[en] The starting point of this thesis is the calculation of the five-point amplitude for the scattering of two distinct scalars with the emission of one graviton in the final state for Einstein-Hilbert gravity. We find that the result, expressed in Sudakov variables, corresponds to the sum of two gauge invariant contributions written in terms of a new two scalar - two graviton effective vertex. A similar calculation is carried out in Quantum Chromodynamics (QCD) for the scattering of two distinct quarks with one extra gluon in the final state. The effective vertices which appear in both cases are then evaluated in the multi-Regge limit (where the emitted on-shell graviton is well separated in rapidity from the scalar particles) reproducing the well-known result obtained by Lipatov where the Einstein-Hilbert graviton emission vertex from two off-shell gravitons can be related to the product of two QCD gluon emission vertices. After this we investigate tree-level five-point amplitudes in scalar-QCD (sQCD) expressed in terms of Sudakov variables and find the equivalent ?gravitational? counterparts using the so-called color-kinematics duality proposed by Bern, Carrasco, and Johannson. Taking the multi-Regge limit in the gravitational amplitudes, we show that those pieces in the coupling of two Reggeized gravitons to one on-shell graviton directly stemming from the double copy of the vertex for two Reggeized gluons to one on-shell gluon are universal and properly reproduced by the duality.In the second part of the thesis we study the applicability of the colorkinematics duality to the scattering of two now distinguishable scalar matter particles with gluon emission in QCD, or graviton emission in Einstein gravity. Our previous analysis suggested that a direct use of the Bern-Carrasco-Johansson double-copy prescription to matter amplitudes does not reproduce the gravitational amplitude in multi-Regge kinematics. However, minimal extensions of thecalculation eliminate this obstacle. Here we present two approaches: introduction of a scalar contact interaction, or relaxing distinguishibility of the scalars. In both cases new diagrams allow for a full reconstruction of the correct multi-Regge limit on the gravitational side. Both modifications correspond to pure theories obtained by dimensional reduction from higher-dimensional gauge theories.

[es] El punto de partida la tesis es el c?lculo de la amplitud de dispersi?n a cinco puntos de dos escalares de diferentes sabores con la emisi?n de un gravit?n en la teor?a de Einstein. El resultado corresponde a la suma de dos contribuciones invariantes gauge escritas en t?rminos de un nuevo v?rtice efectivo para dos escalares y dos gravitones. Un c?lculo similar se lleva a cabo en Cromodin?mica Cu?ntica (QCD) para la amplitud de dispersi?n de dos quarks distinguibles con la emisi?n de un glu?n. Los v?rtices efectivos que aparecen en ambos casos son evaluado en el llamado l?mite de cinem?tica multi-Regge, reproduciendo el conocido resultado obtenido por Lipatov en el que el v?rtice de emisi?n del graviton se puede relacionar con el producto de dos v?rtices de emisi?n de un glu?n. En la segunda parte de la tesis se estudia la aplicabilidad de la dualidad color-cinem?tica (color-kinematics duality) a la dispersi?n de dos part?culas escalares distinguibles con emisi?n de gluones en QCD, o emisi?n de gravitones en gravedad de Einstein. Nuestro an?lisis indica que un uso directo de laprescripci?n de doble copia Bern-Carrasco-Johansson a amplitudes con materia no reproduce la amplitud gravitacional en la cinem?tica de multi-Regge. Sin embargo, extensiones m?nimas del c?lculo eliminan este obst?culo. Aqu? se presentan dos enfoques: la introducci?n de una interacci?n de contacto escalar, o la relajaci?n de la distinguibilidad de los escalares. En ambos casos nuevos diagramas permiten una reconstrucci?n completa del l?mite correcto de Regge en la amplitud gravitacional. Ambas modificaciones se corresponden con teor?as obtenidas por reducci?n dimensional de teor?as de gauge puras en dimensiones superiores.