Complex Scalars Research Articles

Constraining minimal anomaly free U(1) extensions of the Standard Model

We consider a class of minimal anomaly free $\mathrm{U}(1)$ extensions of the Standard Model with three generations of right-handed neutrinos and a complex scalar. Using electroweak precision constraints, new 13 TeV LHC data, and considering theoretical limitations such as perturbativity, we show that it is possible to constrain a wide class of models. By classifying these models with a single parameter, $\kappa$, we can put a model independent upper bound on the new $\mathrm{U}(1)$ gauge coupling $g_z$. We find that the new dilepton data puts strong bounds on the parameters, especially in the mass region $M_{Z'}\lesssim 3~ \mathrm{TeV}$.

Symmetries and couplings of non-relativistic electrodynamics

We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell’s equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a U(1) current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent z.

Neutrino mass, dark matter and anomalous magnetic moment of muon in a U 1 L μ − L τ $$ \mathrm{U}{(1)}_L{{}_{{}_{\mu}}}_{-}{{}_L}_{{}_{\tau }} $$ model

The observation of neutrino masses, mixing and the existence of dark matter are amongst the most important signatures of physics beyond the Standard Model (SM). In this paper, we propose to extend the SM by a local $L_\mu - L_\tau$ gauge symmetry, two additional complex scalars and three right-handed neutrinos. The $L_\mu - L_\tau$ gauge symmetry is broken spontaneously when one of the scalars acquires a vacuum expectation value. The $L_\mu - L_\tau$ gauge symmetry is known to be anomaly free and can explain the beyond SM measurement of the anomalous muon $({\rm g-2})$ through additional contribution arising from the extra $Z_{\mu\tau}$ mediated diagram. Small neutrino masses are explained naturally through the Type-I seesaw mechanism, while the mixing angles are predicted to be in their observed ranges due to the broken $L_\mu-L_\tau$ symmetry. The second complex scalar is shown to be stable and becomes the dark matter candidate in our model. We show that while the $Z_{\mu\tau}$ portal is ineffective for the parameters needed to explain the anomalous muon $({\rm g-2})$ data, the correct dark matter relic abundance can easily be obtained from annihilation through the Higgs portal. Annihilation of the scalar dark matter in our model can also explain the Galactic Centre gamma ray excess observed by Fermi-LAT. We show the predictions of our model for future direct detection experiments and neutrino oscillation experiments.

String theory origin of constrained multiplets

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector $A_\mu$, three complex scalars $\phi^i$ and four 4d fermions $\lambda^0$, $\lambda^i$. These transform, in addition to the more familiar N=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear N=1 multiplets: four chiral multiplets $S$, $Y^i$ that satisfy $S^2=SY^i=0$ and contain the worldvolume fermions $\lambda^0$ and $\lambda^i$; and four chiral multiplets $W_\alpha$, $H^i$ that satisfy $S W_\alpha=0$ and $S \bar D_{\dot \alpha} \bar H^{\bar \imath}=0$ and contain the vector $A_\mu$ and the scalars $\phi^i$. We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet $\Phi$ that satisfies $S(\Phi-\bar \Phi)=0$, which is particularly interesting for inflationary cosmology.

Quality in Use Analysis to Evaluate User Experience of Open Source Software Compatible with MATLAB

Mathematical and statistical open source software (OSS) has played a vital and positive role in computing statistics, performing numerical computations, and solving for real and complex scalars. There is an enormous need to apply quality models to this type of software. In this paper, we present an inclusive set of current quality models and demonstrate their application to OSS. As very little research has been carried out on the quality in use assessment of mathematical software, this work investigates the application of the quality in use model inspired by ISO/IEC 25010 on three OSS products: Scilab, R-Language, and GNU Octave. We can confidently state that Scilab, R-Language, and GNU Octave perform similarly in terms of effectiveness, efficiency, productivity, and cognitive load. However, Scilab outperforms GNU Octave slightly when it comes to error safety.

