Strong Coupling Constant: E, Quark, Unification

[kurious]

The strong coupling constant is given by
a (E)= 12 PI/ (33 - 2NF) H [E^2 / LAMBDA^2

nf = number of quarks in pair production.
Three questions:
What is E the energy of?
If there were more than six quarks how would this affect the strong coupling constant?
If forces can be unified why doesn't the electric coupling constant vary too?

 

[vanesch]

E is the energy scale at which we use our renormalized perturbation expansion ; it should be "close" to the energy of the real or virtual particles considered.
Let me explain:
you know that the non-renormalized perturbation series can be written down, but diverges for non-trivial values of the bare coupling. By rewriting the bare coupling as a function of the "actual" coupling (by inverting the functional relationship between the bare coupling and a "defining interaction" at a certain energy) we find finite expressions for the perturbation terms - this is the procedure of renormalization. However, it turns out that if you then want to use this expansion for interactions far away from the defining energy scale, you need to use a lot of terms (a lot of higher order Feynman diagrams), which is a pain. So you can now displace the "defining interaction energy" to another scale, but then of course you will find another relationship between the (redefined) actual coupling and the bare coupling ; or if you prefer, between the redefined actual coupling, and the original coupling at the original defining scale. This relationship is what you wrote down.
The nice thing is that if you work in the neighbourhood of the redefined scale with the redefined coupling, then you don't need as much diagrams to get to the same result (more or less).

In QCD it is a bit complicated, but let us take QED as an example:
there is a natural scale to define the EM coupling: that is for two electrons at rest at large distance, we want to find back Coulomb's law (with its coefficient e^2/4pi epsilon_0).
So the original defining scale is the rest mass of the electron in an electron-electron interaction. It is the original definition of alpha_0.
If you now use that alpha_0 to consider electron-positron collisions at 500 GeV, you need to sum quite some diagrams ; however, if you *redefine* alpha(500GeV) as what you would have for an electron-electron interaction at that energy, and you work it out as a function of alpha_0 (in order to do so you have to sum several diagrams of course), then an electron-positron interaction at 500 GeV (or 400 or 600 GeV for that matter) will already give you a good result when calculated at treelevel, with alpha(500GeV).

This is the "rescaling" of the coupling constant, and the resulting "running of the coupling constant".

cheers,
Patrick.

 

[kurious]

coupling constant

Does the force between nucleons increases if the number of quarks in the equation is greater?
Also, is this a strong coupling constant only or does it account for the colour force too?

 

[vanesch]

The coupling constant you've written down is the QCD coupling constant, so the colour coupling constant. There is not really such a thing as a "strong coupling constant" for the strong force between nucleons, because that force is believed to be a kind of "remnant" force of the colour force, a bit such as Van der Waals forces between neutral molecules (for example making up ice) are remnant forces of the electromagnetic interaction between nucleae and electrons, the stray field, say. That's why nuclear physics is so difficult, theoretically, and why people resort to all kinds of phenomenological models.

cheers,
Patrick.

 

[kurious]

colour force

Surely there is something wrong with using a colour force to describe quark interactions and this makes unification theories hard to achieve.
Colour charge is constantly changing but electric charge and rest mass are
stable parameters.Perhaps the reason why the colour force is so strong
relates to the reason why gravity is stronger than we'd expect from Newtonian principles.Perhaps the colour force needs to be more relativistic.

 

[selfAdjoint]

Surely there is something wrong with using a colour force to describe quark interactions and this makes unification theories hard to achieve.
Colour charge is constantly changing but electric charge and rest mass are
stable parameters.Perhaps the reason why the colour force is so strong
relates to the reason why gravity is stronger than we'd expect from Newtonian principles.Perhaps the colour force needs to be more relativistic.

The reasons that color force behaves the way it does are all well-understood in the Standard model. The reasons electric charge does what it does are also well understood in terms of this model. It all hangs together very well. Bringing gravity into it would mess up all the finely tuned logic, and really isn't necessary at all.

Your objections arise because you are trying to apply over-simple logic to a system you don't fully understand yet. Recall Einstein's saying: Everything should be made as simple as possible, BUT NO SIMPLER!

 

[kurious]

colour force

I do understand the establishment's version of the colour force.
However, a theory that relies on computers to make predictions - IBM were called into predict the mass of a glueball- doesn't sound like a theory to me!
I think people only accept qcd because they haven't got an alternative which won't blow the standard model-and its 20 or so experimentally obtained input parameters- to pieces.

 

[vanesch]

However, a theory that relies on computers to make predictions - IBM were called into predict the mass of a glueball- doesn't sound like a theory to me!

I don't understand the logic of that statement, unless you claim that beyond a certain computational complexity (limited by what can be done on 10 pages of paper with a pencil) nature can't be described. What's the point ?
A lot of modern science and technology requires computer computations, such as finite element modelling, Monte Carlo integration etc..., what's wrong with that ?

cheers,
Patrick.

 

[kurious]

computations and quark mass

The standard model can't predict the rest masses of all known and unknown particles - something is missing from it.I have found an equation by trial and error that predicts all quark masses:




EQUATION THAT PREDICTS QUARK REST MASSES

The following equation generates the masses, in Gev, associated with the six quarks:
Down, up, strange, charm, bottom, top and predicts the masses of two new quarks labelled X1 and X2.


M = 12.50 x 10 ^3pi(n – 5) / 2 0 x ( n – 4 ) ^2 x 10 ^39( n – 3 ) / 2 x 10^ 57 x q ^n (5)

M = f (n) q n

Where n is an odd numbered integer and q is the magnitude of the electric charge associated with the mass. The equation was based on the idea that
mass = constant x q n and that the constant depends on n and is different for each quark pair - the pairs are next to each other in the table.



