Higgs Boson = Universe is False Vacuum?

In summary, recent studies have explored the stability of the Higgs vacuum by examining the potential's quartic term and its running with energy scale. If this term becomes negative before reaching the Planck scale, the vacuum is not stable. The results of these studies, including those by Alekhin et al and Degrassi et al, suggest that the Higgs vacuum may be metastable, meaning it could eventually decay to a more stable state. However, the exact results may vary depending on technical details and uncertainties in measurements.
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The question of stability of the Higgs vacuum has to do with the shape of the potential, in particular, with the sign of the quartic term, [itex]\lambda h^4[/itex]. If [itex]\lambda [/itex] is positive, then the potential is bounded from below, so that there is a true vacuum at a finite value of the Higgs field, [itex] \langle h \rangle = v[/itex]. This is the case that is usually drawn when people discuss the Higgs mechanism. If [itex]\lambda [/itex] is negative, then the potential is unbounded from below and there is no global minimum. Depending on the quadratic and other terms, there can be a local minimum, which is the false vacuum. Given a long enough period of time, we can have tunneling through the barrier, after which the Higgs field value rolls off to infinity. If the tunneling time is sufficiently long (the age of the universe is the relevant scale here), we can call the vacuum metastable.

At lowest order (tree-level), the coefficients in the Higgs potential can be determined from the weak coupling constant and W/Z and Higgs masses. However, because of quantum effects, the coefficients actually "run" with energy scale according to the renormalization group. Large Higgs value corresponds to a large energy scale (the Higgs field h has units of mass), so the renormalization corrections can get large compared to the tree-level terms. The corrections can be determined in terms of parameters like the masses of all of the other particles participating in the SM interaction, especially the top quark. A detailed formula for the running of [itex]\lambda[/itex] is eq (52) in http://arxiv.org/abs/1205.6497, which is cited in the Alekhin et al paper you linked to. This formula depends on technical details like Yukawa couplings and anomalous dimensions. The formula (63) is a simpler looking formula that boils experimental data into a value for [itex]\lambda(M_t) [/itex] at the scale set by the top quark mass.

The relevant analysis is then to take the value of [itex]\lambda(M_t) [/itex] given by (63) and then use (52) to run its value to large scales. If the sign goes negative before reaching the Planck scale, then the vacuum is not stable. If the tunneling time is longer than the present age of the universe, we distinguish the vacuum as metastable. I'm not 100% certain what Alekhin et al have done differently other than extract a value for the top quark pole mass that has a much larger uncertainty than the one considered by Degrassi et al. Both papers find the same stability bound, but of course the Alekhin et al result has a larger error bar.
 

1. What is the Higgs Boson and how does it relate to the Universe being a False Vacuum?

The Higgs Boson is a subatomic particle that is responsible for giving mass to other particles. According to the Standard Model of particle physics, the Higgs field permeates the entire Universe and interactions with this field give particles their mass. Some theories suggest that the Higgs field could be in a false vacuum state, meaning that it is not at its lowest energy state. This could have implications for the stability and fate of the Universe.

2. How was the Higgs Boson discovered and why is it important?

The Higgs Boson was discovered in 2012 by the Large Hadron Collider (LHC) at CERN. This discovery confirmed the existence of the Higgs field and provided evidence for the Standard Model of particle physics. The Higgs Boson is important because it helps explain the origin of mass and is crucial for our understanding of the fundamental building blocks of the Universe.

3. What evidence supports the idea that the Universe is in a False Vacuum state?

There is currently no direct evidence that the Universe is in a False Vacuum state, but several theories suggest this could be a possibility. Some calculations predict that the Higgs field could be in a false vacuum state, which could have implications for the stability of the Universe. Additionally, some observations of the cosmic microwave background radiation and the expansion of the Universe are consistent with the idea of a False Vacuum state.

4. What are the potential consequences of the Universe being a False Vacuum?

If the Universe is indeed in a False Vacuum state, it could have significant consequences for the stability and future of our Universe. Some theories suggest that the Universe could eventually transition to a lower energy state, causing a catastrophic event known as a vacuum decay. This could have implications for the existence of matter and the structure of the Universe.

5. How are scientists studying the Higgs Boson and the False Vacuum state?

Scientists are continuing to study the properties of the Higgs Boson and its interactions with other particles at the LHC and other particle accelerators around the world. They are also using observations of the Universe and advanced mathematical models to explore the possibility of a False Vacuum state and its implications. Further research and experiments are needed to fully understand the role of the Higgs Boson in the Universe and the possibility of a False Vacuum state.

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