Double Pole Research Articles

Higher-order relativistic corrections to gluon fragmentation into spin-triplet S-wave quarkonium

We compute the relative-order-v^4 contribution to gluon fragmentation into quarkonium in the 3S1 color-singlet channel, using the nonrelativistic QCD (NRQCD) factorization approach. The QCD fragmentation process contains infrared divergences that produce single and double poles in epsilon in 4-2epsilon dimensions. We devise subtractions that isolate the pole contributions, which ultimately are absorbed into long-distance NRQCD matrix elements in the NRQCD matching procedure. The matching procedure involves two-loop renormalizations of the NRQCD operators. The subtractions are integrated over the phase space analytically in 4-2epsilon dimensions, and the remainder is integrated over the phase-space numerically. We find that the order-v^4 contribution is enhanced relative to the order-v^0 contribution. However, the order-v^4 contribution is not important numerically at the current level of precision of quarkonium-hadroproduction phenomenology. We also estimate the contribution to hadroproduction from gluon fragmentation into quarkonium in the 3PJ color-octet channel and find that it is significant in comparison to the complete next-to-leading-order-in-alpha_s contribution in that channel.

Generalized universality of higher transverse moments of quark transverse momentum dependent correlators

The color gauge-invariant transverse momentum dependent (TMD) quark correlators contain process dependent gauge links in the bilocal matrix elements. In this paper, we split these process dependent correlators into universal TMD correlators, which in turn can be parametrized in universal TMD distribution functions. The process dependence is contained in gluonic pole factors, of which the value is determined by the gauge link. The operator structures of the universal TMD correlators are identified using transverse moments. In this paper, specific results for double transverse weighting of quark TMDs are given. In particular, we show that for a spin 1/2 target one has three universal time-reversal even leading `pretzelocity distributions', two of which involve double gluonic pole matrix elements and come with process dependent gluonic pole factors. We generalize the results for single and double weighting to TMD correlators of any specific rank, illustrating it for unpolarized, spin 1/2 and spin 1 targets.

Interactions of breathers and solitons of a generalized variable-coefficient Korteweg-de Vries-modified Korteweg-de Vries equation with symbolic computation

Under investigation in this paper is a generalized variable-coefficient Korteweg-de Vries-modified Korteweg-de Vries equation which describes certain atmospheric blocking phenomenon. Lax pair and infinitely many conservation laws are obtained. With the help of the Hirota method and symbolic computation, the one-, two- and three-soliton solutions are given. Besides, breather and double pole solutions are derived. Propagation characteristics and interactions of breathers and solitons are discussed analytically and graphically. Results also show that the soliton changes its type between depression and elevation periodically. Parabolic-like breather and double pole are depicted. Conditions of the depression and elevation solitons are also given.

Collinear and soft limits of multi-loop integrands in $ \mathcal{N} = 4 $ Yang-Mills

It has been argued in arXiv:1112.6432 that the planar four-point integrand in N=4 super Yang-Mills theory is uniquely determined by dual conformal invariance together with the absence of a double pole in the integrand of the logarithm in the limit as a loop integration variable becomes collinear with an external momentum. In this paper we reformulate this condition in a simple way in terms of the amplitude itself, rather than its logarithm, and verify that it holds for two- and three-loop MHV integrands for n>4. We investigate the extent to which this collinear constraint and a constraint on the soft behavior of integrands can be used to determine integrands. We find an interesting complementarity whereby the soft constraint becomes stronger while the collinear constraint becomes weaker at larger n. For certain reasonable choices of basis at two and three loops the two constraints in unison appear strong enough to determine MHV integrands uniquely for all n.

FOCUSING mKdV BREATHER SOLUTIONS WITH NONVANISHING BOUNDARY CONDITION BY THE INVERSE SCATTERING METHOD

Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain an explicit breather solution with nonzero vacuum parameter b of the focusing modified Korteweg–de Vries (mKdV) equation. Moreover, taking the limiting case of zero frequency, we obtain a generalization of the double pole solution introduced by M. Wadati et al.

