Scalar Loop Research Articles

AdS Higgs mechanism from double trace deformed CFT

Explicit breaking of a global symmetry in a conformal field theory is holographically dual to giving mass to a gauge field living in AdS via the Higgs mechanism. We show that if this breaking is induced via a double trace deformation the Higgs mechanism is induced via a scalar loop diagram. The mass can be calculated analytically in both bulk and field theory and we find perfect agreement. While representing familiar physics, the mechanism is identical to how the graviton picks up a mass in the holographic dual of a conformal field theory coupled to a bath.

A robust GNSS sensors in presence of signal blockage for USV application

Unmanned surface vehicle (USV) can navigate autonomously via the global navigation satellite system (GNSS). However, the traditional GNSS scalar tracking loop easily loses lock in low carrier-to-noise ratio (CNR) situations, such as signal occlusion and weak signals. Meanwhile, an increase in the carrier/code phase error leads to an increase in the measurement error of the navigation filter, which decreases the accuracy of the position estimation. To solve this problem, this paper proposes a carrier and code tracking structure based on a forward and backward Kalman filter to dynamically adjust the gain of the vector tracking loop. The carrier and code phase errors calculated by the loop discriminators were linearly transformed into pseudo-range rate and pseudo-range errors after filtering and smoothing, which were used as the measurements of the navigation filter. The signal CNR was used to adaptively adjust the measurement noise covariance matrix of the loop filters. The field tests used a commercial receiver’s navigation solution as the reference. In the stationary test, the proposed structure reduced the localization error by 44.3% compared with the traditional methods. In kinematic experiments, the proposed structure reduced the carrier and code phase errors in a harsh signal environment and improved the positioning accuracy at the source. The test results demonstrate that the proposed GNSS tracking method can provide a possible solution for the development of navigation systems for USV.

The QED four-photon amplitudes off-shell: Part 1

The present paper is the first in a series of four where we use the worldline formalism to obtain the QED four-photon amplitude completely off-shell. We present the result explicitly in terms of hypergeometric functions, and derivatives thereof, for both scalar and spinor QED. The formalism allows us to unify the scalar and spinor loop calculations, avoiding the usual breaking up of the amplitude into Feynman diagrams, and to achieve manifest transversality at the integrand level as well as UV finiteness term by term by an optimized version of the integration-by-parts procedure originally introduced by Bern and Kosower for gluon amplitudes. The full permutation symmetry is maintained throughout, and the amplitudes get projected naturally into the basis of five tensors introduced by Costantini et al. in 1971. Since in many applications of the “four-photon box” some of the photons can be taken in the low-energy limit, and the formalism makes it easy to integrate out any such leg, apart from the case of general kinematics (part 4) we also treat the special cases of one (part 3) or two (part 2) photons taken at low energy. In this first part of the series, we summarize the application of the worldline formalism to the N-photon amplitudes and its relation to Feynman diagrams, derive the optimized tensor-decomposed integrands of the four-photon amplitudes in scalar and spinor QED, and outline the computational strategy to be followed in parts 2 to 4. We also give an overview of the applications of the four-photon amplitudes, with an emphasis on processes that involve some off-shell photons. The case where all photons are taken at low energy (the “Euler-Heisenberg approximation”) is simple enough to be doable for arbitrary photon numbers, and we include it here for completeness.

Performance Left on the Table: An Evaluation of Compiler Autovectorization for RISC-V

Next-generation length-agnostic vector instruction set architecture (ISA) designs, the RISC-V vector extension, and ARM’s scalable vector extension enable software portability across hardware implementations with different vector engines. While traditional, fixed-length single-instruction–multiple-data ISA instructions, such as Intel AVX and ARM Neon, enjoy mature compiler support for automatic vectorization, compiler support is still emerging for these length-agnostic ISAs. This work studies the compiler shortcomings that constitute the gap in autovectorization capabilities between length-agnostic and fixed-length architectures. We examine LLVM’s support for both the RISC-V vector extension and traditional vector ISAs. We study a set of synthetic scalar loops to compare the breadth of support in the two settings, and we examine a real benchmark suite to compare autovectorized to hand-vectorized RISC-V code. We use both studies to distill a set of recommendations for engineering improvements and future research in compilers and programming models for length-agnostic vector programming.

