Massive Vector Research Articles

Schwarzschild quasi-normal modes of non-minimally coupled vector fields

We study perturbations of massive and massless vector fields on a Schwarzschild black-hole background, including a non-minimal coupling between the vector field and the curvature. The coupling is given by the Horndeski vector-tensor operator, which we show to be unique, also when the field is massive, provided that the vector has a vanishing background value.We determine the quasi-normal mode spectrum of the vector field, focusing on the fundamental mode of monopolar and dipolar perturbations of both even and odd parity, as a function of the mass of the field and the coupling constant controlling the non-minimal interaction. In the massless case, we also provide results for the first two overtones, showing in particular that the isospectrality between even and odd modes is broken by the non-minimal gravitational coupling.We also consider solutions to the mode equations corresponding to quasi-bound states and static configurations. Our results for quasi-bound states provide strong evidence for the stability of the spectrum, indicating the impossibility of a vectorization mechanism within our set-up. For static solutions, we analytically and numerically derive results for the electromagnetic susceptibilities (the spin-1 analogs of the tidal Love numbers), which we show to be non-zero in the presence of the non-minimal coupling.

Investigating the geometric structure of neural activation spaces with convex hull approximations

Neural networks have achieved great success in many tasks, including data classification and pattern recognition. However, how neural networks work and what representations they learn are still not fully understood. For any data sample fed into a neural network, we wondered how its corresponding vectors expanded by activated neurons change throughout the layers and why the final output vector could be classified or clustered. To formally answer these questions, we define the data sample outputs of each layer as activation vectors and the space expanded by them as the activation space. Then, we investigate the geometric structure of the high-dimensional activation spaces of neural networks by studying the geometric characters of the massive activation vectors through approximated convex hulls. We find that the different layers of neural networks have different roles, where the former and latter layers can disperse and gather data points, respectively. Moreover, we also propose a novel classification method based on the geometric structures of activation spaces, called nearest convex hull (NCH) classification, for the activation vectors in each layer of a neural network. The empirical results show that the geometric structure can indeed be utilized for classification and often outperforms original neural networks. Finally, we demonstrate that the relationship among the convex hulls of different classes could be a good metric to help us optimize neural networks in terms of over-fitting detection and network structure simplification.

Massive Vector Form Factors to Three Loops.

We compute the three-loop nonsinglet corrections to the photon-quark form factors taking into account the full dependence on the virtuality of the photon and the quark mass. We combine the method of differential equations in an effective way with expansions around regular and singular points. This allows us to obtain results for the form factors with an accuracy of about eight to twelve digits in the whole kinematic range.

Moffat MOdified Gravity (MOG)

Scalar Tensor Vector Gravity (STVG) or MOdified Gravity (MOG) is a metric theory of gravity with dynamical scalar fields and a massive vector field introduced in addition to the metric tensor. In the weak field approximation, MOG modifies the Newtonian acceleration with a Yukawa-like repulsive term due to a Maxwell–Proca type Lagrangian. This associates matter with a fifth force and a modified equation of motion. MOG has been successful in explaining galaxy rotation curves, cosmological observations and all other solar system observations without the need for dark matter. In this article, we discuss the key concepts of MOG theory. Then, we discuss existing observational bounds on MOG weak field parameters. In particular, we will present our original results obtained from the X-COP sample of galaxy clusters.

