Vacuum Expectation Value Research Articles

Polarization of the Conformal Vacuum in the Milne Universe

The vacuum expectation values of the field squared and energy-momentum tensor for a massless scalar field are investigated in the Milne universe with general number of spatial dimensions. The vacuum state depends on the choice of the mode functions in the canonical quantization procedure and we assume that the field is prepared in the conformal vacuum. As the first step an integral representation for the difference of the Wightman functions corresponding to the conformal and Minkowski vacua is derived. The mean field squared and energy-momentum tensor are obtained in the coincidence limit. It is shown that the Minkowski vacuum state is interpreted as a thermal one with respect to the conformal vacuum. The thermal factor is of the Bose-Einstein type in odd dimensional space and of the Fermi-Dirac type in even number of spatial dimensions.

Maximally symmetric three-Higgs-doublet model

We consider the general Three-Higgs Doublet Model (3HDM) and identify all limits that lead to exact SM alignment. After discussing the underlying symmetries that can naturally enforce such an alignment, we focus on the most economic setting, called here the Maximally Symmetric Three-Higgs Doublet Model (MS-3HDM). The potential of the MS-3HDM obeys an $\mathrm{Sp(6)}$ symmetry, softly broken by bilinear masses and explicitly by hypercharge and Yukawa couplings through renormalisation-group effects, whilst the theory allows for quartic coupling unification up to the Planck scale. Besides the two ratios of vacuum expectation values, $\tan\beta_{1,2}$, the MS-3HDM is predominantly governed by only three input parameters: the masses of the two charged Higgs bosons, $M_{h_{1,2}^{\pm}}$, and their mixing angle $\sigma$. Most remarkably, with these input parameters, we obtain definite predictions for the entire scalar mass spectrum of the theory, as well as for the SM-like Higgs-boson couplings to the gauge bosons and fermions. The predicted deviations of these couplings from their SM values might be probed at future precision high-energy colliders. The new phenomenological aspects of the MS-3HDM with respect to the earlier studied MS-2HDM are discussed.

Mean field squared and energy–momentum tensor for the hyperbolic vacuum in dS spacetime

We evaluate the Hadamard function and the vacuum expectation values (VEVs) of the field squared and energy–momentum tensor for a massless conformally coupled scalar field in (D+1)-dimensional de Sitter (dS) spacetime foliated by spatial sections of negative constant curvature. It is assumed that the field is prepared in the hyperbolic vacuum state. An integral representation for the difference of the Hadamard functions corresponding to the hyperbolic and Bunch–Davies vacua is provided that is well adapted for the evaluation of the expectation values in the coincidence limit. It is shown that the Bunch–Davies state is interpreted as thermal with respect to the hyperbolic vacuum. An expression for the corresponding density of states is provided. The relations obtained for the difference in the VEVs for the Bunch–Davies and hyperbolic vacua are compared with the corresponding relations for the Fulling–Rindler and Minkowski vacua in flat spacetime. The similarity between those relations is explained by the conformal connection of dS spacetime with hyperbolic foliation and Rindler spacetime. As a limiting case, the VEVs for the conformal vacuum in the Milne universe are discussed.

The multicritical point principle as the origin of classical conformality and its generalizations

Abstract The multicritical point principle is one of the interesting theoretical possibilities that can explain the fine-tuning problems of the universe. It simply claims that “the coupling constants of a theory are tuned to one of the multicritical points, where some of the extrema of the effective potential are degenerate.” One of the simplest examples is the vanishing of the second derivative of the effective potential around a minimum. This corresponds to the so-called classical conformality, because it implies that the renormalized mass m2 vanishes. More generally, the form of the effective potential of a model depends on several coupling constants, and we should sweep them to find all the multicritical points. We study the multicritical points of a general scalar field ϕ at one-loop level under the circumstance that the vacuum expectation values of the other fields are all zero. For simplicity, we also assume that the other fields are either massless or so heavy that they do not contribute to the low-energy effective potential of ϕ. This assumption makes our discussion very simple because the resultant one-loop effective potential is parametrized by only four effective couplings. Although our analysis is not completely general because of the assumption, it can still be widely applicable to many models of the Coleman–Weinberg mechanism and its generalizations. After classifying the multicritical points at low-energy scales, we will briefly mention the possibility of criticalities at high-energy scales and their implications for cosmology.

