Dimensions Of Operators Research Articles

Dark matter perspective of left-right symmetric gauge model

We consider an incarnation of left-right symmetric model with a local gauge symmetry of SU(3)C⊗SU(2)L⊗U(1)L⊗SU(2)R⊗U(1)R. Heavy scalars and fermions present in the 27 of E6 are included in the matter sector along with the Standard Model (SM) fermions. Two such colour singlet fermions, N and LS, transforming as bi-doublet and singlet under SU(2) s respectively, can be potential candidates for Dark Matter (DM). Assignment of U(1) charges for the matter fields restricts some of the exotic fermions to interact with the SM fermions. We study in some details the prospect of such fermionic dark matters by calculating relic densities and direct detection cross-sections by treating both these particles as relics. In such a two component Dark Matter scenario, LS having smaller interaction with the SM, will dominantly contribute to relic density. However, it cannot be detected at earth bound experiments with their present sensitivity. On the contrary, N having higher rate of interaction with the SM particle has too large annihilation cross-section thus contributes very little to relic density. In fact, its interaction with the SM is too high such that N-nucleon cross-section for a wide range of N mass is higher than the experimental limits from XENON, LUX or PICO. However, such a high N-nucleon cross-section can be tamed by assuming additional dimension-6 operators involving N and SM quarks. We derive limits on the strengths of such interactions from experimental data.

Bootstrapping traceless symmetric $O(N)$ scalars

We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of O(N)O(N) with two indices t_{ij}tij. We obtain upper bounds on operator dimensions for all the relevant representations and several values of NN. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case N=4N=4, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model ARP^{3}ARP3. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving tt and the lowest dimension scalar singlet.

The Implementation of Accounting Information Systems for its Role in Marketing and Management Processes

Abstract Nowdays the technological innovations evolve faster and in this conditions it is necessary to examine how this technology affects the accounting profession in the same way as it has affected everyday aspects. Accounting is transformed into something more than simple recording, summarizing and reporting of transactions exceeding these routines and practical functions and extending throughout the organization including, delegated functions, processing methodologies, controls and expected outputs, which considered all together as “the system “. It includes all dimensions of business operations, including the flow of financial data across the organization and beyond. Consequently, this paper aims to address issues such as how knowledge about IT deal from accounting professionals and how they further develop their professional development during the subsequent training. This paper shows the importance of the IT knowledge in accounting, marketing, management and decision making. We conclude the paper by giving a short overview relying on the analysis of data collected from a survey.

Joint Power and 3D Trajectory Optimization for UAV-Enabled Wireless Powered Communication Networks With Obstacles

Unmanned aerial vehicle (UAV)-enabled wireless powered communication networks (WPCNs) are promising technologies in 5G/6G wireless communications, while there are several challenges about UAV power allocation and scheduling to enhance the energy utilization efficiency, considering the existence of obstacles. In this work, we consider a UAV-enabled WPCN scenario that a UAV needs to cover the ground wireless devices (WDs). During the coverage process, the UAV needs to collect data from the WDs and charge them simultaneously. To this end, we formulate a joint-UAV power and three-dimensional (3D) trajectory optimization problem (JUPTTOP) to simultaneously increase the total number of the covered WDs, increase the time efficiency, and reduce the total flying distance of UAV so as to improve the energy utilization efficiency in the network. Due to the difficulties and complexities, we decompose it into two sub optimization problems, which are the UAV power allocation optimization problem (UPAOP) and UAV 3D trajectory optimization problem (UTTOP), respectively. Then, we propose an improved non-dominated sorting genetic algorithm-II with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -means initialization operator and Variable dimension mechanism (NSGA-II-KV) for solving the UPAOP. For UTTOP, we first introduce a pretreatment method, and then use an improved particle swarm optimization with Normal distribution initialization, Genetic mechanism, Differential mechanism and Pursuit operator (PSO-NGDP) to deal with this sub optimization problem. Simulation results verify the effectiveness of the proposed strategies under different scales and settings of the networks.