Coupling vector and pseudoscalar mesons to study baryon resonances

A study of meson-baryon systems with total strangeness -1 is made within a framework based on the chiral and hidden local symmetries. These systems consist of octet baryons, pseudoscalar and vector mesons. The pseudoscalar meson-baryon (PB) dynamics has been earlier found determinant for the existence of some strangeness -1 resonances, for example, $\Lambda(1405)$, $\Lambda(1670)$, etc. The motivation of the present work is to study the effect of coupling the closed vector meson-baryon (VB) channels to these resonances. To do this, we obtain the $PB \rightarrow PB$ and $VB \rightarrow VB$ amplitudes from the t-channel diagrams and the $PB \leftrightarrow VB$ amplitudes are calculated using the Kroll-Ruddermann term where, considering the vector meson dominance phenomena, the photon is replaced by a vector meson. The calculations done within this formalism reveal a very strong coupling of the VB channels to the $\Lambda(1405)$ and $\Lambda(1670)$. In the isospin 1 case, we find an evidence for a double pole structure of the $\Sigma (1480)$ which, like the isospin 0 resonances, is also found to couple strongly to the VB channels. The strong coupling of these low-lying resonances to the VB channels can have important implications on certain reactions producing them.

Exceptional points and non-Hermitian degeneracy of resonances in a two-channel model

We study the mixing and degeneracy of two unbound energy eigenstates (resonances) in a two coupled channel model of scattering and reactions. We derive the necessary and sufficient conditions for existence of an exceptional point in the extended spectrum of bound and resonance energy eigenvalues in this model and show that these are not the same as in the single channel case. When these conditions are satisfied, in the complex energy plane, the two simple resonance poles of the scattering matrix merge into one double pole at the exceptional point. In parameter space, the surface of the eigenenergies has a branch point of square root type and branch cuts in its real and imaginary parts that start at the exceptional point and extend in opposite directions. The rich phenomenology of crossings and anticrossings of energies and widths of the doublet of unbound states, as well as the changes of identity of the poles of the scattering matrix observed when one control parameter is varied while the other is kept constant, is fully explained in terms of sections of the eigenenergy surfaces.

국가대표 크로스컨트리 스키 선수들의 Double Poling 기술의 운동학적 분석

【This study aimed to examine the kinematic characteristics of the national elite cross-country skiers' double poling technique and to provide the quantitative data for better performance. Four male elite cross-country roller skiers skied maximum velocity with Double Pole technique. The cycle characteristics with angles of elbow, hip, and knee joint were analyzed. The results showed that CM velocity of the body was increased with the third cycle, the cycle time and length were also increased. The poling time and recovery time rate showed with 32.79%, 67.44% respectively. The joint angles with elbow, hip and knee were $106^{\circ}$ , $133.14^{\circ}$ $156.87^{\circ}$ at pole in event, $158.94^{\circ}$ , $65.7^{\circ}$ , $140.19^{\circ}$ at pole out event. Elite skiers should decrease double poling time rate and increase recovery time rate in order to improve the double poling performance. The cycle length and velocity of the double poling should be increased for the better performance. The elbow angle should be minimized at pole in event with maximum extension until pole out event. The hip and knee angles should be increased for the recovery phase.】

Radiometric Timing of High-Voltage Circuit-Breaker Opening Operations

This paper demonstrates the feasibility of radiometric on-line circuit breaker timing. The timing test is crucial and can reveal a wide range of faults or defects. The work presented concentrates on the timing of gas-insulated substation (GIS) circuit breakers, which due to their enclosed nature pose a variety of challenges not encountered in air insulated substations (AIS). It is demonstrated how key events in the arcing process such as arc ignition and extinctions can be identified from the emitted electromagnetic pulses and how this information can be used to assess the integrity of the circuit breaker being monitored. The results are backed by site measurements of a high voltage reactor switching SF6 double pole puffer breaker. The proposed technique can readily be extended to monitor closing operations as well as being adapted to monitor other types of circuit breakers.