Gaugings of four-dimensionalN=3supergravity andAdS4/CFT3holography

We study matter-coupled $N=3$ gauged supergravity in four dimensions with various semisimple gauge groups. When coupled to $n$ vector multiplets, the gauged supergravity contains $3+n$ vector fields and $3n$ complex scalars parametrized by $SU(3,n)/SU(3)\times SU(n)\times U(1)$ coset manifold. Semisimple gauge groups take the form of $G_0\times H\subset SO(3,n)\subset SU(3,n)$ with $H$ being a compact subgroup of $SO(n+3-\textrm{dim}(G_0))$. The $G_0$ groups considered in this paper are of the form $SO(3)$, $SO(3,1)$, $SO(2,2)$, $SL(3,\mathbb{R})$ and $SO(2,1)\times SO(2,2)$. We find that $SO(3)\times SO(3)$, $SO(3,1)$ and $SL(3,\mathbb{R})$ gauge groups admit a maximally supersymmetric $AdS_4$ critical point. The $SO(2,1)\times SO(2,2)$ gauge group admits a supersymmetric Minkowski vacuum while the remaining gauge groups admit both half-supersymmetric domain wall vacua and $AdS_4$ vacua with completely broken supersymmetry. For the $SO(3)\times SO(3)$ gauge group, there exists another supersymmetric $N=3$ $AdS_4$ critical point with $SO(3)_{\textrm{diag}}$ symmetry. We explicitly give a detailed study of various holographic RG flows between $AdS_4$ critical points, flows to non-conformal theories and supersymmetric domain walls in each gauge group. The results provide gravity duals of $N=3$ Chern-Simons-Matter theories in three dimensions.

The role of flavon cross couplings in leptonic flavour mixing

In models with discrete flavour symmetries, flavons are critical to realise specific flavour structures. Leptonic flavour mixing originates from the misalignment of flavon vacuum expectation values which respect different residual symmetries in the charged lepton and neutrino sectors. Flavon cross couplings are usually forbidden, in order to protect these symmetries. Contrary to this approach, we show that cross couplings can play a key role and give raise to necessary corrections to flavour-mixing patterns, including a non-zero value for the reactor angle and CP violation. For definiteness, we present two models based on $A_4$. In the first model, all flavons are assumed to be real or pseudo-real, with 7 real degrees of freedom in the flavon sector in total. A sizable reactor angle associated with nearly maximal CP violation is achieved, and, as both originate from the same cross coupling, a sum rule results with a precise prediction for the value of the Dirac CP-violating phase. In the second model, the flavons are taken to be complex scalars, which can be connected with supersymmetric models and multi-Higgs models. The complexity properties of flavons provide new sources for generating the reactor angle. Models in this new approach introduce very few degrees of freedom beyond the Standard Model and can be more economical than those in the framework of extra dimension or supersymmetry.

Curved Dyonic Domain Walls in Four Dimensions

<span>In this short paper we show the existence of solitonic solutions of four dimensional ungauged N=1 <span>supergravity coupled to arbitrary vector and chiral multiplets whose Ricci scalar curvature is constant. <span>The Ricci scalar of spacetimes indeed depends on the <span><em>σ</em><span>-model, namely the complex scalars and their first <span>derivative. Then, we give two explicit models, namely static domain walls and static spherical symmetric <span>black holes which are related to our previous works.</span></span></span></span><br /></span></span></span>

Dark radiative inverse seesaw mechanism

We present a minimal model that simultaneously accounts for neutrino masses and the origin of dark matter (DM) and where the electroweak phase transition is strong enough to allow for electroweak baryogenesis. The Standard Model is enlarged with a Majorana fermion, three generations of chiral fermion pairs, and a single complex scalar that plays a central role in DM production and phenomenology, neutrino masses, and the strength of the phase transition. All the new fields are singlets under the SM gauge group. Neutrino masses are generated via a new variant of radiative inverse seesaw where the required small mass term is generated via loops involving DM and no large hierarchy is assumed among the mass scales. The model offers all the advantage of low-scale neutrino mass models as well as a viable dark matter candidate that is testable with direct detection experiments.