QUARK CHARGE n MASS (Gev) )

DOWN - 1/3 -1 0.0088

UP + 2/3 -1 0.0044

X1 -1/3 +1 0.084

X2 +2/3 +1 0.16

STRANGE -1/3 +3 0.21

CHARM +2/3 +3 1.72

BOTTOM -1/3 +5 5.20

TOP +2/3 +5 167.25

I now understand why this equation works and I am going to submit it to a journal later in the year.The quark at N= +1 doesn't exist because of the colour force .This equation enables the rest mass of the muon to be predicted accurately too! Basically the constant k bypasses the need to do quantum field theory.

 

[vanesch]

M = 12.50 x 10 3pi (n – 5) / 2 0 x ( n – 4 ) 2 x 10 39 ( n – 3 ) / 2 x 10 57 x q n

Could you retype your equation, because as such it is not very readable.
If I interpret it the way it is written as a product, M = 0 for n = 5 and n = 3.
So this can't be what you mean. I guess you mean a SUM of terms.

cheers,
Patrick.

 

[kurious]

retyped equation

The standard model can't predict the rest masses of all known and unknown particles - something is missing from it.I have found an equation by trial and error that predicts all quark masses:




EQUATION THAT PREDICTS QUARK REST MASSES

The following equation generates the masses, in Gev, associated with the six quarks:
Down, up, strange, charm, bottom, top and predicts the masses of two new quarks labelled X1 and X2.


M = 12.50 x 10 ^3pi(n – 5) / 2 0 x ( n – 4 ) ^2 x 10 ^39( n – 3 ) / 2 x 10^ 57 x q ^n (5)

M = f (n) q n

Where n is an odd numbered integer and q is the magnitude of the electric charge associated with the mass. The equation was based on the idea that
mass = constant x q n and that the constant depends on n and is different for each quark pair - the pairs are next to each other in the table.



QUARK CHARGE n MASS (Gev) )

DOWN - 1/3 -1 0.0088

UP + 2/3 -1 0.0044

X1 -1/3 +1 0.084

X2 +2/3 +1 0.16

STRANGE -1/3 +3 0.21

CHARM +2/3 +3 1.72

BOTTOM -1/3 +5 5.20

TOP +2/3 +5 167.25

I now understand why this equation works and I am going to submit it to a journal later in the year.The quark at N= +1 doesn't exist because of the colour force .This equation enables the rest mass of the muon to be predicted accurately too! Basically the constant k bypasses the need to do quantum field theory.

--------------------------------------------------------------------------------

 

[Haelfix]

'Colour charge is constantly changing but electric charge and rest mass are
stable parameters.'

Kurious, I suggest holding off on learning or postulating about QCD, until you have taken a couple courses in quantum mechanics, special relativity and a particle phenomenology class.

I mean, QCD really is complete jibberish if you haven't taken these courses with the adequate mathematical rigor, and the questions you ask reflect this.

If you insist on theorizing, then there is an appropriate board for that elsewhere on the forums.

 

[kurious]

qcd and maths

I have taken courses in QM and special relativity.
As for qcd, I only use experimentally obtained values of the colour force for my theories.I don't bother with the detailed maths of qcd because I think there is good reason to think the theory is badly flawed.The gold standard for the standard model is to be able to predict the masses of all known or unknown particles. It cannot - it does not.Electric charge and rest mass are constant with time-in general-but colour charge changes.How can something that is not changing be reconciled with something that is.How can a god be a mortal ?

 

[vanesch]

The gold standard for the standard model is to be able to predict the masses of all known or unknown particles. It cannot - it does not

The "gold standard" of the standard model is to predict correctly many different differential cross sections of particle collisions. It does a good job at it. As the masses of the particles are the free parameters of the theory, of course it doesn't predict them. It would of course be nice if we had an extension of the standard model that gives us the particle masses ; but a real theoretical prediction and not a curve fit of course ! Everybody can fit a parametrized expression to experimentally obtained masses and then claim to have predicted them, but there is no point in doing that.

cheers,
Patrick.

 

[Haelfix]

'Electric charge and rest mass are constant with time-in general-but colour charge changes.'

Yes, and that statement is goobledygook and nonsensical w.r.t to quantum field theory. I'll let you figure out why.

You do realize that most masses for general fields in the standard model are and were predicted and subsequently verified? Eg several fundamentals and most composite fields. Most of the ones we didn't know, and use as input parameters were also bounded .

The theory is remarkably self consistent, and no serious physicist even debates the validity of the SDM in its appropriate regime.

 

[kurious]

particle masses

A theory that is right would give the exact rest masses of all particles.
And it would be able to explain why quarks and leptons occur in related groups.John Baez is asking if anyone knows this on his "open questions in physics" website.But above all the standard model should have helped to formulate a GUT which accounts for where the missing antimatter is?
Got any ideas? I have.The antimatter is all around us in tiny fragments-destroyed by a chain reaction shortly after the big bang.GUTs need to give rise to a particle that can account for this decay of antimatter.They do not even account for the non-decay of a proton.Physicists have been trying to unify all the forces for decades now.GR doesn't go with QM despite everyone's
efforts.I think there are more forces to be found and that the idea that light is the fastest moving entity in the universe needs to be abandoned-there is no theoretical proof that light is the fastest moving thing-indeed there is no
theory which can derive the speed of light naturally.