Factorization Formula Research Articles

On factorized Lax pairs for classical many-body integrable systems

In this paper, we study the factorization formulae for the Lax matrices of the classical Ruijsenaars–Schneider and Calogero–Moser models. We review the already known results and discuss their possible origins. The first origin comes from the IRF-Vertex relations and the properties of the intertwining matrices. The second origin is based on the Schlesinger transformations generated by modifications of underlying vector bundles. We show that both approaches provide explicit formulae for [Formula: see text]-matrices of the integrable systems in terms of the intertwining matrices (and/or modification matrices). In the end, we discuss the Calogero–Moser models related to classical root systems. The factorization formulae are proposed for a number of special cases.

Resummation of soft and Coulomb corrections for toverline{t}h production at the LHC

In this paper, a combined resummation of soft and Coulomb corrections is performed for the associated production of the Higgs boson with a top quark pair at the LHC. We illustrate the similarities and critical differences between this process and the toverline{t} production process. We show that up to the next-to-leading power, the total cross section for toverline{t}h production admits a similar factorization formula in the threshold limit as that for tt production. This fact, however, is not expected to hold at higher powers. Based on the factorization formula, we perform the resummation at the improved next-to-leading logarithmic accuracy, and match to the next-to-leading order result. This allows us to give NLL′+NLO predictions for the total cross sections at the LHC. We find that the resummation effects enhance the NLO cross sections by about 6%, and significantly reduce the scale dependence of the theoretical predictions.

Semi-classical calculations of the α decay half-lives for even–even nuclei

The half-lives of the [Formula: see text] decay for even–even nuclei having [Formula: see text] (164 nuclei) have been calculated by using the Wentzel–Kramers–Brillouin (WKB) method together Bohr–Sommerfeld (BS) quantization condition for cosh potential in two-different forms with and without the isospin effects for six different parameter sets. By comparing the obtained results with the experimental values, the rms deviations have been computed. It is obtained that when the cosh potential is used in 2 different type forms, the rms values are also changed and the better one for obtaining the half-lives is cosh-2 form. Even if the isospin-dependent potential does not have so much effect on rms values in this sort of WKB with BS calculations with cosh potential forms, considering the isospin effect together the isospin-dependent nuclear diffuseness parameter have a strong influence on the rms values. New hindrance factor formula based on liquid drop model was used in order to show the influence of hindrance factor on the [Formula: see text] decay half-lives. It is pointed out that this new function of the hindrance factor does not depend on the magic numbers, it contains fewer free parameters and using of this improves the calculations positively. New estimates by using present model have also been made for even–even nuclei having with [Formula: see text] which do not have the measured [Formula: see text] decay half-lives yet and they have been compared the results of the ImSahu model. The present results would provide useful information and knowledge for the explanation of half-lives of [Formula: see text] decay of nuclei and future possible experimental studies.

MR-based wall shear stress measurements in fully developed turbulent flow using the Clauser plot method

In arterial blood flow wall shear stress (WSS) quantifies the frictional force that flowing blood exerts on a vessel wall. WSS can be directly estimated from phase-contrast (PC) MR velocity measurements and has been suggested as a biomarker in cardio-vascular diseases. We present and investigate the application of the Clauser plot method for estimating WSS in fully developed turbulent stationary flow using PC velocity measurements. The Clauser plot method estimates WSS from the logarithmic region of boundary layer in fully developed turbulent stationary flow. The Clauser plot method was evaluated using 2D PC-MR phantom measurements at 3 T for different in-plane resolutions at various Reynolds numbers. WSS values derived from the Clauser plot were compared to results from Laser Doppler Velocimetry (LDV) measurements and theoretical results calculated using the friction factor formula for smooth pipe flow. For all Reynolds numbers, WSS values derived from the Clauser plot were in good agreement with results from LDV measurements and values using the friction factor formula (relative deviations ∼5%). Furthermore, Clauser plot derived results were almost independent of spatial resolution, in contrast to WSS results obtained with our in-house software tool for MR-based WSS quantification showing relative deviations of more than 100%. In fully developed turbulent flow, the Clauser plot method provides highly consistent WSS independent of the underlying spatial resolution. Therefore, it renders a valuable approach for MR-based WSS estimates in controllable flow settings. Although its direct in vivo applicability is severely limited because of the different flow character, it may serve as helpful approach for validation of MR-based WSS quantification algorithms prior to their clinical application.

