Additional Scalar Field Research Articles

CriticalO(N)models above four dimensions: Small-Nsolutions and stability

We explore O(N) models in dimensions $4<d<6$. Specifically, we investigate models of an O(N) vector field coupled to an additional scalar field via a cubic interaction. Recent results in $d=6-\epsilon$ have uncovered an interacting ultraviolet fixed point of the renormalization group (RG) if the number N of components of the vector field is large enough, suggesting that these models are asymptotically safe. We set up a functional RG analysis of these systems to address three key issues: Firstly, we find that in $d=5$ the interacting fixed point exists all the way down to N=1. Secondly, we show that the standard O(N) universality classes are actually embedded in those of the cubic models, in that the latter exhibit the same values for (most of) the critical exponents, but feature an additional third RG relevant direction. Thirdly, we address the critical question of global stability of the fixed-point potential to test whether the fixed point can underly a viable quantum field theory.

Solving the wrong hierarchy problem

Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity- and $\mathbb{Z}_2$-symmetric theories where the Standard Model Higgs potential has two vacua. The parity or $\mathbb{Z}_2$ copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. We show this mechanism postdicts the top Yukawa to be within $1 \sigma$ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.

Radiative corrections to the Higgs boson couplings in the model with an additional real singlet scalar field

We calculate renormalized Higgs boson couplings with gauge bosons and fermions at the one-loop level in the model with an additional isospin singlet real scalar field. These coupling constants can deviate from the predictions in the standard model due to tree-level mixing effects and one-loop contributions of the extra neutral scalar boson. We investigate how they can be significant under the theoretical constraints from perturbative unitarity and vacuum stability and also the condition of avoiding the wrong vacuum. Furthermore, comparing with the predictions in the Type I two Higgs doublet model, we numerically demonstrate how the singlet extension model can be distinguished and identified by using precision measurements of the Higgs boson couplings at future collider experiments.

Renormalizable model for neutrino mass, dark matter, muon g − 2 and 750 GeV diphoton excess

We discuss a possibility to explain the 750 GeV diphoton excess observed at the LHC in a three-loop neutrino mass model which has a similar structure to the model by Krauss, Nasri and Trodden. Tiny neutrino masses are naturally generated by the loop effect of new particles with their couplings and masses to be of order 0.1-1 and TeV, respectively. The lightest right-handed neutrino, which runs in the three-loop diagram, can be a dark matter candidate. In addition, the deviation in the measured value of the muon anomalous magnetic moment from its prediction in the standard model can be compensated by one-loop diagrams with exotic multi-charged leptons and scalar bosons. For the diphoton event, an additional isospin singlet real scalar field plays the role to explain the excess by taking its mass of 750 GeV, where it is produced from the gluon fusion production via the mixing with the standard model like Higgs boson. We find that the cross section of the diphoton process can be obtained to be a few fb level by taking the masses of new charged particles to be about 375 GeV and related coupling constants to be order 1.

Impact of other scalar fields on oscillons after hilltop inflation

Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations in 2+1 dimensions to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically form, and consider the coupling to an additional scalar field which, depending on the value of the coupling parameter, can get resonantly enhanced from the inhomogeneous inflaton field. We find that three cases are realized: without a parametric resonance, the additional scalar field has no effects on the oscillons. For a fast and strong parametric resonance of the other scalar field, oscillons are strongly suppressed. For a delayed parametric resonance, on the other hand, the oscillons get imprinted on the other scalar field and their stability is even enhanced compared to the single-field oscillons.

