Related papers: Summing One-Loop Graphs at Multi-Particle Threshol…
In this letter we present a recursive method for computing one-loop off-shell amplitudes in colored quantum field theories. First, we generalize the perturbiner method by recasting the multiparticle currents as generators of off-shell tree…
We identify a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities. One-loop amplitudes for massless supersymmetric gauge theories fall into this…
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, for various models of random (multi)graphs. For our proofs we introduce the notion of \emph{patchworks} to describe the possible…
We consider the tree amplitudes of production of $n_2$ scalar particles by $n_1$ particles of another kind, where both initial and final particles are at rest and on mass shell, in a model of two scalar fields with $O(2)$ symmetric…
We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized $D$-dimensional unitarity. It allows automated computations of both cut-constructible {\it and} rational parts of one-loop scattering…
Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in…
Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded…
We investigate flows on graphs whose links have random capacities. For binary trees we derive the probability distribution for the maximal flow from the root to a leaf, and show that for infinite trees it vanishes beyond a certain threshold…
At very high energies scattering amplitudes in a spontaneously broken gauge theory into multi-particle final states are known to grow factorially with the number of particles produced. Using simple scalar field theory models with and…
We provide a new set of on-shell recursion relations for tree-level scattering amplitudes, which are valid for any non-trivial theory of massless particles. In particular, we reconstruct the scattering amplitudes from (a subset of) their…
We compute the probability of producing $n$ particles from few colliding particles in the unbroken $(3+1)$-dimensional $\lambda\phi^4$ theory. To this end we numerically implement semiclassical method of singular solutions which works at…
This is part of a series of papers describing the new curve integral formalism for scattering amplitudes of the colored scalar tr$\phi^3$ theory. We show that the curve integral manifests a very surprising fact about these amplitudes: the…
We show that one-loop amplitudes in massless gauge theories can be determined from single cuts. By cutting a single propagator and putting it on-shell, the integrand of an n-point one-loop integral is transformed into an (n+2)-particle tree…
We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help…
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…
Starting from tree and one-loop tachyon amplitudes of open string theory in the presence of a constant B-field, we explore two problems. First we show that in the noncommutative field theory limit the amplitudes reduce to tree and one-loop…
We study the problem of computing the tightest upper and lower bounds on the probability that the sum of $n$ dependent Bernoulli random variables exceeds an integer $k$. Under knowledge of all pairs of bivariate distributions denoted by a…
I derive the set of recurrence relations between the amplitudes of multiparticle production at threshold in the standard large-N limit of the O(N)-symmetric phi^4$ theory which sums all relevant diagrams with arbitrary number of loops. I…
We study multiparticle production in the unbroken $(3+1)$-dimensional $\lambda\phi^4$ theory using the semiclassical method of singular solutions. We show that the probabilities of these processes are exponentially suppressed in terms of a…
We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules,…