Showing papers on "Scalar potential published in 2019"

Analytic Description of Primordial Black Hole Formation from Scalar Field Fragmentation

Abstract: Primordial black hole (PBH) formation is a more generic phenomenon than was once thought. The dynamics of a scalar field in inflationary universe can produce PBHs under mild assumptions regarding the scalar potential. In the early universe, light scalar fields develop large expectation values during inflation and subsequently relax to the minimum of the effective potential at a later time. During the relaxation process, an initially homogeneous scalar condensate can fragment into lumps via an instability similar to the gravitational (Jeans) instability, where the scalar self-interactions, rather than gravity, play the leading role. The fragmentation of the scalar field into lumps (e.g. Q-balls or oscillons) creates matter composed of relatively few heavy "particles", whose distribution is subject to significant fluctuations unconstrained by comic microwave background (CMB) observations and unrelated to the large-scale structure. If this matter component comes to temporarily dominate the energy density before the scalar lumps decay, PBHs can be efficiently produced during the temporary matter-dominated era. We develop a general analytic framework for description of PBH formation in this class of models. We highlight the differences between the scalar fragmentation scenario and other commonly considered PBH formation models. Given the existence of the Higgs field and the preponderance of scalar fields within supersymmetric and other models of new physics, PBHs constitute an appealing and plausible candidate for dark matter.

New constraints on classical de Sitter: flirting with the swampland

Abstract: We study the existence and stability of classical de Sitter solutions of type II supergravities with parallel Dp-branes and orientifold Op-planes. Together with the dilaton and volume scalar fields, we consider a third one that distinguishes between parallel and transverse directions to the Dp/Op. We derive the complete scalar potential for these three fields. This formalism allows us to reproduce known constraints obtained in 10d, and to derive new ones. Specifying to group manifolds with constant fluxes, we exclude a large region of parameter space, forbidding de Sitter solutions on nilmanifolds, semi-simple group manifolds, and some solvmanifolds. In the small remaining region, we identify a stability island, where the three scalars could be stabilized in any de Sitter solution. We discuss these results in the swampland context.

Higgs scalar potential in asymptotically safe quantum gravity

Abstract: The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem, and a possible explanation of an---asymptotically---vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted.

A Strong Scalar Weak Gravity Conjecture and Some Implications

Abstract: We propose a new version of the scalar Weak Gravity Conjecture (WGC) which would apply to any scalar field coupled to quantum gravity. For a single scalar it is given by the differential constraint (V″)2 ≤ (2V‴2 − V″V′′′′) $$ {M}_{\mathrm{p}}^2 $$ , where V is the scalar potential. It corresponds to the statement that self-interactions of a scalar must be stronger than gravity for any value of the scalar field. We find that the solutions which saturate the bound correspond to towers of extremal states with mass $$ {m}^2\left(\phi \right)={m}_0^2/\left({\left(R/m\right)}^2+1/{(nR)}^2\right) $$ , with R2 = eϕ, consistent with the emergence of an extra dimension at large or small R and the existence of extended objects (strings). These states act as WGC states for the scalar ϕ. It is also consistent with the distance swampland conjecture with a built-in duality symmetry. All of this is remarkable since neither extra dimensions nor string theory are put in the theory from the beginning, but they emerge. This is quite analogous to how the 11-th dimension appears in M-theory from towers of Type IIA solitonic D0-branes. From this constraint one can derive several swampland conjectures from a single principle. In particular one finds that an axion potential is only consistent if f ≤ Mp, recovering a result already conjectured from other arguments. The conjecture has far reaching consequences and applies to several interesting physical systems: i) Among chaotic inflation potentials only those asymptotically linear may survive. ii) If applied to the radion of the circle compactification of the Standard Model to 3D with Dirac neutrinos, the constraint implies that the 4D cosmological constant scale must be larger than the mass of the lightest neutrino, which must be in normal hierarchy. It also puts a constraint on the EW scale, potentially explaining the hierarchy problem. This recovers and improves results already obtained by applying the AdS swampland conjecture, but in a way which is independent from UV physics. iii) It also constraints simplest moduli fixing string models. The simplest KKLT model is compatible with the constraints but the latter may be relevant for some choices of parameters.

