Vacuum Expectation Value Research Articles

Mean-Field Phase Transitions in Tensorial Group Field Theory Quantum Gravity.

Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field theory (TGFT) has recently led to much progress in its application to phenomenology, in particular, cosmology. This application relies on the assumption of a phase transition to a nontrivial vacuum (condensate) state describable by mean-field theory, an assumption that is difficult to corroborate by a full RG flow analysis due to the complexity of the relevant TGFT models. Here, we demonstrate that this assumption is justified due to the specific ingredients of realistic quantum geometric TGFT models: combinatorially nonlocal interactions, matter degrees of freedom, and Lorentz group data, together with the encoding of microcausality. This greatly strengthens the evidence for the existence of a meaningful continuum gravitational regime in group-field and spin-foam quantum gravity, the phenomenology of which is amenable to explicit computations in a mean-field approximation.

W-boson mass anomaly from a general SU(2) L scalar multiplet* *Supported in part by the National Key Research and Development Program of China (2021YFC2203003, 2020YFC2201501) and the National Natural Science Foundation of China (NSFC) (12005254, 12147103)

We explain the W-boson mass anomaly by introducing an scalar multiplet with general isospin and hypercharge {in the case without its vacuum expectation value}. It is shown that the dominant contribution from the scalar multiplet to the W-boson mass arises at the one-loop level, which can be expressed in terms of the electroweak (EW) oblique parameters T and S at leading order. We first rederive the general formulae of T and S induced by a scalar multiplet of EW charges, confirming the results in literature. We then study several specific examples of great phenomenological interest by applying these general expressions. As a result, it is found that the model with a scalar multiplet in an real representation with cannot generate the required correction because it leads to vanishing values of T and S. However, the cases with scalars in a complex representation under with a general hypercharge can explain the excess observed by CDF-II owing to nonzero T and S. We further consider the strong constraints from the perturbativity and EW global fit of the precision data and vary the isospin representation and hypercharge of the additional scalar multiplet to assess the extent of the model to solve the W-boson mass anomaly. It turns out that these constraints play important roles in setting limits on the model parameter space. We also briefly describe the collider signatures of the extra scalar multiplet, especially when it contains long-lived, heavy, highly charged states.

Особливості структури і фізико-хімічних властивостей міді, отриманої способом електронно-променевого випаровування-конденсації у вакуумі

Особливості структури і фізико-хімічних властивостей міді, отриманої способом електронно-променевого випаровування-конденсації у вакуумі

Features of the structure and physico-chemical properties of copper produced by the method of electron beam evaporation and condensation in vacuum

Features of the structure and physico-chemical properties of copper produced by the method of electron beam evaporation and condensation in vacuum

Bottom quark and tau lepton masses in a toy textrm{SU}(6) model

We study a toy textrm{SU}(6) model with the symmetry breaking pattern of the extended 331 symmetry of textrm{SU}(3)_c otimes textrm{SU}(3)_W otimes textrm{U}(1)_X. A “fermion-Higgs mismatching” symmetry breaking pattern is proposed for more realistic model building. Within such symmetry breaking pattern, only one Higgs doublet develops vacuum expectation value for the spontaneous electroweak symmetry breaking, and gives tree-level top quark mass. A natural VEV splittings in the 331 breaking Higgs fields gives tree-level masses to both bottom quark and tau lepton. The 125,textrm{GeV} SM-like Higgs boson discovered at the LHC can have Yukawa couplings to bottom quark and tau lepton as in the SM prediction, and this suggests the 331 symmetry breaking scale to be sim {{{mathcal {O}}}}(10),textrm{TeV}.

EFT of conformal symmetry breaking

Conformal symmetry can be spontaneously broken due to the presence of a defect or other background, which gives a symmetry-breaking vacuum expectation value (VEV) to some scalar operators. We study the effective field theory of fluctuations around these backgrounds, showing that it organizes as an expansion in powers of the inverse of the VEV, and computing some of the leading corrections. We focus on the case of spacelike defects in a four-dimensional Lorentzian theory relevant to the pseudoconformal universe scenario, although the conclusions extend to other kinds of defects and to the breaking of conformal symmetry to Poincar\'e symmetry.

