Higgs field in the early universe

[skydivephil]

As i understand it, at some point in the early unvierse, the Higgs field was off, then it swtiched on. Is this correct? I can't find when this is supposed to have happened, does anyone know?

 

[Mordred]

Depends on which Supersymmetry GUT model. in the SU(5) model it correlates the breaking of SU(5) to SU(3)*SU(2)*U(1), not sure where it sits in the SO(10) GUT model. However it would be when fermions and weak gauge bosons first gain mass. In the Georgi-Glashow model (outdated) which correlates to above, the break is at the GUT Epoch, or grand unification scale. roughly 10¹⁶GeV

according to Wiki
"The electromagnetic interaction was modeled with the weak interaction, whose force carriers are W and Z bosons, traversing minuscule distance, in electroweak theory (EWT). Electroweak interaction would operate at such high temperatures as soon after the presumed Big Bang, but, as the early universe cooled, split into electromagnetic and weak interactions. The strong interaction, whose force carrier is the gluon, traversing minuscule distance among quarks, is modeled in quantum chromodynamics (QCD). EWT, QCD, and the Higgs mechanism, whereby the Higgs field manifests Higgs bosons that interact with some quantum particles and thereby endow those particles with mass, comprise particle physics' Standard Model (SM). Predictions are usually made using calculational approximation methods, although such perturbation theory is inadequate to model some experimental observations (for instance bound states and solitons). Still, physicists widely accept the Standard Model as science's most experimentally confirmed theory."

http://en.wikipedia.org/wiki/Fundamental_interaction

Georgi-Glashow model SU(5)*SU(3)*SU(2)*U(1)
http://en.wikipedia.org/wiki/Georgi–Glashow_model

here is a review of various GUT models.
see section 2.4.1
http://arxiv.org/pdf/hep-ph/9402266v5.pdf

here are a couple others covering S0(10)
http://arxiv.org/pdf/0904.1556.pdf
http://pdg.lbl.gov/2...11-rev-guts.pdf

 

[skydivephil]

Thank you for that Modred , this look slike the same energy scale as inflation is supposed to happen. So i preumse its at the same time, is that right? Also given you say its model dependant what are the range of estimates with regards to inflaiton. do some models say before inflationa and others after or ...?

Also is this related for the motivation to suggest that the bubble universes in eternal inflation have different constants? or is that solely based upon the string theory landscape? I am not trying to argue if eternal inflaiton or string landscape is correct or not, I have no opinion, but I just want to undersdtand how these issues are related (or not). Thanks

 

[Mordred]

Again this also depends on which inflation model is true, there is 60 different inflation models, including numerous Higg's inflation models. The simple answer is we don't know for sure. In the Georgi-Glashow model inflation happened slightly after at the beginning of the electroweak epoch. which follows the GUT epoch.

Not sure on the bubble universe portion however

 

[phsopher]

As i understand it, at some point in the early unvierse, the Higgs field was off, then it swtiched on. Is this correct? I can't find when this is supposed to have happened, does anyone know?

The electroweak symmetry is restored in the Standard Model above the temerature of the order of 100 GeV. As the universe cooled down below this point the Higgs would have obtained a non-zero vacuum expectation value (VEV) giving weak gauge bosons and fermions (other than neutrinos) their masses.

It should be noted though, that since the Higgs is a light field during inflation it would also obtain a VEV in our observable patch during that era. So electroweak symmetry would have been broken during inflation as well. So the brief likely history of the Higgs would be: fist a condesate would be generated during inflation and subsequently decay after inflation is over, then the thermal bath produced by the decay of the inflaton would restore electroweak symmetry until the universe cooled down beyond 100 GeV breaking the symmetry again.

I think electroweak phase transition is covered, at least brifly, in most standard cosmology textbooks. For example

Physical Foundations of Cosmology by Mukhanov

 

[Mordred]

isn't the value 100GeV the strong coupling constant becomes weak or strong? according to Mukhanov? if your copy is the same as mine its equation 4.3.1.