Axion boson stars

Abstract: We study novel solitonic solutions to Einstein-Klein-Gordon theory in the presence of a periodic scalar potential arising in models of axion-like particles. The potential depends on two parameters: the mass of the scalar field ma and the decay constant fa; the standard case of the QCD axion is recovered when ma ∝ 1/fa. When fa → ∞ the solutions reduce to the standard case of "mini" boson stars supported by a massive free scalar field. As the energy scale fa of the scalar self-interactions decreases we unveil several novel features of the solution: new stability branches emerge at high density, giving rise to very compact, radially stable, boson stars. Some of the most compact configurations acquire a photon sphere. When fa is at the GUT scale, a boson star made of QCD axions can have a mass up to ten solar masses and would be more compact than a neutron star. Gravitational-wave searches for these exotic compact objects might provide indirect evidence for ultralight axion-like particles in a region not excluded by the black-hole superradiant instability.

Electroweak phase transition with composite Higgs models: calculability, gravitational waves and collider searches

Abstract: We study the strong first order electroweak phase transition (SFOEWPT) with the SO(6)/SO(5) composite Higgs model, whose scalar sector contains one Higgs doublet and one real singlet. Six benchmark models are built with fermion embeddings in 1, 6, and 15 of SO(6). We show that SFOEWPT cannot be triggered under the minimal Higgs potential hypothesis, which assumes the scalar potential is dominated by the form factors from the lightest composite resonances. To get a SFOEWPT, the contributions from local operators induced by physics above the cutoff scale are needed. We take the 6 + 6 model as an example to investigate the gravitational waves prediction and the related collider phenomenology.

Gravitational Waves as a Probe of Left-Right Symmetry Breaking

Abstract: Left-right symmetry at high energy scales is a well-motivated extension of the Standard Model. In this paper we consider a typical minimal scenario in which it gets spontaneously broken by scalar triplets. Such a realization has been scrutinized over the past few decades chiefly in the context of collider studies. In this work we take a complementary approach and investigate whether the model can be probed via the search for a stochastic gravitational wave background induced by the phase transition in which SU(3)C × SU(2)L × SU(2)R × U(1)B−L is broken down to the Standard Model gauge symmetry group. A prerequisite for gravitational wave production in this context is a first-order phase transition, the occurrence of which we find in a significant portion of the parameter space. Although the produced gravitational waves are typically too weak for a discovery at any current or future detector, upon investigating correlations between all relevant terms in the scalar potential, we have identified values of parameters leading to observable signals. This indicates that, given a certain moderate fine-tuning, the minimal left-right symmetric model with scalar triplets features another powerful probe which can lead to either novel constraints or remarkable discoveries in the near future. Let us note that some of our results, such as the full set of thermal masses, have to the best of our knowledge not been presented before and might be useful for future studies, in particular in the context of electroweak baryogenesis.

Magnetohydrodynamics as Superfluidity.

Abstract: We show that relativistic magnetohydrodynamics (MHD) can be recast as a novel theory of superfluidity. This new theory formulates MHD just in terms of conservation equations, including dissipative effects, by introducing appropriate variables such as a magnetic scalar potential, and providing necessary and sufficient conditions to obtain equilibrium configurations. We show that this scalar potential can be interpreted as a Goldstone mode originating from the spontaneous breaking of a one-form symmetry, and present the most generic constitutive relations at one derivative order for a parity-preserving plasma in this new superfluid formulation.

Linear confinement of a scalar and spin-0 particle in a topologically trivial flat Gödel-type space-time

Abstract: In the previous work (Ahmed, Eur Phys J C 78(7):598, 2018), we investigated the relativistic quantum effects on a scalar and spin-half particles in a topologically trivial flat Godel-type space-time. We have found that the energy eigenvalues of the system are influenced by the vorticity parameter characterizing the space-time. In the present work, we investigate the linear confinement of a scalar particle on the Klein–Gordon equation with a linear and Coulomb-type scalar potential in this flat Godel-type solution. The energy eigenvalues of the system get modifies due to the presence of scalar potentials, and the vorticity parameter. In addition, we study the relativistic quantum motion of spin-0 particles with vector and scalar potentials of Coulomb-type and analyze the effects on the energy eigenvalues.

