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We investigate in details the gravitational wave (GW) from the first-orderphase transition (PT) in the extended standard model of particle physics with adimension-six operator, which is capable of exhibiting the recently discoveredslow first-order PT in addition to the usually studied fast first-order PT. Tosimplify the discussion, it is sufficient to work with an example of a toymodel with the sextic term, and we propose an unified description for both slowand fast first-order PTs. We next study the full one-loop effective potentialof the model with fixed/running renormalization-group (RG) scales. Compared tothe prediction of GW energy density spectrum from the fixed RG scale, we findthat the presence of running RG scale could amplify the peak amplitude byamount of one order of magnitude while shift the peak frequency to the lowerfrequency regime, and the promising regime of detection within the sensitivityranges of various space-based GW detectors shrinks down to a lower cut-offvalue of the sextic term rather than the previous expectation.

The gravitational waves from the first-order phase transition with a dimension-six operator