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 inflation, characterised by $f_{\rm NL}^{\rm loc}$. We present methodology to measure loc}$ from Dark Energy Survey (DES) data using 2-point angular correlation function (ACF) with scale-dependent bias. One focuses work integral constraint. This condition appears when estimating mean number density galaxies and key in obtaining unbiased constraints. The methods are analysed for two types simulations: $\sim 246$ GOLIAT-PNG N-body small area simulations NL}$ equal -100 100, 1952 Gaussian ICE-COLA mocks NL}=0$ that follow DES redshift distribution. use ensemble show importance constraint measuring PNG, where we recover fiducial values within $1\sigma$ including In contrast, found bias $\Delta f_{\rm NL}\sim 100$ not it. For DES-like scenario, forecast NL} \sim 23$, equivalent $1.8\sigma$, IC value NL}=100$. validate our analysis realistic setup finding it robust different choices: best-fit estimator, effect IC, BAO damping, covariance, scale choices. measurement $\sigma(f_{\rm NL})=31$ DES-Y3 sample, ACF $1\ {\rm deg}<\theta<20\ deg}$ range.