Analytic Description of Primordial Black Hole Formation from Scalar Field Fragmentation

Abstract: Primordial black hole (PBH) formation is a more generic phenomenon than was once thought. The dynamics of a scalar field in inflationary universe can produce PBHs under mild assumptions regarding the scalar potential. In the early universe, light scalar fields develop large expectation values during inflation and subsequently relax to the minimum of the effective potential at a later time. During the relaxation process, an initially homogeneous scalar condensate can fragment into lumps via an instability similar to the gravitational (Jeans) instability, where the scalar self-interactions, rather than gravity, play the leading role. The fragmentation of the scalar field into lumps (e.g. Q-balls or oscillons) creates matter composed of relatively few heavy "particles", whose distribution is subject to significant fluctuations unconstrained by comic microwave background (CMB) observations and unrelated to the large-scale structure. If this matter component comes to temporarily dominate the energy density before the scalar lumps decay, PBHs can be efficiently produced during the temporary matter-dominated era. We develop a general analytic framework for description of PBH formation in this class of models. We highlight the differences between the scalar fragmentation scenario and other commonly considered PBH formation models. Given the existence of the Higgs field and the preponderance of scalar fields within supersymmetric and other models of new physics, PBHs constitute an appealing and plausible candidate for dark matter.

The Spectrum of Teleparallel Gravity

Abstract: The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential.

Scalar electroweak multiplet dark matter

Abstract: We revisit the theory and phenomenology of scalar electroweak multiplet thermal dark matter. We derive the most general, renormalizable scalar potential, assuming the presence of the Standard Model Higgs doublet, H, and an electroweak multiplet Φ of arbitrary SU(2)L rank and hypercharge, Y. We show that, in general, the Φ-H Higgs portal interactions depend on three, rather than two independent couplings as has been previously considered in the literature. For the phenomenologically viable case of Y = 0 multiplets, we focus on the septuplet and quintuplet cases, and consider the interplay of relic density and spin-independent direct detection cross section. We show that both the relic density and direct detection cross sections depend on a single linear combination of Higgs portal couplings, λeff. For λeff ∼ $$ \mathcal{O} $$ (1), present direct detection exclusion limits imply that the neutral component of a scalar electroweak multiplet would comprise a subdominant fraction of the observed DM relic density.

Unitary inflaton as decaying dark matter

Abstract: We consider the inflation model of a singlet scalar field (sigma field) with both quadratic and linear non-minimal couplings where unitarity is ensured up to the Planck scale. We assume that a Z2 symmetry for the sigma field is respected by the scalar potential in Jordan frame but it is broken explicitly by the linear non-minimal coupling due to quantum gravity. We discuss the impacts of the linear non-minimal coupling on various dynamics from inflation to low energy, such as a sizable tensor-to-scalar ratio, a novel reheating process with quartic potential dominance, and suppressed physical parameters in the low energy, etc. In particular, the linear non-minimal coupling leads to the linear couplings of the sigma field to the Standard Model through the trace of the energy-momentum tensor in Einstein frame. Thus, regarding the sigma field as a decaying dark matter, we consider the non-thermal production mechanisms for dark matter from the decays of Higgs and inflaton condensate and show the parameter space that is compatible with the correct relic density and cosmological constraints.

Vacuum stability and symmetry breaking in left-right symmetric model

Abstract: We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry breaking and the existence of a correct vacuum. We then compare results obtained from the derived conditions with those from numerical minimization of the scalar potential. Finally, we discuss the renormalization group analysis of the scalar quartic couplings through an example study that satisfies vacuum stability, perturbativity, unitarity and experimental bounds on the physical scalar masses.