Separation behavior of As, Zn and Cd trace impurities in the deep vacuum purification process of refined lead

Environmentally friendly vacuum distillation has been employed to purify refined lead (99.996%), aiming to separate low-boiling point trace impurities of As, Zn and Cd in refined lead and to provide a foundation for the preparation of high-purity lead (5 N) and ultrapure lead (6 N). In this paper, the low-boiling point trace impurities As, Zn and Cd in refined lead are removed by low-temperature vacuum distillation (LTVD). Detailed analysis of the initial and purified lead was performed by glow discharge mass spectrometry (GDMS) to reveal that Cd and Zn were evaporated as volatiles and were removed from the refined lead in a crucible. Correspondingly, the contents of Zn and Cd impurities decreased from 4 ppmw and 1 ppmw to 0.006 ppmw and 0.01 ppmw, respectively. In contrast to the removal efficiencies of Zn and Cd by LTVD, the removal efficiency of As impurities is only 4%. To cope with this, a novel high-temperature pyrolysis-zone condensation (HTP-ZC) vacuum purification process is proposed for further As separation. The HTP-ZC results indicate that As, Cd and Zn are condensed as residues and removed in the condensation stage. Removal efficiencies of 99.96% for As, 99.98% for Zn, and approximately 100% for Cd were achieved. This approach, with huge industrialization potential, pushes the direct yield of the product to 90% and effectively removes trace impurities with low boiling points, such as As, Cd and Zn, in refined lead. The proposed HTP-ZC process has the potential to stably, cleanly and efficiently produce high-purity lead and ultrapure lead.

Dark matter to baryon ratio from scalar triplets decay in type-II seesaw

We propose a minimal model for the cosmic coincidence problem Omega _mathrm{DM}/Omega _B sim 5 and neutrino mass in a type-II seesaw scenario. We extend the standard model of particle physics with a mathrm SU(2) singlet leptonic Dirac fermion chi , which represents the candidate of dark matter (DM), and two triplet scalars Delta _{1,2} with hierarchical masses. In the early Universe, the CP violating out-of-equilibrium decay of lightest Delta generates a net B-L asymmetry in the visible sector (comprising of SM fields), where B and L represents the total baryon and lepton number respectively. A part of this asymmetry gets transferred to the dark sector (comprising of DM chi ) through a dimension eight operator which conserves B-L. Above the electroweak phase transition, the B-L asymmetry of the visible sector gets converted to a net B-asymmetry by the B+L violating sphalerons, while the B-L asymmetry of the dark sector remains untouched which we see today as relics of DM. We show that the observed DM abundance can be explained for a DM mass about 8 GeV. We then introduce an additional singlet scalar field phi which mixes with the SM-Higgs to annihilate the symmetric component of the DM resonantly which requires the singlet scalar mass to be twice the DM mass, i.e. around 16 GeV, which can be searched at collider experiments. In our model, the active neutrinos also get small masses by the induced vacuum expectation value (vev) of the triplet scalars Delta _{1,2}. In the later part of the paper we discuss all the constraints on model parameters coming from invisible Higgs decay, Higgs signal strength, DM direct detection and relic density of DM.

Does vacuum saturation work for the higher-dimensional vacuum condensates in the QCD sum rules?

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the [Formula: see text]-type and [Formula: see text]-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter [Formula: see text] to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the [Formula: see text] leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.

Yukawa coupling unification in non-supersymmetric SO(10) models with an intermediate scale

We discuss the possibility of unifying in a simple and economical manner the Yukawa couplings of third generation fermions in a non-supersymmetric SO(10) model with an intermediate symmetry breaking, focusing on two possible patterns with intermediate Pati-Salam and minimal left-right groups. For this purpose, we assume a minimal Yukawa sector at high energy, starting with two Higgs bi-doublets at the intermediate scale which then simply reduce to a two Higgs doublet model at the electroweak scale. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalization group running which are generated by the heavy fields that appear at the intermediate symmetry breaking scale. We then study the running of the Yukawa couplings of the top quark, bottom quark and tau lepton at two-loops in these two breaking schemes, when the appropriate matching conditions are imposed. We find that the unification of the third family Yukawa couplings can be achieved while retaining a viable spectrum, provided that the ratio of the vacuum expectation values of the two Higgs doublet fields is large, tan⁡β≈60.

