Effect of Peak Absolute Magnitude of Type Ia Supernovae and Sound Horizon Values on Hubble Tension using DESI results

We apply data-motivated priors on the peak absolute magnitude of Type Ia supernovae ($M$) and the sound horizon at the drag epoch ($r_d$), to study how the $M-r_d$ degeneracy affects low redshift measurements of the Hubble constant, and then compare these estimates to the Planck estimated value of the Hubble constant. We use the data from Pantheon$+$, Cosmic Chronometers, and the Dark Energy Spectroscopic Instrument Data Release 1 (DESI DR1) Baryon Acoustic Oscillations (BAO) results for this purpose. We reaffirm the fact that there is a degeneracy between $M$ and $r_d$, and modifying the $r_d$ values to reconcile the discrepancy in Hubble constant values also requires a change in the peak absolute magnitude $M$. For certain $M$ and $r_d$ priors, the discrepancy is found to reduce to be as low as (1.2-2) $\sigma$ when considering the spatially flat $\Lambda$CDM model. We also notice that for our datasets considered, the Gaussian prior combination of $M \in \mathcal{N} (-19.253,0.027)$ (obtained from SH0ES) and $r_d \in \mathcal{N} (147.05,0.3)$ Mpc (determined from Planck CMB measurements) is least favored as compared to other prior combinations for the $\Lambda$CDM model.