  One of the simplest ways to account for the observed W-boson mass shift is to
introduce the $SU(2)_L$ triplet Higgs boson with zero hypercharge, whose vacuum
expectation value is about 3 GeV. If the triplet is heavy enough at
$\mathcal{O}(1)$ TeV, it essentially contributes only to $T$ parameter without
any conflict to the observation. The presence of a complex triplet Higgs boson
raises the $SU(2)_L$ gauge coupling constant to $\alpha_2(M_{\rm PL} )\simeq
1/44$ at the Planck scale. Thanks to this larger gauge coupling constant, we
show that the electroweak axion vacuum energy explains the observed
cosmological constant provided that the axion field is located near the hill
top of the potential at present.