Two-field cosmological α -attractors with Noether symmetry

Abstract: We study Noether symmetries in two-field cosmological α-attractors, investigating the case when the scalar manifold is an elementary hyperbolic surface. This encompasses and generalizes the case of the Poincare disk. We solve the conditions for the existence of a ‘separated’ Noether symmetry and find the form of the scalar potential compatible with such, for any elementary hyperbolic surface. For this class of symmetries, we find that the α-parameter must have a fixed value. Using those Noether symmetries, we also obtain many exact solutions of the equations of motion of these models, which were studied previously with numerical methods.

Metastable Vacua in Large-$N$ QCD$_3$

Abstract: We reexamine the vacuum structure of three-dimensional quantum chromodynamics (QCD$_3$) with gauge group $SU(N)$, $N_f$ fundamental quark flavors, and a level-$k$ Chern-Simons term. This analysis can be reliably carried out in the large-$N$, fixed $N_f, k$ limit of the theory, up to certain assumptions that we spell out explicitly. At leading order in the large-$N$ expansion we find $N_f + 1$ distinct, exactly degenerate vacuum superselection sectors with different patterns of flavor-symmetry breaking. The associated massless Nambu-Goldstone bosons are generically accompanied by topological Chern-Simons theories. This set of vacua contains many candidate phases previously proposed for QCD$_3$. At subleading order in the large-$N$ expansion, the exact degeneracy between the different superselection sectors is lifted, leading to a multitude of metastable vacua. If we dial the quark masses, different metastable vacua can become the true vacuum of the theory, leading to a sequence of first-order phase transitions. This intricate large-$N$ dynamics can be captured by the previously proposed bosonic dual theories for QCD$_3$, provided these bosonic duals are furnished with a suitable scalar potential. Interestingly, this potential must include terms beyond quartic order in the scalar fields.

Constraints on holographic multifield inflation and models based on the Hamilton-Jacobi formalism

Abstract: In holographic inflation, the 4D cosmological dynamics is postulated to be dual to the renormalization group flow of a 3D Euclidean conformal field theory with marginally relevant operators. The scalar potential of the 4D theory—in which inflation is realized—is highly constrained, with use of the Hamilton–Jacobi equations. In multifield holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wave functions contain no oscillatory phases independent of the momenta). We show that this result is exact, independent of the number of fields, the field space geometry, and the shape of the inflationary trajectory followed in multifield space. In the specific case where the multifield trajectory is a straight line or confined to a plane, it can be understood as the existence of an upper bound on the dynamical masses m of extra fields of the form m≤3H/2 up to slow roll corrections. This bound corresponds to the analytic continuation of the well-known Breitenlohner–Freedman bound found in anti–de Sitter spacetimes in the case when the masses are approximately constant. The absence of underdamped oscillations implies that a detection of “cosmological collider” oscillatory patterns in the non-Gaussian bispectrum would not only rule out single-field inflation, but also holographic inflation or any inflationary model based on the Hamilton–Jacobi equations. Hence, future observations have the potential to exclude, at once, an entire class of inflationary theories, regardless of the details involved in their model building.

Dark matter bound states via emission of scalar mediators

Abstract: If dark matter (DM) couples to a force carrier that is much lighter than itself, then it may form bound states in the early universe and inside haloes. While bound-state formation via vector emission is known to be efficient and have a variety of phenomenological implications, the capture via scalar emission typically requires larger couplings and is relevant to more limited parameter space, due to cancellations in the radiative amplitude. However, this result takes into account only the trilinear DM-DM-mediator coupling. Theories with scalar mediators include also a scalar potential, whose couplings may participate in the radiative transitions. We compute the contributions of these couplings to the radiative capture, and determine the parameter space in which they are important.

E9 exceptional field theory. Part I. The potential

Abstract: We construct the scalar potential for the exceptional field theory based on the affine symmetry group E9. The fields appearing in this potential live formally on an infinite-dimensional extended spacetime and transform under E9 generalised diffeomorphisms. In addition to the scalar fields expected from D = 2 maximal supergravity, the invariance of the potential requires the introduction of new constrained scalar fields. Other essential ingredients in the construction include the Virasoro algebra and indecomposable representations of E9. Upon solving the section constraint, the potential reproduces the dynamics of either eleven-dimensional or type IIB supergravity in the presence of two isometries.

