  The inconsistent Hubble constant values derived from cosmic microwave
background (CMB) observations and from local distance-ladder measurements may
suggest new physics beyond the standard $\Lambda$CDM paradigm. It has been
found in earlier works that, at least phenomenologically, non-standard
recombination histories can reduce the $\gtrsim 4\sigma$ Hubble tension to
$\sim 2\sigma$. Following this path, we vary physical and phenomenological
parameters in RECFAST, the standard code to compute ionization history of the
universe, to explore possible physics beyond standard recombination. We find
that the CMB constraint on the Hubble constant is sensitive to the Hydrogen
ionization energy and $2s \rightarrow 1s$ two-photon decay rate, both of which
are atomic constants, and is insensitive to other details of recombination.
Thus, the Hubble tension is very robust against perturbations of recombination
history, unless exotic physics modifies the atomic constants during the
recombination epoch.