Forbidden scalar dark matter and dark Higgses

As experimental searches for WIMP dark matter continue to yield null results, models beyond the WIMP paradigm have proliferated in order to elude ever improving observational constraints, among them that of sub-GeV dark matter mediated by a massive vector portal (a dark photon) associated with a new dark U(1) gauge symmetry. It has been previously noted that for a significant range of the parameter space of this class of models, the annihilation of dark matter particles into a pair of dark photons can dominate the freeze-out process even when this process is kinematically forbidden for dark matter at rest — this is known as the “forbidden dark matter” (FDM) regime. Prior studies of this regime, however, assume that any “dark Higgs” associated with breaking the dark U(1) and imparting mass to the dark photon is decoupled from the dark matter and as such plays no role in the freeze-out process. In this paper, we explore the effects of a dark Higgs on sub-GeV dark matter phenomenology in this FDM regime by considering the simplest possible construction in which there exist non-trivial dark matter-dark Higgs couplings: a model with a single complex scalar DM candidate coupled directly to the dark Higgs field. We find that for a wide range of parameter space, the dark Higgs can alter the resulting relic abundance by many orders of magnitude, and that this effect can remain significant even for a small dark matter-dark Higgs coupling constant. Considering measurements from direct detection and measurements of the CMB, we further find that points in this model’s parameter space which recreate the appropriate dark matter relic abundance suffer only mild constraints from other sources at present, but may become accessible in near-future direct detection experiments.

Compact stars in the Einstein dark energy model

We investigate the properties of high density compact objects in a vector type theory, inspired by Einstein's 1919 theory of elementary particles, in which Einstein assumed that elementary particles are held together by gravitational as well as electromagnetic type forces. From a modern perspective, Einstein's theory can be interpreted as a vector type model, with the gravitational action constructed as a linear combination of the Ricci scalar, of the trace of the matter energy-momentum tensor, and of a massive self-interacting vector type field. To obtain the properties of stellar models we consider the field equations for a static, spherically symmetric system, and we investigate numerically their solutions for different equations of state of quark and neutron matter, by assuming that the self-interaction potential of the vector field either vanishes or is quadratic in the vector field potential. We consider quark stars described by the MIT bag model equation of state and in the Color Flavor Locked phase, as well as compact stars consisting of a Bose-Einstein Condensate of neutron matter, with neutrons forming Cooper pairs. Constant density stars, representing a generalization of the Interior Schwarzschild solution of general relativity, are also analyzed. Also, we consider the Douchin-Haensel (SLy) equation of state. The numerical solutions are explicitly obtained in both standard general relativity, and the Einstein dark energy model and an in depth comparison between the astrophysical predictions of these two theories are performed. As a general conclusion of our study, we find that for all the considered equations of state a much larger variety of stellar structures can be obtained in the Einstein dark energy model, including classes of stars that are more massive than their general relativistic counterparts.

Gauge invariant operators in the SU(2) Higgs model: Ward identities and renormalization

The renormalization properties of two local gauge invariant composite operators $(O,{R}_{\ensuremath{\mu}}^{a})$ corresponding, respectively, to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are analyzed to all orders in perturbation theory by means of the algebraic renormalization in the $SU(2)$ Higgs model, with a single scalar in the fundamental representation, when quantized in the Landau gauge in Euclidean space-time. The present analysis generalizes earlier results presented in the case of the $U(1)$ Higgs model. A powerful global Ward identity, related to an exact custodial symmetry, is derived for the first time, with deep consequences at the quantum level. In particular, the gauge invariant vector operators ${R}_{\ensuremath{\mu}}^{a}$ turn out to be the conserved Noether currents of the above-mentioned custodial symmetry. As such, these composite operators do not renormalize, as expressed by the fact that the renormalization $Z$-factors of the corresponding external sources, needed to define the operators ${R}_{\ensuremath{\mu}}^{a}$ at the quantum level, do not receive any quantum corrections. Using this Ward identity, one can also prove that the longitudinal component of the two-point correlation function $⟨{R}_{\ensuremath{\mu}}^{a}(p){R}_{\ensuremath{\nu}}^{b}(\ensuremath{-}p)⟩$ exhibits only a tree level nonvanishing contribution which, moreover, is momentum independent, thus it is not associated to any physical propagating mode. Finally, we point out that the renowned nonrenormalization theorem for the ghost-antighost-vector boson vertex in Landau gauge remains true to all orders, also in the presence of the Higgs field.