The Fate of Dense Scalar Stars

Abstract: Long-lived pseudo-solitonic objects, known as oscillons/oscillatons, which we collectively call real scalar stars, are ubiquitous in early Universe cosmology of scalar field theories. Typical examples are axions stars and moduli stars. Using numerical simulations in full general relativity to include the effects of gravity, we study the fate of real scalar stars and find that depending on the scalar potential they are either meta-stable or collapse to black holes. In particular we find that for KKLT potentials the configurations are meta-stable despite the asymmetry of the potential, consistently with the results from lattice simulations that do not include gravitational effects. For ?-attractor potentials collapse to black holes is possible in a region of the parameter space where scalar stars would instead seem to be meta-stable or even disperse without including gravity. Each case gives rise to different cosmological implications which may affect the stochastic spectrum of gravitational waves.

On the inexistence of solitons in Einstein–Maxwell-scalar models

Abstract: Three non-existence results are established for self-gravitating solitons in Einstein–Maxwell-scalar models, wherein the scalar field is, generically, non-minimally coupled to the Maxwell field via a scalar function . Firstly, a trivial Maxwell field is considered, which yields a consistent truncation of the full model. In this case, using a scaling (Derrick-type) argument, it is established that no stationary and axisymmetric self-gravitating scalar solitons exist, unless the scalar potential energy is somewhere negative in spacetime. This generalises previous results for the static and strictly stationary cases. Thus, rotation alone cannot support self-gravitating scalar solitons in this class of models. Secondly, constant sign couplings are considered. Generalising a previous argument by Heusler for electro-vacuum, it is established that no static self-gravitating electromagnetic-scalar solitons exist. Thus, a varying (but constant sign) electric permittivity alone cannot support static Einstein–Maxwell-scalar solitons. Finally, the second result is generalised for strictly stationary, but not necessarily static, spacetimes, using a Lichnerowicz-type argument, generalising previous results in models where the scalar and Maxwell fields are not directly coupled. The scope of validity of each of these results points out the possible paths to circumvent them, in order to obtain self-gravitating solitons in Einstein–Maxwell-scalar models.

A new N=1 AdS4 Vacuum of Maximal Supergravity

Abstract: The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N=8, SO(8) gauged supergravity using Machine Learning software has led to a discovery of a new N=1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3)xZ2-invariant truncation of the N=8 theory to an N=1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the N=1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3)xZ2-invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional Z2^3-invariant scalar manifold (SU(1,1)/U(1))^7, for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new N=1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an N=1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

Axion boson stars

Abstract: We study novel solitonic solutions to Einstein-Klein-Gordon theory in the presence of a periodic scalar potential arising in models of axion-like particles. The potential depends on two parameters: the mass of the scalar field $m_a$ and the decay constant $f_a$; the standard case of the QCD axion is recovered when $m_a\propto1/f_a$. When $f_a\to\infty$ the solutions reduce to the standard case of "mini" boson stars supported by a massive free scalar field. As the energy scale $f_a$ of the scalar self-interactions decreases we unveil several novel features of the solution: new stability branches emerge at high density, giving rise to very compact, radially stable, boson stars. Some of the most compact configurations acquire a photon sphere. When $f_a$ is at the GUT scale, a boson star made of QCD axions can have a mass up to ten solar masses and would be more compact than a neutron star. Gravitational-wave searches for these exotic compact objects might provide indirect evidence for ultralight axion-like particles in a region not excluded by the black-hole superradiant instability.

Symmetries and Mass Degeneracies in the Scalar Sector

Abstract: We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that (CP4)n is the identity operator only for integer n values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZWW vertices.

Charting the phase diagram of QCD3

Abstract: We study the phase diagram of SU (N) gauge theory in three space-time dimensions with a Chern-Simons term at level k, coupled to two sets of fundamental fermions with masses m1 and m2, respectively. The two-dimensional phase diagram that we propose shows a rich structure and widens in an interesting way previous results in the literature, to which it reduces in some limits. We present several checks of our proposal, including consistency with boson/fermion dualities. In this respect, we extensively comment on the structure of the scalar potential which is needed on the bosonic side of the duality.

