Does the CC depend on symmetry breaking?

[friend]

I wonder if symmetry breaking of the U(1)SU(2)SU(3) symmetries of the standard model have anything to do with the calculation of the cosmological constant. Do we assume that the symmetries are broken or unbroken in the current calculation of the CC?

As I recall, one way symmetry is broken in the SM is by changes in the potentials in the lagrangian. And I suppose that setting the potentials to zero or a constant value would change the calculation of the CC. I wonder if this would be enough to account for the 120 orders of magnitude between calculated and observed values of the CC.

Any thoughts on the subject would be appreciated. Thanks in advance.

 

[friend]

Correct me if I'm wrong, but it does seem as though the lesser the real particle density there is in the universe the faster its acceleration of expansion. In the original inflation the universe was dominated by the inflaton field that drove an exponential rate of expansion until the field collapsed into particles at which time the universe ceased accelerating in its expansion. And at late times the particle density has decreased, and expansion has accelerated again.

So with particles representing isolated sources of potential, be it gravitational or electric or color charges, this causes there to be changes in potential that breaks symmetry. I wonder how this influences the calculation of the CC. This example seems to indicate that the less the potential changes the more the acceleration rate.

 

[friend]

For starters, if we were to set all potentials to zero in the lagrangian, would the CC be infinite or zero?

 

[bapowell]

For starters, if we were to set all potentials to zero in the lagrangian, would the CC be infinite or zero?

What do you mean by "set all potentials to zero"? The Higgs potential is zero at the VEV of the field; while the VEV is nonzero. Is this what you're talking about?

 

[friend]

What do you mean by "set all potentials to zero"? The Higgs potential is zero at the VEV of the field; while the VEV is nonzero. Is this what you're talking about?

I'm not sure how they calculate the cosmological constant in QFT. If I remember right, it is the vacuum energy of all the various quantum fields that exist. By vacuum energy, I think that means no particles and no sources of potential. And we get a CC calculated to be 120 orders of magnitude more than observed.

If there are no potential energy sources involved in the vacuum energy, does that mean that the standard model symmetries are not broken in the usual calculation for the CC? Or maybe this is a separate issue.

 

[bapowell]

The CC is calculated in QFT by summing the zero-point energies of all modes of each field up to some prescribed cut off, generally taken to be the Planck scale. This calculation, since it pertains to the current universe, is done with the Standard Model symmetries broken, i.e. the masses of leptons are included. But, since these masses are so tiny relative to the cut off, they could probably be assumed to be zero without affecting the result. In other words, the huge vacuum energy associated with the SM particles is due to the large UV cutoff of the theory.

 

[suprised]

I And I suppose that setting the potentials to zero or a constant value would change the calculation of the CC..

Sure it does. But there are several contributions to the CC, the vacuum energy of the Higgs field at the minimum of its potential is just one. There is no meaning in particle field theory of the absolute value, so a constant term can always be added. In gravity, that term matters however. A version of the fine tuning problem is that the natural value would be in the order of the characteristic scale of that symmetry breaking, say 100GeV, while the value of the CC is many orders of magnitude smaller. So there is no good rationale to choose this small value.

In Susy theories, the vacuum energy at a minimum with unbroken Susy is zero, and this was one of the main motivations for studying Susy field theories in flat space; in particular at those times when it was thought that the CC in Nature would be zero.

But that doesn't really help - the problem reappers when considering the chiral symmertry breaking in QCD via the quark condensate, just at a lower scale, where Susy is broken anyway (near 1GeV, say).

In addition, there a quantum corrections to the vacuum energy, the leading being the 1-loop correction which is divergent in QFT, except when it is forbidden by supersymmetry again. But fine tuning problems reappear the moment Susy is brokken. In string theory the quantum corrections to the CC are at least finite and not divergent, but still the fine tuning problem is there. There were a lot of toy models trying to generate a hierarchy by non-perturbatve effects etc.