Accessing Gluon Parton Distributions in Large Momentum Effective Theory.

Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula for these renormalized quasi-PDFs from which one can extract the gluon PDFs.

Traditional Uses of Some Wild Plants in Kale and Acıpayam Provinces in Denizli

Aim of study: With this study, it was aimed to determine some wild plants in the traditional uses in daily lives by local people for healing, treatment, food, spices, equipment, etc. purposes.Area of study: The study area was Kale and Acıpayam provinces in Denizli between April and October 2016.Material and Methods: Plant materials were provided from villagers and county of Kale and Acıpayam districts. In the identification of plants, "Flora of Turkey and the East Aegean Islands" and "List of Turkish Plants" were used. To determine this, totally 60 people were interviewed face to face. The Informants' Consensus Factor (FIC) and Use Value (UV) formulas were used to analyze the data.Main results: As a result of the surveys conducted with 60 people, 48 plant taxa belonging to 29 families have been identified. It has been determined that the plants with traditional use in the region are mostly used for the treatment of stomach disorders, respiratory diseases and pain relief. The most used parts of the plants have been leaves. The highest UV is Olea europaea L. var. sylvestris L. (0.65), and the lowest UV is Pulicaria dysenterica (L.) Bernh.. (0.05). The highest FIC value (0.86) is cold and flu.Research highlights: Although Viscum album subsp. austriacum (Wiesb.) Vollman has been found to be used for different diseases in the literature, its use as a vasodilator drug was first determined by this study.

Fatigue strength evaluation of thin plate butt joints considering initial deformation

In addition to dislocation and welding angle deformation during the processing of welded joints of thin plates, additional curvature deformation will occur in the thin plates, which is defined as the initial deformation of the plates. Due to the existence of dislocation and angular deformation, additional secondary bending moment effect will appear in the welded structure, which will affect the stress concentration at the weld toe. Therefore, DNV and IIW specifications recommend the stress amplification factor formula caused by welding imperfections. However, the current evaluation formula is mostly applicable to the stress concentration correction of thick plate welded structures, which does not consider the additional initial deformation effect caused by thin plate welding. Therefore, on the basis of the revised formula for thick plates, the stress amplification factor considering the initial deformation effect of thin plates is derived in this paper, and the calculation results are compared with those in traditional codes. Nonlinear finite element calculation results and fatigue test results are used to verify the feasibility and validity of the formula. The results show that, when considering the initial deformation of welding plates, the traditional code formula has a large error, and the revised calculation results are in good agreement with the finite element calculation results, which can accurately reflect the stress concentration effect at the welding toe of the thin plates butt joints.

Intrinsic fluctuation and susceptibility in somatic cell reprogramming process**Project supported by the National Natural Science Foundation of China (Grant Nos. 11775091 and 11474117).

Based on the coherent feedforward transcription regulation loops in somatic cell reprogramming process, a stochastic kinetic model is proposed to study the intrinsic fluctuations in the somatic cell reprogramming. The Fano factor formulas of key genes expression level in the coherent feedforward transcription regulation loops are derived by using of Langevin theory. It is found that the internal fluctuations of gene expression levels mainly depend on itself activation ratio and degradation ratio. When the self-activation ratio (or self-degradation ratio) is increased, the Fano factor increases reaches a maximum and then decreases. The susceptibility is used to measure the sensitivity of steady-state response to the variation in systemic parameters. It is found that with the increase of the self-activation ratio (or self-degradation ratio), the susceptibility of steady-state increases at first, it reaches a maximum, and it then decreases. The magnitude of the maximum is increased with the increase of activated ratio by the upstream transcription factor.