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field ϕ nonminimally coupled to the Ricci scalar R of the form F(ϕ)R. The scalar field has a self-interacting potential and sits at its vacuum expectation value ϕv far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value ϕc close to 0. This allows the existence of scalarized NS solutions connecting ϕv with ϕc whose difference is significant, whereas the field is located in the vicinity of ϕ=ϕv for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field ϕ finally approaches the asymptotic value ϕv without spoiling a successful cosmological evolution. After ϕ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

Constraints on the doublet left-right symmetric model from Higgs data

We study the constraints on the doublet left-right symmetric model (DLRSM) arising due to the Higgs data. The SU(2)L symmetry of this model is broken by three vacuum expectation values, κ1, κ2 and vL. Most studies of this model assume that the ratios r = κ2/κ1 and w = vL/κ1 are very small. In this work, we study the constraints imposed on r and w by the Higgs data from LHC. We consider the most general scalar potential and calculate the masses of the CP-even scalars and the couplings of the lightest of these scalars to itself, to W and Z gauge bosons and to the third generation quarks. We find that there is no lower bound on either r or w. Equating the mass of the lightest CP-even scalar to 125 GeV leads to an upper limit w < 6.7. The requirement that the Yukawa coupling of the quarks to the Higgs bidoublet of the model should be perturbative yields the upper bounds r < 0.8 and w < 3.5. The Yukawa coupling of the bottom quark to the lightest CP-even scalar strongly disfavours value of r, w < 0.1 and shows a marked preference for values of w ∼ mathcal{O} (1).

Spontaneous Lorentz symmetry breaking effects on GRBs jets arising from neutrino pair annihilation process near a black hole

The study of neutrino pair annihilation into electron-positron pairs (nu {bar{nu }}rightarrow e^-e^+) is astrophysically well-motivated because it is a possible powering mechanism for the gamma-ray bursts (GRBs). In this paper, we estimate the gamma-ray energy deposition rate (EDR) arising from the annihilation of the neutrino pairs in the equatorial plane of a slowly rotating black hole geometry modified by the broken Lorentz symmetry (induced by a background bumblebee vector field). More specifically, owing to the presence of a dimensionless Lorentz symmetry breaking (LSB) parameter l arising from nonminimal coupling between the bumblebee field with nonzero vacuum expectation value and gravity, the metric solution in question differs from the standard slowly rotating Kerr black hole. By idealizing the thin accretion disk temperature profile in the two forms of isothermal and gradient around the bumblebee gravity-based slow rotating black hole, we investigate the influence of spontaneous LSB on the nu {bar{nu }}-annihilation efficiency. For both profiles, we find that positive values of LSB parameter l>0 induce an enhancement of the EDR associated with the neutrino-antineutrino annihilation. Therefore, the process of powering the GRBs jets around bumblebee gravity modified slowly rotating geometry is more efficient in comparison with standard metric. Using the observed gamma-ray luminosity associated with different GRBs types (short, long, and ultra-long), we find, through the analysis of the EDR in the parameter space l-a (a^2ll 1), some allowed ranges for the LSB parameter l.

The anomalous shift of the weak boson mass and the quintessence electroweak axion

One of the simplest ways to account for the observed W-boson mass shift is to introduce the SU(2) L triplet Higgs boson with zero hypercharge, whose vacuum expectation value is about 3 GeV. If the triplet is heavy enough at TeV, it essentially contributes only to T parameter without any conflict with the observation. The presence of a complex triplet Higgs boson raises the SU(2) L gauge coupling constant to α 2(M PL) ≃ 1/44 at the Planck scale. Thanks to this larger gauge coupling constant, we show that the electroweak axion vacuum energy explains the observed cosmological constant provided that the axion field is located near the hill top of the potential at present.

Non-perturbative analysis for a massless minimal quantum scalar with V(ϕ) = λϕ 4/4! + βϕ 3/3! in the inflationary de Sitter spacetime

