Observational bounds on a possible electron-to-proton mass ratio variation and constraints in the lepton-specific 2HDM

In this work, we test a possible redshift variation of the electron-to-proton mass ratio, $\mu =m_e\mathrm{/}{m}_p$, directly from galaxy cluster gas mass fraction measurements and type Ia supernovae observations. Our result reveals no variation of $\mu$ within 1~$\sigma$. From the point of view of Particle Physics, we can use the precision on these results to constrain the parameter space of models beyond the Standard Model of electroweak interactions. We exemplify this by focusing on a specific Two-Higgs doublet model (2HDM), where the second scalar doublet couples exclusively to leptons. An important parameter in the model concerns the ratio between its vacuum expectation values, defined by $\tan \beta \equiv v_2\mathrm{/}{v}_1$. In our approach, we can constrain the inverse parameter $(\cot \beta )$ to an optimal value, $(\cot \beta )=(2.003\pm 0.081)\cdot {10}^{-3}$, with the highest vacuum expectation value for 2HDM, $v_2$, estimated at around $240.57\pm 2.93$~GeV. Also, by taking into account the discrepancy in the anomalous magnetic moment of the muon found between theory and experiment, we can reduce the validity region for this model and establish bounds on the scalar masses, in light of our findings from galaxy cluster data for $\mu$. This study contributes valuable insights to the understanding of the interface between Particle Physics and Astrophysics, establishing a new interrelationship between data on the large-scale structure of the Universe and subatomic Physics.