A Review on Process and Practices in Operation and Design Modification of Ejectors

This work reviews the current operational condition and activities on design modification for different applications of ejectors. Ejectors being a simple mechanical system capable of performing multiple fluid related functions (vacuum generation, pumping, mixing, condensing and heat exchanging), have been an essential part of several industrial processes. Two areas have been emphasized; internal flow and application-based modifications in components of ejectors. The geometry and inlet flow conditions were found to be the prime influencing factor of its performance. The objective and application-based modifications were performed on the primary nozzle, secondary nozzle, mixing chamber, throat and diffuser. The resultant performance was found to be dependent on operational condition and fluid type. This emphasizes the requirement of application-based design selection of the technology. In addition, the flow dynamics of condensing, non-condensing, particle and slurry flow has been studied based on available literatures. The one-point final objective is to identify the usability of primary water jet ejectors for active vapor transport and condensation, to replace vacuum pump and condenser in compact domestic water desalination system.

Application of a combined safety approach for the evaluation of safety margin during a Loss of Condenser Vacuum event

A combined safety approach, which uses a best-estimate computer code and adopts conservative assumptions for safety systems availability, is developed and applied to the safety margin evaluation for the Loss of Condenser Vacuum (LOCV) of the 1000 MWe Korean Nuclear Power Plant. The Multi-dimensional Analysis of Reactor Safety-KINS standard (MARS-KS) code is selected as a best-estimate code and the PAPIRUS program is used to obtain different initial operational conditions through random sampling of control variables. During an LOCV event, fuel integrity is not threatened by the increase in Departure from Nuclear Boiling Ratio (DNBR). However, the high pressure in the primary coolant system and the secondary system might affect the system integrity. Thus, the peak pressure becomes a major safety concern. Transient analyses are performed for 124 cases of different initial conditions and the most conservative case, which results in the highest system pressure is selected. It is found the suggested methodology gives similar peak pressures when compared to those predicted from existing methodologies. The proposed approach is expected to minimize the time and efforts required to identify the conservative plant conditions in the existing conservative safety methodologies.

Pseudo-Goldstone dark matter in SO(10)

We propose a pseudo-Goldstone boson dark matter (pGDM) particle in $SO(10)$ grand unified theory (GUT). Due to its Goldstone nature, this pGDM evades the direct DM detection experiments which, otherwise, severely constrain the parameter space of DM models. In $SO(10)$, the pGDM is embedded as a linear combination of the Standard Model (SM) singlet scalars in ${\bf 16_H}$ and ${\bf 126_H}$ representations. We consider two scenarios for the intermediate route of $SO(10)$ symmetry breaking (SB) to the SM: $SU(5) \times U(1)_X$ and Pati-Salam the $SU(4)_c \times SU(2)_L \times SU(2)_R$ (4-2-2) gauge groups. The vacuum expectation value of ${\bf 126_H}$, which triggers the breaking of $U(1)_X$ and 4-2-2 symmetry in the two scenarios, respectively, determines the pGDM lifetime whose astrophysical lower bound provides one of the most stringent constraints. For the 4-2-2 route to $SO(10)$, the successful SM gauge coupling unification requires the 4-2-2 breaking scale to be ${\cal O} (10^{11})$ GeV, and most of the parameter space is excluded. For the $SU(5) \times U(1)_X$ route, on the other hand, the $U(1)_X$ breaking scale can be significantly higher, and a wide range of the parameter space is allowed. Furthermore, the proton lifetime in the $SU(5)$ case is predicted to be $4.53 \times 10^{34}$ years, which lies well within the sensitivity reach of the Hyper-Kamiokande experiment. We also examine the constraints on the model parameter space from the Large Hadron Collider and the indirect DM search by Fermi-LAT and MAGIC experiments.