$\alpha$_s is 0.13 at $\cong$100GeV

he after explains the strength of strong interactions should be come infinite at q²=$\Lambda$²_qcd he also explains that this is based on a one loop approximation. where he is discussing the quantum chromodynamic portion. The Higg's interactions isn't even involved at this stage

That value you described is only a descriptive for when the strong coupling becomes weak or strong. the thing is the QCD coupling constant decreases at higher portions where the QED coupling constant increases at higher temperatures. Where they converge is when they unify.

http://en.wikipedia.org/wiki/Coupling_constant#Running_coupling

the unification of the coupling constants is covered on 3.1 page 30 based on the SU(5) minimal extension of the SM model.

http://arxiv.org/pdf/hep-ph/9402266v5.pdf

edit forgot to include the Yukawa coupling, there is 3 coupling constants not two. electroweak, strong and yukawa coupling constants

I had to look for the line I needed in regards to the higgs
Introducing spontaneous symmetry breaking via the Higgs-mechanism. This introduced gauge boson masses without explicitly breaking the gauge symmetry This is the SU(5) extension. the above is the SU(3)*SU(2)*U1) portion or rather a specific part of it

 

[Mordred]

Thinking about it I don't recall any of my cosmology textbooks covering SUSY. they usually describe GUT without including super symmetry. I have 6 cosmology textbooks and I don't recall any of them even mentioning the Higg's

Mind you I haven't finished reading Linde's yet but he mentioned he made it free for distribution as its outdated
http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde

 

[phsopher]

The OP is asking when the Higgs is turned on. I interpret this to mean the time when the Higgs obtains a non-zero VEV thus breaking the electroweak symmetry and giving masses to weak gauge bosons, quarks and leptons. This happens at $T\sim \mathcal O(\text{100 GeV})$. I don't have my copy of Mukhanov with me, but in this online copy, see section 4.4.5, page 176 (I'm not sure if I'm allowed to post this link since it's for an entire book, but since it's on a university webpage I assume it's ok).

I don't understand what point you are making. The strong coupling constant becomes small roughly above the the QCD phase transition scale which is 100 MeV so QCD is perturbative at the electroweak scale (100 GeV).

I don't want to comment about Grand Unification because 1) I don't know anything about it, 2) I think GUTs and the like are speculative, for all we know SM is valid all the way up to the Planck scale$^*$ (would require top mass lower than central value to ensure stability of the vacuum, though) and 3) in my estimation this is not what the OP is after.

Thinking about it I don't recall any of my cosmology textbooks covering SUSY. they usually describe GUT without including super symmetry. I have 6 cosmology textbooks and I don't recall any of them even mentioning the Higg's

Mind you I haven't finished reading Linde's yet but he mentioned he made it free for distribution as its outdated
http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde

The electroweak phase transition happens in the pure Standard Model. You don't need SUSY or GUTs. Maybe I'm wrong that most textbooks cover it. I know that Mukhanov does as already established and Peacock briefly mentions it (page 305) and it was mentioned in my cosmology course so I extrapolated from these and assumed that it's discussed in some fashion in most textbooks.

__________________________
$^*$ Of course you still need additional sectors for inflation, dark matter, neutrino masses etc.

 

[Mordred]

Fair enough like I stated earlier it depends on the model. My understanding is that neither the Gut SM nor the MSSM models work completely. Best hope being on the SO(10)

In regards to SO(10) my understanding (still studying it) the higgs turns on earlier. As well as in the MSSM minimal super symmetric model.

I guess the only correct answer is that it is anyones guess lol

 

[phsopher]

Fair enough like I stated earlier it depends on the model. My understanding is that neither the Gut SM nor the MSSM models work completely. Best hope being on the SO(10)

In regards to SO(10) my understanding (still studying it) the higgs turns on earlier. As well as in the MSSM minimal super symmetric model.

