Note on differential operators, CHY integrands, and unifying relations for amplitudes

An elegant unified web for amplitudes of various theories was given by Cachazo, He and Yuan in the CHY framework a few years ago. Recently, similar web has also been constructed by Cheung, Shen and Wen, which relies on a set of differential operators. In this note, by acting these differential operators on CHY-integrands systematically, we have established the relation between these two approaches. Thus, amplitudes for all theories which have CHY representations, include gravity theory, Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory and its extension, bi-adjoint scalar theory, $\phi^4$ theory, non-linear sigma model, as well as special Galileon theory, have been included in the unified web rooted from gravity theory.Comment: 20 page

Single transverse spin asymmetry of prompt photon production

We study the single transverse spin asymmetry of prompt photon production in high energy proton-proton scattering. We include the contributions from both the direct and fragmentation photons. While the asymmetry for direct photon production receives only the Sivers type of contribution, the asymmetry for fragmentation photons receives both the Sivers and Collins types of contributions. We make a model calculation for quark-to-photon Collins function, which is then used to estimate the Collins asymmetry for fragmentation photons. We find that the Collins asymmetry for fragmentation photons is very small, thus the single transverse spin asymmetry of prompt photon production is mainly coming from the Sivers asymmetry in direct and fragmentation photons. We make predictions for the prompt photon spin asymmetry at RHIC energy, and emphasize the importance of such a measurement.Comment: 11 pages 7 figures, additional discussion, 1 figure added, matches published version in Phys. Lett.