off-shell correlation functions. We obtain new results ranging from full one loop at mass dimension twelve to five loops at mass dimension six. We explore the structure of the anomalous dimension matrix with an emphasis on its zeros, and investigate the effects of conformal and orthonormal operators. For the real scalar, the zeros can be explained by a ‘non-renormalization’ rule recently derived by Bern et al. For the complex scalar we find two new selection rules for mixing n- and (n− 2)-field operators, with n the maximal number of fields at a fixed mass dimension. The first appears only when the (n− 2)-field operator is conformal primary, and is valid at one loop. The second appears in more generic bases, and is valid at three loops. Finally, we comment on how the Hilbert series we construct may be used to provide a systematic enumeration of a class of evanescent operators that appear at a particular mass dimension in the scalar EFT.

Monte Carlo Evaluation of the Continuum Limit of the Two-Point Function of the Euclidean Free Real Scalar Field Subject to Affine Quantization

We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point function near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic result and therefore numerical methods are necessary.

Spatio-temporal correlation functions in scalar turbulence from functional renormalization group

We provide the leading behavior at large wavenumbers of the two-point correlation function of a scalar field passively advected by a turbulent flow. We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a stochastic vector field with a Gaussian distribution, and then a scalar advected by a homogeneous and isotropic turbulent flow described by the Navier–Stokes equation, under the assumption that the scalar is passive, i.e., that it does not affect the carrier flow. We show that at large wavenumbers, the two-point correlation function of the scalar in the Kraichnan model decays as an exponential in the time delay, in both the inertial and dissipation ranges. We establish the expression, both from a perturbative and from a nonperturbative calculation, of the prefactor, which is found to be always proportional to k2. For a real scalar, the decay is Gaussian in t at small time delays, and it crosses over to an exponential only at large t. The assumption of delta-correlation in time of the stochastic velocity field in the Kraichnan model, hence, significantly alters the statistical temporal behavior of the scalar at small times.

Di-Higgs blind spots in gravitational wave signals

Conditions for strong first-order phase transition and generation of observable gravitational wave (GW) signals are very restrictive to the profile of the Higgs potential. Working in the minimal extension of the SM with a new gauge singlet real scalar, we show that the production of signals relevant for future GW experiments, such as LISA, can favor depleted resonant and non-resonant di-Higgs rates at colliders for phenomenologically relevant regimes of scalar mixing angles and masses for the heavy scalar. We perform a comprehensive study on the emergence of these di-Higgs blind spot configurations in GWs and also show that di-boson channels, ZZ and WW, can restore the phenomenological complementarities between GW and collider experiments in these parameter space regimes.

Dark matter physics in dark SU(2) gauge symmetry with non-Abelian kinetic mixing

We investigate a model of dark sector based on non-Abelian $SU(2{)}_{D}$ gauge symmetry. This dark gauge symmetry is broken into discrete ${Z}_{2}$ via vacuum expectation values of two real triplet scalars, and an $SU(2{)}_{D}$ doublet Dirac fermion becomes ${Z}_{2}$---odd particles whose lighter component makes stable dark matter candidate. The standard model and dark sector can be connected via the scalar mixing and the gauge kinetic mixing generated by higher dimensional operators. We then discuss relic density of dark matter and implications to collider physics in the model. The most unique signatures of this model at the LHC would be the dark scalar (${\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}$) productions where it subsequently decays into: (1) a fermionic dark matter (${\ensuremath{\chi}}_{l}$) and a heavy dark fermion (${\ensuremath{\chi}}_{h}$) pair, ${\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\overline{\ensuremath{\chi}}}_{l}{\ensuremath{\chi}}_{h}({\overline{\ensuremath{\chi}}}_{h}{\ensuremath{\chi}}_{l})$, followed by ${\ensuremath{\chi}}_{h}$ decays into ${\ensuremath{\chi}}_{l}$ and non-Abelian dark gauge bosons (${X}_{i}$'s) which decays into SM fermion pair ${\overline{f}}_{\mathrm{SM}}{f}_{\mathrm{SM}}$ resulting in the reaction $pp\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{\overline{\ensuremath{\chi}}}_{h}{\ensuremath{\chi}}_{l}({\overline{\ensuremath{\chi}}}_{l}{\ensuremath{\chi}}_{h})\ensuremath{\rightarrow}{f}_{\mathrm{SM}}{\overline{f}}_{\mathrm{SM}}{\ensuremath{\chi}}_{l}{\overline{\ensuremath{\chi}}}_{l}$, (2) a pair of ${X}_{i}$'s followed by ${X}_{i}$ decays into a DM pair or the SM fermions resulting in the reaction, $pp\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Phi}}}_{1}^{{(}^{\ensuremath{'}})}\ensuremath{\rightarrow}{X}_{i}{X}_{i}\ensuremath{\rightarrow}{\overline{\ensuremath{\chi}}}_{l}{\ensuremath{\chi}}_{l}{f}_{\mathrm{SM}}{\overline{f}}_{\mathrm{SM}}$ or even number of ${f}_{\mathrm{SM}}{\overline{f}}_{\mathrm{SM}}$ pairs.