We consider a massless, minimally coupled quantum scalar field theory with an asymmetric self interaction, V(ϕ) = λϕ 4/4! + βϕ 3/3! (λ > 0) in the inflationary de Sitter spacetime. The potential is bounded from below. While the β=0 case has been much well studied, the motivation behind taking such a hybrid potential corresponds to the fact that it might generate finite negative vacuum expectation values of V(ϕ) as well of ϕ, leading to some dynamical screening of the inflationary cosmological constant Λ, at late times, with the initial conditions, 〈ϕ〉 = 0 = 〈V(ϕ)〉. In this work we first compute the vacuum expectation values of ϕ, ϕ 2 and V(ϕ), using the late time, non-perturbative and infrared effective stochastic formalism. The backreactions to the inflationary Λ are estimated. We also compute the dynamically generated mass of the scalar field using 〈ϕ 2〉. We next compute 〈ϕ 2〉 using quantum field theory with respect to the initial Bunch-Davies vacuum at one and two loops, using the Schwinger-Keldysh formalism. These results show non-perturbative secular logarithms, growing with the cosmological time. Using next a recently proposed renormalisation group inspired formalism, we attempt to find out a resummed 〈ϕ 2〉. We have been able to resum some part of the same which contains contributions only from the local self energy. The corresponding dynamically generated mass is computed. Comparison of the stochastic and the quantum field theory results shows that they differ numerically, although they have similar qualitative behaviour. Possible reasons for such quantitative mismatch is discussed. The manifestation of strong non-classical effects in the results found via both the formalisms has been emphasised.

Preparation of Poly(4-methyl-1-pentene) Membranes by Low-Temperature Thermally Induced Phase Separation

As a widely used method for the preparation of membranes, thermally induced phase separation (TIPS) is usually performed at high temperatures (200–260 °C) and has the disadvantages of high energy consumption, usage of large amounts of solvents, and easy decomposition of polymers. To solve these problems, this article presents a low-temperature thermally induced phase separation (LT-TIPS) method for the preparation of porous poly(4-methyl-1-pentene) (PMP) membranes at 70 °C. The PMP/cyclohexane solution was cast on a glass plate and quenched in water for a few minutes, and then the solvent was recovered by vacuum evaporation and condensation. The effects of quenching medium, quenching temperature, time, wet membrane thickness, and polymer concentration on the membrane porosity and air permeability were studied. The results showed that the elevated quenching temperature and extended quenching time in water favor the increase of air permeability. The increase of wet membrane thickness and polymer concentration results in reduced air permeability. The method displays convenience in process control, low energy consumption, less solvent usage, easy recovery of solvent, and environmental friendliness, exhibiting great promises for the preparation of membranes.

Some new observations for the Georgi-Machacek scenario with triplet Higgs scalars

The Georgi-Machacek model, introducing a complex and a real scalar triplet as additional components of the electroweak symmetry breaking sector, enables substantial triplet contributions to the weak gauge boson masses, subject to the equality of the complex and the real triplet vacuum expectation values (vev) via a custodial SU(2) symmetry. We present an updated set of constraints on this scenario, from collider data (including those from 137/139~fb$^{-1}$ of luminosity at the Large Hadron Collider), available data on the 125-GeV scalar, indirect limits and also theoretical restrictions from vacuum stability and unitarity. It is found that some bounds get relaxed, and the phenomenological potential of the scenario is more diverse, if the doubly charged scalar in the spectrum can decay not only into two like-sign $W$'s but also into one or two singly charged scalars. Other interesting features are noticed in a general approach, such as substantial $\gamma\gamma$ and $Z\gamma$ branching ratios of the additional custodial singlet scalar, and appreciable strength of the trilinear interaction of a charged scalar, the $W$ and the $Z$. Finally,, we take into account the possibility of custodial SU(2) breaking, resulting in inequality of the real and the complex scalar vevs which too in principle may allow large triplet contribution to weak boson masses. Illustrative numerical results on the modified limits and predictions are presented, once more taking into account all the constraints mentioned above.

Dual electroweak phase transition in the two-Higgs-doublet model with the S3 discrete symmetry

In this work, dual electroweak phase transition (EWPT) consisting of two phases, is carefully studied in the two-Higgs-doublet model with the $S_3$ discrete symmetry. The role of $S_3$ here is to further separate the stages of the electroweak phase transition, compared to that of the original two-Higgs-doublet model (2HDM). The strength of the electroweak phase transition $(S)$ in the model under consideration is large enough for the first-order EWPT, specifically $1 < S < 2.8$. The ratio between the two vacuum expectation values (VEVs), $\tan\beta = v_2/v_1$, is proven to have no effects on the strength of the phase transition. This ratio only affects the mass domain that causes the first-order phase transition. Furthermore, in this paper we will show clearly that when studying the EWPT in models of more than one scalar field that generates masses, one needs to analyze the problem of phase transition under multiple stages. In other words, the effect of the first stage of symmetry breaking to the second one, is to simplify by suggestion that vacuum expectation value of the Higgs boson responsible for the initial stage is proportional to that of the field for the next stage.