Study of the projected sensitivity on the anomalous quartic gauge couplings via Zγγ production at the CLIC

Gauge boson self-couplings are completely defined by the non-Abelian gauge symmetry of the Standard Model (SM). For this reason, a direct search for these couplings is extremely significant in understanding the gauge structure of the SM. The possible deviation from the SM predictions of gauge boson self-couplings would be a sign of the presence of new physics beyond the SM. In this work, we study the sensitivities on the anomalous couplings defined by dimension-8 operators related to the $ZZ\gamma\gamma$ and $Z\gamma\gamma\gamma$ quartic vertices through the process $e^+e^- \to Z\gamma\gamma$ with Z-boson decaying to charged leptons at the Compact Linear Collider (CLIC). We analyze the center-of-mass energy of 3 TeV, integrated luminosities of ${\cal L}=1, 4, 5$ $\rm ab^{-1}$, systematic uncertainties of $\delta_{sys}=0\%, 3\%, 5\%$, unpolarized and polarized electron beams and considering the Initial State Radiation and Beamstrahlung effects for extraction of expected sensitivity on the anomalous $f_ {T,j}/\Lambda^4$ couplings at $95\%$ confidence level, which are especially sensitive to the $Z\gamma\gamma$ channel. It is clear from the results that we expect better limits on the couplings if the systematic error is improved. The best limits obtained on the anomalous quartic couplings for the process $e^+e^- \to Z\gamma\gamma$ with $\sqrt{s}= 3$ TeV, ${\cal L}=5$ $\rm ab^{-1}$, and $\delta_{sys}=0\%$ can be approximately improved up to about 1.1 times better than the limits obtained with $\delta_{sys}=5\%$. Our sensitivities on the anomalous quartic couplings can set more stringent sensitivity by two orders of magnitude concerning the best sensitivity derived from the current experimental limits. Finally, with initial electron beam polarization, the sensitivity of the anomalous quartic couplings improves by almost a factor of 1.2.

Building blocks of the flavourful SMEFT RG

A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow. The anomalous dimension matrix of the Standard Model Effective Field Theory (SMEFT) encodes clues to where to find relics of heavy new physics in data, but its unwieldy 2499 × 2499 size (at operator dimension 6) makes it difficult to draw general conclusions. In this paper, we study the flavour structure of the SMEFT one loop anomalous dimension matrix of dimension 6 current-current operators, a 1460 × 1460 submatrix. We take an on-shell approach, laying bare simple patterns by factorising the entries of the matrix into their gauge, kinematic and flavour parts. We explore the properties of different diagram topologies, and make explicit the connection between the IR-finiteness of certain diagrams and their gauge and flavour structure. Through a completely general flavour decomposition of the Wilson coefficient matrices, we uncover new flavour selection rules, from which small subsystems emerge which mix almost exclusively amongst themselves. We show that, for example, if we neglect all Yukawa couplings except for that of the top quark, the selection rules produce block diagonalisation within the current-current operators in which the largest block is a 61 × 61 matrix. We provide all the ingredients of the calculations in comprehensive appendices, including SM and SMEFT helicity amplitudes, and explicit results for phase space integrals and gauge contractions. This deconstruction of the matrix, and its resulting block-diagonalisation, provides a first step to understanding the IR-relevant directions in the SMEFT parameter space, hence closing in on natural places for heavy new physics to make itself known.

The epsilon expansion of the O(N) model with line defect from conformal field theory

We employ the axiomatic framework of Rychkov and Tan to investigate the critical O(N) vector model with a line defect in (4 − ϵ) dimensions. We assume the fixed point is described by defect conformal field theory and show that the critical value of the defect coupling to the bulk field is uniquely fixed without resorting to diagrammatic calculations. We also study various defect localized operators by the axiomatic method, where the analyticity of correlation functions plays a crucial role in determining the conformal dimensions of defect composite operators. In all cases, including operators with operator mixing, we reproduce the leading anomalous dimensions obtained by perturbative calculations.