Addendum to “Leptophilic U(1) massive vector bosons from large extra dimensions: Reexamination of constraints from LEP data” [Phys. Lett. B 820 (2021) 136585

Very recently, we proposed an explanation of the discrepancy between the measured anomalous magnetic moment of the muon and the Standard Model (SM) prediction in which the dominant contribution to (g−2)μ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. In this addendum we reexamine the bounds on 4-fermion contact interactions from precise electroweak measurements and show that the constraints on KK masses and couplings are more severe than earlier thought. However, we demonstrate that our explanation remains plausible if a few KK modes are lighter than LEP energy, because if this were the case the contribution to the 4-fermion scattering from the internal propagator would be dominated by the energy and not by the mass. To accommodate the (g−2)μ discrepancy we assume that the lepton number L does not partake in the hypercharge and propagates in one extra dimension (transverse to the SM branes): for a mass of the lowest KK excitation of 60 GeV (lower than the LEP energy), the string scale is roughly 10 TeV while the L gauge coupling is of order ∼10−1.

The final Kasner regime inside black holes with scalar or vector hair

The final (close to the singularity) dynamical behavior of the metric inside black holes with massive charged scalar or vector hair is analyzed for general anisotropic and inhomogeneous initial conditions. These solutions are relevant to a holographic realization of superconductivity. It is shown that the dynamics falls within the scope of the “cosmological billiard” description and that in both cases, the corresponding hyperbolic billiard region has infinite volume so that the system ultimately settles down to a final Kasner regime. For massive vector hair, the conclusion holds because the longitudinal mode plays the same role as a scalar field. There exists, however, a measure-zero subset of solutions characterized by vanishing longitudinal modes that exhibit a chaotic behavior with an infinite number of BKL oscillations as one goes to the singularity.

τRR minimization in presence of hypermultiplets

We compute τRR minimization in gauged supergravity for M-theory and String Theory truncations with both massless and massive vector multiplets. We explicitly compute, as anticipated in [1], that massive vector fields at the vacuum require the introduction of a constraint through a Lagrange multiplier. We illustrate this explicitly in two examples, namely the U(1)2-invariant truncation dual to the mABJM model and the ISO(7) truncation in massive IIA, the latter being a theory with both electric and magnetic gauging. We revisit the vacuum constraints at AdS4 and show how the supergravity analysis matches the results of the field theory dual computation.

Moffat\u2019s modified gravity tested on X-COP galaxy clusters

Scalar tensor vector gravity (STVG) is a fully covariant Lorentz invariant alternative theory of gravity also known as MOdified Gravity (MOG) which modifies General Relativity by inclusion of dynamical massive vector field and scalar fields. In STVG the mass mu of the vector field phi _{mu } and the gravitational constant G acquire the status of dynamical fields. We use the reconstructed total cluster mass of the X-COP sample obtained from X-ray observations by XMM-Newton telescope in combination with Sunyaev–Zel’dovich (SZ) effect observed within Planck all-sky survey to estimate the alpha and mu parameters of MOG theory. The obtained values are consistent with previous fits by other authors. Hence the MOG is passing another test and proves its consistency strengthening thereby its stance of being a promising alternative to General Relativity.

Constraining mathcal{CP} -violation in the Higgs-top-quark interaction using machine-learning-based inference

While mathcal{CP} violation in the Higgs interactions with massive vector boson is already tightly constrained, the mathcal{CP} nature of the Higgs interactions with fermions is far less constrained. In this work, we assess the potential of machine-learning-based inference methods to constrain mathcal{CP} violation in the Higgs top-Yukawa coupling. This approach enables the use of the full available kinematic information. Concentrating on top-associated Higgs production with the Higgs decaying to two photons, we derive expected exclusion bounds for the LHC and the high-luminosity phase of the LHC. We also study the dependence of these bounds on the Higgs interaction with massive vector bosons and their robustness against theoretical uncertainties. In addition to deriving expected exclusion bounds, we discuss at which level a non-zero mathcal{CP} -violating top-Yukawa coupling can be distinguished from the SM. Moreover, we analyze which kinematic distributions are most sensitive to a mathcal{CP} -violating top-Yukawa coupling.