Taylor's theorem for matrix functions with applications to condition number estimation

We derive an explicit formula for the remainder term of a Taylor polynomial of a matrix function. This formula generalizes a known result for the remainder of the Taylor polynomial for an analytic function of a complex scalar. We investigate some consequences of this result, which culminate in new upper bounds for the level-1 and level-2 condition numbers of a matrix function in terms of the pseudospectrum of the matrix. Numerical experiments show that, although the bounds can be pessimistic, they can be computed much faster than the standard methods. This makes the upper bounds ideal for a quick estimation of the condition number whilst a more accurate (and expensive) method can be used if further accuracy is required. They are also easily applicable to more complicated matrix functions for which no specialized condition number estimators are currently available.

Single-superfield helical-phase inflation

Large-field inflation in supergravity requires the approximate global symmetry needed to protect flatness of the scalar potential. In helical-phase inflation, the U(1) symmetry of the Kähler potential is assumed, the phase part of the complex scalar of a chiral superfield plays the role of inflaton, and the radial part is strongly stabilized. The original model of helical phase inflation, proposed by Li, Li and Nanopoulos (LLN), employs an extra (stabilizer) superfield. We propose a more economical new class of the helical phase inflationary models without a stabilizer superfield. As the specific examples, the quadratic, the natural, and the Starobinsky-type inflationary models are studied in our approach.

ϵ-Weak Cauchy sequences and a quantitative version of Rosenthal's [formula omitted]-theorem

A bounded sequence (xn) in a Banach space is called ϵ-weak Cauchy, for some ϵ>0, if for all x⁎∈BX⁎ there exists some n0∈N such that |x⁎(xn)−x⁎(xm)|<ϵ for all n≥n0 and m≥n0. It is shown that given ϵ>0 and a bounded sequence (xn) in a Banach space then either (xn) admits an ϵ-weak Cauchy subsequence or, for all δ>0, there exists a subsequence (xmn) with the following property. If I is a finite subset of N and ϕ:I→N∖I is any map then‖∑n∈Iλn(xmn−xmϕ(n))‖≥(ϵπ−δ)∑n∈I|λn| for every sequence of complex scalars (λn)n∈I. This provides an alternative proof for Rosenthal's ℓ1-theorem and strengthens its quantitative version due to Behrends. As a corollary we obtain that for any uniformly bounded sequence (fn) of complex-valued functions, continuous on the compact Hausdorff space K and satisfying lim⁡supn,m→∞|fn(t)−fm(t)|≤ϵ, for some ϵ>0 and all t∈K, there exists a subsequence (fjn) satisfying lim⁡supn,m→∞|∫K(fjn−fjm)dμ|≤2ϵ, for every Radon measure μ on K.

Constrained inflaton due to a complex scalar

We reexamine inflation due to a constrained inflaton in the model of a complex scalar. Inflaton evolves along a spiral-like valley of special scalar potential in the scalar field space just like single field inflation. Sub-Planckian inflaton can induce sufficient e-foldings because of a long slow-roll path. In a special limit, the scalar spectral index and the tensor-to-scalar ratio has equivalent expressions to the inflation with monomial potential φn. The favorable values for them could be obtained by varying parameters in the potential. This model could be embedded in a certain radiative neutrino mass model

Constrained inflaton due to a complex scalar

We reexamine inflation due to a constrained inflaton in the model of a complex scalar. Inflaton evolves along a spiral-like valley of special scalar potential in the scalar field space just like single field inflation. Sub-Planckian inflaton can induce sufficient e-foldings because of a long slow-roll path. In a special limit, the scalar spectral index and the tensor-to-scalar ratio has equivalent expressions to the inflation with monomial potential φn. The favorable values for them could be obtained by varying parameters in the potential. This model could be embedded in a certain radiative neutrino mass model

