We use large-scale lattice simulations to compute the rate of baryon number violating processes ( the sphaleron rate ) , the Higgs field expectation value , and the critical temperature in the Standard Model across the electroweak phase transition temperature .
While there is no true phase transition between the high-temperature symmetric phase and the low-temperature broken phase , the cross-over is sharply defined at T _ { c } = ( 159 \pm 1 ) GeV .
The sphaleron rate in the symmetric phase ( T > T _ { c } ) is \Gamma / T ^ { 4 } = ( 18 \pm 3 ) \alpha _ { W } ^ { 5 } , and in the broken phase in the physically interesting temperature range 130 \mbox { GeV } < T < T _ { c } it can be parametrized as \log ( \Gamma / T ^ { 4 } ) = ( 0.83 \pm 0.01 ) T / { GeV } - ( 147.7 \pm 1.9 ) .
The freeze-out temperature in the early Universe , where the Hubble rate wins over the baryon number violation rate , is T _ { * } = ( 131.7 \pm 2.3 ) GeV .
These values , beyond being intrinsic properties of the Standard Model , are relevant for e.g .
low-scale leptogenesis scenarios .