Loop Integrals Research Articles

Loops, recursions, and soft limits for fermionic correlators in (A)dS

Study of correlation functions in AdS/CFT and in-in correlators in de Sitter space often requires the computation of Witten diagrams. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches have been developed to simplify computations. However, in momentum space, these methods have been limited to fields with integer spin. In this paper, we formulate tools for evaluating Witten diagrams with spin−12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{spin}-\\frac{1}{2} $$\\end{document} fields in momentum space and discuss where they differ from the corresponding integer-spin analysis. We formulate our tools explicitly for massless fermions and present how appropriate Weight shifting operators with respect to the external kinematics can be used to obtain the generalization to fermions with integer mass (in units of 1/lAdS). We apply these tools to loop Witten diagrams and also discuss their use for evaluating in-in correlators in dS. In cases where we can evaluate the loop integrals, we find their transcendentality is lower than the corresponding scalar field results. Further, we classify the nature of IR divergences encountered for interacting massive scalars and fermions. We also prove a novel Weinberg-like soft theorem for gauge fields coupled to matter in AdS and show that the universal terms in the leading soft factor are sensitive to the spin of the matter field. These generalize the recently discovered soft theorems for pure Yang-Mills to Yang-Mills with matter.

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ3, ζ5 to the cusp anomalous dimension.

Phase transition and gravitational waves in maximally symmetric composite Higgs model

In this paper we study phase transitions in a maximally symmetric composite Higgs model with next-to-minimal coset, where a pseudoscalar singlet emerges alongside the Higgs doublet. The maximal symmetry guarantees the finiteness of the radiatively generated scalar potential. We explore the scenario involving an explicit source of CP violation in the strong sector, which induces a ℤ2 asymmetric scalar potential, and consequently leads to nonzero vacuum expectation value for the singlet. Current experimental bounds from the LHC are imposed on the masses of the composite resonances, while the CP violating interactions of the pseudo Nambu-Goldstone bosons are tightly constrained from the measurements of the electric dipole moment of the electron. We compute the finite temperature corrections to the potential, incorporating the momentum-dependent form factors in the loop integrals to capture the effect of the strong dynamics. The impact of the resonances from the strong sector on the finite temperature potential are exponentially suppressed. The presence of explicit CP violation leads to strong first-order phase transition from a false vacuum to the electroweak vacuum where the pseudoscalar singlet has a non-zero vacuum expectation value. We illustrate that, as a result of such phase transitions, the production of potentially observable gravitational waves at future detectors will offer a complementary avenue to probe the composite Higgs models, distinct from collider experiments.

On the topological number in Kelvin’s circulation of inviscid fluids

Kelvin’s circulation, as a loop integral of the velocity field, is first shown to be equal to ΓC=2πΔnΓ1+constant in an inviscid fluid, with Γ1 a unit circulation. The integer Δn is interpreted as the number of net 2π-rotations of the velocity vector in one cyclicality along the circulation loop and hence it is a topological number. Different from the linkage number in the helicity invariant, which only exists in 3D space, the topological number in the circulation invariant is independent of the spatial dimension. A further study reveals that this new topological phase 2πΔn is rooted at the gauge invariance of the circulation and it is a counterpart of the Berry’s phase in the quantum system.

FeynCalc 10: Do multiloop integrals dream of computer codes?

In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version include greatly improved capabilities for doing multiloop calculations, including topology identification and minimization, optimized tensor reduction, rewriting of scalar products in terms of inverse denominators, detection of equivalent or scaleless loop integrals, derivation of Symanzik polynomials, Feynman parametric as well as graph representation for master integrals and initial support for handling differential equations and iterated integrals. In addition to that, the new release also features completely rewritten routines for color algebra simplifications, inclusion of symmetry relations between arguments of Passarino–Veltman functions, tools for determining matching coefficients and quantifying the agreement between numerical results, improved export to ▪ and first steps towards a better support of calculations involving light-cone vectors.

On gauge amplitudes first appearing at two loops

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

Power stabilization of a terahertz-frequency quantum-cascade laser using a photonic-integrated modulator

We demonstrate a technique to stabilize the emission from a 3.4-THz quantum-cascade laser against power drifts, using a recently developed photonic integrated circuit (PIC) structure formed by coupling a racetrack resonator with a ridge waveguide. This structure enables a dynamic power-control range of ±15% and locking over >600 s using a proportional–integral control loop. The resonator yields a 50% weaker perturbation to the laser emission frequency when compared with direct laser modulation, and hence offers the prospect of simultaneous, quasi-independent control of power and frequency. Progress towards integrating the PIC with a precision micromachined rectangular metallic waveguide module has also been demonstrated, with power modulation of the principal laser emission line being observed during pulsed operation.