Inflation with an extra light scalar field after Planck

Bayesian inference techniques are used to investigate situations where an additional light scalar field is present during inflation and reheating. This includes (but is not limited to) curvaton-type models. We design a numerical pipeline where ≃ 200 inflaton setups × 10 reheating scenarios = 2000 models are implemented and we present the results for a few prototypical potentials. We find that single-field models are remarkably robust under the introduction of light scalar degrees of freedom. Models that are ruled out at the single-field level are not improved in general, because good values of the spectral index and the tensor-to-scalar ratio can only be obtained for very fine-tuned values of the extra field parameters and/or when large non-Gaussianities are produced. The only exception is quartic large-field inflation, so that the best models after Planck are of two kinds: plateau potentials, regardless of whether an extra field is added or not, and quartic large-field inflation with an extra light scalar field, in some specific reheating scenarios. Using Bayesian complexity, we also find that more parameters are constrained for the models we study than for their single-field versions. This is because the added parameters not only contribute to the reheating kinematics but also to the cosmological perturbations themselves, to which the added field contributes. The interplay between these two effects lead to a suppression of degeneracies that is responsible for having more constrained parameters.

From OPE to chiral perturbation theory in holographic QCD

The soft wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply with the OPE. We study also the axial two-point function using the same modified dilaton field and an additional scalar field to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, F π and L 10 , are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.

Scalar dark matter in the B−L model

The U(1)B−L extension of the Standard Model requires the existence of right-handed neutrinos and naturally realizes the seesaw mechanism of neutrino mass generation. We study the possibility of explaining the dark matter in this model with an additional scalar field, ϕDM, that is a singlet of the Standard Model but charged under U(1)B−L. An advantage of this scenario is that the stability of ϕDM can be guaranteed by appropriately choosing its B−L charge, without the need of an extra ad hoc discrete symmetry. We investigate in detail the dark matter phenomenology of this model. We show that the observed dark matter density can be obtained via gauge or scalar interactions, and that semi-annihilations could play an important role in the latter case. The regions consistent with the dark matter density are determined in each instance and the prospects for detection in future experiments are analyzed. If dark matter annihilations are controlled by the B−L gauge interaction, the mass of the dark matter particle should lie below 5 TeV and its direct detection cross section can be easily probed by XENON1T; if instead they are controlled by scalar interactions, the dark matter mass can be much larger and the detection prospects are less certain. Finally, we show that this scenario can be readily extended to accommodate multiple dark matter particles.

Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime

We investigate stability of the Higgs effective potential in curved spacetime. To this end, we consider the gauge-less top-Higgs sector with an additional scalar field. Explicit form of the terms proportional to the squares of the Ricci scalar, the Ricci tensor and the Riemann tensor that arise at the one-loop level in the effective action has been determined. We have investigated the influence of these terms on the stability of the scalar effective potential. The result depends on background geometry. In general, the potential becomes modified both in the region of the electroweak minimum and in the region of large field strength.

Dark matter and neutrino masses from a scale-invariant multi-Higgs portal

We consider a classically scale invariant version of the Standard Model, extended by an extra dark $SU(2)_X$ gauge group. Apart from the dark gauge bosons and a dark scalar doublet which is coupled to the Standard Model Higgs through a portal coupling, we incorporate right-handed neutrinos and an additional real singlet scalar field. After symmetry breaking \`a la Coleman-Weinberg, we examine the multi-Higgs sector and impose theoretical and experimental constraints. In addition, by computing the dark matter relic abundance and the spin-independent scattering cross section off a nucleon we determine the viable dark matter mass range in accordance with present limits. The model can be tested in the near future by collider experiments and direct detection searches such as XENON 1T.

Assuming Regge trajectories in holographic QCD: from OPE to chiral perturbation theory

The soft wall model in holographic QCD has Regge trajectories but wrong oper- ator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply with the OPE. We study also the axial two-point function us- ing the same modified dilaton field and an additional scalar fie ld to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, Fπ and L10, are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocat- ing Digamma function to study QCD two-point functions in different momentum regions.

