Related papers: Solving for tadpole coefficients in one-loop ampli…

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…

We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multiloop integrals derived in previous…

We calculate at two-loop order the complex-valued scattering amplitude related to the twice-iterated scalar-isovector boson-exchange between nucleons. In comparison to the once-iterated boson-exchange amplitude it shows less dependence on…

In the Type II superstring the 4-point function for massless NS-NS bosons at one-loop is well known [1][14]. The overall constant factor in this amplitude is very important because it needs to satisfy the unitarity and S-duality conditions…

For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the…

We report on the development of tools to calculate loop integrals and amplitudes beyond one loop. In particular, we review new features of the program SecDec which can be used for the numerical evaluation of parametric integrals like…

We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n+2 particles in five…

We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by…

Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method…

A method for calculating coefficient functions of the operator product expansion, which was previously derived for the non-singlet case, is generalized for the singlet coefficient functions. The resulting formula defines coefficient…

Spectral methods based on integral transforms may be efficiently used to solve differential equations in some special cases. This paper considers a different approach in which algorithms are proposed to calculate integral Laguerre transform…

We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining…

We develop an analytic approximation for the coincidence limit of a massive scalar propagator in an arbitrary spatially flat, homogeneous and isotropic geometry. We employ this to compute the one loop corrections to the inflaton effective…

We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1+1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its…

We present a calculation of the rational terms in two-loop all-plus gluon amplitudes using $D$-dimensional unitarity. We use a conjecture of separability of the two loops, and then a simple generalization of one-loop $D$-dimensional…

The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…

A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…

Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing…

We find a direct map that determines moduli-space integrands for one-loop superstring amplitudes in terms of field-theory loop integrands in the BCJ form. The latter can be computed using efficient unitarity methods, so our map provides an…

This paper presents an evaluation of the wave function coefficients for conformally coupled scalars at both one and two-loop levels at leading order in the coupling constant, in momentum space. We take cues from time-dependent interactions…