Thrust distribution in Higgs decays at the next-to-leading order and beyond

We present predictions for the thrust distribution in hadronic decays of the Higgs boson at the next-to-leading order and the approximate next-to-next-to-leading order. The approximate NNLO corrections are derived from a factorization formula in the soft/collinear phase-space regions. We find large corrections, especially for the gluon channel. The scale variations at the lowest orders tend to underestimate the genuine higher order contributions. The results of this paper is therefore necessary to control the perturbative uncertainties of the theoretical predictions. We also discuss on possible improvements to our results, such as a soft-gluon resummation for the 2-jets limit, and an exact next-to-next-to-leading order calculation for the multi-jets region.

New factorization relations for Yang-Mills amplitudes

A double-cover extension of the scattering equation formalism of Cachazo, He and Yuan (CHY) leads us to conjecture covariant factorization formulas of n-particle scattering amplitudes in Yang-Mills theories. Evidence is given that these factorization relations are related to Berends-Giele recursions through repeated use of partial fraction identities involving linearized propagators.

Calculations of the deuteron form factors

On the received coefficients of the analytical forms for deuteron wave function in coordinate representation in form r^(l+1)*exp(-A*r) for the modern realistic nucleon-nucleon potentials NijmI, NijmII, Nijm93, Reid93 and Argonne v18 are calculated charge GC(p), quadrupole GQ(p) and magnetic GM(p) deuteron form factors. An original dipole fit for proton and neutron isoscalar electric and magnetic form factors is used for calculations. Theoretical calculations of values of the deuteron form factor are compared with their experimental data of world collaborations (Bates, BLAST, Bonn, JLab, Mainz, Naval Research Lab, NIKHEF, Orsay, Saclay, SLAC, Stanford, VEPP3 and VEPP4) and reviews (Abbott, Boden, Garcon and Karpius). The change of the sign of form factors is in the pulse regions at 4.7-4.9 fm-1 for GC; at 12.8-14.7 fm-1 for GQ; at 6.3-8.1 and 11.4-12.2 fm-1 for GM. The theoretical values for the form factors GQ(0) and GM(0) were calculated at the boundary condition for the momentum at p2=0. Calculated positions of the zero for deuteron form factors are compared with values for other potential models. The peculiarities of parametrizations of deuteron form factors for theoretical approaches and fits of theoretical calculations to experimental values, which are described in the cited literature, are analyzed. Formulas for spherical and quadrupole form factors are writed, which are expressed in terms of the coefficients for the indicated deuteron wave function. At large values of momentum the asymptotics of the deuteron form factors are determined by the coefficients of the analytical forms for deuteron wave function, nucleon isoscalar form factors and the order of momentum in the denominator. The further use of deuteron form factors for obtaining polarization observables in processes involving deuteron as a projectile is discussed.

Analysis of the Responses of Science Teacher Candidates to Force Concept Inventory by Concentration Factor

This study aims to obtain information about the modelling situations related to the topic by performing concentration analysis of teacher candidates' responses to Force Concept Inventory (FCI). The research was conducted using survey model, which is a quantitative research method. The study was carried out in the fall semester of the academic year 2015–2016 among 95 freshman teacher candidates enrolled in the Science Education Program of the Faculty of Education at a university in the Western Black Sea region. The data collection tool employed was FCI. In this context, concentration score, concentration factor and concentration deviation formulas were used. In light of the results obtained, it was determined that the responses of teacher candidates correspond to the null model, meaning that it is a result of a random reaction. It was suggested that this method of analysis could be used to develop more effective multiple-choice tests and comprehensively assess the learning situation of a class in depth.

Approximate Wiener--Hopf Factorization and Monte Carlo Methods for Lévy Processes

In the present paper, we justify the convergence formulas for approximate Wiener--Hopf factorization to exact formulas for factors from a broad class of Levy processes. Another result obtained here...