Relaxed superconductors

Momentum relaxation can be built into many holographic models without sacrificing homogeneity of the bulk solution. In this paper we study two such models: one in which translational invariance is broken in the dual theory by spatially-dependent sources for massless scalar fields and another that features an additional neutral scalar field. We turn on a charged scalar field in order to explore the condensation of a charged scalar operator in the dual theories. After demonstrating that the relaxed superconductors we construct are thermodynamically relevant, we find that the finite DC electrical conductivity of the normal phase is replaced by a superfluid pole in the broken phase. Moreover, when the normal phase possesses a Drude behaviour at low frequencies, the optical conductivity of the broken phase at low frequencies can be described by a two-fluid model that is a sum of a Drude peak and a superfluid pole, as was found recently for inhomogeneous holographic superconductors. We also study cases in which this low-frequency behavior does not hold. We find that the Drude description is accurate when the retarded current-current correlator has a purely-dissipative pole that is well-separated from the rest of the excitations.

Nonthermal two component dark matter model for Fermi-LAT γ-ray excess and 3.55 keV X-ray line

A two component model of nonthermal dark matter is formulated to simultaneously explain the Fermi-LAT results indicating a $\gamma$-ray excess observed from our Galactic Centre in the 1-3 GeV energy range and the detection of an X-ray line at 3.55 keV from extragalactic sources. Two additional Standard Model singlet scalar fields $S_2$ and $S_3$ are introduced. These fields couple among themselves and with the Standard Model Higgs doublet $H$. The interaction terms among the scalar fields, namely $H$, $S_2$ and $S_3$, are constrained by the application of a discrete $\mathbb{Z}_2\times \mathbb{Z}^\prime_2$ symmetry which breaks softly to a remnant $\mathbb{Z}^{\prime \prime}_2$ symmetry. This residual discrete symmetry is then spontaneously broken through an MeV order vacuum expectation value $u$ of the singlet scalar field $S_3$. The resultant physical scalar spectrum has the Standard Model like Higgs as $\chi_{{}_{{}_1}}$ with $M_{\chi_{{}_{{}_1}}}\sim 125$ GeV, a moderately heavy scalar $\chi_{{}_{{}_2}}$ with $50 \,\,{\rm GeV} \leq M_{\chi_{{}_{{}_2}}}\leq 80\,\,{\rm GeV}$ and a light $\chi_{{}_{{}_3}}$ with $M_{\chi_{{}_{{}_3}}} \sim 7$ keV. There is only tiny mixing between $\chi_{{}_{{}_1}}$ and $\chi_{{}_{{}_2}}$ as well as between $\chi_{{}_{{}_1}}$ and $\chi_{{}_{{}_3}}$. The lack of importance of domain wall formation in the present scenario from the spontaneous breaking of the discrete symmetry ${\mathbb{Z}_2^{\prime\prime}}$, provided $u\leq 10$ MeV, is pointed out. We find that our proposed two component dark matter model is able to explain successfully both the above mentioned phenomena $-$ the Fermi-LAT observed $\gamma$-ray excess (from the $\chi_{{}_{{}_2}} \rightarrow {\rm b} \bar{\rm b}$ decay mode) and the observation of the X-ray line (from the decay channel $\chi_{{}_{{}_3}}\rightarrow\gamma \gamma$) by the XMM-Newton observatory.

Son-Yamamoto relation and holographic renormalization group flows

Motivated by the Son-Yamamoto (SY) relation which connects the three point and two-point correlators we consider the holographic RG flows in the bottom-up approach to holographic QCD via the Hamilton-Jacobi (HJ) equation with respect to the radial coordinate . It is shown that the SY relation is diagonal with respect to the RG flow in the 5d YM-CS model while the RG equation acquires the inhomogeneous term in the model with the additional scalar field which encodes the chiral condensate.

Higgs and gravitational scalar fields together induce Weyl gauge

A common biquadratic potential for the Higgs field $h$ and an additional scalar field $\phi$, non minimally coupled to gravity, is considered in locally scale symmetric approaches to standard model fields in curved spacetime. A common ground state of the two scalar fields exists and couples both fields to gravity, more precisely to scalar curvature $R$. In Einstein gauge ($\phi = const$, often called "Einstein frame"), also $R$ is scaled to a constant. This condition makes perfect sense, even in the general case, in the Weyl geometric approach. There it has been called {\em Weyl gauge}, because it was first considered by Weyl in the different context of his original scale geometric theory of gravity of 1918. Now it seems to get new meaning as a combined effect of electroweak theory and gravity, and their common influence on atomic frequencies.

