External Momenta Research Articles

Direct numerical computation and its application to the higher-order radiative corrections

The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the progress of DCM to several scalar multi-loop integrals after the presentation in ACAT2016. Also the discussion is given on the application of DCM to physical 2-loop processes including numerator functions.

Anomalies in finite amplitudes: Two-dimensional single and triple axial-vector triangles

An explicit and detailed investigation about the two-dimensional (2D) single and triple axial-vector triangles is presented. Such amplitudes are related to the 2D axial-vector two-point function (AV) through contractions with the external momenta. Given this fact, before considering the triangles, we give a clear point of view for the AV anomalous amplitude. Such point of view is constructed within the context of an alternative strategy to handle the divergences typical of the perturbative solutions of quantum field theory. In the referred procedure all amplitudes in all theories, formulated in odd and even space–time dimensions, renormalizable or not, are treated on the same footing. After performing, in a very detailed way, all the calculations, we conclude that the same phenomenon occurring in the AV amplitude is present also in the finite single and triple axial-vector triangles. The conclusion gives support to the thesis that the phenomenon is present in pseudo-amplitudes belonging to a chain where the divergent AV one is only the simplest structure. It is expected that the same must occur in all even space–time dimensions. In particular, in four dimensions, the single and triple axial box amplitudes must exhibit anomalies too.

Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals

Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives in the Baikov or parametric representations lead to identities which involve dimension shifts. These dimension shifts can be avoided by imposing a certain constraint on the total derivatives. The solutions of this constraint turn out to be a specific type of syzygies which correspond to logarithmic vector fields along the Gram determinant formed of the independent external and loop momenta. We present an explicit generating set of solutions in Baikov representation, valid for any number of loops and external momenta, obtained from the Laplace expansion of the Gram determinant. We provide a rigorous mathematical proof that this set of solutions is complete. This proof relates the logarithmic vector fields in question to ideals of submaximal minors of the Gram matrix and makes use of classical resolutions of such ideals.

Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters

Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can be inferred. For an improved theory accuracy, we compute all two-loop corrections involving the strong coupling for the Higgs-boson mass spectrum of the MSSM with complex parameters. Apart from the dependence on the strong coupling, these contributions depend on the weak coupling and Yukawa couplings, leading to terms of mathcal {O}{left( alpha alpha _sright) } and mathcal {O}{left( sqrt{alpha _{q_1}}sqrt{alpha _{q_2}}alpha _sright) }, (q_{1,2}=t,b,c,s,u,d). The full dependence on the external momentum and all relevant mass scales is taken into account. The calculation is performed in the Feynman-diagrammatic approach which is flexible in the choice of the employed renormalization scheme. For the phenomenological results presented here, a renormalization scheme consistent with higher-order corrections included in the code FeynHiggs is adopted. For the evaluation of the results, a total of 513 two-loop two-point integrals with up to five different mass scales are computed fully numerically using the program SecDec. A comparison with existing results in the limit of real parameters and/or vanishing external momentum is carried out, and the impact on the lightest Higgs-boson mass is discussed, including the dependence on complex phases. The new results will be included in the public code FeynHiggs.

Japan

Economic OutlookVolume 42, Issue 3 p. 55-56 Article Japan First published: 31 July 2018 https://doi.org/10.1111/1468-0319.12363AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract GDP grew by a solid 1.7% in 2017, supported by strongly expanding global trade. For this year, we expect growth to ease to 1.2%, dampened by slowing external momentum and weak domestic demand in Q1. Although GDP dropped 0.2% q/q in Q1, we expect this setback to be temporary and look for reasonable, broad-based growth during the rest of 2018. Monthly indicators of consumption and trade look positive and suggest a recovery in Q2. The outlook for investment also remains broadly positive, although sentiment has moderated somewhat since the start of the year. Protectionism, particularly the threat of US tariffs on Japanese cars, remains a key downside risk for our forecast. Volume42, Issue3July 2018Pages 55-56 RelatedInformation

Analytic representations of mK , FK , mη , and Fη in two loop SU(3) chiral perturbation theory

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in $SU(3)$ chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at $p^2=m_P^2$ ($P=\pi, K, \eta$). Recalling that there are three mass scales in this theory, $m_\pi$, $m_K$ and $m_\eta$, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for $m_\pi$ and $F_\pi$, the pion mass and decay constant. We provide fully analytic exact expressions for $m_K$ and $m_\eta$, the kaon and eta masses, and $F_K$ and $F_\eta$, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for $m_K$, $F_K$, $m_\eta$ and $F_\eta$ that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for $m_\pi$ and $F_\pi$ may be obtained, the latter having been used in conjunction with the results for $F_K$ to produce a recently published analytic representation of $F_K/F_\pi$.