How Inflationary Gravitons Affect the Force of Gravity

We employ an unregulated computation of the graviton self-energy from gravitons on the de Sitter background to infer the renormalized result. This is used to quantum-correct the linearized Einstein equation. We solve this equation for the potentials that represent the gravitational response to a static, point mass. We find large spatial and temporal logarithmic corrections to the Newtonian potential and to the gravitational shift. Although suppressed by a minuscule loop-counting parameter, these corrections cause perturbation theory to break down at large distances and late times. Another interesting fact is that gravitons induce up to three large logarithms, whereas a loop of massless, minimally coupled scalars produces only a single large logarithm. This is in line with corrections to the graviton mode function: a loop of gravitons induces two large logarithms, whereas a scalar loop gives none.

Scalar and vector tracking loop simulation based on a uniform semi-analytic model and robustness analysis in multipath/NLOS situations

Scalar and vector tracking loop simulation based on a uniform semi-analytic model and robustness analysis in multipath/NLOS situations

Lepton anomalous magnetic moment with singlet-doublet fermion dark matter in a scotogenic U(1)Lμ−Lτ model

We study an extension of the minimal gauged ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ model including three right-handed singlet fermions and a scalar doublet to explain the anomalous magnetic moments of muon and electron simultaneously. The presence of an in-built ${Z}_{2}$ symmetry under which the right-handed singlet fermions and $\ensuremath{\eta}$ are odd, gives rise to a stable dark matter candidate along with light neutrino mass in a scotogenic fashion. In spite of the possibility of having positive and negative contributions to muon and electron ($g\ensuremath{-}2$) respectively from vector boson and charged scalar loops, the minimal scotogenic ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ model cannot explain both muon and electron ($g\ensuremath{-}2$) simultaneously while being consistent with other experimental bounds. We then extend the model with a vectorlike lepton doublet which not only leads to a chirally enhanced negative contribution to electron ($g\ensuremath{-}2$) but also leads to the popular singlet-doublet fermion dark matter scenario. With this extension, the model can explain both electron and muon ($g\ensuremath{-}2$) while being consistent with neutrino mass, dark matter and other direct search bounds. The model remains predictive at high energy experiments like collider as well as low energy experiments looking for charged lepton flavor violation, dark photon searches, in addition to future ($g\ensuremath{-}2$) measurements.

Design and Implementation of Vector Tracking Loop for High-Dynamic GNSS ReceiverDesign and Implementation of Vector Tracking Loop for High-Dynamic GNSS Receiver.

For the tracking of high-dynamic satellite navigation signals, the conventional scalar tracking loop (STL) is vulnerable. Frequent signal-tracking interruption affects the continuity of navigation. The vector tracking loop (VTL) can overcome this disadvantage. However, there are some difficulties in implementing existing vector tracking methods on a real-time hardware receiver, such as the synchronization problem and computation load. This paper proposes an implementation framework of VTL based on a partial open-loop numerically controlled oscillator (NCO) control mode that can be implemented with minor modifications on an existing receiver platform. The structure of VTL, the design of the navigation filter, and the key points of hardware implementation are introduced in detail. Lastly, the VTL performance was verified by a GPS simulator test. The results show that the proposed VTL can run in real-time and be significantly improved in the tracking continuity of high-dynamic signals, tracking sensitivity, positioning accuracy, and recovery time for interrupted signals compared with those of STL.

GPS Vector Tracking Loop with Fault Detection and Exclusion

In this paper, both the integrity monitoring and fault detection and exclusion (FDE) mechanisms are incorporated into the vector tracking loop (VTL) architecture of the Global Positioning System (GPS) receiver for reliability enhancement. For the VTL, the tasks of signal tracking and navigation state estimation no longer process separately and a single extended Kalman filter (EKF) is employed to simultaneously track the received signals and estimate the receiver’s position, velocity, etc. In contrast to the scalar tracking loop (STL) which utilizes the independent parallel tracking loop approach, the VTL technique is beneficial from the correlation of each satellite signal and user dynamics. The VTL approach provides several important advantages. One of the merits is that the tracking loop can be assisted for overcoming the problem of signal blockage. Although the VTL architectures provide several important advantages, they suffer some fundamental drawbacks. For example, the errors in the navigation solutions may degrade the tracking accuracy. The most significant drawback is that failure of tracking in one channel may affect the entire tracking loop and possibly lead to loss of lock. For reliability enhancement, the EKF based integrity monitoring and FDE algorithms are developed to prevent the error from spreading into the entire tracking loop. The integrity monitoring is utilized to check the possible fault in the pseudorange and the pseudorange rate, followed by the FDE mechanism employed to exclude the abnormal satellite signals. Performance assessment and evaluation for the proposed approach will be presented.

