5,692 research outputs found
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
Expansion of Einstein-Yang-Mills Amplitude
In this paper, we provide a thorough study on the expansion of single trace
Einstein-Yang-Mills amplitudes into linear combination of color-ordered
Yang-Mills amplitudes, from various different perspectives. Using the gauge
invariance principle, we propose a recursive construction, where EYM amplitude
with any number of gravitons could be expanded into EYM amplitudes with less
number of gravitons. Through this construction, we can write down the complete
expansion of EYM amplitude in the basis of color-ordered Yang-Mills amplitudes.
As a byproduct, we are able to write down the polynomial form of BCJ numerator,
i.e., numerators satisfying the color-kinematic duality, for Yang-Mills
amplitude. After the discussion of gauge invariance, we move to the BCFW
on-shell recursion relation and discuss how the expansion can be understood
from the on-shell picture. Finally, we show how to interpret the expansion from
the aspect of KLT relation and the way of evaluating the expansion coefficients
efficiently.Comment: 50 pages, 1 figure, Revised versio
3-(3,5-Dimethyl-1H-pyrazol-1-yl)propanamide
In the crystal of the title compound, C8H13N3O, molecules are linked by intermolecular N—H⋯N and N—H⋯O hydrogen bonds into a three-dimensional network. Additional stabilization is provided by weak intermolecular C—H⋯O hydrogen bonds
3-[3-(2-Pyridyl)-1H-pyrazol-1-yl]propanamide
In the title compound, C11H12N4O, the pyrazole and pyridine rings are nearly coplanar [dihedral angle = 1.87 (5)°]. Adjacent molecules are linked by N—H⋯N and N—H⋯O hydrogen bonds into a linear chain running along the c axis
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