7,851 research outputs found
Amplitude Relations in Non-linear Sigma Model
In this paper, we investigate tree-level scattering amplitude relations in
non-linear sigma model. We use Cayley parametrization. As was shown in
the recent works [23,24] both on-shell amplitudes and off-shell currents with
odd points have to vanish under Cayley parametrization. We prove the off-shell
identity and fundamental BCJ relation for even-point currents. By taking
the on-shell limits of the off-shell relations, we show that the color-ordered
tree amplitudes with even points satisfy -decoupling identity and
fundamental BCJ relation, which have the same formations within Yang-Mills
theory. We further state that all the on-shell general KK, BCJ relations as
well as the minimal-basis expansion are also satisfied by color-ordered tree
amplitudes. As a consequence of the relations among color-ordered amplitudes,
the total -point tree amplitudes satisfy DDM form of color decomposition as
well as KLT relation.Comment: 27 pages, 8 figures, 4 tables, JHEP style, improved versio
Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
In this paper, we derive generalized Bern-Carrasco-Johansson relations for
color-ordered Yang-Mills amplitudes by imposing gauge invariance conditions and
dimensional reduction appropriately on the new discovered graphic expansion of
Einstein-Yang-Mills amplitudes. These relations are also satisfied by
color-ordered amplitudes in other theories such as color-scalar theory,
bi-scalar theory and nonlinear sigma model (NLSM). As an application of the
gauge invariance induced relations, we further prove that the three types of
BCJ numerators in NLSM , which are derived from Feynman rules, Abelian Z-theory
and Cachazo-He- Yuan formula respectively, produce the same total amplitudes.
In other words, the three distinct approaches to NLSM amplitudes are equivalent
to each other.Comment: 40pages, 2 figure
Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
For a physical field theory, the tree-level amplitudes should possess only
single poles. However, when computing amplitudes with Cachazo-He-Yuan (CHY)
formulation, individual terms in the intermediate steps will contribute
higher-order poles. In this paper, we investigate the cancelation of
higher-order poles in CHY formula with Pfaffian as the building block. We
develop a diagrammatic rule for expanding the reduced Pfaffian. Then by
organizing diagrams in appropriate groups and applying the cross-ratio
identities, we show that all potential contributions to higher-order poles in
the reduced Pfaffian are canceled out, i.e., only single poles survive in
Yang-Mills theory and gravity. Furthermore, we show the cancelations of
higher-order poles in other field theories by introducing appropriate
truncations, based on the single pole structure of Pfaffian.Comment: 30 pages,6 figures,1 table, footnote adde
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