Support Vector Machine Assisted GPS Navigation in Limited Satellite Visibility

This paper investigates performance improvement via the incorporation of the support vector machine (SVM) into the vector tracking loop (VTL) for the Global Positioning System (GPS) in limited satellite visibility. Unlike the traditional scalar tracking loop (STL), the tracking and navigation modules in the VTL are not independent anymore since the user’s position can be determined by using the information from other satellites and can be predicted on the basis of the states of the user. The method proposed in this paper makes use of the SVM to bridge the GPS signal and prevent the error growth due to signal outage. Similar to the neural network, the SVM is motivated by its ability to approximate an unknown nonlinear input-output mapping through supervised training. The SVM is employed for predicting adequate numerical control oscillator (NCO) inputs, i.e., providing better prediction of residuals for the Doppler frequency and code phase in order to maintain regular operation of the navigation system. When the navigation processing is in good condition, the SVM is at the training stage, and the output information from the discriminator and navigation filter is adopted as the inputs. Other machine learning (ML) algorithms such as the radial basis function neural network (RBFNN) and the Adaptive Network-Based Fuzzy Inference System (ANFIS) are employed for comparison. Performance evaluation for the SVM assisted architecture as compared to the RBFNN- and ANFIS-assisted methods and the un-assisted VTL will be carried out and the performance evaluation during GPS signal outage will be presented. The proposed design is very useful for navigation during the environment of limited satellite visibility to effectively overcome the problem in the environment of GPS outage.

GPS Vector Tracking Receivers with Rate Detector for Integrity Monitoring

In this paper, the integrity monitoring algorithm based on a Kalman filter (KF) based rate detector is employed in the vector tracking loop (VTL) of the Global Positioning System (GPS) receiver. In the VTL approach, the extended Kalman filter (EKF) simultaneously tracks the received signals and estimates the receiver’s position, velocity, etc. In contrast to the scalar tracking loop (STL) that uses the independent parallel tracking loop approach, the VTL technique uses the correlation of each satellite signal and user dynamics and thus reduces the risk of loss lock of signals. Although the VTL scheme provides several important advantages, the failure of tracking in one channel may affect the entire system and lead to loss of lock on all satellites. The integrity monitoring algorithm can be adopted for robustness enhancement. In general, the standard integrity monitoring algorithm can timely detect the step type erroneous signals. However, in the presence of ramp type slowly growing erroneous signals, detection of such type of error takes much more time since the error cannot be detected until the cumulative exceeds the specified threshold. The integrity monitoring based on the rate detector possesses good potential for resolving such problem. The test statistic based on the pseudorange residual in association with the EKF is applied for determination of whether the test statistic exceeds the allowable threshold values. The fault detection and exclusion (FDE) mechanism can then be employed to exclude the hazardous erroneous signals for the abnormal satellites to assure normal operation of GPS receivers. Feasibility of the integrity monitoring algorithm based on the EKF based rate detector will be demonstrated. Performance assessment and evaluation will be presented.

Gradient effects on false vacuum decay in gauge theory

We study false vacuum decay for a gauged complex scalar field in a polynomial potential with nearly degenerate minima. Radiative corrections to the profile of the nucleated bubble as well as the full decay rate are computed in the planar thin-wall approximation using the effective action. This allows to account for the inhomogeneity of the bounce background and the radiative corrections in a self-consistent manner. In contrast to scalar or fermion loops, for gauge fields one must deal with a coupled system that mixes the Goldstone boson and the gauge fields, which considerably complicates the numerical calculation of Green's functions. In addition to the renormalization of couplings, we employ a covariant gradient expansion in order to systematically construct the counterterm for the wave-function renormalization. The result for the full decay rate however does not rely on such an expansion and accounts for all gradient corrections at the chosen truncation of the loop expansion. The ensuing gradient effects are shown to be of the same order of magnitude as non-derivative one-loop corrections.

