Parity-odd Four-Point Correlation Function from DESI Data Release 1 Luminous Red Galaxy Sample

TL;DR

This work measures the parity-odd $4$PCF of DESI DR1 LRGs using both auto- and cross-correlation tests and explores two covariance frameworks: a full analytic covariance and a compressed-hybrid approach. While the uncorrected analytic covariance can imply a local $\sim4\sigma$ detection, incorporating cross-statistics to diagnose data–mock covariance mismatch reduces the significance, yielding results consistent with zero parity violation. The analysis identifies fiber assignment and volume replication as key systematics that require calibration, and demonstrates that a hybrid-covariance approach with mode compression stabilizes results across patches. Overall, the parity-odd signal in DR1 is consistent with zero, with improved completeness in future DESI data expected to enhance sensitivity to potential parity-violating physics.

Abstract

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 DESI DR1 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 DESI DR1 LRG sample is consistent with zero. We note, 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.

Figures (13)

• Figure 1: Footprint of DESI-DR1 LRG. The color map shows the number of targets sharing the same unique identifier, which combines the tile ID and fiber location. This quantity is closely correlated with the sample completeness: higher values of NTILE indicate higher completeness. For this paper, we specifically studied two regions, the ${\rm NGC}_1$ and ${\rm NGC}_2$, which have the highest numbers of targets sharing the same identifier (also see Table \ref{['tab:statistic']}).
• Figure 2: Measurement of the parity-odd 4PCFs using the DESI-DR1 LRG sample in NGC. The top two panels show a subset of the angular channels ($\ell_1,\ell_2,\ell_3$) for the coefficients of the connected 4PCF, weighted by $r_1r_2r_3$. Points with error bars (red) are the measurement from the data; the black curves with shaded gray regions indicate the $1\sigma$ standard deviation from the Abacus simulations with altMTL fiber assignment scheme. The bottom panel shows the arrangement of the three radial bins.
• Figure 3: Simlar to Fig. \ref{['fig:4PCF_Iron_AbacusAltmtl_NGC_6ells_odd']}, this figure shows the measurement of the parity-odd 4PCFs using the DESI-DR1 LRG sample in SGC. The top two panels show a subset of the angular channels ($\ell_1,\ell_2,\ell_3$) for the coefficients of the connected 4PCF, weighted by $r_1r_2r_3$. Points with error bars (blue) are the measurement from the data; the black curves with shaded gray regions indicate the $1\sigma$ standard deviation from the Abacus simulations with altMTL fiber assignment scheme. The bottom panel shows the arrangement of the three radial bins.
• Figure 4: Distribution of the auto-correlation $\chi^2$ for the parity-odd connected 4PCF, using the full DESI DR1 LRG sample and combining the NGC and SGC, with each using the corresponding covariance. The panel shows a comparison between simulations and data, as well as the detection significance of the parity-odd 4PCF using the analytic covariance matrix. We used the range $20\, {h^{-1}\rm{Mpc}} <r<160\,{h^{-1}\rm{Mpc}}$ without additional radial cuts ($\Delta r=0$). The vertical lines indicate the statistics for the DESI data. The dashed line represents the correction derived from the cross-statistics in Eq. \ref{['eqn:chi2_delta_c']}, with the uncertainty shown as the shaded region, estimated from the EZmock. The filled colored histograms correspond to Abacus-FFA; the circled histogram corresponds to Abacus-altMTL; the hashed histogram corresponds to EZmock-FFA. The black curves show the theoretical $\chi^2$ distribution. Additionally, the distribution of the altMTL mocks and the data have been calibrated by multiplying by the ratios deriving from the fiber implementations in the FFA and altMTL mocks, whereas the Abacus mocks are rescaled for the volume effect.
• Figure 5: Distribution of both types of cross-correlation statistics ($\chi^2_\times$ (left and middle) and $\chi^2_{\Delta}$ (right)) for the parity-odd 4PCF between the NGC and SGC of the DESI DR1 LRG sample. This figure compares simulations with data using the analytic covariance matrix. For all the panels, the filled grey histograms are for the EZmock-FFA, the purple histograms are for the Abacus mocks, and the black solid or dashed curves denote the theoretical $\chi^2_\times$ distribution, modeled as a Gaussian centered at zero with the width predicted by Eq. \ref{['eqn:var_chi2x']}. Left: The Vertical line indicates the DESI data statistics, which is consistent with zero with a negative value. Middle: filled purple histograms correspond to the Abacus-Complete mocks, and the hatched histogram represents the Abacus-altMTL mocks. We find that the Abacus mocks do not center around zero due to the limited volume effect (for more discussion see below). Right: The Vertical line again indicates the DESI data statistics. The filled grey histograms correspond to the EZmock-FFA, while the purple histograms show the Abacus mocks. The dark hatched histogram is for Abacus-altMTL without applying correction. The light dashed histogram is for the corrected Abacus-altMTL using Eq. \ref{['eqn:chi2_Delta_tot_avg']} given the shifted Abacus center in the Type-I cross correlation shown in the middle panel.