Position-space representation of charged particles\u2019 propagators in a constant magnetic field as an expansion over Landau levels

We have obtained propagators in the position space as an expansion over Landau levels for the charged scalar particle, fermion, and massive vector boson in a constant external magnetic field. The summation terms in the resulting expressions consisted of two factors, one being rotationally invariant in the 2-dimensional Euclidean space perpendicular to the direction of the field, and the other being Lorentz-invariant in the 1+1-dimensional space-time. The obtained representations are unique in the sense that they allow for the simultaneous study of the propagator from both space-time and energetic perspectives which are implicitly connected. These results contribute to the development of position-space techniques in QFT and are expected to be of use in the calculations of loop diagrams.

Emotional Calculation Method of Rural Tourist Based on Improved SPCA-LSTM Algorithm

New technologies such as big data and cloud computing provide new means and tools for rural development. The big rural tourism, with its convenience, quickness, and low threshold, presents great convenience for tourists’ emotional calculation and has become one of the main sources of tourism big data. Under the guidance of big data theory and emotion theory, this paper proposes an emotional calculation method of rural tourists based on improved SPCA-LSTM algorithm, taking big text data as data source. Firstly, the improved TF-IDF algorithm is designed to highlight the importance of feature items, and the word vector trained by word2vec model is applied to represent the rural tourism data text. Then, a weighted sparse PCA (RSPCA) is constructed to reduce the dimension of massive word vector features. RSPCA introduces the weighted l 1 optimization framework and LASSO regression model into the mathematical model of PCA algorithm and establishes a new data dimension reduction model. Thereupon, the long-term and short-term memory convolution network with attention mechanism is employed to extract text features. Finally, the feature vector is utilized to calculate the rural tourist’s emotion by softmax function. The experimental results indicate that the improved SPCA-LSTM algorithm, whose performance index is better than other existing algorithms, is effective in calculating tourists’ emotions. Also, it is more suitable for the research of tourist sentiment calculation in the era of big data.

Quasinormal modes of Proca fields in a Schwarzschild-AdS spacetime

We present new results concerning the Proca massive vector field in a Schwarzschild-AdS black hole geometry. We provide a first principles analysis of Proca vector fields in this geometry using both the vector spherical harmonic (VSH) separation method and the Frolov-Krtou\v{s}-Kubiz\v{n}\'{a}k-Santos (FKKS) method that separates the relevant equations in spinning geometries. The analysis in the VSH method shows, on one hand, that it is arduous to separate the scalar-type from the vector-type polarizations of the electric sector of the Proca field, and on the other hand, it displays clearly the electric and the magnetic mode sectors. The analysis in the FKKS method is performed by taking the nonrotating limit of the Kerr-AdS spacetime, and shows that the ansatz decouples the polarizations in the electric mode sector even in the nonrotating limit. On the other hand, it captures only two of the three possible polarizations, the magnetic mode sector is missing. The reason for the absence of this polarization is related to the degeneracy of the principal tensor in static spherical symmetric spacetimes. The degrees of freedom and quasinormal modes in both separation methods of the Proca field are found. The frequencies of the quasinormal modes are also computed. For the electric mode sector in the VSH method the frequencies are found through an extension, which substitutes number coefficients by matrix coefficients, of the Horowitz-Hubeny numerical procedure, whereas for the magnetic mode sector in the VSH method and the electric sector of the FKKS method it is shown that a direct use of the procedure can be made. The values of the quasinormal mode frequencies obtained for each method are compared and showed to be in good agreement with each other. This further supports the analytical approaches presented here for the behavior of the Proca field in a Schwarzschild-AdS black hole background.