Triple Higgs boson production at the Large Hadron Collider with Two Real Singlet scalars

We investigate the production of three Higgs bosons in the Two Real Singlet extension of the Standard Model, where the scalar sector is augmented by two additional real scalar fields which are singlets under the Standard Model gauge group. The model contains three neutral CP-even scalars, allowing for resonant production and asymmetric decay chains. We focus on the signature pp → h3→ h1h2→ h1h1h1, where we identify h3 as the heaviest scalar state, h2 as the second heaviest and the lightest, h1, as the Standard Model-like Higgs boson discovered by the Large Hadron Collider experiments. The dominant final state occurs when all three Higgs bosons decay to bottom-anti-bottom quark pairs, h1→ boverline{b} , leading to 6 b-jets. Taking into account all current theoretical and experimental constraints, we determine the discovery prospects for this channel in future runs of the Large Hadron Collider, as well as in the high-luminosity phase.

Beyond the Standard Model effective field theory: The singlet extended Standard Model

One of the assumptions of simplified models is that there are a few new particles and interactions accessible at the LHC and all other new particles are heavy and decoupled. The effective field theory (EFT) method provides a consistent method to test this assumption. Simplified models can be augmented with higher order operators involving the new particles accessible at the LHC. Any UV completion of the simplified model will be able to match onto these beyond the Standard Model EFTs (BSM-EFT). In this paper we study the simplest simplified model: the Standard Model extended by a real gauge singlet scalar. In addition to the usual renormalizable interactions, we include dimension-5 interactions of the singlet scalar with Standard Model particles. As we will show, even when the cutoff scale is 3 TeV, these new effective interactions can drastically change the interpretation of Higgs precision measurements and scalar searches. In addition, we discuss how power counting in a BSM-EFT depends strongly on the processes and parameter space under consideration. Finally, we propose a $\chi^2$ method to consistently combine the limits from new particle searches with measurements of the Standard Model. Unlike imposing a hard cut off on heavy resonance rates, our method allows fluctuations in individual channels that are consistent with global fits.

The Deformation of an $(\alpha, \beta)$-Metric

In this paper, we will continue our investigation on the new recently introduced $(\alpha, \beta)$-metric $F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}$ in \cite{Pis}; where $\alpha$ is a Riemannian metric; $\beta$ is a 1-form, and $a\in \left(\frac{1}{4},+\infty\right)$ is a real positive scalar. We will investigate the deformation of this metric, and we will investigate its properties.

Unruh-DeWitt detector responses for complex scalar fields in de Sitter spacetime

We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field ϕ, in the (3 + 1)-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to ϕ†ϕ. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter α-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed.

The scalar chemical potential in cosmological collider physics

Non-analyticity in co-moving momenta within the non-Gaussian bispectrum is a distinctive sign of on-shell particle production during inflation, presenting a unique opportunity for the “direct detection” of particles with masses as large as the inflationary Hubble scale (H). However, the strength of such non-analyticity ordinarily drops exponentially by a Boltzmann-like factor as masses exceed H. In this paper, we study an exception provided by a dimension-5 derivative coupling of the inflaton to heavy-particle currents, applying it specifically to the case of two real scalars. The operator has a “chemical potential” form, which harnesses the large kinetic energy scale of the inflaton, {overset{cdot }{phi}}_0^{1/2}approx 60H , to act as an efficient source of scalar particle production. Derivative couplings of inflaton ensure radiative stability of the slow-roll potential, which in turn maintains (approximate) scale-invariance of the inflationary correlations. We show that a signal not suffering Boltzmann suppression can be obtained in the bispectrum with strength fNL ∼ mathcal{O} (0.01–10) for an extended range of scalar masses lesssim {overset{cdot }{phi}}_0^{1/2} , potentially as high as 1015 GeV, within the sensitivity of upcoming LSS and more futuristic 21-cm experiments. The mechanism does not invoke any particular fine-tuning of parameters or breakdown of perturbation-theoretic control. The leading contribution appears at tree-level, which makes the calculation analytically tractable and removes the loop-suppression as compared to earlier chemical potential studies of non-zero spins. The steady particle production allows us to infer the effective mass of the heavy particles and the chemical potential from the variation in bispectrum oscillations as a function of co-moving momenta. Our analysis sets the stage for generalization to heavy bosons with non-zero spin.

Decay of boson stars with application to glueballs and other real scalars

One of the most interesting candidates for dark matter are massive real scalar particles. A well-motivated example is from a pure Yang-Mills hidden sector, which locks up into glueballs in the early universe. The lightest glueball states are scalar particles and can act as a form of bosonic dark matter. If self-interactions are repulsive this can potentially lead to very massive boson stars, where the inward gravitational force is balanced by the repulsive self-interaction. This can also arise from elementary real scalars with a regular potential. In the literature it has been claimed that this allows for astrophysically significant boson stars with high compactness, which could undergo binary mergers and generate detectable gravitational waves. Here we show that previous analyses did not take into proper account $3 \to 2$ and $4 \to 2$ quantum mechanical annihilation processes in the core of the star, while other work misinterpreted the classical $3 \to 1$ process. In this work, we compute the annihilation rates, finding that massive stars will rapidly decay from the $3 \to 2$ or $4 \to 2$ processes (while the $3 \to 1$ process is typically small). Using the Einstein-Klein-Gordon equations, we also estimate the binding energy of these stars, showing that even the densest stars do not have quite enough binding energy to prevent annihilations. For such boson stars to live for the current age of the universe and to be consistent with bounds on dark matter scattering in galaxies, we find the following upper bound on their mass for $O(1)$ self-interaction couplings: $M_*<10^{-18}M_{sun}$ when $3 \to 2$ processes are allowed and $M_*<10^{-11}M_{sun}$ when only $4 \to 2$ processes are allowed. We also estimate destabilization from parametric resonance which can considerably constrain the phase space further. Furthermore, such stars are required to have very small compactness to be long lived.