I guess the only correct answer is that it is anyones guess lol

Like I said I don't know anything about the GUTs so I may be well off the mark here but it was my understanding that the higgs responsible for the symmetry breaking at the GUT scale would have to be a different Higgs, that is, not the Standard Model Higgs responsible for electroweak symmetry breaking. Is this not the case? I mean, we've probed electroweak physics in accelerators so we know how that works and so in my opinion the electroweak phase transition is something that happened in the universe regardless of higher energy extensions of the standard model.

 

[Mordred]

How many Higg's fields.Bosons are there lol? I certainly don't know.

see alternate models, Higgs
The Minimal Standard Model as described above is the simplest known model for the Higgs mechanism with just one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector favoured by theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0, a CP-odd neutral Higgs boson A0, and two charged Higgs particles H±. Supersymmetry ("SUSY") also predicts relations between the Higgs-boson masses and the masses of the gauge bosons, and could accommodate a 125 GeV/c2 neutral Higgs boson.

http://en.wikipedia.org/wiki/Higgs_boson

The standard model is U(1)*SU(2)*SU(3) this portion has 4 Higg's particles including its anti particle

The SU(5)*SU(3)*SU(2)*U(1) MSSM needs 12 Higg's goldstone bosons forthe lie algebra if memory serves right. However I'm still learning lie algebra so I could be wrong.

So in that sense your correct in that its a different Higg's in a way lol Not sure how the SO(10) works yet but some of the numbers I've seen on it involve 72 higgs

 

[bapowell]

Why all this talk about GUTs? The OP is presumably interested in the SM Higgs which has only to do with the electroweak scale. Phsopher is correct in that the temperature-corrected potential generates a local maximum below the transition temperature. Before this time (at higher temperatures) the Higgs vacuum was symmetric and the Higgs was "off".

 

[Mordred]

As i understand it, at some point in the early unvierse, the Higgs field was off, then it swtiched on. Is this correct? I can't find when this is supposed to have happened, does anyone know?

That's up to the OP to let us know Bapowell, some point in the early universe could very well include GUT. Either way the question is answered, and for the record I never stated Phsopher was incorrect, we were discussing if its possible the Higg's occurs earlier than the predictions of the standard model

by the way wiki has the electroweak scale at 246 GeV, makes me wonder where the difference is (not that we can trust wiki 100%)

http://en.wikipedia.org/wiki/Electroweak_scale
could this be why?

"Physically, it describes the moment in our universe evolution when electric and
weak forces differentiate. At temperature scales above 100 GeV, MSM Lagrangian exhibits the gauge symmetry:"
SU(3)_c*SU(2)_L*U(1)_Y
SU(3)_c
refers to the color symmetry and plays no role in our rendition of the electroweak phase transition."
that was why I questioned the 100GeV value in post 6see equation 3.5
http://www.staff.science.uu.nl/~proko101/DoruSticlet_pt2.pdf

answer 246 GeV Minimal standard model, as I stated the electroweak scale depends on the model used
in the MSSM models the electroweak scale is roughly 10¹⁵
edit however the SUSY scale may be too high in the MSSM model so I wouldn't place any faith in MSSM. Least from what I've been reading

 

[Chronos]

Lawrence Krauss suggests SU(10) is favored by BICEP2 data - http://arxiv.org/abs/1404.0634.

 

[Mordred]

nice paper, I'm starting to like the SO(10) model, the seesaw mechanism takes some getting used to though lol by the way here is two papers on SO(10). For one thing it accounts for right hand neutrinos. Recall those dark matter articles showing the potential of being observed

http://arxiv.org/pdf/1003.6102v1.pdf

http://cds.cern.ch/record/392392/files/9907211.pdf

this one is a 220 page dissertation
http://arxiv.org/pdf/hep-ph/0508153v1.pdf

 

[bapowell]

answer 246 GeV Minimal standard model, as I stated the electroweak scale depends on the model used
in the MSSM models the electroweak scale is roughly 10¹⁵
edit however the SUSY scale may be too high in the MSSM model so I wouldn't place any faith in MSSM. Least from what I've been reading

I think you are quoting the MSSM GUT scale there (supposing your units are GeV). What does SUSY have to do with electroweak symmetry breaking?