Reinforcement learning using a swarm intelligence based neural network

This paper proposes a new reinforcement learning method using the SWarm Intelligence-trained Neural Network (SWINN) to efficiently generate solutions to various real-world problems. The swarm intelligence algorithm Particle Swarm Optimization (PSO) is combined with a Training Resource Allocator (TRA) in SWINN for specific problems. TRA, as a heuristic global search method, controls the allocation of training resources to different candidate topologies of artificial neural networks (ANNs) to expedite the system convergence, while PSO is applied as a local search algorithm to adjust the ANN’s connection weights. To evaluate the performance of the SWINN algorithm, two reinforcement learning case studies: the double pole balance (a.k.a. double inverted pendulum) problem and a mobile robot localization problem are conducted. Simulation results successfully demonstrate that SWINN offers performance that is competitive with modern neuroevolutionary techniques, and is viable for real-world problems.

Scalar-flat Kähler metrics with conformal Bianchi V symmetry**Dedicated to Maciej Przanowski on the occasion of his 65th birthday.

We provide an affirmative answer to a question posed by Tod (1995, Twistor Theory (New York: Dekker)), and construct all four-dimensional Kähler metrics with vanishing scalar curvature which are invariant under the conformal action of the Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterize the associated solutions of the SU(∞) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.

Automation of the stabilization diagrams for subspace based system identification

For the continuous real-time monitoring of structures, the realization of a fully automatic real time system identification without any human intervention is the most crucial step. In this study, a new technique for the automation of the stability diagrams is developed that uses the modal phase collinearity (MPC) in order to quantify the spatial consistency of the identification results. In the new technique, the stabilization diagram is modeled as a histogram composed of overlapping bins. New strategies for the multiple occurrence of poles in the neighboring bins and double poles within a bin are developed. A new cluster validity index is proposed which can solve the problem caused by the scale of measurements and which can be directly calculated from non-normalized data. The threshold limits are defined for the proposed index. The results of the study show that the automation of the pole selection process from the stabilization diagrams is successfully realized. It is also shown that for local modes, the MPC value will be substantially smaller as compared to the global modes and can be used as a quick, efficient and powerful measure of global versus local response behavior.

Exceptional Point of the Neutral Heavy Higgs System H 2–H 3

We study the singularity of the surface that represents the masses of the isolated doublet of heavy, neutral Higgs bosons, H2–H3, in a toy model based on the MSSM with CP violation, in parameter space. These two heavy, neutral Higgs bosons are coherent and, for large values of the masses, nearly degenerate. In this scenario, mixing between the mass eigenstates of the H2–H3 system could be very large and exact degeneracy is possible. As function of the Lagrangian parameters, the physical mass of the doublet has an algebraic branch point of rank one at the exceptional point where the two masses are equal. The real and imaginary parts of the masses in the doublet have branch cuts that start at the same branch point but extend in opposite directions in parameter space. Associated with this branch point, the propagator of the mixing doublet of neutral heavy Higgs bosons has a double pole in the complex s-plane of the energy squared. We computed the mass surface of the isolated doublet of H2–H3 bosons as function of the Lagrangian parameters in the neighbourhood of the exceptional point in a toy model of the system H2–H3. We also computed the trajectories of the poles of the transition matrix for values of the Lagrangian parameters close to the exceptional point and explained the characteristic change of identity seen in these trajectories in the s-plane as a manifestation of the topology of the two-sheeted mass surfaces in the space of Lagrangian parameters.

Coalescence of metastable states in chemical reactions: double poles of the scattering matrix and exceptional points

Accidental degeneracy of two scattering resonances in chemical reactions is discussed. A novel analytical parameterization for the scattering matrix elements valid in the presence of two interacting resonances is derived and applied to investigate the coalescence of metastable states leading to double poles in the partial-wave amplitude. We show how double poles can manifest themselves in reaction cross-sections and discuss their relationship with exceptional points. The presence of two degenerate resonances interacting with each other can create a peculiar double-peak structure in the reaction probability. At the energy where the two decaying states coalesce the scattering matrix has a double pole and correspondingly the reaction probability reaches its minimum value. This novel formula has been tested with the well-established data obtained for the F + H2 reaction, for which previous studies have revealed the existence of two interfering resonance pathways. The good agreement of model predictions and quantum scattering calculations shows that the present approach is reliable. Hence, we claim that it provides a way for the observation of interacting resonances in molecular collisions. Resonance positions and partial widths can be obtained by fitting the numerically calculated state-to-state reaction probabilities to the square modulus of the novel expression for the scattering matrix elements derived in the paper.

