arXiv subjects
Publications and source records attributed to Petros Draggiotis.
We discuss briefly the first numerical implementation of the Loop-Tree Duality (LTD) method. We apply the LTD method in order to calculate ultraviolet and infrared finite multi-leg one-loop Feynman integrals. We attack scalar and tensor integrals with up to six legs (hexagons). The LTD method shows an excellent performance independently of the number of external legs.
We present a first numerical implementation of the Loop-Tree Duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then, we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and present explicit results for scalar integrals with up to five external legs (pentagons) and tensor integrals with up to six legs (hexagons). The LTD method features an excellent performance independently of the number of external legs.
We review the recent progress on the numerical implementation of the Loop-Tree Duality Method (LTDM) for the calculation of scattering amplitudes. A central point is the analysis of the singularities of the integrand. In the framework of the LTDM some of these singularities cancel out. The ones left over are dealt with by contour deformation. We present details on how to achieve this as well as first results.
We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
We review the recent developments of the loop-tree duality method, focussing our discussion on analysing the singular behaviour of the loop integrand of the dual representation of one-loop integrals and scattering amplitudes. We show that within the loop-tree duality method there is a partial cancellation of singularities at the integrand level among the different components of the corresponding dual representation. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.
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 publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.
We present a systematic method to evaluate the splitting functions for tree-level QCD processes where m partons approach the collinear limit. The splitting functions are computed by deriving on-shell recursion equations, which are similar to the Berends-Giele recursion relations for off-shell currents.
We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its application to two- and three-loop scalar master integrals and discuss the structure of the occurring cuts.
The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two- and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.
TeV gravity models provide a scenario for black hole formation at energies much smaller than G_N^(-1/2) \sim 10^19 GeV. In particular, the collision of a ultrahigh energy cosmic ray with a dark matter particle in our galactic halo or with another cosmic ray could result into a black hole of mass between 10^4 and 10^11 GeV. Once produced, such object would evaporate into elementary particles via Hawking radiation. We show that the interactions among the particles exiting the black hole are not able to produce a photosphere nor a chromosphere. We then evaluate how these particles evolve using the jet-code HERWIG, and obtain a final diffuse flux of stable 4-dimensional particles peaked at 0.2 GeV. This flux consists of an approximate 43% of neutrinos, a 28% of electrons, a 16% of photons and a 13% of protons. Emission into the bulk would range from a 1.4% of the total energy for n=2 to a 16% for n=6.
We study the properties of black holes of mass 10^4--10^{11} GeV in models with the fundamental scale of gravity at the TeV. These black holes could be produced in the collision of a ultrahigh energy cosmic ray with a dark matter particle in our galactic halo or with another cosmic ray. We show that QCD bremsstrahlung and pair production processes are unable to thermalize the particles exiting the black hole, so a chromosphere is never formed during Hawking evaporation. We evaluate with HERWIG the spectrum of stable 4-dim particles emitted during the Schwarzschild phase and find that in all cases it is peaked at energies around 0.2 GeV, with an approximate 43% of neutrinos, 28% of photons, 16% of electrons and 13% of protons. Bulk gravitons are peaked at higher energies, they account for a 0.4% of the particles (16% of the total energy) emitted by the most massive black holes in n=6 extra dimensions or just the 0.02% of the particles (1.4% of the energy) emitted by a 10 TeV black hole for n=2.
We present a numerical implementation of generalized unitarity. We will show that we are able to obtain the box coefficients of any 1 loop gluonic amplitude, for an arbitrary helicity configuration and for any number of external particles.
We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and we compute the mean and variance of this distribution for several theories. We show the distribution's `fine structure', arising from topological sum rules, can be obtained.