Precision photon spectra for wino annihilation

We provide precise predictions for the hard photon spectrum resulting from neutral SU(2)W triplet (wino) dark matter annihilation. Our calculation is performed utilizing an effective field theory expansion around the endpoint region where the photon energy is near the wino mass. This has direct relevance to line searches at indirect detection experiments. We compute the spectrum at next-to-leading logarithmic (NLL) accuracy within the framework established by a factorization formula derived previously by our collaboration. This allows simultaneous resummation of large Sudakov logarithms (arising from a restricted final state) and Sommerfeld effects. Resummation at NLL accuracy shows good convergence of the perturbative series due to the smallness of the electroweak coupling constant — scale variation yields uncertainties on our NLL prediction at the level of 5%. We highlight a number of interesting field theory effects that appear at NLL associated with the presence of electroweak symmetry breaking, which should have more general applicability. We also study the importance of using the full spectrum as compared with a single endpoint bin approximation when computing experimental limits. Our calculation provides a state of the art prediction for the hard photon spectrum that can be easily generalized to other DM candidates, allowing for the robust interpretation of data collected by current and future indirect detection experiments.

Centrality and Energy Dependence of Charged Particles in $p+A$ and $A+A$ Collisions from Running Coupling $k_{\mathrm {T}}$-factorization

We extend the numerical analysis of the energy and centrality dependence of particle multiplicities at midrapidity in high-energy p+A and A+A collisions from a running coupling $k_T$-factorization formula made in~\cite{Dumitru:2018gjm} by considering two unintegrated gluon distributions that were left out. While a good agreement with the experimental data in A+A collisions is achieved, improving the description of those observables in p+A collisions calls for a better understanding of the proton unintegrated gluon distribution at larger values of $x$ and also the use of a realistic impact parameter dependence.

A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions

A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions

A Time-Integral Crack Propagation Model Considering Thickness Effect

The crack propagation mechanism of thick plates is difficult to describe accurately, and thus, it is difficult to predict the lifetimes of thick plate structural cracks in extreme construction environments. In this paper, a theoretical model of the time-integrated crack propagation that accounts for the thickness effect is established. The constraint factor is introduced to characterize the thickness effect of crack propagation, and the constraint factor formula was obtained by fitting the experimental results. The results of the fatigue crack growth tests and the crack propagation theoretical predictions for Q345D specimens showed the time-integrated crack propagation model predicts the crack propagation more accurately in the initial stage and during the stable expansion stage of crack propagation. These results have guiding significance for the fatigue life prediction of equipment with thick plate structural features.

Unraveling high-energy hadron structures with lattice QCD

Parton distribution functions are key quantities for us to understand the hadronic structures in high-energy scattering, but they are difficult to calculate from lattice QCD. Recent years have seen fast development of the large-momentum effective theory which allows extraction of the x-dependence of parton distribution functions from a quasi-parton distribution function that can be directly calculated on lattice. The extraction is based on a factorization formula for the quasi-parton distribution function that has been derived rigorously in perturbation theory. A systematic procedure that includes renormalization, perturbative matching, and power corrections has been established to calculate parton distribution functions. Latest progress from lattice QCD has shown promising signs that it will become an effective tool for calculating parton physics.

Inclusive decays of ηc and ηb at NNLO with large nf resummation

Based on the nonrelativistic QCD factorization theorem, we resum QCD corrections to the inclusive decay rate of $\eta_c$ and $\eta_b$ in the large-$n_f$ limit using bubble chain resummation. By employing dimensional regularization, we show explicitly the cancellation of the infrared renormalon ambiguity in the factorization formula at leading order in $v$ in the large-$n_f$ limit, where $v$ is the typical heavy quark velocity inside the meson. We also make predictions of the ratio of the inclusive decay rate to the decay rate into two photons. By comparing our results with a fixed-order calculation we conclude that resummation of QCD corrections is crucial in making an unambiguous prediction. We also find significant corrections beyond the large-$n_f$ limit for the decay of $\eta_c$, which may imply that QCD corrections need to be resummed beyond the large-$n_f$ limit to make an accurate prediction of the decay rate.

On the structure of the conformal higher-spin wave operators

We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t ≤ s. In the case of the usual Fradkin-Tseytlin fields t = 1 this gives a systematic derivation of the factorization formulas known in the literature while for t > 1 the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.