Effective Mass-to-Charge Ratio of Electroweak or QED Vacuum

[SonnetsAndMath]

Apologies if my question is confused, because I'm beginner in field theory: adding up all corrections, can we talk about an effective (at least approximate) overall mass-to-charge ratio for the electroweak or QED vacuums?

Suppose we want to talk about the relative strength of electric-to-gravitational vacuum polarization effects on the QED or electroweak vacuum. I realize I might already be in speculative territory with gravitational vacuum polarization effects, but I expect there to be some ratio between the coupling constants for the vacuum, between inverse square laws that couple to the mass and the charge respectively. (For my purposes, the Newtonian limit of gravity might be sufficient, here.)

I'd expect the ratio for the QED vacuum, and maybe the electroweak, to be on order of the electron's or the proton's mass-to-charge ratio, but it'd be extremely helpful if someone could point me to one or more sources for a more accurate estimate. I'm having difficulty finding this on the internet in general, perhaps because I don't know what search terms to use.

 

[SonnetsAndMath]

Maybe it would help the forum answer my question, or help someone else looking for an answer to a similar question, if I explained some of what I've worked out toward this end.

First of all, I assume that the temperature of a massless boson gas is high enough that particles of the Standard Model are available to the breakdown of a typical particle in the gas. However, the temperature is also below electroweak unification scale. For the specific prediction I'm attempting to make, the temperature of the boson gas I need to work with is approximately 6.5 trillion K. This boson gas can be assumed (approximately or exactly) only to interact gravitationally, not electromagnetically. (Suppose it's a "toy" dark matter/energy candidate. Actually, it's both this and a hypothetical graviton.)

What I'm trying to quantify is its gravitational effect on the apparent (Standard Model) vacuum. We know that a high energy photon gas can polarize the vacuum, while a mechanism for gravitational polarization of the vacuum might not be clear. However, we can say that the energy density of the electric field of the gas couples to the square of the charge:
$$E_e \sim -\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r},$$
while (approximately) the energy density of the gravitational field of the gas couples to the square of the mass:
$$E_g \sim -G \frac{m_1 m_2}{r}.$$
In Planck units, we take both force constants as equal to one, and the relative coupling of the respective field energies of the gas to the vacuum should be some function of Standard Model squared natural charges over squared natural masses.

Numerically, the sum of the squared charges over the sum of the squared masses of every particle species in the Standard Model seems to hit my target. (With or without my hypothetical graviton candidate included.) Is the sum of the squared masses over of the sum of the squared charges, for every particle in the Standard Model, a meaningful quantification of the relative strength of electromagnetism and gravity on the vacuum? Again, we are assuming all particles of the Standard Model are available to the high temperature gas, but we are significantly below electroweak unification temperature.

(Thank you in advance for your help.)

 

[mitchell porter]

If I were trying to calculate gravitational vacuum polarization, I might start semiclassical (QFT in curved space-time), and then once I had some idea of what I was doing, I'd try to repeat the calculation in terms of gravitons.

However, what really caught my attention is "the sum of the squared masses of every particle species in the Standard Model" - since that quantity is not so far from the square of the Higgs vev.

 

[SonnetsAndMath]

Thank you for the response. My cosmology with this model is extremely unstable, which probably indicates that I have to abandon it as posed, which might indicate that the factor I mentioned is purely ad hoc. (There are other ways to proceed, but not in terms of vacuum polarization, for now.)

 

[fresh_42]

Closed on pending moderation.

My cosmology with this model is extremely unstable, which probably indicates ...

Please make sure to stay on the mainstream, scientific side of the line. Personal theories must have been published in a reputable journal before they were allowed to discuss on PF. Of course scientific discussions in general sometimes touch this line, especially at the boundaries of reserach. If in doubt, please support your arguments by appropriate quotations.

Thread re-opened.