  By adding the dimension-six operator for the Higgs potential (denoted
$\mathcal{O}_6$) in Standard Model, we have a first-order electroweak phase
transition (EWPT) whose strength is larger than unity. The cutoff parameter of
the dimension-six Higgs operator ($\Lambda$) is found to be in the range
593-860 GeV with the Wilson parameter equals to unity; it is also shown that
the greater the $\Lambda$, the lower the phase transition strength and the
larger the Wilson parameter, the wider the domain of $\Lambda$. At zero
temperature, the sphaleron energy is calculated with a smooth ansatz and an
ansatz with scale-free parameters, thereby we find that smooth profiles are not
more accurate than profiles with scale-free parameters. Then, using the
one-loop effective Higgs potential with the inclusion of $\mathcal{O}_6$
instead of all possible dimension-six operators, we directly calculate the
electroweak sphaleron energy at finite temperature with the scale-free
parameters ansatz and show that the decoupling condition is satisfied during
the phase transition. Moreover, we can reevaluate the upper bound of the cutoff
scale inferred from the first-order phase transition. In addition, with the
upper bound of the cutoff parameter (about 800-860 GeV), EWPT is a solution to
the energy scale of the dimension-six operators. There is an extended
conclusion that EWPT can only be solved at a large energy scale than that of
SM.