Inflationary behavior ofR2gravity in a conformal framework

Models of inflation are tightly constrained by the PLANCK satellite data. Among them, Starobinsky's model with an exponential type potential seems to be challenged by the recent BICEP2 results. The model is based on the existence of $\,~ R^2$ terms in the Einstein-Hilbert action, which have their origin in the conformal-anomaly. Conformal (or Weyl) gravitational theories are relevant when matter fields become effectively massless; i.e. their masses are negligible in comparison with the spacetime curvature. These theories may include other, additional scalar fields. We show that their presence under general conditions does not destabilize the inflationary behaviour encountered in the Starobinsky model, although the issue of the exact quantitative agreement with existing data, like the tensor to scalar ratio, rests on the choice of parameters.

Dark Energy coupling with electromagnetism as seen from future low-medium redshift probes

Beyond the standard cosmological model where the late-time accelerated expansion of the universe is driven by a cosmological constant, the observed expansion can be reproduced as well by the introduction of an additional dynamical scalar field. In this case, the field is expected to be naturally coupled to the rest of the theory's fields, unless a (still unknown) symmetry suppresses this coupling. Therefore, this would possibly lead to some observational consequences, such as space-time variations of nature's fundamental constants. In this paper we investigate the coupling between a dynamical Dark Energy model and the electromagnetic field, and the corresponding evolution of the fine structure constant (α) with respect to the standard local value α0.

Phase Field Approximation of Dynamic Brittle Fracture

AbstractThe numerical assessment of fracture has gained importance in fields like the safety analysis of technical structures or the hydraulic fracturing process. The modelling technique discussed in this work is the phase field method which introduces an additional scalar field. The smooth phase field distinguishes broken from undamaged material and thus describes cracks in a continuum. The model consists of two coupled partial differential equations ‐ the equation of motion including the constitutive behaviour of the material and a phase field evolution equation. The crack growth follows implicitly from the solution of this system of PDEs. The numerical solution with finite elements can be accelerated with an algorithm that performs computationally extensive tasks on a graphic processing unit (GPU). A numerical example illustrates the capability of the model to reproduce realistic features of dynamic brittle fracture. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Cosmology in generalized Horndeski theories with second-order equations of motion

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\chi$ associated with the gravitational sector, we take into account multiple scalar fields $\phi_I$ ($I=1,2\cdots,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I=\partial_{\mu}\phi_I\partial^{\mu}\phi_I$. These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $\phi_I$ are generally suppressed relative to that for the dark energy field $\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

Quantifying the `naturalness' of the curvaton model

We investigate the probability of obtaining an observable curvature perturbation, using as an example the minimal curvaton-higgs (MCH) model. We determine ``probably observable'' and ``probably excluded'' regions of parameter space assuming generic initial conditions and applying a stochastic approach for the curvaton's evolution during inflation. Inflation is assumed to last longer than the Nobs ≃ 55 observable e-folds, and the total number of e-folds of inflation determines the particular ranges of parameters that are probable. For the MCH model, these ``probably observable'' regions always lie within the range 8 × 104 GeV ⩽ mσ ⩽ 2 × 107 GeV, where mσ is the curvaton mass, and the Hubble scale at horizon exit is chosen as H* = 1010 GeV. Because the ``probably observable'' region depends on the total duration of inflation, information on parameters in the Lagrangian from particle physics and from precision CMB observations can therefore provide information about the total duration of inflation, not just the last Nobs e-folds. This method could also be applied to any model that contains additional scalar fields to determine the probability that these scalar fields contribute to the curvature perturbation.