Integration of CTCF loops, methylome, and transcriptome in differentiating LUHMES as a model for imprinting dynamics of the 15q11-q13 locus in human neurons.

Human cell line models, including the neuronal precursor line LUHMES, are important for investigating developmental transcriptional dynamics within imprinted regions, particularly the 15q11-q13 Angelman (AS) and Prader-Willi (PWS) syndrome locus. AS results from loss of maternal UBE3A in neurons, where the paternal allele is silenced by a convergent antisense transcript UBE3A-ATS, a lncRNA that terminates at PWAR1 in non-neurons. qRT-PCR analysis confirmed the exclusive and progressive increase in UBE3A-ATS in differentiating LUHMES neurons, validating their use for studying UBE3A silencing. Genome-wide transcriptome analyses revealed changes to 11 834 genes during neuronal differentiation, including the upregulation of most genes within the 15q11-q13 locus. To identify dynamic changes in chromatin loops linked to transcriptional activity, we performed a HiChIP validated by 4C, which identified two neuron-specific CTCF loops between MAGEL2-SNRPN and PWAR1-UBE3A. To determine if allele-specific differentially methylated regions (DMR) may be associated with CTCF loop anchors, whole genome long-read nanopore sequencing was performed. We identified a paternally hypomethylated DMR near the SNRPN upstream loop anchor exclusive to neurons and a paternally hypermethylated DMR near the PWAR1 CTCF anchor exclusive to undifferentiated cells, consistent with increases in neuronal transcription. Additionally, DMRs near CTCF loop anchors were observed in both cell types, indicative of allele-specific differences in chromatin loops regulating imprinted transcription. These results provide an integrated view of the 15q11-q13 epigenetic landscape during LUHMES neuronal differentiation, underscoring the complex interplay of transcription, chromatin looping, and DNA methylation. They also provide insights for future therapeutic approaches for AS and PWS.

One-loop calculations in the chirality-flow formalism

In a few recent papers we introduced the chirality-flow formalism, which builds on the spinor-helicity formalism, but incorporates the Fierz identity into the Feynman rules. Calculations at tree level are thereby trivial, often to the extent that it is possible to immediately write down a tree-level Feynman diagram in terms of spinor inner products. This simplification persists in tree-level computer implementations, giving very sizable speedups. In the present paper, we argue that there is also a significant simplification of the Lorentz structure at the one-loop level when using the four-dimensional formulation of the four-dimensional helicity scheme. As at tree level, the gauge reference vector for external gauge bosons, and the simplified Lorentz structure lead to significant shortening of the calculations. Additionally, we find that the possible terms in a tensor decomposition of loop integrals are highly constrained, and therefore the tensor reduction procedure is simplified. Published by the American Physical Society 2024

Smoothed asymptotics: From number theory to QFT

Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultraviolet regularization scheme for loop integrals in quantum field theory which we call η regularization. This reveals a connection between the elimination of divergences in divergent series of powers and the preservation of gauge invariance in the regularization of loop integrals in quantum field theory. In particular, we note that a method for regularizing the series of natural numbers so that it converges to minus one-twelfth inspires a regularization scheme for non-Abelian gauge theories coupled to Dirac fermions that preserves the Ward identity for the vacuum polarization tensor and other higher point functions. We also comment on a possible connection to Schwinger proper time integrals. Published by the American Physical Society 2024

Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the λϕ4 model

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field ϕ(x) locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional λϕ4 terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling λ. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the λϕ4 QFT.

Low-energy theorems and linearity breaking in anomalous amplitudes

This study seeks a better comprehension of anomalies by exploring (n+1)-point perturbative amplitudes in a 2n-dimensional framework. The involved structures combine axial and vector vertices into odd tensors. This configuration enables diverse expressions, considered identities at the integrand level. However, connecting them is not automatic after loop integration, as the divergent nature of amplitudes links to surface terms. The background to this subject is the conflict between the linearity of integration and the translational invariance observed in the context of anomalies. That prohibits the simultaneous satisfaction of all symmetry and linearity properties, constraints that arise through Ward identities and relations among Green functions. Using the method known as Implicit Regularization, we show that trace choices are a means to select the amount of anomaly contributions appearing in each symmetry relation. Such an idea appeared through recipes to take traces in recent works, but we introduce a more complete view. We also emphasize low-energy theorems of finite amplitudes as the source of these violations, proving that the total amount of anomaly remains fixed regardless of any choices.

