11268 1907.06041 10.1007/JHEP09(2019)085 85 85 String correlators: recursive expansion, integration-by-parts and scattering equations Regular Article - Theoretical Physics 1 41 2019 9 11 2019 7 29 2019 9 3 2019 9 3 2019 9 11 The Author(s) 2019 13130 2019 2019 9 9 Song He songhe@itp.ac.cn Fei Teng fei.teng@physics.uu.se Yong Zhang yongzhang@itp.ac.cn grid.9227.e 0000000119573309 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics Chinese Academy of Sciences Beijing 100190 China grid.410726.6 0000 0004 1797 8419 School of Physical Sciences University of Chinese Academy of Sciences No.19A Yuquan Road Beijing 100049 China grid.8993.b 0000 0004 1936 9457 Department of Physics and Astronomy Uppsala University 75108 Uppsala Sweden Abstract We further elaborate on the general construction proposed in [1], which connects, via tree-level double copy, massless string amplitudes with color-ordered QFT amplitudes that are given by Cachazo-He-Yuan formulas. The current paper serves as a detailed study of the integration-by-parts procedure for any tree-level massless string correlator outlined in the previous letter. We present two new results in the context of heterotic and (compactified) bosonic string theories. First, we find a new recursive expansion of any multitrace mixed correlator in these theories into a logarithmic part corresponding to the CHY integrand for Yang-Mills-scalar amplitudes, plus correlators with the total number of traces and gluons decreased. By iterating the expansion, we systematically reduce string correlators with any number of subcycles to linear combinations of Parke-Taylor factors and similarly for the case with gluons. Based on this, we then derive a CHY formula for the corresponding (DF)2 + YM + ϕ 3 amplitudes. It is the first closed-form result for such multitrace amplitudes and thus greatly extends our result for the single-trace case. As a byproduct, it gives a new CHY formula for all Yang-Mills-scalar amplitudes. We also study consistency checks of the formula such as factorizations on massless poles. Keywords Scattering Amplitudes Bosonic Strings Gauge Symmetry ArXiv ePrint: 1907.06041