We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of 𝒩=4 SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025) 107], which includes a regularization preserving dual conformal invariance (DCI). As a new ingredient, we introduce a simple method, allowing to factor out the dependence on the DCI cross ratios from the contribution of each region. The remaining integrals are then essentially simplified by taking successive limits of vanishing external invariants. For 3 out of 82 regions contributing to the most complicated integral ℐ_5^(3) we were not able to perform the integration even after these simplifications. For these three regions, we perform the integration-by-parts (IBP) reduction in parametric representation and evaluate the resulting locally finite integrals using HyperInt.

We compute the potential-graviton contributions to the conservative scattering angle of two non-spinning bodies in maximal supergravity at fifth order in Newton's constant, including second-order self-force effects. Our goal is to tackle the challenging integrals arising at this order in Einstein gravity, but within the technically simpler framework of supergravity. The calculation employs the scattering-amplitude framework, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. The final result is expressed as a series expansion around the static limit, thereby avoiding the explicit evaluation of intricate special functions. This series solution for the master integrals applies, as well, to the corresponding computation in general relativity. Remarkably, we observe nontrivial cancellations among contributions associated with Calabi-Yau integrals, alongside a distinct contribution governed by a Heun differential equation.

We present a three-loop analysis of the scattering amplitude of five nearly massless W-bosons in planar maximally supersymmetric Yang-Mills theory. The basis of the master integrals is established, making use of the unitarity-cut sewing technique in six-dimensional N=(1,1) super-Yang-Mills theory. Its dimensional reduction down to four allows us to generate masses for internal and external states. We descend on the special Coulomb branch of maximally supersymmetric Yang-Mills theory by setting all propagator masses to zero. Employing explicit expressions for all integrals that we calculated in a companion paper, we find a concise representation for this infrared-sensitive observable. We confirm its exponentiation, both for infrared and finite terms. The infrared double logarithm manifests the anticipated universality through the octagon anomalous dimension as its governing coefficient. Unlike our previous two-loop result, this consideration reveals that each of the three independent kinematic structures furnishing the amplitude possesses its own function of 't Hooft coupling.

We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase-space integrals without reversed unitarity. We present an Euler integral representation similar to the Lee-Pomeransky representation and explicitly describe a recursive IBP reduction and dimensional shift relations for the general case of n denominators. On the level of master integrals, applying a differential equation approach, we explicitly calculate the previously unknown angular integrals with four denominators for any number of masses to finite order in ε. Extending the idea of dimensional recurrence, we explore the decomposition of angular integrals into branch integrals reducing the number of scales in the master integrals from (n + 1)n/2 to n + 1. To showcase the potential of this method, we calculate the massless three denominator integral and establish all-order results in ε, including a resummation of soft logarithms.

We study the small-mass asymptotic behavior of so-called angular integrals, appearing in phase-space calculations in perturbative quantum field theory. For this purpose we utilize the strategy of expansion by regions, which is a universal method both for multiloop Feynman integrals and various parametric integrals. To apply the technique to angular integrals, we convert them into suitable parametric integral representations, which are accessible to existing automation tools. We use the code asy.m to reveal regions contributing to the asymptotic expansion of angular integrals. To evaluate the contributions of these regions in an epsilon expansion we apply the method of Mellin-Barnes representation. Our approach is checked against existing results on angular integrals revealing a connection between contributing regions and angular integrals constructed from an algebraic decomposition. We explicitly calculate the previously unknown asymptotics for angular integrals with three and four denominators and formulate a conjecture for the leading asymptotics and the pole part for a general number of denominators and masses.

Abstract We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N $$ \mathcal{N} $$ = 8 supergravity at the fifth post-Minkowskian order and to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present the solution to the differential equations for all master integrals necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in N $$ \mathcal{N} $$ = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in N $$ \mathcal{N} $$ = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

This study examines the influence of the mechanical processing of a titanium nitride based powder mixture on the change in the morphology of the CO2 laser treated surface, the weld pool morphology, and its cross-sectional structure. Ultrafine titanium nitride particles used as nanomodifier, which have low wettability in the metal melt and are not entrained by its convective flows, accumulate in the subsurface and reduce the structural modification efficiency in the bulk of the treated material. Processing of the modifying Ti + TiN mixture for 9 min leads to the formation of composite particles (5-7 pm) in which ultrafine titanium nitride particles are uniformly distributed over the surface and volume. The composite particles melt during laser irradiation and form ultrafine titanium nitride particles of nanomodifier cladded with a thin titanium layer, which have a smaller contact angle. As a result, the particles are more evenly distributed over the weld pool and the number of crystallization centers increases, leading to the formation of a fine homogeneous structure of the material. The microhardness increases by 32%, and its standard deviation decreases by a factor of 1.5 3.0.

We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N= 8 supergravity at the fifth post-Minkowskian order and to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present the solution to the differential equations for all master integrals necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in N = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in N = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

The reasons for the occurrence of exothermic processes of oxidation of nitric acid solutions with reducing agents are analyzed. The main condition is heating the mixtures to temperatures (Tst), above which the release of heat as a result of a chemical reaction begins to exceed its removal from the system. An analysis of the characteristics of exothermic processes obtained experimentally for solutions with reducing agents has been carried out. The effect of irradiation of solutions on the Tst value is small, while other parameters of exothermic processes decrease - heat release, the self-heating value, and the volume of released gases. Necessary and sufficient parameters have been identified to assess the explosion hazard of heating operations of these solutions. Conditions have been established to ensure safety during the evaporation of nitric acid solutions with reducing agents.