Loops in AdS: from the spectral representation to position space

We compute a family of scalar loop diagrams in AdS. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree- level exchange or contact diagrams. An important example is the computation of the finite coupling 4-point function of the large-N conformal O(N ) model on AdS3. Remarkably, the re-summation of bubble diagrams is equal to a certain contact diagram: the {overline{D}}_{1,1,frac{3}{2},frac{3}{2}}left(z,overline{z}right) function. Another example is a scalar with ϕ4 or ϕ3 coupling in AdS3: we compute various 4-point (and higher point) loop bubble diagrams with alternating integer and half- integer scaling dimensions in terms of a finite sum of contact diagrams and tree-level exchange diagrams. The 4-point function with external scaling dimensions differences obeying ∆12 = 0 and ∆34 = 1 enjoys significant simplicity which enables us to compute in quite generality. For integer or half-integer scaling dimensions, we show that the M -loop bubble diagram can be written in terms of Lerch transcendent functions of the cross- ratios z and overline{z} . Finally, we compute 2-point bulk bubble diagrams with endpoints in the bulk, and the result can be written in terms of Lerch transcendent functions of the AdS chordal distance. We show that the similarity of the latter two computations is not a coincidence, but arises from a vertex identity between the bulk 2-point function and the double-discontinuity of the boundary 4-point function.

Calculation of disconnected quark loops in lattice QCD * * Supported by National Natural Science Foundation of China (11335001)

Calculation of disconnected quark loops in lattice QCD is very time consuming. Stochastic noise methods are generally used to estimate these loops. However, stochastic estimation gives large errors in the calculations of disconnected diagrams. We use the symmetric multi-probing source (SMP) method to estimate the disconnected quark loops, and compare the results with the noise method and the spin-color explicit (SCE) method on a quenched lattice QCD ensemble with lattice volume and lattice spacing fm. The results show that the SMP method is very suitable for the calculation of pseudoscalar disconnected quark loops. However, the SMP and SCE methods do not have an obvious advantage over the noise method in the evaluation of the scalar disconnected loops.

Vector Tracking Loop-Based GNSS NLOS Detection and Correction: Algorithm Design and Performance Analysis

This article deals with the non-line-of-sight (NLOS) reception issue in the field of global navigation satellite system (GNSS). The NLOS reception has attracted a significant amount of attention because it is one of the main factors that limit the GNSS position accuracy in urban areas. In this article, we dig into the baseband signal processing level to explore a new solution to the NLOS detection and correction by means of the vector tracking loop (VTL). The NLOS effects on both conventional scalar tracking loops (STLs) and VTL are derived mathematically. Based on this, an NLOS detection algorithm is developed using metrics, such as the equivalent noise bandwidth, the time delay of multicorrelator peaks, as well as code discriminator outputs. Once detected, the NLOS-induced measurement error is corrected before being fed forward into the navigation estimator to improve the position accuracy. Two field tests in urban areas in Hong Kong are conducted to illustrate the effectiveness of the proposed method in real applications. The NLOS correction performance is also assessed using simulated NLOS receptions with controllable time delays and reflection coefficients, which reveals how the proposed algorithm performs in different NLOS scenarios.

Performance assessment of GNSS scalar and vector frequency tracking loops

This paper focuses on two types of frequency lock loops (FLL) in Global Navigation Satellite System (GNSS) receivers, namely the conventional scalar frequency lock loop (SFLL) and the vector frequency lock loop (VFLL).The VFLL has been proven to have a better tracking performance than the SFLL in scenarios such as intermittent signal outages, high dynamics, etc. However, the FLL tracking performance under the equivalent noise bandwidth has not been explored in literature. To do this, we implemented three kinds of FLL, i.e., the SFLL, the weighted least square-based vector frequency loop (WLS-VFLL), and the extended Kalman filter-based vector tracking loop (EKF-VFLL). All these FLLs have the same noise bandwidth, based on which we made a fair comparison between them. The experimental static data and simulated high- dynamic data have been tested. Results show that the EKF-VFLL has a similar tracking performance with WLS-VFLL under static environment, both better than the SFLL. In high- dynamic environment, the advantages of EKF-VFLL are more prominent than the other two methods. Furthermore, EKF-VFLL takes the longest time in terms of computational efficiency.

