The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear combination of so-c
alled master integrals. To do this, public (AIR, FIRE, REDUZE, LiteRed, KIRA) and private codes based on solving integration by parts relations are used. However, the choice of the master integrals provided by these codes is not always optimal. We present an algorithm to improve a given basis of the master integrals, as well as its computer implementation; see also a competitive variant [1].
Multi-principal-element alloys, including high-entropy alloys, experience segregation or partially-ordering as they are cooled to lower temperatures. For Ti$_{0.25}$CrFeNiAl$_{x}$, experiments suggest a partially-ordered B2 phase, whereas CALculation
of PHAse Diagrams (CALPHAD) predicts a region of L2$_{1}$+B2 coexistence. We employ first-principles density-functional theory (DFT) based electronic-structure approach to assess stability of phases of alloys with arbitrary compositions and Bravais lattices (A1/A2/A3). In addition, DFT-based linear-response theory has been utilized to predict Warren-Cowley short-range order (SRO) in these alloys, which reveals potentially competing long-range ordered phases. The resulting SRO is uniquely analyzed using concentration-waves analysis for occupation probabilities in partially-ordered states, which is then be assessed for phase stability by direct DFT calculations. Our results are in good agreement with experiments and CALPHAD in Al-poor regions ($x le 0.75$) and with CALPHAD in Al-rich region ($0.75 le {x} le 1$), and they suggest more careful experiments in Al-rich region are needed. Our DFT-based electronic-structure and SRO predictions supported by concentration-wave analysis are shown to be a powerful method for fast assessment of competing phases and their stability in multi-principal-element alloys.
FIRE is a program performing reduction of Feynman integrals to master integrals. The C++ version of FIRE was presented in 2014. There have been multiple changes and upgrades since then including the possibility to use multiple computers for one reduc
tion task and to perform reduction with modular arithmetic. The goal of this paper is to present the current version of FIRE.
The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the interface a
t constant speed subject to time-independent loading. By means of the Laplace and Fourier transforms the problem is formulated as a vector Riemann-Hilbert problem. When the distance from the crack to the boundary grows to infinity the problem admits a closed-form solution. In the general case, a method of partial matrix factorization is proposed. In addition to factorizing some scalar functions it requires solving a certain system of integral equations whose numerical solution is computed by the collocation method. The stress intensity factors and the associated weight functions are derived. Numerical results for the weight functions are reported and the boundary effects are discussed. The weight functions are employed to describe propagation of a semi-infinite crack beneath the half-plane boundary at piecewise constant speed.
New features of the Mathematica code FIRE are presented. In particular, it can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by parts reduction to master integrals for quite complicated familie
s of Feynman integrals. As as an example, we consider four-loop massless propagator integrals for which LiteRed provides reduction rules and FIRE assists to apply these rules. So, as a by-product one obtains a four-loop variant of the well-known three-loop computer code MINCER. We also describe various ways to find additional relations between master integrals for several families of Feynman integrals.
Magnetic design proposed for a damping ring (DR) is based on second generation HTS cabling technology applied to the DC windings with a yoke and mu-metal-shimmed pole to achieve ~2T high-quality field within a 86 mm gap and 32-40 cm period. Low level
s of current densities (~90-100A/mm2) provide a robust, reliable operation of the wiggler at higher heat loads, up to LN2 temperatures with long leads, enhanced flexibility for the cryostats and infrastructure in harsh radiation environment, and reduced failure rate compared to the baseline SC ILC DR wiggler design at very competitive cost.
We evaluate a Laurent expansion in dimensional regularization parameter $epsilon=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using a recently developed method of one of the present co
authors (R.L.) and extending thereby results by Baikov and Chetyrkin obtained at transcendentality weight seven. We observe only multiple zeta values in our results. Therefore, we conclude that all the four-loop massless propagator integrals, with any integer powers of numerators and propagators, have only multiple zeta values in their epsilon expansions up to transcendentality weight twelve.
We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present
coauthors (R.L.). We observe only multiple zeta values in our results.
We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically imp
roved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane $omega cd x=0$ defined by a light-like four-vector $omega$. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.
Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, th
e constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.