Double insertions of SMEFT operators in gluon fusion Higgs boson production

Deviations from the Standard Model (SM) can be parametrized in terms of the SM effective field theory (SMEFT), which is typically truncated at dimension-6. Including higher dimension operators---as well as considering simultaneous insertions of multiple dimension-6 operators---may be necessary in some processes, in order to correctly capture the properties of the underlying UV theory. As a step toward clarifying this in the Higgs boson production in gluon fusion process, we study double insertions of dimension-6 operators in the 1-loop virtual amplitude. We present needed Feynman rules up to $\mathcal{O}(1/{\mathrm{\ensuremath{\Lambda}}}^{4})$ and we numerically study the impact of various approximations to the $\mathcal{O}(1/{\mathrm{\ensuremath{\Lambda}}}^{4})$ expansion.

Dark states with electromagnetic form factors at electron colliders

Electromagnetically neutral dark sector particles may feebly interact with photons through higher dimensional effective operators, such as mass-dimension 5 magnetic and electric dipole moment, and a mass-dimension 6 anapole moment and charge radius operators. In this work, we use hypercharge gauge field form factors to treat dark states, which will induce not only electromagnetic form factors but also the corresponding $Z$ boson operators. Taking a Dirac fermion $\chi$ as an example, we investigate the probes of searching for such dark states at current and future $e^+e^-$ collider experiments including BESIII, STCF, Belle II and CEPC via monophoton searches. Comparing to current experiments, we find that electron colliders including BESIII, STCF, Belle II, which operate with the center-of-mass at several GeV, have leading sensitivity on the corresponding electromagnetic form factors for the mass-dimension 5 operators with dark states lighter than several GeV, while they can not provide competitive upper limits for the mass-dimension 6 operators. Future CEPC operated with the center-of-mass on and beyond the mass of $Z$-boson with competitive luminosity can probe the unexplored parameter space for dark states with mass-dimension 5 (6) operators in the mass region of $m\lesssim 100 $ GeV (10 MeV $\lesssim m\lesssim 100 $ GeV).

Analytic continuation of harmonic sums with purely imaginary indices near the integer values

We present a simple algebraic method for the analytic continuation of harmonic sums with integer real or purely imaginary indices near negative and positive integers. We provide a MATHEMATICA code for exact expansion of harmonic sums in a small parameter near these integers. As an application, we consider the analytic continuation of the anomalous dimension of twist-1 operators in the ABJM model, which contains nested harmonic sums with purely imaginary indices. We found that in the BFKL-like limit the result has the same single-logarithmic behavior as in [Formula: see text] SYM and QCD, however, we did not find a general expression for the “BFKL Pomeron” eigenvalue in this model. For the slope function, we found full agreement with the expansion of the known general result and give predictions for the first three perturbative terms in the expansion of the next-to-slope function. The proposed method of analytic continuation can also be used for other generalization of nested harmonic sums.

Comments on epsilon expansion of the O(N) model with boundary

The O(N) vector model in the presence of a boundary has a non-trivial fixed point in (4 − ϵ) dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is investigated at the leading order in the ϵ-expansion by diagrammatic and axiomatic approaches. In the latter, we extend the framework of Rychkov and Tan for the bulk theory to the case with a boundary and calculate the conformal dimensions of boundary composite operators with attention to the analyticity of correlation functions. In both approaches, we obtain consistent results.

Dark Contributions to h → μ + μ – in the Presence of a μ-Flavored Vector-Like Lepton

A simple extension of the standard model (SM) with a μ-flavored vector-like lepton (VLL) doublet and a real singlet scalar can have an interesting implication to the h → μ + μ – decay while offering the simplest possible explanation for the dark matter (DM) phenomenology. Assuming the real singlet scalar to be a viable DM candidate, it has been shown that the muon Yukawa coupling can have a negative contribution at the one-loop order if the 2nd generation SM leptons are allowed to couple with the VLL doublet. The stringent direct detection bounds corresponding to a real singlet scalar DM can easily be relaxed if the SM quark sector was augmented with a dimension-6 operator at some new physics (NP) scale Λ NP. Thus, this model presents a significant phenomenological study where the muon Yukawa coupling can be corrected within a real singlet scalar DM framework. The considered parameter space can be tested/constrained through the high luminosity run of the LHC (HL-LHC) and future direct detection experiments.

