Primordial non-Gaussianity with angular correlation function: Integral constraint and validation for des

Local primordial non-Gaussianity (PNG) is a promising observable of the underlying physics of inflation, characterized by flocNL. We present the methodology to measure flocNLfrom the Dark Energy Survey (DES) data using the two-point angular correlation function (ACF) with scale-dependent bias. One of the focuses of the work is the integral constraint (IC). This condition appears when estimating the mean number density of galaxies from the data and is key in obtaining unbiased flocNLconstraints. The methods are analysed for two types of simulations: ~246 GOLIAT-PNG N-body small area simulations with fNLequal to -100 and 100, and 1952 Gaussian ICE-COLA mocks with fNL= 0 that follow the DES angular and redshift distribution. We use the ensemble of GOLIAT-PNG mocks to show the importance of the IC when measuring PNG, where we recover the fiducial values of fNL within the 1σ when including the IC. In contrast, we found a bias of fNL~ 100 when not including it. For a DES-like scenario, we forecast a bias of fNL~ 23, equivalent to 1.8σ, when not using the IC for a fiducial value of fNL= 100. We use the ICE-COLA mocks to validate our analysis in a realistic DES-like set-up finding it robust to different analysis choices: best-fitting estimator, the effect of IC, BAO damping, covariance, and scale choices. We forecast a measurement of fNLwithin σ(fNL) = 31 when using the DES-Y3 BAO sample, with the ACF in the 1 deg < θ < 20 deg range.