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I just read an article about the correlation between the Higgs boson mass and the stability (or metastability) of vacuum, so I want to ask to someone this:

When someone is talking about the electroweak vacuum lifetime, does it refer to a certain region of space, the time needed for quantum tunnelling to occur once in the whole vacuum, the lifetime of the entire vacuum or something else?

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I believe that no one has established a definition that is accurate up to order-one prefactors – that the lifetime is only being calculated as an order-of-magnitude estimate. This order-of-magnitude estimate is meant to be relevant for the real Universe.

In the real Universe, the volume where a dangerous decay may start is proportional to $c^3\tau^3$ where $\tau$ is the lifetime. So if the probability of the nucleation of a "bubble of the new vacuum" is $$\gamma=\frac{dP}{d\Omega} = \frac{dP}{dt\cdot dV}$$ per unit spacetime four-volume, I believe that by the lifetime, people just mean $$\tau =\left({\gamma}{c^3}\right)^{-1/4} $$ up to number-one prefactors that are not specified and it's somewhat likely that the normalization is exactly as I wrote it. Note that $\gamma$ has units of ${\rm m}^{-3}{\rm s}^{-1}$ which gets converted to ${\rm s}^{-4}$ with the multiplication by $c^3$.

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Motl what you mean for "real universe" ? – user27494 Sep 3 '13 at 12:24
I mean the universe around us - with its particular dependence of the Hubble constant on time and with the age of 13.8 billion years. The Hubble constant's dependence on the cosmological evolution implies that the current radius of observable universe is about 40+ billion light years etc. Most models that talk about the electroweak vacuum stability of course talk about more general universes whose particle physics agrees with the observed particle physics, may disagree in some respects, and these theories are of course usable within many different cosmologies. – Luboš Motl Sep 3 '13 at 13:43
This is the paper pag 5 fig. 3 as you can see it's not so clear.. But acoording to the fact that we're living on the edge of the metastability/stability bound i suppose that our vacuum could be a loooooong living one..i hope – user27494 Sep 20 '13 at 15:32

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