We study the form factor of the lowest component of the stress-tensor multiplet away from the origin of the moduli space in the spontaneously broken, aka Coulomb, phase of the maximally supersymmetric Yang-Mills theory for decay into three massive W-bosons. The calculations are done at two-loop order by deriving and solving canonical differential equations in the asymptotical limit of nearly vanishing W-masses. We confirm our previous findings that infrared physics of `off-shell observables' is governed by the octagon anomalous dimension rather than the cusp. In addition, the form factor in question possesses a nontrivial remainder function, which was found to be identical to the massless case, upon a proper subtraction of infrared logarithms (and finite terms). However, the iterative structure of the object is more intricate and is not simply related to the previous orders in coupling as opposed to amplitudes/form factors at the origin of the moduli space.

It is shown how the well-known large mass expansion can be simplified to obtain more terms of the expansion in an analytic form. Expanding two-loop four-point Feynman integrals which contribute to the process $H \to ggg$ is used as an example.

We compute the potential-photon contributions to the classical relativistic scattering angle of two charged non-spinning bodies in electrodynamics through fifth order in the coupling. We use the scattering amplitudes framework, effective field theory, and multi-loop integration techniques based on integration by parts and differential equations. At fifth order, the result is expressed in terms of cyclotomic polylogarithms. Our calculation demonstrates the feasibility of the corresponding calculations in general relativity, including the evaluation of the encountered four-loop integrals.

Feynman integral reduction by means of integration-by-parts identities is a major power gadget in a theorist toolbox indispensable for calculation of multiloop quantum effects relevant for particle phenomenology and formal theory alike. An algorithmic approach consists of solving a large sparse non-square system of homogeneous linear equations with polynomial coefficients. While an analytical way of doing this is legitimate and was pursued for decades, it undoubtedly has its limitations when applied in complicated circumstances. Thus, a complementary framework based on modular arithmetic becomes critical on the way to conquer the current `what is possible' frontier. This calls for use of supercomputers to address the reduction problem. In order to properly utilize these computational resources, one has to efficiently optimize the technique for this purpose. Presently, we discuss and implement various methods which allow us to significantly improve performance of Feynman integral reduction within the FIRE environment.

Показано, как можно упростить хорошо известное разложение фейнмановских интегралов при большой массе, чтобы получить больше членов разложения в аналитической форме. В качестве примера используется разложение двухпетлевых четырехточечных интегралов Фейнмана, которые дают вклад в процесс $H \to ggg$.

Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle virtualities. The latter serve as regulators of infrared divergences, thus making these observables finite in four space-time dimensions. In this paper, we use the method of canonical differential equations for calculation of (non)planar double box integrals in the near mass-shell kinematical regime, i.e., where virtualities of external particles are much smaller than the Mandelstam variables involved. We deduce a basis of master integrals with uniform transcendental weight based on the analysis of leading singularities by means of the Baikov representation as well as an array of complementary techniques. We dub the former asymptotically canonical since it is valid in the near mass-shell limit of interest. We iteratively solve resulting differential equations up to weight four in terms of multiple polylogarithms.

We calculate the total Born cross section of the $e^+e^-$-pair production by an electron in the field of a nucleus (trident process) using the modern multiloop methods. For general energies we obtain the cross section in terms of converging power series. The threshold asymptotics and the high-energy asymptotics are obtained analytically. In particular, we obtain additional contribution to the Racah formula due to the identity of the final electrons. Besides, our result for the leading term of the high-energy asymptotics reveals a typo in an old Racah paper [Racah1937].

FIRE is a program which performs integration-by-parts (IBP) reduction of Feynman integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat by Robert Lewis to simplify rational functions. We present an upgrade of FIRE which incorporates a new library FUEL initially described in a separate publication, which enables a flexible choice of third-party computer algebra systems as simplifiers, as well as efficient communications with some of the simplifiers as C++ libraries rather than through Unix pipes. We achieve significant speedups for IBP reduction of Feynman integrals involving many kinematic variables, when using an open source backend based on FLINT newly added in this work, or the Symbolica backend developed by Ben Ruijl as a potential successor of FORM.

We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N = 8 supergravity at the fifth post-Minkowskian order to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present all master integrals and solve their associated differential equations necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in N = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in N = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

A successful LINAC operation at Synchrotron Radiation Facility−Siberian Circular Photon Source (SRF SKIF) is directly related to the improvement of diagnostic methods for measuring the transverse profile and longitudinal distribution of the beam charge, which, in turn, requires the use of new materials or methods for their production. The thermal outgassing has been measured from aerogel and electrophoretically deposited P43 phosphor used in the LINAC diagnostic system of SRF SKIF.

We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic. These IBPs are indispensable in modern approaches to evaluation of multiloop Feynman integrals by means of differential equations. Modular arithmetic is far more superior to algebraic implementations when one deals with high-multiplicity situations involving a large number of Lorentz invariants. We introduce a new method based on balanced relations which allows one to achieve the goal of a robust functional restoration with minimal data input. The technique is implemented as a Mathematica package Reconstruction.m in the FIRE6 environment and thus successfully demonstrates a proof of concept.