SCIENTIFIC-METHODICAL ASPECT OF IMPROVING HUMAN COMPUTER COMMUNICATION SYSTEM IN SOFTWARE DEVELOPMENT

Effective human-computer communication (HCC) systems are crucial in software development to ensure user satisfaction, productivity, and system efficiency. This paper explores scientific and methodical approaches to enhance HCC systems, focusing on principles from human-computer interaction (HCI), usability engineering, and cognitive psychology. The research emphasizes iterative design processes, user-centered methodologies, and the integration of feedback loops to optimize interface design and user experience. Case studies and empirical data illustrate the effectiveness of these approaches in improving HCCsystems, highlighting their impact on software usability and user engagement.

Loop corrections in the separate universe picture

In inflationary models that produce a spike of power on short scales, back-reaction of small-scale substructure onto large-scale modes is enhanced. Loop corrections that quantify this back-reaction have been evaluated by a number of authors. We argue that the separate universe framework provides a highly convenient tool for such computations. Each loop of interest is characterized by large hierarchies in wavenumber and horizon exit time. The separate universe framework highlights important factorizations involving these hierarchies. We interpret each loop correction in terms of a simple, classical, back-reaction model, and clarify the meaning of the different volume scalings that have been reported in the literature. We argue that significant back-reaction requires both short-scale nonlinearities and long-short couplings that modulate the short-scale power spectrum. In the absence of long-short couplings, only incoherent “shot noise”-like effects are present, which are volume-suppressed. Dropping the shot noise, back-reaction from a particular scale is controlled by a product of f NL-like parameters: an equilateral configuration measuring the nonlinearity of the short-scale modes, and a squeezed configuration measuring the long-short coupling. These may carry important scale dependence controlling the behaviour of the loop in the decoupling limit where the hierarchy of scales becomes large. In single-field models the long-short coupling may be controlled by this hierarchy, in which case the net back-reaction would be safely suppressed. We illustrate our framework using explicit computations in a 3-phase ultra-slow-roll scenario. Our analysis differs from earlier treatments of this model, which did not consistently include the effect of small-scale modes. Finally, we discuss different choices for the smoothing scale used in the separate universe framework and argue the effect can be absorbed into a renormalization of local operators. This complicates interpretation of the loop, because the analytic part of each loop integral is degenerate with unknown, ultraviolet-sensitive contributions.

γ5 schemes and the interplay of SMEFT operators in the Higgs-gluon coupling

We calculate the four-top-quark operator contributions to Higgs production via gluon fusion in the Standard Model effective field theory. The four-top operators enter for the first time via two-loop diagrams. Owing to their chiral structure they contain γ5, so special care needs to be taken when using dimensional regularization for the loop integrals. We use two different schemes for the continuation of γ5 to D space-time dimensions in our calculations and present a mapping for the parameters in the two schemes. This generically leads to an interplay of different operators, such as four-top operators, chromomagnetic operators, or Yukawa-type operators at the loop level. We validate our results by examples of matching onto UV models. Published by the American Physical Society 2024

Scaling analysis of nuclear power plant (APR1400) utilizing ATLAS integral effect test result of A5.1 (Counterpart test for LSTF 1% cold-leg break LOCA)

ATLAS is the thermal hydraulic integral effect test loop that can simulate the same pressure and temperature condition with nuclear power plant. It was designed with a height ratio of 1/2 and a volume ratio of 1/288 with reference to APR1400. The counterpart test against LSTF which was named as A5.1 test was performed within the OECD/NEA ATLAS international joint research project to compare major thermal hydraulic phenomena between two test facilities. The main scenario for the A5.1 test is the LSTF SB-CL-32 test. The SB-CL-32 test is a 1% horizontal small break loss of coolant accident (SBLOCA) at the cold leg with cold leg injection of the emergency core cooling system (ECCS) and accident management (AM) action.From the counterpart test results, the significant differences were found in the viewpoint of the thermal–hydraulic phenomena. It was concluded that the different result were caused by the different design characteristic of each test facility because they referred the different nuclear power plant. Thus, the applicability of the ATLAS test results to its reference nuclear power plant was evaluated by utilizing ATLAS A5.1 test results which was the counterpart test with the LSTF.The transient scenario and initial and boundary conditions of the A5.1 test were adopted to APR1400 after applying scaling ratios of ATLAS. The MARS-KS code was utilized to analyzed thermal hydraulic behaviors of APR1400 and the analysis results were compared with the scaled A5.1 test result. From the result of comparison, it was concluded that the ATLAS test results predicted the thermal hydraulic behavior of the nuclear power plant well. Thus, it was confirmed that ATLAS is a well-designed integral effect test facility which is designed with an appropriate scaling method.