So it seems that the problem of the CC is of a different nature than what can be captured in particle field theory, and that was a wrong track. Most likely it can't be addressed without a full theory of quantum gravity. Some ideas were tested in string theory, apart from anthropic arguments (ie, novel kind of stringy symmetries that prohibit a CC despite broken Susy, but nothing ever really worked out).

 

[friend]

Thanks guys. I feel like I'm learning something. I only dabble in physics for it philosophical value, and I have my own way of looking at things. I don't have a complete picture, and it's nice to get some perspective from people like you.

The CC is calculated in QFT by summing the zero-point energies of all modes of each field up to some prescribed cut off, generally taken to be the Planck scale. This calculation, since it pertains to the current universe, is done with the Standard Model symmetries broken, i.e. the masses of leptons are included.

So am I to understand that the Higgs mechanism is applicable to the virtual particles of the vacuum energy of the CC?

A version of the fine tuning problem is that the natural value would be in the order of the characteristic scale of that symmetry breaking, say 100GeV, while the value of the CC is many orders of magnitude smaller.

This makes it sound as if the scale of symmetry breaking (and thus whether there is breaking or not) is extremely relevant to the calculated value of the CC. Is this correct?

Thanks.

 

[bapowell]

A version of the fine tuning problem is that the natural value would be in the order of the characteristic scale of that symmetry breaking, say 100GeV, while the value of the CC is many orders of magnitude smaller. So there is no good rationale to choose this small value.

This is confusing. Why should the energy of the true vacuum have anything whatever to do with the scale of the SSB? Why is it "natural" to expect they'd be of similar magnitude?

 

[bapowell]

So am I to understand that the Higgs mechanism is applicable to the virtual particles of the vacuum energy of the CC?

Yes, to the extent that massive particles that get their mass from the Higgs are included in the summation.

 

[friend]

Yes, to the extent that massive particles that get their mass from the Higgs are included in the summation.

As I understand it, there is some expectation value for the higg field to interact with a particle field per unit of time and provide mass to the virtual particle. And there is the expectation value for the life of a virtual particle. Is it true that it is very likely that a particle will interact with the higgs and gain mass during the time that the virtual particle exists? And if so, then is this still true at higher energy virtual particles that exist for a shorter time? It would seem that at high enough energies there would be a decreased likelyhood that a virtual particle would gain mass. And if this is true, then I assume this would mean that higher energy modes would contribute less to the CC then before, since they might not have time to gain mass and thus energy. Is this taken into account, or am I way off here?

 

[bapowell]

There is no probability associated with the interaction between a particular quantum field and the Higgs. The interaction appears as an explicit coupling between the quantum field and the Higgs VEV in the dynamics, and so it applies to real and virtual excitations alike at all times and energy scales (up to the cut off of the theory, of course).

 

[suprised]

This is confusing. Why should the energy of the true vacuum have anything whatever to do with the scale of the SSB? Why is it "natural" to expect they'd be of similar magnitude?

Well in a generic potential with coeffs of order one, with regard to some scale, that's what you get.

 

[friend]

This is confusing. Why should the energy of the true vacuum have anything whatever to do with the scale of the SSB? Why is it "natural" to expect they'd be of similar magnitude?

There is no probability associated with the interaction between a particular quantum field and the Higgs.

Just a moment. I'm not quite convinced. As I recall, there is an energy scale at which symmetry is unbroken because the higgs does not interact to give mass to particles that produces the generations of mass that breaks symmetry. So this seems to indicate that the higgs mechanism is energy dependent. I'm also thinking in terms of other particle interactions that have a cross section and a probability of interaction. So when I think of higgs bosons interacting with electrons, I think of interaction rates... that might depend on how long the particle exists. At least this is the picture I got from somewhere. Or I could be misinformed. Maybe you could give other kinds of particle interaction examples to support your point so I don't think this higgs mechanism is a special case. Maybe you can construct a summary. I could use the reminder. Thanks. I do appreciate your efforts.