Minimal scenario of criticality for electroweak scale, neutrino masses, dark matter, and inflation

We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman–Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a Z_2 symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling xi |H|^2 R that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for xi =25 and that the heaviest right-handed neutrino is predicted to have a mass around 10^{14}mathrm{GeV} to meet the current cosmological observations. Such a small value of xi can be realized by the Higgs-portal coupling lambda _{SH}simeq 0.32 and the vacuum expectation value of the additional neutral scalar langle phi rangle simeq 2.7 TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section 1.8times 10^{-9} pb, and the mass of additional neutral scalar 190 GeV.

Wilson loop correlators in mathcal{N} = 2 superconformal quivers

We complete the program of [1] about perturbative approaches for mathcal{N} = 2 superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of AdS5 × S5 with the aim of testing possible holographic perspectives of quiver theories in mathcal{N} = 2.

Phase transitions in the logarithmic Maxwell O(3)-sigma model

We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell’s term and subject to a so-called Gausson’s self-dual potential. To carry out this study, it is numerically shown that this model supports topological solutions in 3-dimensional spacetime. In fact, to obtain the topological solutions, we assume a spherically symmetrical ansatz to find the solutions, as well as some physical behaviors of the vortex, as energy and magnetic field. It is presented a planar view of the magnetic field as an interesting configuration of a ring-like profile. To calculate the differential configurational complexity (DCC) of structures, the spatial energy density of the vortex is used. In fact, the DCC is important because it provides us with information about the possible phase transitions associated with the structures located in the Maxwell–Gausson model in 3D. Finally, we note from the DCC profile an infinite set of kink-like solutions associated with the parameter that controls the vacuum expectation value.

Scale-invariance, dynamically induced Planck scale and inflation in the Palatini formulation

We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.

The Fundamental Scale of QCD

There are several scales in the QCD as the theory of strong interaction: the vacuum gluonic condensate (as the divergence of the dilatation current), the nucleon mass as the basic mass scale in our universe, which is connected to the string tension $\sigma$, and the perturbative QCD scale $\Lambda_{\rm QCD}$, which defines the scale of the renormalized perturbative expansions. In this paper we connect all these scales to the vacuum condensate, using the field correlator method, where the string tension is expressed in terms of nonlocal field correlators, which are connected to the local condensates, while the perturbative $\Lambda_V$ is connected to $\sigma$ in the framework of the Background Perturbation Theory (BPT). We also demonstrate how the IR singularities and IR renormalons disappear in BPT making the resulting theory internally consistent.

Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermality of Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters sin theta and Delta m. As opposed to bosons, we find q>1, which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

Theory space of one unitary matrix model and its critical behavior associated with Argyres–Douglas theory

The lowest critical point of one unitary matrix model with cosine plus logarithmic potential is known to correspond with the [Formula: see text] Argyres–Douglas (AD) theory and its double scaling limit derives the Painlevé II equation with parameter. Here, we consider the critical points associated with all cosine potentials and determine the scaling operators, their vacuum expectation values (vevs) and their scaling dimensions from perturbed string equations at planar level. These dimensions agree with those of [Formula: see text] AD theory.

Detectable Gravitational Wave Signals from Affleck-Dine Baryogenesis.

In Affleck-Dine baryogenesis, the observed baryon asymmetry of the Universe is generated through the evolution of the vacuum expectation value of a scalar condensate. This scalar condensate generically fragments into nontopological solitons (Q balls). If they are sufficiently long-lived, they lead to an early matter domination epoch, which enhances the primordial gravitational wave signal for modes that enter the horizon during this epoch. The sudden decay of the Q balls results in a rapid transition from matter to radiation domination, producing a sharp peak in the gravitational wave power spectrum. Avoiding the gravitino over-abundance problem favors scenarios where the peak frequency of the resonance is within the range of the Einstein telescope and/or DECIGO. This observable signal provides a mechanism to test Affleck-Dine baryogenesis.

Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules * *Supported by National Natural Science Foundation of China (11775079)

In this study, we investigate the , , , , , , , and pentaquark molecular states with and without strangeness via the QCD sum rules in detail, focusing on the light flavor, , breaking effects, and make predictions for new pentaquark molecular states besides assigning , , , , and self-consistently. In the future, we can search for these pentaquark molecular states in the decay of , , and . Furthermore, we discuss high-dimensional vacuum condensates in detail.