Deep learning framework for solving Fokker–Planck equations with low-rank separation representation

An insightful deep learning framework is proposed to solve the well-known Fokker–Planck (FP) equations that quantify the evolution of the probability density function. It efficiently reduces the demand of training data in acquiring precise integrations of special normalization conditions via neural network (NN). Instead of all hypercubic discrete points, the inputs of each NN only require one-dimensional discrete data, and this also avoids the exponential increase in training data as the dimension increase. Without loss of generality, to solve a d-dimensional FP equation, d NNs are employed and assembled into a low-rank separation representation. The FP equation, boundary conditions, and integral operators are then re-expressed in the sense of the separation representation. It enables the constructed loss function to perform simple vector operations, in that complicated d-dimensional operators are replaced by a set of one dimensional operators. A tractable strategy is presented for the selection of separation rank inspired by the potential function of the given system, although selecting an appropriate separation rank is still an open issue. Typical numerical examples reveal that the proposed algorithm is effective and superior for solving FP equations. The suggested framework could be applied and extended in various areas of engineering and applied sciences.

Exploration roles and responsibilities of trade unions in preventing and responding to emergencies against epidemics: The case of COVID-19.

The coronavirus disease 209 (COVID-19) pandemic has been affecting various strata of society including different guilds. Each of these segments has its role to play in controlling epidemics. Accordingly, this study aimed to explore trade unions' roles and responsibilities in the prevention and emergency response to epidemic, including the COVID-19 pandemic. The present qualitative research was conducted using directed content analysis. Participants were selected by a purposeful sampling method. Data were collected through semistructured interviews and field notes and validated through Lincoln and Guba's (1985) evaluative criteria. Data were analyzed by MAXQDA software. Data analysis, constant comparison, and class integration provided a total of seven main themes, which were extracted into four domains of Plan, Implementation, Review, and Action. The main themes were categorized into the dimensions of each domain, so that the Plan domain included three dimensions of union/guild contexts, leadership and staff participation, and planning. The Implementation domain included two dimensions of support and operations. The Assessment domain had a performance evaluation dimension, and the Action domain was made up of an improvement dimension. Relying on their organizational and social capacities, trade unions can facilitate the leadership and participation of employees and communities for appropriate policies and making resilient decisions to control epidemics and other roles and responsibilities related to health.

A new general approach for obtaining matrix product operators for spin Hamiltonians with periodic boundary conditions

This article concerns the matrix product operators for one-dimensional spin Hamiltonians under open and periodic boundary conditions. A novel approach called ‘the dynamics of blocks’ is proposed to obtain the matrix product operators in the case of Hamiltonians with periodic boundary conditions. This approach works universally for any Hamiltonian with two-particle as well as single-particle interactions. The main significance of the proposed approach is that, the dimensions of the matrix product operators obtained are the same for both open and periodic boundary conditions. This method gives us a generic way of constructing MPOs for any Hamiltonian with arbitrary neighboring interactions, immaterial of how the interaction strength falls. A general numerical implementation of the ‘dynamics of blocks’ method is also carried out. The DMRG algorithm was implemented, and the ground state eigenvalue was obtained using these MPOs to numerically validate the method.

Dark matter from a conformal Dark Sector

We consider theories in which a dark sector is described by a Conformal Field Theory (CFT) over a broad range of energy scales. A coupling of the dark sector to the Standard Model breaks conformal invariance. While weak at high energies, the breaking grows in the infrared, and at a certain energy scale the theory enters a confined (hadronic) phase. One of the hadronic excitations can play the role of dark matter. We study a “Conformal Freeze-In” cosmological scenario, in which the dark sector is populated through its interactions with the SM at temperatures when it is conformal. In this scenario, the dark matter relic density is determined by the CFT data, such as the dimension of the CFT operator coupled to the Standard Model. We show that this simple and highly predictive model of dark matter is phenomenologically viable. The observed relic density is reproduced for a variety of SM operators (“portals”) coupled to the CFT, and the resulting models are consistent with observational constraints. The mass of the COFI dark matter candidate is predicted to be in the keV-MeV range.

Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite ε

Using numerical conformal bootstrap technology we perform a non-perturbative study of the Ising CFT and its spectrum from infinitesimal to finite values of ε = 4 – d. Exploiting the recent navigator bootstrap method in conjunction with the extremal functional method, we test various qualitative and quantitative features of the ε-expansion. We follow the scaling dimensions of numerous operators from the perturbatively controlled regime to finite coupling. We do this for ℤ2-even operators up to spin 12 and for ℤ2-odd operators up to spin 6 and find a good matching with perturbation theory. In the finite coupling regime we observe two operators whose dimensions approach each other and then repel, a phenomenon known as level repulsion and which can be analyzed via operator mixing. Our work improves on previous studies in both increased precision and the number of operators studied, and is the first to observe level repulsion in the conformal bootstrap.

AdS_5 vacua and holographic RG flows from 5D N=4 gauged supergravity

We study five-dimensional N=4 gauged supergravity coupled to five vector multiplets with SO(2)_Dtimes SO(3)times SO(3) gauge group. There are four supersymmetric AdS_5 vacua in the truncation to SO(2)_{text {diag}} invariant scalars. Two of these vacua preserve the full N=4 supersymmetry with SO(2)_Dtimes SO(3)times SO(3) and SO(2)_Dtimes SO(3)_{text {diag}} symmetries. These have an analogue in N=4 gauged supergravity with SO(2)times SO(3)times SO(3) gauge group. The other two AdS_5 vacua preserve only N=2 supersymmetry with SO(2)_{text {diag}}times SO(3) and SO(2)_{text {diag}} symmetry. The former has an analogue in the previous study of SO(2)_Dtimes SO(3) gauge group while the latter is a genuinely new N=2AdS_5 vacuum. These vacua should be dual to N=2 and N=1 superconformal field theories (SCFTs) in four dimensions with different flavour symmetries. We give the full scalar mass spectra at all of the AdS_5 critical points which provide information on conformal dimensions of the dual operators. Finally, we study holographic RG flows interpolating between these AdS_5 vacua and find a new class of solutions. In addition to the RG flows from the trivial SO(2)_Dtimes SO(3)times SO(3)N=4 critical point, at the origin of the scalar manifold, to all the other critical points, there is a family of RG flows from the trivial N=4 critical point to the new SO(2)_{text {diag}}N=2 critical point that pass arbitrarily close to the SO(2)_Dtimes SO(3)_{text {diag}}N=4 critical point.

Dimension-five baryon-number violation in low-scale Pati-Salam models

The gauge bosons of Pati-Salam do not mediate proton decay at the renormalisable level, and for this reason it is possible to construct scenarios in which $SU(4) \otimes SU(2)_{R}$ is broken at relatively low scales. In this Letter we show that such low-scale models generate dimension-5 operators that can give rise to nucleon decays at unacceptably large rates, even if the operators are suppressed by the Planck scale. We find an interesting complementarity between the nucleon-decay limits and the usual meson-decay constraints. Furthermore, we argue that these operators are generically present when the model is embedded into $SO(10)$, lowering the suppression scale. Under reasonable assumptions, the lower limit on the breaking scale can be constrained to be as high as $\mathcal{O}(10^{8})$ GeV.

The leading trajectory in the 2+1D Ising CFT

We study the scattering of lumps in the 2+1-dimensional Ising CFT, indirectly, by analytically continuing its spectrum using the Lorentzian inversion formula. We find evidence that the intercept of the model is below unity: j* ≈ 0.8, indicating that scattering is asymptotically transparent corresponding to a negative Lyapunov exponent. We use as input the precise spectrum obtained from the numerical conformal bootstrap. We show that the truncated spectrum allows the inversion formula to reproduce the properties of the spin-two stress tensor to 10−4 accuracy and we address the question of whether the spin-0 operators of the model lie on Regge trajectories. This hypothesis is further supported by analytics in the large-N O(N) model. Finally, we show that anomalous dimensions of heavy operators decrease with energy at a rate controlled by (j* − 1), implying regularity of the heavy spectrum.