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Electroweak unification is discussed in the Big Bang model and variant proposals, and there is a transition at energies of 100 GeV where the EW symmetry is unbroken and a quark gluon plasma phase dominates.

In my answer to the question

>What accelerator energies and types would be needed to explore electroweak unification, and if accessible, what would be the likely observables?

the relevant plots for this question can be found and links for the progress of phenomenology up to now.

It was not possible to find any reference to electroweak symmetry breaking in the models proposed to fit the LHC experiments plasma data, even though the claim is that the quark gluon plasma studies the early stages of the universe.

In this proposal for the proposed future FCC collider I found that even for its high energies the mean energy density is less than the 100 GeV seen in the Big Bang histories, it will be of order 40GeV, while LHC plasmas are of order 20GeV energy density.

The phase diagram which includes quark gluon plasma explains this , quark gluon plasma is necessary but not sufficient for electroweak symmetry to be restored.

BUT the lab experiments are nucleus on nucleus, individual measurements. As it is a quantum phenomenon, there should be the tail of phase space at high energies which would have higher energy densities, even to 100 GeV , considering the TeV available at LHC. Those specific interactions should have crossed the 100 GeV , and the symmetry should be restored.

This means among other things that all quarks produced will have zero mass. As a consequence the probability of getting flavor particle antiparticle pairs should be equal. For example a top-antitop would have the same probability to be created as a bottom anti-bottom or as charm anti-charm in the final jet output from the plasma.

There have been differences found in various production rates, but nowhere did I find a hint that restoration of electroweak symmetry could be contributing to this in the phenomenological models used.

My question is: am I wrong? because I did not go into the models carefully?

Is the contribution of restoration of electroweak symmetry in the tails of distributions taken into account in the quark gluon plasma phenomenology for LHC energies, and it is not statistically expected to be detectable?

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The QGP is a macroscopic system, and the main source of fluctuations is ordinary thermal fluctuations. This means that we can use the standard text book formula $$ \Delta E =\sqrt{k_BT^2C_V} $$ for fluctuations of the energy. Here, $C_V$ is the specific heat at constant volume. Let's take a non-interacting equation of state $$ \epsilon = N_d \frac{\pi^2}{30}T^4 $$ where $\epsilon=E/V$ is the energy density, and $N_d$ is the number of degrees of freedom. Then $$ \frac{\Delta E}{E}=\frac{2}{\pi}\sqrt{\frac{30}{N_d}} \frac{1}{\sqrt{T^3V}} $$ For illustration let's take $T=300$ MeV, $V=1\,{\rm fm}^3$ (a little bigger than the size of a proton), and $N_d=37$. I get a mean energy of about 12 GeV, and fluctuations $\Delta E/E\sim 30\%$. These are sizeable fluctuations, but $\epsilon \sim (200 GeV)^4$, required for the EW phase transition, corresponds to $10^{11}$ $GeV/{\rm fm}^3$. This is a fluctuation by more than $10^{10}$ sigma!

At this point the whole estimate is of course a little questionable. This is in the tail of the distribution, where, indeed, quantum fluctuations are presumably more important than thermal fluctuations. More importantly, I assumed a canonical distribution, but I looked for a fluctuation in which the total energy in a $1\,{\rm fm}^3$ volume is bigger than the energy available in the nucleus-nucleus collision (about 2000 TeV).

This suggests that I should probably think about this differently. What I am asking for is not an energy fluctuation, but a volume fluctuation. I have a total energy available of about 2000 TeV, and I am asking whether the system can fluctuate to a volume so that the local energy density in that volume is above the critical energy density for the EW phase transition (about $(200\,{\rm GeV})^4$). The volume is about $(0.02\,{\rm fm})^3$, so I am asking that the colliding nuclei (radius about 5 fm) fluctuate down in size to about 0.02 fm. This probability is not zero (I could try to estimate it along the lines of estimating exclusive hard scattering reactions in QCD), but it is clearly very, very small.

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  • $\begingroup$ where did you get the fourth power? it is not in the formula. also a fermi is 10^-15 meters $\endgroup$ – anna v May 6 at 13:43
  • $\begingroup$ The critical temperature of the EW phase transition is $O(100\, GeV)$, so the critical energy density is $O((100\, GeV)^4)$. $\endgroup$ – Thomas May 6 at 15:00
  • $\begingroup$ " $$ \epsilon = N_d \frac{\pi^2}{30}T^$ $$is the $ in the exponent of the temperature supposed to be "4" ? you give no links to check. $\endgroup$ – anna v May 6 at 19:36
  • $\begingroup$ Should be 4, simply Stefan-Boltzmann for noninteracting Bosons/Fermions $\endgroup$ – Thomas May 6 at 23:27

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