 

[phsopher]

How many Higg's fields.Bosons are there lol? I certainly don't know.

see alternate models, Higgs
The Minimal Standard Model as described above is the simplest known model for the Higgs mechanism with just one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector favoured by theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0, a CP-odd neutral Higgs boson A0, and two charged Higgs particles H±. Supersymmetry ("SUSY") also predicts relations between the Higgs-boson masses and the masses of the gauge bosons, and could accommodate a 125 GeV/c2 neutral Higgs boson.

http://en.wikipedia.org/wiki/Higgs_boson

The standard model is U(1)*SU(2)*SU(3) this portion has 4 Higg's particles including its anti particle

The SU(5)*SU(3)*SU(2)*U(1) MSSM needs 12 Higg's goldstone bosons forthe lie algebra if memory serves right. However I'm still learning lie algebra so I could be wrong.

So in that sense your correct in that its a different Higg's in a way lol Not sure how the SO(10) works yet but some of the numbers I've seen on it involve 72 higgs

What I'm getting at is that when you say that in some models the Higgs turns on earlier do you mean that other higgses turn on earlier or that the SM one does? I don't see why it would be that latter. We've probed the energies up to 10 TeV in accelerators, if new physics pushed the symmetry breaking scale to higher energies wouldn't we have seen it in accelerators? Since SM works at energies up to 10 TeV and there is a symmetry breaking phase transition at $T\sim \mathcal O(\text{100 GeV})$ in the SM then it must have happened in the early universe.

by the way wiki has the electroweak scale at 246 GeV, makes me wonder where the difference is (not that we can trust wiki 100%)

http://en.wikipedia.org/wiki/Electroweak_scale
could this be why?

"Physically, it describes the moment in our universe evolution when electric and
weak forces differentiate. At temperature scales above 100 GeV, MSM Lagrangian exhibits the gauge symmetry:"
SU(3)_c*SU(2)_L*U(1)_Y
SU(3)_c
refers to the color symmetry and plays no role in our rendition of the electroweak phase transition."
that was why I questioned the 100GeV value in post 6

246 GeV is the vacuum expectation value of the Higgs in the broken phase. The temperature at which the transition happens depends on the masses of the Higgs, weak gauge bosons and the top quark; see Mukhanov, equation (4.137). It will be somewhat different though of the same order. Also I said of order 100 GeV though perhaps I have neglected to continue to say that throughout all my posts.

Lawrence Krauss suggests SU(10) is favored by BICEP2 data - http://arxiv.org/abs/1404.0634.

While this essay did win the first prize in the Gravity Research Foundation contest, it feels somewhat numerological to me. BICEP2 suggests 10^16 GeV. You know where else I've seen that number? It's the unification scale if you assume supersymmetry with not too heavy superpartners and SO(10) GUT. Ergo BICEP2 favors SO(10)?

 

[Mordred]

I think you are quoting the MSSM GUT scale there (supposing your units are GeV). What does SUSY have to do with electroweak symmetry breaking?

the standard model is a good low energy approximation, however it does not explain right hand neutrinos, dark matter, there is also the proton decay problem. How does it even explain the Higg's mass at 125GeV?
the SO(10) (non SUSY) model does cover right hand neutrinos. There is also numerous papers dealing with electro-weak vacuum and how it could potentially tie into inflation.
but according to you the Higgs field is and I quote "off" above the electroweak scale. If that's the case then explain these articles. How can one define OFF when it obviously has influences above 246 GeV? A different Higg's that is a poor argument.

or its off, but its not off when your talking the GUT scale, that doesn't make one iota of sense. Considering the purpose of any particle physics model is to define and explain all the particles and their interactions at any temperature scale, GUT just happens to be one of the goals in that. Their are countless papers that discuss the limitations of the standard model. I've been posting numerous papers throughout this post that all mention the standard model limitations. Why do you think the standard model has extensions?