Research on adaptive feedforward control method for Tiltrotor Aircraft/Turboshaft engine system based on radial basis function neural network

The paper proposes an adaptive feedforward control approach based on a radial basis function neural network to address the issue of poor disturbance rejection capability in conventional integrated control methods for tiltrotor aircraft propulsion systems. Firstly, a comprehensive simulation model of the tiltrotor aircraft and turboshaft engine is established, and its accuracy is validated against the results of the General Tiltrotor Integrated Simulation Code. Building upon this, a cascade Proportional-integral control parameter design method based on separation principles is proposed to tackle the problem of designing control parameters for the Proportional Integral main loop structure. Subsequently, an adaptive feedforward control method that takes into account both aircraft-induced disturbances and model uncertainties for turboshaft engines is presented using a Radial Basis Function neural network. This approach includes a nonlinear estimator capable of estimating load disturbances and a Radial Basis Function adaptive feedforward controller. Furthermore, stability proof of the closed-loop system is provided based on Lyapunov function analysis. Finally, digital simulations and hardware-in-the-loop experiments are conducted based on a typical tiltrotor flight mission. The results demonstrate that the proposed method effectively mitigates the power turbine drop compared to the conventional Proportional Integral controller with collective pitch feedforward.

Subtleties in triangle loops for Ds+→ρ+η→π+π0η in a0(980) production

We address a general problem in the evaluation of triangle loops stemming from the consideration of the range of the interaction involved in some of the vertices, as well as the energy dependence of the width of some unstable particles in the loop. We find sizeable corrections from both effects. We apply that to a loop relevant to the Ds+→π+π0η decay, and find reductions of about a factor of 4 in the mass distribution of invariant mass of the πη in the region of the a0(980). The method used is based on the explicit analytical evaluation of the q0 integration in the d4q loop integration, using Cauchy’s residues method, which at the same time offers an insight on the convergence of the integrals and the effect of form factors and cutoffs. Published by the American Physical Society 2024

A reduced smoothed integration scheme of the cell‐based smoothed finite element method for solving fluid–structure interaction on severely distorted meshes

AbstractThis article describes an inexpensive partitioned coupling strategy for computational fluid–structure interaction (FSI) admitting negative‐Jacobian elements. The emphasis is very much on a reduced smoothed integration (RSI) scheme of the cell‐based smoothed finite element method (CSFEM) using four‐node quadrilateral (Q4) elements for a cost‐effective solution to the Navier–Stokes (NS) equations. In the discrete fluid field, each Q4 element is considered as one single smoothing cell so as to diminish the smoothed integration loops substantially. However, the RSI scheme does not respect the stability condition of smoothed Galerkin weak‐form integral in the CSFEM. To tackle this issue, a simple hourglass control is introduced to the under‐integrated formulation of the NS solver. Importantly, the stabilized RSI scheme has an inbuilt advantage of its enormous tolerance towards negative‐Jacobian elements. The developed technique is easy‐to‐implement and has been tested in various FSI examples adopting both fine and distorted meshes.

Path-Following Sliding Mode Controller for an Electric Vehicle Considering Actuator Dynamics

This study introduced a novel path-following controller tailored to electric vehicles equipped with a steer-by-wire system, i.e., the steering angle of the vehicle was defined by an electrical actuator. The control objective was to force the proper steering angle of the vehicle, which permits following a desired path. The system presupposed that an external algorithm that utilized sensor data provided the lateral movement references while maintaining a steady longitudinal velocity for the vehicle. The proposed control scheme was based on a robust sliding mode steering controller to manage the vehicle’s lateral movement. Furthermore, a brushless DC (BLDC) motor was considered as the steering actuator, which was controlled by a field-oriented controller (FOC), which was based on four internal proportional–integral (PI) control loops for precise steering actuation. To assess the performance of the proposed control scheme, numerical simulations were obtained, which demonstrated its effectiveness in achieving the control objective.