Entropy production, thermodynamic fluxes and transport coefficients of an interface between two electromagnetic fluids with spin

The purpose of this wok is to obtain a complete description of the entropy production within the framework of non equilibrium thermodynamics for the case of an isotropic material interface between two one-component immiscible fluids when both of them are magnetizable and polarizable and external and internal angular momentum are included. All physical variables are allowed to be singular along the interface with the exception of the magnetic field and electric field. The set of conservation laws for the interface are derived and the explicit form of the entropy production is obtained. Taking into account spacial and time reversal symmetries, we establish the phenomenological relations between the fluxes and thermodynamic forces. We conclude by providing an example where constraints for the values of the transport coefficients are obtained as a consequence of conditions which must be fulfilled to guarantee that the matrix of transport coefficients remains positive definite.

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

We introduce a more general set of kinematic renormalization schemes than the original momentum (MOM) subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter $\omega$ which tags the external momentum of one of the legs of the $3$-point vertex functions in Quantum Chromodynamics (QCD). In each of the three new schemes we renormalize QCD in the Landau and maximal abelian gauges and establish the three loop renormalization group functions in each gauge. As an application we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

Postcapture stabilization of space robots considering actuator failures with bounded torques

Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper presents a novel control strategy for stabilization of a space robot in postcapture considering actuator failures and bounded torques. In the control strategy, the motion of the manipulator is not regarded as a disturbance to the base; in contrast, it is utilized to compensate for the limitation of the control torques by means of an inverse dynamical model of the system. Different scenarios where actuators are external mechanisms or momentum exchange devices have been carried out, and for actuator failures, both single- and two-actuator failures have been considered. Regarding to the performance of actuators, control torques are bounded. In cases that either single or two actuators have failed, the base can be stabilized kinematically when actuators are external mechanisms, but can only be stabilized dynamically when only momentum exchange devices are used. Finally, a space robot with a seven-degree-of-freedom manipulator in postcapture is studied to verify the validity and feasibility of the proposed control scheme. Simulation results show that the whole system can be stabilized rapidly.

A new approach on anti-vortex devices at water intakes including a submerged water jet

A new approach on anti-vortex methods as hydraulic-based anti-vortex was investigated experimentally in the present study. In the investigated method, a submerged water jet is used as the anti-vortex mechanism. The added jet acts as a source of external momentum. This leads to change the intake-induced hydrodynamic pattern in the near-field of the intake structure, which can prevent formation of undesirable intake vortices. The experiments were carried out on a horizontal pipe intake. By performing 570 test cases in two different categories, including the inclined jet with respect to the axis of the intake, and the inclined jet with respect to the water surface, the effects of the jet inclination angle on the anti-vortex performance were investigated. It was found that the inclined jet with respect to the water surface is the best alternative to consider as the water jet injection pattern. Results showed that using the inclined jet with respect to the water surface can simply reduce the amounts of the expected water jet momentum more than 50% compared to that of the similar condition of the horizontal injection pattern. Moreover, it was concluded that the intake critical submergence can easily be minimized using the inclined jet with respect to the water surface.

Gluons and gravitons at one loop from ambitwistor strings

We present new and explicit formulae for the one-loop integrands of scattering amplitudes in non-supersymmetric gauge theory and gravity, valid for any number of particles. The results exhibit the colour-kinematics duality in gauge theory and the double-copy relation to gravity, in a form that was recently observed in supersymmetric theories. The new formulae are expressed in a particular representation of the loop integrand, with only one quadratic propagator, which arises naturally from the framework of the loop-level scattering equations. The starting point in our work are the expressions based on the scattering equations that were recently derived from ambitwistor string theory. We turn these expressions into explicit formulae depending only on the loop momentum, the external momenta and the external polarisations. These formulae are valid in any number of spacetime dimensions for pure Yang-Mills theory (gluon) and its natural double copy, NS-NS gravity (graviton, dilaton, B-field), and we also present formulae in four spacetime dimensions for pure gravity (graviton). We perform several tests of our results, such as checking gauge invariance and directly matching our four-particle formulae to previously known expressions. While these tests would be elaborate in a Feynman-type representation of the loop integrand, they become straightforward in the representation we use.

Top-forms of leading singularities in nonplanar multi-loop amplitudes

The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we can decompose the on-shell diagrams by removing external BCFW bridges to a planar diagram whose top-form is well known now. The top-form of the on-shell diagram with the auxiliary line can be obtained by adding the BCFW bridges in an inverse order as discussed in our former paper (Chen et al. in Eur Phys J C 77(2):80 2017). To get the top-form of the original diagram, the soft limit of the auxiliary line is needed. We obtain the evolution rule for the Grassmannian integral and the geometry constraint in the soft limit. This completes the top-form description of leading singularities in nonplanar scattering amplitudes of mathcal {N}=4 Super Yang–Mills (SYM), which is valid for arbitrary higher-loops and beyond the Maximally-Helicity-Violation (MHV) amplitudes.