There is plenty of research going on, that show the Higg's interactions beyond what is defined by the standard model. The first set explains what it has to do with the electro-weak symmetry breaking.

"The exact way particles in the Standard Model obtain mass is a question to which various
answers exist but none has been shown to be true in experiment. One possibility in the
Standard Model is that particles obtain mass through spontaneous symmetry breaking at
the scale of the electroweak force. Spontaneous symmetry breaking can be understood with
a \Mexican hat" depicting a potential for a particle (see figure 1.1) where a ball (particle)
that is initially placed at the tip of the hat (maximum potential, i.e. at high energies) and is
symmetric under rotations takes up a specific value when it tips of the top of the hat into the
rim; the picture is then no longer invariant under rotations. Electroweak symmetry breaking
(EWSB), also called the Higg's mechanism, is the process of spontaneous symmetry breaking
through which gauge bosons in gauge theories acquire their mass. In this mechanism, they do
so through \eating" or absorbing so-called massless Nambu{Goldstone bosons. The simplest
implementation of this mechanism is addition of an extra Higg's field to the Standard Model.

http://phys.onmybike.nl/StrongEWSB.pdf

here is a book on it
"Electroweak Symmetry Breaking and New Physics at the TeV Scale"
http://www.worldscientific.com/worldscibooks/10.1142/3073

New Approaches to ElectroWeak Symmetry Breaking
http://lpsc.in2p3.fr/GDR-SUSY/tutorial_Annecy06/EWSB_1.pdf

ASI Lectures on Electroweak Symmetry Breaking from Extra Dimensions
http://arxiv.org/abs/hep-ph/0510275

http://arxiv.org/abs/hep-ph/9912343
"Electroweak symmetry breaking remains the foremost problem facing elementary particle
physics at this moment. We expect to come to understand it in scientific detail in the
next decade with the Tevatron and the LHC"
http://arxiv.org/pdf/hep-ph/9912343v3.pdf

Implications of LHC results for TeV-scale physics: signals of electroweak symmetry breaking
https://indico.cern.ch/event/173388/material/0/0.pdf

Electroweak Vacuum Stability in light of BICEP2
http://arxiv.org/abs/1403.6786
"Electroweak Vacuum (In)Stability in an Inflationary Universe"
http://arxiv.org/abs/1301.2846
"Higgs mass implications on the stability of the electroweak vacuum"
http://arxiv.org/pdf/1112.3022.pdf

 

[Mordred]

What I'm getting at is that when you say that in some models the Higgs turns on earlier do you mean that other higgses turn on earlier or that the SM one does? I don't see why it would be that latter. We've probed the energies up to 10 TeV in accelerators, if new physics pushed the symmetry breaking scale to higher energies wouldn't we have seen it in accelerators? Since SM works at energies up to 10 TeV and there is a symmetry breaking phase transition at $T\sim \mathcal O(\text{100 GeV})$ in the SM then it must have happened in the early universe.

246 GeV is the vacuum expectation value of the Higgs in the broken phase. The temperature at which the transition happens depends on the masses of the Higgs, weak gauge bosons and the top quark; see Mukhanov, equation (4.137).

.

The standard model only uses one Higg's field, The calculation of 246 Gev is only with one Higg's field. The research papers I posted in the previous threads, show the relations with the other potential Higg's fields and possibly the seesaw mechanism. (mexican hat).

keep in mind I was very clear that it depends on which model. The choice of models favored is up to the individual. My take is the Higg's sector has a lot of open questions, and more research is needed to truly make any statements one way or the other.

 

[bapowell]

but according to you the Higgs field is and I quote "off" above the electroweak scale. If that's the case then explain these articles. How can one define OFF when it obviously has influences above 246 GeV? A different Higg's that is a poor argument.

or its off, but its not off when your talking the GUT scale, that doesn't make one iota of sense. Considering the purpose of any particle physics model is to define and explain all the particles and their interactions at any temperature scale, GUT just happens to be one of the goals in that. Their are countless papers that discuss the limitations of the standard model. I've been posting numerous papers throughout this post that all mention the standard model limitations. Why do you think the standard model has extensions?

