Parity-odd four-point correlation function from the DESI data release 1 luminous red galaxy sample

The parity-odd four-point function provides a unique probe of fundamental symmetries and potential new physics in the large-scale structure of the Universe. We present measurements of the parity-odd four point function using the Dark Energy Spectroscopic Instrument (DESI) DR1 luminous red galaxy (LRG) sample and assess its detection significance. Our analysis considers both auto- and cross-correlations, using two complementary approaches to the covariance: (i) the full analytic covariance matrix applied to the uncompressed data vector, and (ii) a compressed data vector combined with a hybrid covariance matrix constructed from simulations and analytic estimates. When using the full analytic covariance matrix without corrections, we observe apparent auto-correlation signals with significance up to 4σ. However, this excess is also consistent with a mismatch between the statistical fluctuations estimated from the simulations and those present in the real data. Our findings therefore suggest that the parity-odd signal in the current DESIDR1LRG sample is consistent with zero. Wenote,however, that the low completeness of this sample may have a non-negligible impact on the detection sensitivity. Future data releases with improved completeness will be crucial for further investigation.