Thermodynamics of the Higg's Mechanism

JPBenowitz

As I was taught in my modern physics class the Higg's Field acts like an ideal ferromagnet cooling down to some constant and thus invoking spontaneous symmetry breaking. The process of the Higg's Field cooling down is modeled by the Mexican Hat Potential. What I do not understand about the Higg's Mechanism is the thermodynamics of the field. For the field to cool down it must give off latent heat in the form of particle-antiparticle pairs. These decay channels are dependent upon the Higg's Bosons mass but nevertheless all decay channels are completely comprised of massive particles. So my question is how would the Higg's Field cool down if the Higg's Boson decays into particles it will thereafter instantaneously interact with? Does this necessitate multiple Higg's Fields?

Bill_K

The Higgs field cools down because the Big Bang cools down. THe Big Bang cools down because the universe expands, converting thermal energy into gravitational potential energy.

DrDu

Why? A Higgs particle can also loose energy in scattering with light particles like electrons etc.

JPBenowitz

The problem is that the electron interacts with the Higg's Field and in order for the field to lose a net energy wouldn't it be forced to decay into a particle it does not interact with? The Higg's can decay into photons but as an educated guess I would assume there isn't enough radiation in the universe left over from the initial cooling of the Higg's Field. The Higg's couldn't decay into an electron and a photon due to conservation of charge so where does the extra energy go?

JPBenowitz

The Higg's "Field" is infinite in all directions. It was present before the Big Bang just not at its critical temperature thus having no apparent affect in quantum field theory.

JPBenowitz

Then again... as the scale of the universe gets smaller photons have much more energy so my initial assumption isn't the greatest. But there are two other possibilities, the Higg's doesn't interact with the elusive graviton or gluons.

DrDu

Why? When you fire a bullet into a tank of water, it will transfer its energy to the water molecules precisely because it interacts with them. It is not necessary to create new particles to dissipate energy.

JPBenowitz

We aren't talking about kinetic energy. As I understand the Higg's Field does not behave as a dissipative force like friction. Think of it as an ideal gas in an excited state extending infinitely in all directions emitting photons periodically. In order for this body to cool down its ground state must require more energy than is being released per photon otherwise its average temperature would remain constant. If it is not necessary for a field to dissipate energy in the form of particles how do fields dissipate energy in Quantum Field Theory then?

DrDu

Why not? You seem to imagine a field as a strange object which behaves miraculously different from any other thermodynamic object.

JPBenowitz

So Quantum Fields behave thermodynamically exactly like an ordinary object? How does a field dissipate energy other than decaying into particles?

DrDu

Scattering. Take Compton scattering as an example. There an incoming electromagnetic wave (field) of energy hf is scattered into a wave with lower energy hf'.
In the same way, Higgs bosons may scatter from other particles and reduce their kinetic energy.
Once the gas of Higgs bosons is cold enought scattering of Higgs bosons from each other becomes increasingly important which leads to symmetry breaking.

JPBenowitz

This can't be right though. The Higg's Boson is an excitation of the Higg's Field, it's a virtual particle that violates m^2c^4 = E^2-p^2c^2 such that its energy and momentum are unknown due to the Uncertainty Principle. Mathematically the Higg's Boson doesn't appear as an indices to a scattering matrix they are apart of perturbation theory. You can measure the kinetic energy of the outgoing particles but this doesn't necessarily tell you anything about the kinetic energy of the Higg's due to its violation of energy-momentum.

DrDu

I also read again your original question and I think I understand your problem right now. The Higgs Bosons before symmetry breaking are massless. The new vacuum after symmetry breaking has a finite density of the original Higgs bosons (Consider the ground state of a shifted harmonic oscillator H=p^2+(q-a)^2: calculate the mean number of quanta with that wavefunction for an unshifted Hamiltonian H=p^2+q^2) . It is these original Higgs bosons with which other particles interact when they become massive. When symmetry breaking proceeds, either existing Higgs particles (whether real or virtual) can get scattered into the ground state or new ground state Higgs bosons are directly created when two other particles anihilate.

JPBenowitz

Right, I forgot to clarify that I am strictly speaking of the Higg's Field during symmetry breaking of the inflationary epoch. The Higg's Field is a nonthermal field meaning it does not lose energy as the universe expands and thus is a causal candidate for inflation. My question remains as to what was the initial process that allowed the Higg's Field's energy to reach its nonzero value. In other words is it possible the decay channels evolved during this period for the initial cooling of the field?

JPBenowitz

I'm sorry that was a dumb question haha, of course the decay channels evolved because the very particles the Higg's decays into first have to be created! So I guess my final question is could the elusive dark matter / dark energy particle be hiding in the decay channels of the Higg's in the very early universe?

JPBenowitz

Are there any papers anyone knows of dealing with the mechanism of which the Higg's Field cooled down during the inflationary epoch?

Skitto

I'm thinking the answer would have something to do with what would cause the start of a fractal pattern, the life source of a tree, the equation of the Mandelbrot set, the core, the bang itself and what caused it.