Slow down Mordred. Nobody is saying that the SM is complete, and that there isn't important unknown physics happening at and above the GUT scale. All I'm saying is that above the electroweak scale, the Higgs field responsible for breaking electroweak symmetry is *by definition* off, in the sense that the symmetry is restored. This is absolutely true at the GUT scale, as evidenced by the fact that GUT symmetry breaking occurs many orders of magnitude above the electroweak scale. Phsopher is saying the same thing: the Higgs is turned "on" when it acquires a VEV -- are you saying that the electroweak Higgs has a nonzero VEV above the electroweak scale?

I understand that SUSY corrections affect the electroweak scale a little bit, but not by orders of magnitude. This is why I'm confused over the discussion involving GUTs, SM extensions, etc. To be clear: it's not that these extensions aren't important, but I don't think they have much to do with the electroweak scale.

 

[phsopher]

.

The standard model only uses one Higg's field, The calculation of 246 Gev is only with one Higg's field. The research papers I posted in the previous threads, show the relations with the other potential Higg's fields and possibly the seesaw mechanism. (mexican hat).

keep in mind I was very clear that it depends on which model. The choice of models favored is up to the individual. My take is the Higg's sector has a lot of open questions, and more research is needed to truly make any statements one way or the other.

This doesn't really answer my question, which was that if new physics modifies the electroweak dynamics, such as to push the EW phase transition to higher energies, wouldn't we already have seen that at accelerators. There is no evidence of new physics up to energies of about 10 TeV. Like, bapowell is saying, this doesn't mean that there is no new physics beyond those incuding GUTs or whatever. What I don't understand is why the electroweak phase transition prediction would be modified given the fact that the SM is well tested up to the energies where it is supposed to happen and there is no evidence that beyond standard model physics have any effect at these energies.

 

[Mordred]

The Higg's sector isn't well tested is my understanding. Is the one Higg's mass the only one? Isn't some of the predictions also looking for a 115 GeV Higg's.

On 4 July 2012, the ATLAS and CMS experiments at CERN's Large Hadron Collider announced they had each observed a new particle in the mass region around 126 GeV. This particle is consistent with the Higgs boson but it will take further work to determine whether or not it is the Higgs boson predicted by the Standard Model. The Higgs boson, as proposed within the Standard Model, is the simplest manifestation of the Brout-Englert-Higgs mechanism. Other types of Higgs bosons are predicted by other theories that go beyond the Standard Model.

this research isn't completed yet AFIAK

http://home.web.cern.ch/topics/higgs-boson

 

[bapowell]

Yes, I agree Mordred -- there is very much still to explore regarding the Higgs sector. But my understanding is that the electroweak scale is well pegged, and something happens when this symmetry gets broken. Now, there may well be more than 1 Higgs, but that part of the sector responsible for the phase transition is associated with this energy scale, and is restored at higher energies.

 

[Mordred]

Thats where I am still trying to figure out the seesaw mechanism in SO(10) as it appears to affect the coupling constants. Also the left hand neutrinos and right hand neutrinos appear to gain mass differently. One side gains mass as temperature increases. The other side loses mass at increasing temperatures. The seesaw mechanism is determined by 2higgs doublets. Its admittedly a new model for me so I may have that misunderstood. However if that understanding is correct doesn't that affect the electroweak symmetry? Some of the papers in regards to electroweak symmetry in the TeV scale suggest that is the case


Edit this has some implications.

The seesaw mechanism must have Ma in the TeV range. In the SO(10) otherwise the right hand higgs will decouple.

The seesaw mechanism has a left hand and a right hand Higgs.

 

[Mordred]

figured it out. There is not one but two types of electroweak symmetry breaking.
radiative electroweak symmetry breaking is not the same as the conventional symmetry breaking.