Vortex Dissipation Using a Hydraulic-Based Anti-Vortex Device at Intakes

In the present research, dissipating free surface vortices over the intakes by designing a hydraulic anti-vortex method is studied experimentally. In this method, an up-stream submerged water jet is used as a hydraulic-based anti-vortex mechanism. The imposed jet acts as a point source of external momentum to the formed free surface area. The added momentum changes the hydrodynamic balance of the vortex zone, and leads to instability and disability of the vortex to form and develop. Experiments were conducted on a projected horizontal pipe intake to investigate the efficiency of the proposed anti-vortex hydraulic device on dissipating and preventing formation of free surface vortices. Results show that the efficiency of the imposed jet is dependent on the jet linear momentum and vertical distance between the nozzle and intake positions. Moreover, the critical submergence of the intake can potentially reduce up to the nozzle submergence in which less than 10% of the jet momentum is required by decreasing nozzle submergence about 50%. Finally, an empirical equation is suggested to predict the critical submergence of the intake with respect to the jet linear momentum and the nozzle submergence.

Two Higgs doublet models and brightarrow s exclusive decays

We computed the leading order Wilson coefficients relevant to all the exclusive brightarrow sell ^+ell ^- decays in the framework of the two Higgs doublet model (2HDM) with a softly broken mathbb {Z}_2 symmetry by including the mathcal {O}(m_b) corrections. We elucidate the issue of appropriate matching between the full and the effective theory when dealing with the (pseudo-)scalar operators for which keeping the external momenta different from zero is necessary. We then make a phenomenological analysis by using the measured {mathcal {B}}(B_srightarrow mu ^+mu ^-) and {mathcal {B}}(Brightarrow K mu ^+mu ^-)_{mathrm {high}-q^2}, for which the hadronic uncertainties are well controlled, and we discuss their impact on various types of 2HDM. A brief discussion of the decays with tau -leptons in the final state is provided too.

Collinear factorization violation and effective field theory

The factorization of amplitudes into hard, soft and collinear parts is known to be violated in situations where incoming particles are collinear to outgoing ones. This result was first derived by studying limits where non-collinear particles become collinear. We show that through an effective field theory framework with Glauber operators, these factorization-violating effects can be reproduced from an amplitude that is factorized before the splitting occurs. We confirm results at one-loop, through single Glauber exchange, and at two-loops, through double Glauber exchange. To approach the calculation, we begin by reviewing the importance of Glauber scaling for factorization. We show that for any situation where initial state and final state particles are not collinear, the Glauber contribution is entirely contained in the soft contribution. The contributions coming from Glauber operators are necessarily non-analytic functions of external momentum, with the non-analyticity arising from the rapidity regulator. The non-analyticity is critical so that Glauber operators can both preserve factorization when it holds and produce factorization-violating effects when they are present.

A model of flow separation controlled by dielectric barrier discharge

Flow separation, asan aerodynamic phenomenon, occurs in specific conditions. The conditions are studied in a wind tunnel on different airfoils. The phenomenon can be delayed or suppressed by exerting an external momentum to the flow. Dielectric barrier discharge actuators arranged in a row of 8 and perpendicular to the flow direction can delay flow separation by exerting the momentum. In this study, a mathematical model is developed to predict a parameter, which is utilized to represent flow separation on an NACA0012 airfoil. The model is based on the neuro-fuzzy method applied to experimental datasets. The neuro model is trained in different flow conditions and the parameter is measured by pressure sensors.

Comparison between hydraulic and structural based anti-vortex methods at intakes

Surface vortices are the main reason of flow instability and entraining air and debris into the intakes. Using structural based anti-vortex facilities is a common method for dissipating vortices over the intakes. In the present experimental study, performance of a new hydraulic based anti-vortex method is compared with available structural based anti-vortex methods over the horizontal intakes. In the new approach dynamically high-risk surface vortices are eliminated by imposing a hydraulic jet at the formed vortex zone over the intake. The injected jet acts as a point source of external momentum in order to change the hydrodynamic condition of the formed vortex flow. Results show that the investigated hydraulic based anti-vortex device is more flexible and more hydraulically efficient than the structural based anti-vortex methods, especially when the intake Froude number is higher than 1.3.

Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation

A number of irreducible master integrals for L-loop sunrise and bubble Feynman diagrams with generic values of masses and external momenta are explicitly evaluated via the Mellin-Barnes representation.

An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory

A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of F_{pi } and M_{pi }^2 in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low-energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.

Investigation of intrinsic toroidal rotation scaling in KSTAR

The behaviors of an intrinsic toroidal rotation without any external momentum sources are investigated in KSTAR. In these experiments, pure ohmic discharges with a wide range of plasma parameters are carefully selected and analyzed to speculate an unrevealed origin of toroidal rotation excluding any unnecessary heating sources, magnetic perturbations, and strong magneto-hydrodynamic activities. The measured core toroidal rotation in KSTAR is mostly in the counter-current direction and its magnitude strongly depends on the ion temperature divided by plasma current (Ti/IP). Especially the core toroidal rotation in the steady-state is well fitted by Ti/IP scaling with a slope of ∼−23, and the possible explanation of the scaling is compared with various candidates. As a result, the calculated offset rotation could not explain the measured core toroidal rotation since KSTAR has an extremely low intrinsic error field. For the stability conditions for ion and electron turbulences, it is hard to determine a dominant turbulence mode in this study. In addition, the intrinsic toroidal rotation level in ITER is estimated based on the KSTAR scaling since the intrinsic rotation plays an important role in stabilizing resistive wall modes for future reference.