Research on a chip scale atomic clock driven GNSS/SINS deeply coupled navigation system for augmented performance

Chip scale atomic clock (CSAC) is a recently developed low-profile atomic frequency reference device. Researchers have demonstrated CSAC was able to improve the accuracy of Global navigation satellite system (GNSS) receiver positioning results. However, the work was conducted using scalar tracking loops (STL). It is meaningful to investigate CSAC augmented vector tracking loop (VTL), since the VTL has different architecture with STL. Thus, in this paper, the authors investigated a CSAC driven VTL_DI system for exploring CASC impact on VTL. Firstly, the authors explored 1) whether VTL_DI could operate without regarding clock offset and drifts as VTL_DI integration filter state variables, and 2) whether VTL_DI could provide reliable position with only three satellites in view. Secondly, side-by-side comparative field tests were conducted to evaluate performance improvement: by solution A: VTL_DI supported by CSAC and solution B: a temperature compensated crystal oscillator (TXCO) with more than four satellites and three satellites in view scenarios. It was discovered that the CSAC could enhance the position performance, even if amount of satellites were fewer than four in view. However, VTL_DI system could not guarantee its positioning accuracy without clock offset as state variable, which was different from STL_DI system.

The Explicit Tuning Investigation and Validation of a Full Kalman Filter-Based Tracking Loop in GNSS Receivers

As the development of traditional scalar tracking loops, different additional enhancement techniques in a GNSS receiver are proposed to help improve the positioning service quality. Up to now, Kalman-based tracking loop has gained much attention due to its potential superiorities, it has been widely exploited and studied in different specific applications. But meanwhile, there is still a lack of the detailed exploration regarding the Kalman tuning and the fully in-depth analysis and validation. Based on our former related work, an improved mathematical expression of Kalman gain and proper tractable models are proposed to help the analysis of Kalman tuning. An explicit tuning rule is proposed step by step regarding every single parameter involved and the validation is carried out in real experiments by the comparison of different receivers with different configurations. The results verify the proposed tuning rule and advantages of KF-tracking with proper setting. Thanks to the accurate and reliable signal parameter estimation, it can dramatically relieve the burden of the following processing modules, like PVT, RTK and other similar algorithms.

Radiative effects on false vacuum decay in Higgs-Yukawa theory

We derive fermionic Green's functions in the background of the Euclidean solitons describing false vacuum decay in a prototypal Higgs-Yukawa theory. In combination with appropriate counterterms for the masses, couplings and wave-function normalization, these can be used to calculate radiative corrections to the soliton solutions and transition rates that fully account for the inhomogeneous background provided by the nucleated bubble. We apply this approach to the archetypal example of transitions between the quasi-degenerate vacua of a massive scalar field with a quartic self-interaction. The effect of fermion loops is compared with those from additional scalar fields, and the loop effects accounting for the spacetime inhomogeneity of the tunneling configuration are compared with those where gradients are neglected. We find that scalar loops lead to an enhancement of the decay rate, whereas fermion loops lead to a suppression. These effects get relatively amplified by a perturbatively small factor when gradients are accounted for. In addition, we observe that the radiative corrections to the solitonic field profiles are smoother when the gradients are included. The method presented here for computing fermionic radiative corrections should be applicable beyond the archetypal example of vacuum decay. In particular, we work out methods that are suitable for calculations in the thin-wall limit, as well as others that take account of the full spherical symmetry of the solution. For the latter case, we construct the Green's functions based on spin hyperspherical harmonics, which are eigenfunctions of the appropriate angular momentum operators that commute with the Dirac operator in the solitonic background.

Anomalous neutral gauge boson interactions and simplified models

Trilinear $Z$ boson interactions are sensitive probes both of new sources of $CP$ violation in physics beyond the standard model and of new particle thresholds. Measurements of trilinear $Z$ interactions are typically interpreted in the frameworks of anomalous couplings and effective field theory, both of which require care in interpretation. To obtain a quantitative picture of the power of these measurements when interpreted in a TeV-scale context, we investigate the anatomy of $ZZZ$ interactions and consider two minimal and perturbative simplified models which induce such interactions through new scalar and fermion loops at the weak scale, focusing on $ZZ$ and vector boson fusion-induced $Zjj$ production at the LHC and $ZZ$ production at a future ${e}^{+}{e}^{\ensuremath{-}}$ collider. We show that both threshold and non-threshold effects often are small compared to the sensitivity of the LHC, while the increased sensitivity of a future lepton collider should allow us to constrain such scenarios through associated electroweak precision effects complementary to direct searches at hadron colliders.