"The mechanism of radiative electroweak symmetry breaking occurs through loop corrections, and unlike conventional symmetry breaking where the Higgs mass is a parameter, the radiatively generated Higgs mass is dynamically predicted."

http://arxiv.org/pdf/1209.5416v3.pdf

http://arxiv.org/pdf/hep-ph/9504239v2.pdf

that applies to the MSSM model. oft termed soft breaking. the MSSM GUT papaer I posted in my opening post in the summary mentions two GUT breakings. One at a higher scale than the other. However it considers the conventional one incomplete due to Higg's meta instabilities above roughly 10¹¹GeV

I'll have to see how it applies in the So(10)

 

[Mordred]

there found the difference between the how the TeV affects VeV.

"The vacuum corresponds to the groundstate with minimal potential energy and zero kinetic energy. At high enough temperatures the thermal fluctuations of the Higgs particles about the groundstate become so strong that the coherence is lost, i.e. Φ(x) =constant is not true anymore"

"Both, the fermion and gauge boson masses are generated through the interaction with the Higgs field. Since the interactions are proportional to the coupling
constants, one finds a relation between masses and coupling constants. For the
fermions the Yukawa coupling constant is proportional to the fermion mass and the mass ratio of the W and Z bosons is only dependent on the electroweak mixing angle (see eq. 2.28). This mass relation is in excellent agreement with experimental data after including radiative corrections. Hence, it is the first indirect evidence that the gauge bosons masses are indeed generated by the interaction with a scalar field, since otherwise there is no reason to expect the masses of the charged and neutral gauge bosons to be related in such a specific way via the couplings."
then it explains G cannot be the direct product of the SU(3), SU(2) and U(1) groups, since this would not represent a new unified force with a single coupling constant, but still require three independent coupling constants.

The problems mentioned above can be partly solved by assuming the symmetry
groups SU(3)C⊗SU(2)L⊗U(1)Y are part of a larger group G, i.e.GC SU(3)C⊗SU(2)L⊗U(1)Y
.
(3.1)
The smallest group G is the SU(5) group 1[29], so the minimal extension of the SM towards a GUT is based on the SU(5) group. Throughout this paper we will only consider this minimal extension. The group G has a single coupling constant for all interactions and the observed differences in the couplings at low energy are caused by radiative corrections. As discussed before, the strong coupling constant decreases with increasing energy, while the electromagnetic one increases with
energy, so that at some high energy they will become equal. Since the changes with energy are only logarithmic (eq. 2.45), the unification scale is high, namely of the order of 10¹⁵−10¹⁶ GeV, depending on the assumed particle content in the loop diagrams

That's difference, and where the TeV scale is needed to explore the thermal fluctuations and dynamics of the Higg's particle. In the SUSY GUT models and the SO(10) model, as well as explains the nature behind those articles I posted in.

However the Higg's interactions are described at the TeV scale much higher than VeV=246.
in both SUSY GUT and SO(10) Susy and non SuSY models. So in terms of just the standard model excluding any locality and global issues then VeV would be when the Higg's first turns on.

In the TeV range this isn't true anymore as the Higg's interactions are used outside the standard model exclusive particles in the SUSY, and the Higg's is used for the SO(10) and SU(5) with different Higg's masses at each symmetry breaking step until you reach the standard model particles which used the 126 Higg's were all familiar with.
not to mention this reason
"The vacuum corresponds to the ground state with minimal potential energy and zero kinetic energy. At high enough temperatures the thermal fluctuations of the Higg's particles about the ground state become so strong that the coherence is lost, i.e. Φ(x) =constant is not true anymore"

as well as "The mechanism of radiative electroweak symmetry breaking occurs through loop corrections, and unlike conventional symmetry breaking where the Higgs mass is a parameter, the radiatively generated Higgs mass is dynamically predicted." hence different Higg's masses used at different stages of symmetry breaking.

edit: I also need to retract the statement of electroweak symmetry occurring at 10¹⁵
due to misunderstanding the difference between the SM VeV value and radiative electroweak symmetry breaking