Gauge invariance and localization of vector Kaluza\u2013Klein modes

We investigate the gauge invariance and localization of vector KK modes for a bulk U(1) gauge field under three kinds of localization mechanism on a brane with one extra dimension. By a general KK decomposition for the bulk U(1) gauge field, there are both vector and scalar KK modes on the brane, which couple with each other. We demonstrate that for a localization mechanism with a gauge invariant bulk action of the U(1) gauge field, the effective action of the KK modes on the brane can be formalized to gauge invariant form. However, only the massive vector KK modes and their accompanying scalar ones can be both localized on the brane, which depends on the solution of the brane, the gauge invariance of the massive vector field is finally preserved. For a localization mechanism with a broken gauge invariant bulk action of the field, it is impossible to rebuild the gauge invariance on the brane.

A bispinor formalism for spinning Witten diagrams

We develop a new embedding-space formalism for AdS4 and CFT3 that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS4 and conformal Killing spinors for the boundary CFT3. The more conventional embedding space coordinates XI for the bulk and PI for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin ℓ ≥ 1, we determine its conservation properties at the unitarity bound. In our CFT3 formalism, we identify an mathfrak{so} (5, 5) Lie algebra of differential operators that includes the basic weight-shifting operators. These operators, together with a set of differential operators in AdS4, can be used to relate Witten diagrams with spinning external legs to Witten diagrams with only scalar external legs. We provide several applications that include Compton scattering and the evaluation of an R4 contact interaction in AdS4. Finally, we derive bispinor formulas for the bulk-to-bulk propagators of massive spinor and vector gauge fields and evaluate a diagram with spinor exchange.

The holographic contributions to the sphere free energy

We study which bulk couplings contribute to the S3 free energy F( mathfrak{m} ) of three-dimensional mathcal{N} = 2 superconformal field theories with holographic duals, potentially deformed by boundary real-mass parameters m. In particular, we show that F( mathfrak{m} ) is independent of a large class of bulk couplings that include non-chiral F-terms and all D-terms. On the other hand, in general, F( mathfrak{m} ) does depend non-trivially on bulk chiral F-terms, such as prepotential interactions, and on bulk real-mass terms. These conclusions can be reached solely from properties of the AdS super-algebra, mathfrak{osp} (2|4). We also consider massive vector multiplets in AdS, which in the dual field theory correspond to long single-trace superconformal multiplets of spin zero. We provide evidence that F( mathfrak{m} ) is insensitive to the vector multiplet mass and to the interaction couplings between the massive vector multiplet and massless ones. In particular, this implies that F( mathfrak{m} ) does not contain information about scaling dimensions or OPE coefficients of single-trace long scalar mathcal{N} = 2 superconformal multiplets.

The Role of Longitudinal Polarizations in Horndeski and Macroscopic Gravity: Introducing Gravitational Plasmas

We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation, we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector, and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to molecule deformation. Finally, we investigate the interaction of the massive mode in Horndeski gravity with a noncollisional medium, showing that Landau damping phenomenon can occur in the gravitational sector as well. That allows us to introduce the concept of “gravitational plasma”, where inertial forces associated with the background field play the role of cold ions in electromagnetic plasma.

Ultralight dark matter searches with KAGRA gravitational wave telescope

Among various dark matter candidates, bosonic ultralight fields with masses below 1eV are well motivated. Recently, a number of novel approaches have been put forward to search for ultralight dark matter candidates using laser interferometers at various scales. Those include our proposals to search for axion-like particles (ALPs) and vector fields with laser interferometric gravitational wave detectors. ALPs can be searched for by measuring the oscillating polarization rotation of laser light. Massive vector fields weakly coupled to the standard model sector can also be searched for by measuring the oscillating forces acting on the suspended mirrors of the interferometers. In this paper, the current status of the activities to search for such ultralight dark matter candidates using a gravitational wave detector in Japan, KAGRA, is reviewed. The analysis of data from KAGRA’s observing run in 2020 to search for vector dark matter, and the installation of polarization optics to the arm cavity transmission ports of the interferometer to search for ALPs in future observing runs are underway.