 

[friend]

Well in a generic potential with coeffs of order one, with regard to some scale, that's what you get.

Yea... that reminds me of how the interaction strength changes with energy. Isn't that what unification is all about with screening effects changing with energy scale? Doesn't that also mean that the coupling constants are changing with energy scale, "running of the constants" and all that? And doesn't that effect interaction rates? I don't remember exactly. Could use some confirmation one way or the other.

Anyway, if the higgs boson is 125Gev, there is plenty of room between that and the GUT scale. So does the coupling constants with the higgs field change between 125GeV and the GUT scale as well? Or more generally, do they take into account the running of the constants in the calculation of the CC?

 

[bapowell]

Just a moment. I'm not quite convinced. As I recall, there is an energy scale at which symmetry is unbroken because the higgs does not interact to give mass to particles that produces the generations of mass that breaks symmetry. So this seems to indicate that the higgs mechanism is energy dependent.

It is, but the energy relevant to symmetry breaking is the ambient energy of the universe -- essentially the thermal energy associated with the particles that the Higgs is in contact with. The so-called "temperature-corrected" Higgs potential is symmetric; only after the temperature of the universe drops does it develop a false vacuum.

I'm also thinking in terms of other particle interactions that have a cross section and a probability of interaction. So when I think of higgs bosons interacting with electrons, I think of interaction rates... that might depend on how long the particle exists. At least this is the picture I got from somewhere. Or I could be misinformed.

That's the correct picture when imagining how Higgs bosons -- the particles themselves -- interact with other particles, like electrons. But the mass generated via the Higgs arises as a result of the interaction of particles and the Higgs field, which happens to have a nonzero value in space (the VEV). When I wrote earlier about there being no probability associated with the interaction, I was referring to the coupling between quantum fields and the Higgs VEV -- not Yukawa-type couplings between the other quantum fields and the Higgs field. My mistake, sorry for the confusion.

 

[suprised]

Yea... that reminds me of how the interaction strength changes with energy. Isn't that what unification is all about with screening effects changing with energy scale? Doesn't that also mean that the coupling constants are changing with energy scale, "running of the constants" and all that? And doesn't that effect interaction rates? I don't remember exactly. Could use some confirmation one way or the other.

Anyway, if the higgs boson is 125Gev, there is plenty of room between that and the GUT scale. So does the coupling constants with the higgs field change between 125GeV and the GUT scale as well? Or more generally, do they take into account the running of the constants in the calculation of the CC?

Sure, there is the usual renormalization taking place. But there is no "calculation" of the CC in particle field theory, because the first quantum correction is infinite anyway. So you can attribute any number to it, whatever you like, since it is undetermined in field theory (unless if you assume unbroken SUSY in flat space, when it is zero; or you may softly break SUSY and then compute it).

Whatever, as said this problem most likely cannot be properly addressed, much less solved, in particle field theory alone, this attempt appears to have been the wrong starting point.

 

[friend]

Whatever, as said this problem most likely cannot be properly addressed, much less solved, in particle field theory alone, this attempt appears to have been the wrong starting point.

You seem to be suggesting that new physics is needed to solve the CC problem. Do you have any favorite theories as to what that might be? I would perfer to think we may be doing something wrong in our current calculations and exhaust that option before trying something completely new.

For example, we're told that all the forces unite at the GUT scale. And I'm told that the UV divergence cause a higher than measured CC. But if everything unites at the GUT, I wonder how that unified field would contribute to the CC from the GUT scale to the Planck scale. (How many orders of magnitude is that?) Would the first quantum corrections diverge for that unified field? I know that bapowell would say that the unified field is only applicable in hot environments, not the present environment. But I'm accustomed to thinking of temperature in terms of the average energy of particles as they collide. So I would have a tendency to consider the unified field even when the virtual particles of the vacuum are colliding with each other at those energy levels.