On the inexistence of solitons in Einstein-Maxwell-scalar models

Abstract: Three non-existence results are established for self-gravitating solitons in Einstein-Maxwell-scalar models, wherein the scalar field is, generically, non-minimally coupled to the Maxwell field via a scalar function $f(\Phi)$. Firstly, a trivial Maxwell field is considered, which yields a consistent truncation of the full model. In this case, using a scaling (Derrick-type) argument, it is established that no stationary and axisymmetric self-gravitating scalar solitons exist, unless the scalar potential energy is somewhere negative in spacetime. This generalises previous results for the static and strictly stationary cases. Thus, rotation alone cannot support self-gravitating scalar solitons in this class of models. Secondly, constant sign couplings are considered. Generalising a previous argument by Heusler for electro-vacuum, it is established that no static self-gravitating electromagnetic-scalar solitons exist. Thus, a varying (but constant sign) electric permittivity alone cannot support static Einstein-Maxwell-scalar solitons. Finally, the second result is generalised for strictly stationary, but not necessarily static, spacetimes, using a Lichnerowicz-type argument, generalising previous results in models where the scalar and Maxwell fields are not directly coupled. The scope of validity of each of these results points out the possible paths to circumvent them, in order to obtain self-gravitating solitons in Einstein-Maxwell-scalar models.

Two-real-scalar-singlet extension of the SM: LHC phenomenology and benchmark scenarios.

Abstract: We investigate the LHC phenomenology of a model where the Standard Model (SM) scalar sector is extended by two real scalar singlets. A $\mathbb{Z}_2\otimes\mathbb{Z}_2'$ discrete symmetry is imposed to reduce the number of scalar potential parameters, which is spontaneously broken by the vacuum expectation values of the singlet fields. As a result, all three neutral scalar fields mix, leading to three neutral CP-even scalar bosons, out of which one is identified with the observed Higgs boson at 125 GeV. We explore all relevant collider signatures of the three scalars in this model. Besides the single production of a scalar boson decaying directly to SM particle final states, we extensively discuss the possibility of resonant multi-scalar production. The latter includes decays of the produced scalar boson to two identical scalars ("symmetric decays"), as well as to two different scalars ("asymmetric decays"). Furthermore, we discuss the possibility of successive decays to the lightest scalar states ("cascade decays"), which lead to experimentally spectacular three- and four-Higgs final states. We provide six benchmark scenarios for detailed experimental studies of these Higgs-to-Higgs decay signatures.

The Application of Theta Method to Potential Field Gradient Tensor Data for Edge Detection of Complex Geological Structures

Abstract: Edge detection of magnetized structures is an important application of magnetic filters for geological interpretations. In this way, one can mention methods of the potential field derivatives which are categorized into: methods based on scalar potential field and potential field gradient tensor (PGT) data. Using five independent signal components, methods based on the PGT matrices have higher accuracy than methods based on scalar potential field data. Investigations of various methods of edge detection show that as geologic conditions become more complex, they greatly lose their efficacy and sometimes suffer from distortions. These distortions probably result from the Gibbs phenomenon which occurs in the process of computing the potential field data derivatives. This phenomenon creates false edges and incorrect interpretations of data. The thetaPGT method addresses this phenomenon by combining the PGT matrix and the previously derived theta map method. The maximum value of thetaPGT delineates the horizontal edge of geologic contacts. Achieved results by applying the thetaPGT method on simple and then complex synthetic magnetic models demonstrates higher accuracy of the proposed method in comparison with the analytic signal, theta and horizontal directional theta (HDT) methods. The new method has no sensitivity to depth and strike, and also doesn’t create additional edges. Furthermore, it has lower noise sensitivity and significantly reduces the effect of the Gibbs phenomenon. Finally, applying this method on real magnetic data from the Varzeghan area, northwest Iran, with respect to other methods reveals more details of structures in the area and characterized false faults resulting from the Gibbs phenomenon.