Well-posedness of non-autonomous linear evolution equations for generators whose commutators are scalar

We prove the well-posedness of non-autonomous linear evolution equations for generators $${A(t): D(A(t)) \subset X \to X}$$ whose pairwise commutators are complex scalars, and in addition, we establish an explicit representation formula for the evolution. We also prove well-posedness in the more general case where instead of the onefold commutators only the p-fold commutators of the operators A(t) are complex scalars. All these results are furnished with rather mild stability and regularity assumptions: Indeed, stability in X and strong continuity conditions are sufficient. Additionally, we improve a well-posedness result of Kato for group generators A(t) by showing that the original norm continuity condition can be relaxed to strong continuity. Applications include Segal field operators and Schrodinger operators for particles in external electric fields.

A subexponential vector-valued Bohnenblust–Hille type inequality

Bayart, Pellegrino and Seoane recently proved that the polynomial Bohnenblust–Hille inequality for complex scalars is subexponential. We show that a vector-valued polynomial Bohnenblust–Hille inequality on complex Banach lattices is also subexponential for some special cases. Our main result recovers the best known constants of the classical polynomial inequality provided in [4].

Accidental dark matter: Case in the scale invariant localB−Lmodel

We explore the idea of accidental dark matter (aDM) stability in the scale invariant local $U(1)_{B-L}$ model, which is a theory for neutrino and at the same time radiatively breaks scale invariance via quantum mechanical dynamics in the $U(1)_{B-L}$ sector. A real singlet scalar can be accidental DM with an accidental $Z_2$, by virtue of both extended symmetries. A $U(1)_{B-L}$ charged complex scalar can also be a viable accidental DM due to an accidental (or remanent) $Z_3$. They can reproduce correct relic density via the annihilations through the conventional Higgs portal or dark Higgs portal. The dark Higgs portal scenario is in tension with the LHC bound on $Z_{B-L}$, and only heavy DM of a few TeVs can have correct relic density. In particular, DM may trigger spontaneous breaking of scale Invariance (SISB). The situation is relaxed significantly in the $Z_3$ case due to the effective semi-annihilation mode and then light DM can be accommodated easily. In addition, the $Z_3$ model can accommodate the GeV scale $\gamma-$ray excess from the galactic center (GC) via semi-annihilation into pseudo Goldstone boson (PGSB). The best fit is achieved at a DM about 52 GeV, with annihilation cross section consistent with the thermal relic density. The invisible Higgs branching ratio is negligible because the Higgs portal quartic coupling is very small $\lambda_{h\phi} \lesssim 10^{-3}$.

Simple recursion relations for general field theories

On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.

Static BPS black holes in U(1) gauged supergravity

We consider the flow equations for 1/4-BPS asymptotically AdS4 static black holes in Fayet-Iliopoulos gauged supergravity, using very special geometry identities to obtain a simplified form in the most general case. Under mild assumptions on the form of the solution, we analyse the flow equations and find an explicit solution for arbitrary gauging and charge vectors. Comparing with the corresponding attractor equations, we find that the solution is given in terms of exactly the same vector of parameters, implying that all regular attractors can be extended to full black hole solutions. We present explicit examples of black hole solutions with all complex scalars and allowed charges turned on, within the STU model and its truncations.

Thermal dark matter implies new physics not far above the weak scale

In this work we complete a model independent analysis of dark matter constraining its mass and interaction strengths with data from astro- and particle physics experiments. We use the effective field theory framework to describe interactions of thermal dark matter particles of the following types: real and complex scalars, Dirac and Majorana fermions, and vector bosons. Using Bayesian inference we calculate posterior probability distributions for the mass and interaction strengths for the various spin particles. The observationally favoured dark matter particle mass region is 10-100 GeV with effective interactions that have a cut-off at 0.1-1 TeV. This mostly comes from the requirement that the thermal abundance of dark matter not exceed the observed value. Thus thermal dark matter coupled with present data implies new physics most likely under 10 TeV.