Anomalous dimensions at four loops in [formula omitted] superconformal Chern–Simons theories

In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N = 6 superconformal Chern–Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU ( 4 ) , the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the logarithm of the renormalization constant.

Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

The derivative nonlinear Schrödinger (DNLS) equation, which governs the propagation of the femtosecond optical pulse in a monomodal optical fiber, is analytically studied in this Letter. Breather and double-pole solutions are derived from the two-soliton solution with the choice of parameters. It is found that the parameters in the DNLS equation cannot only control the phase and propagation direction of the breather and double pole, but also influence the interaction period of the breather. Elastic collisions between a breather and a dark/anti-dark soliton are studied by the qualitative analysis and graphical illustration. The stability of the breather and double-pole solutions is also analyzed.

Multivariate hypergeometric cascades, isomonodromy problems and Ward ansätze

The Ward ansätze in twistor theory generate solutions of the anti-self-dual Yang–Mills equations from solutions of the wave equation in spacetime. The theory has a straightforward generalization in which the ‘spacetime’ is an open set in the Grassmannian Gr(2, N). The linear ‘wave equation’ in this case has special solutions, called the generalized confluent hypergeometric functions, which are equivariant under the natural action of Jordan groups on spacetime. Using the generalized Penrose–Ward transform, Ward ansätze of increasing weight arising from such hypergeometric functions give a cascade of solutions to isomonodromy problems for systems of ordinary differential equations, generally with irregular singularities. The extended construction is explored in detail, and two examples are given. In the first, solutions of the Schlesinger equations are constructed from the Lauricella FD functions; in the second, solutions of the isomonodromy problem for systems with two double poles and any number of simple poles are obtained from the generalized Bessel functions.

Reinforcement learning using swarm intelligence-trained neural networks

This article proposes a new reinforcement learning method using the swarm intelligence-trained neural network (SWINN) to generate solutions to various real-world problems efficiently. The swarm intelligence algorithm, particle swarm optimisation (PSO), is combined with a training resource allocator (TRA) in SWINN for specific problems. TRA, as a heuristic global search method, controls the allocation of training resources to different candidate topologies of artificial neural networks (ANNs) to expedite the system convergence, while PSO is applied as a local search algorithm to adjust the ANNs connection weights. To evaluate the performance of the SWINN algorithm, two reinforcement learning case studies: the double pole balance (a.k.a. double inverted pendulum) problem and a mobile robot localisation problem are conducted. Extensive simulation results successfully demonstrate that SWINN offers performance that is competitive with modern neuroevolutionary techniques, and is viable for real-world problems.

Augmented Recursion For One-loop Amplitudes

We present a semi-recursive method for calculating the rational parts of one-loop amplitudes when recursion produces double poles. We illustrate this with the graviton scattering amplitude M^{1-loop}(1-, 2+, 3+, 4+, 5+).

Monodromy Jordan blocks, b-functions and poles of zeta functions for germs of plane curves

We study the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a germ of a holomorphic function in two variables. It was known that there is at most one double pole for (any of) these zeta functions which is then given by the log canonical threshold of the function at the singular point. If the germ is reduced Loeser showed that such a double pole always induces a monodromy eigenvalue with a Jordan block of size 2. Here we settle the non-reduced situation, describing precisely in which case such a Jordan block of maximal size 2 occurs. We also provide detailed information about the Bernstein–Sato polynomial in the relevant non-reduced situation, confirming a conjecture of Igusa, Denef and Loeser.