Constraints on the simultaneous variation of the fine structure constant and electron mass in light of DESI BAO data

We study the cosmological constraints of the time variation of the electron mass $m_e$ and the fine-structure constant $\alpha$, using data of cosmic microwave background, supernovae light curve and baryon acoustic oscillation (BAO) data including the recent DESI BAO DR2 measurements. The results are slightly depending on the BAO data set included in the analysis. The latest DESI BAO DR2 data strongly indicates that $m_e$ or $\alpha$ is slightly larger than the previous data from 6DF+SDSS and DESI BAO DR1. We also compare the varying $m_e$ model, the varying $\alpha$ model, and the simultaneous variation of $m_e$ and $\alpha$. When considering the Hubble tension, a larger electron mass is the most promising option and the variation of the fine-structure constants does not alleviate the tension.