Finite temperature energy–momentum tensor in compactified cosmic string spacetime

In this paper we analyze the expectation value of the field squared and the energy–momentum tensor associated with a massive charged scalar quantum field with a nonzero chemical potential propagating in a high-dimensional compactified cosmic string spacetime in thermal equilibrium at finite temperature T. Moreover, we assume that the charged quantum field interacts with a very thin magnetic flux running along the core of the idealized cosmic string, and with a magnetic flux enclosed by the compact dimension. These observables are expressed as the vacuum expectation values and the finite temperature contributions coming from the particles and antiparticles excitations. Due to the compactification, the thermal corrections can be decomposed in a part induced by the cosmic string spacetime without compactification, plus a contribution induced by the compactification. This decompositions explicitly follows from the Abel–Plana formula used to proceed the summation over the discrete quantum number associated with the quasiperiodic condition imposed on the quantum field along the compact dimension. The expectations values of the field squared and the energy–momentum tensor are even periodic functions of the magnetic flux with period being the quantum flux, and also even functions of the chemical potential. Our main objectives in this paper concern in the investigation of the thermal corrections only. In this way we explicitly calculate the behavior of these observables in the limits of low and high temperature. We show that the temperature enhance the induced densities. In addition some graphs are also included in order to exhibit these behaviors.

Neutrino capture on tritium as a probe of flavor vacuum condensate and dark matter

We show that the study of neutrino capture on tritium, for non-relativistic neutrinos, can allow to distinguish among the various neutrino models, eventually prove the quantum field theory condensation effects and permit to test the hypothesis according to which the flavor vacuum energy gives a contribution to the dark matter of the universe. Indeed, we show that the capture rate depends on the neutrino model considered, and that it brings an imprint of the flavor vacuum condensate. Experiments like PTOLEMY, designed to reveal the cosmic neutrino background, then can give an indication of the existence of the dark matter component induced by neutrino mixing.

Confinement in QCD: novelties

We report on recent progress in understanding confinement of colour in QCD as dual superconductivity of the vacuum. A gauge invariant version of the creation operator of monopoles is constructed whose vacuum expectation value is the order parameter. This order parameter is gauge-invariant from scratch, has no infrared divergences, is finite in the confined phase and vanishes in the deconfined phase. A natural explanation also emerges of why the electric field lines in the flux tubes keep no memory of the colour orientation of the condensing monopoles. A further by-product is that the order parameter can be traded with the two-point vacuum parallel correlator of the chromo-electric field.

Dark energy with a triplet of classical U(1) fields

We present a new mechanism for cosmic acceleration consisting of a scalar field coupled to a triplet of classical U(1) gauge fields. The gauge fields are arranged in a homogeneous, isotropic configuration, with both electric- and magnetic-like vacuum expectation values. The gauge fields provide a mass-like term via a Chern-Simons interaction that suspends the scalar away from its potential minimum, thereby enabling potential-dominated evolution. We show this mechanism can drive a brief period of acceleration, such as dark energy, without the need for fine tunings. We obtain simple analytic results for the dark energy equation of state and dependence on model parameters. In this model, the presence of the gauge field generically leads to a suppression of long-wavelength gravitational waves, with implications for the experimental search for cosmic microwave background B-modes and direct detection of a stochastic gravitational wave background.

A model of pseudo-Nambu–Goldstone dark matter from a softly brokenSU(2) global symmetry with aU(1) gauge symmetry

AbstractA model of the pseudo-Nambu–Goldstone (pNG) dark matter (DM) is proposed. We assume that there is an SU(2)g global symmetry and a U(1)X gauge symmetry in the dark sector, and they are spontaneously broken into a U(1)D global symmetry after a scalar field develops a vacuum expectation value. We add a soft symmetry-breaking term that breaks the SU(2)g global symmetry into the U(1)g global symmetry explicitly. Our model predicts a stable complex pNG particle under the U(1)D global symmetry. One of the virtues of the pNG DM models is that the models can explain the current null results of the direct detection experiments. The small momentum transfer suppresses the scattering amplitudes thanks to the low-energy behavior of the Nambu–Goldstone boson. In our model, the soft symmetry-breaking term is uniquely determined. This is the advantage of our model compared to some earlier works in which some soft symmetry-breaking terms cannot be forbidden but are simply assumed to be absent to avoid the constraints from the direct detection experiments. We calculate the thermal relic abundance of the pNG DM and find that the model can explain the measured value of the DM energy density under some constraints from perturbative unitarity.