Quantifying the Impact of 2D and 3D BAO Measurements on the Cosmic Distance Duality Relation with HII Galaxy observation

The cosmic distance duality relation (CDDR) is a fundamental and practical condition in observational cosmology that connects the luminosity distance and angular diameter distance. Testing its validity offers a powerful tool to probe new physics beyond the standard cosmological model. In this work, for the first time, we present a novel consistency test of CDDR by combining HII galaxy data with a comprehensive set of Baryon Acoustic Oscillations (BAO) measurements. The BAO measurements include two-dimensional (2D) BAO and three-dimensional (3D) BAO, as well as the latest 3D BAO data from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2). We adopt four different parameterizations of the CDDR parameter, η (z), to investigate possible deviations and their evolution with cosmic time. To ensure accurate redshift matching across datasets, we reconstruct the distance measures through a model-independent Artificial Neural Network (ANN) approach. Our analysis uniquely examines two distinct approaches: i) marginalization over the BAO sound horizon rd, and ii) fixing rd to specific values. We find no significant deviation from the CDDR (less than 68% confidence level) in either the marginalized rd or the rd=147. 05 Mpc scenario. However, a slight deviation at the 68% confidence level is found when applying 2D-BAO data with rd=139. 5 Mpc. Furthermore, our analysis shows that all BAO data considered in this work support the validity of the CDDR, where 3D-DESI BAO provides the tightest constraints. We find no tension between 2D and 3D BAO measurements, which confirms their mutual consistency. In addition, the treatment of the sound horizon rd significantly impacts η (z) constraints, which proves its importance in CDDR tests. Finally, the consistency of our results supports the standard CDDR and demonstrates the robustness of our analytical approach.