We obtain the integrand of full-color four-loop three-point form factor of the stress-tensor supermultiplet in N=4 SYM,based on the color-kinematics(CK)duality and generalized unitarity method.Our result not only manifests all dual Jacobi relations via CK duality but also contains 133 free parameters.This suggests the constructibility of the form factor at even higher loops via CK duality.We also find that the planar form factor has a hidden dual conformal symmetry in the lightlike limit of the operator momentum,which is checked up to four loops.
Cosmic shear statistics,such as the two-point correlation function(2PCF),can be evaluated with the PDF-SYM method instead of the traditional weighted-sum approach.It makes use of the full PDF information of the shear estimators,and does not require weightings on the shear estimators,which can in principle introduce additional systematic biases.This work presents our constraints on S8and?mfrom the shear-shear correlations using the PDF-SYM method.The data we use is from the z-band images of the Dark Energy Camera Legacy Survey(DECa LS),which covers about 10000 deg2with more than 100 million galaxies.The shear catalog is produced by the Fourier Quad method,and well tested on the real data itself with the field-distortion effect.Our main approach is called quasi-2D as we do use the photo-z information of each individual galaxy,but without dividing the galaxies into redshift bins.We mainly use galaxy pairs within the redshift interval between 0.2 and 1.3,and the angular range from 4.7 to 180 arcmin.Our analysis yields S8=0.762±0.026 and?m=0.234±0.075,with the baryon effects and the intrinsic alignments included.The results are robust against redshift uncertainties.We check the consistency of our results by deriving the cosmological constraints from auto-correlations ofγ1andγ2separately,and find that they are consistent with each other,but the constraints from theγ1component are much weaker than that fromγ2.It implies a much worse data quality ofγ1,which is likely due to additional shear uncertainties caused by CCD electronics(according to the survey strategy of DECa LS).We also perform a pure 2D analysis,which gives S8=0.81_(-0.04)^(+0.03)and?m=0.25_(-0.05)^(+0.06).Our findings demonstrate the potential of the PDF-SYM method for precision cosmology.
