Some Naive Quark-Model Calculations

[lpetrich]

In another forum, I did some rather naive quark-model calculations, but rather successful ones: mathematical and geometric model for mass of proton.

Much of the thread was taken up with numerological crackpottery, and I noted that there is a well-established mainstream theory of the proton's mass: A rather technical presentation on finding the proton's mass, [hep-ex/0002035] Measurement of the Running of the Fine-Structure Constant, Current advances: The fine-structure constant, Backreaction: Asymptotic Freedom and the Coupling Constant of QCD, Theoretical Elementary Particle Physics Group @ KTH - Research Topics: Grand Unified Theories (GUTs), http://2.bp.blogspot.com/_ws8XY4ubvXg/R1qrf-HmpFI/AAAAAAAAAaY/YR29Ynif3-0/s1600-h/smmssm.jpg, [hep-ph/0012288] Beyond the Standard Model (In Search of Supersymmetry), [1006.1311] Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED, http://www.riken.go.jp/lab-www/theory/colloquium/kinoshita.pdf

The source of my numbers: Particle Data Group. Here, m is mass in MeV and mu is magnetic moment in a unit called the nuclear magneton. In ()'s, the quark content and spin.

Proton (uud,1/2): m = 938.272081, mu = 2.792847351
Neutron (udd,1/2): m = 939.565413, mu = - 1.9130427
Collectively: nucleons

Delta (uuu,uud,udd,ddd,3/2): m = 1210

Lambda (uds,1/2): m = 1115.683, mu = -0.613

Sigma+ (uus,1/2): m = 1189.37, mu = 2.458
Sigma0 (uds,1/2): m = 1192.642, (from transitions, |mu| = 1.61)
Sigma- (dds,1/2): m = 1197.449, mu = -1.160
Sigma-x+ (uus,3/2): m = 1382.80
Sigma-x0 (uds,3/2): m = 1383.7
Sigma-x- (dds,3/2): m = 1387.2

Xi0 (uss,1/2): m = 1314.86, mu = -1.250
Xi- (dss,1/2): m = 1321.71, mu = -0.6507
Xi-x0 (uss,3/2) m = 1531.80
Xi-x- (dss,3/2) m = 1535.0

Omega- (sss,3/2): m = 1672.45, mu = -2.02

Averaging over the up and down quarks, the masses are:
Nucleon: 938.918747
Delta: 1210
Lambda: 1115.683
Sigma: 1193.16
Sigma-x: 1384.6
Xi: 1318.28
Xi-x: 1533.4
Omega: 1672.45

So there is a big splitting due to the QCD spin-spin interaction.

 

[lpetrich]

I'll refer to up and down quarks together as n ones, n for nucleon.

Nucleon: m0 - 3cnn
Delta: m0 + 3cnn
m0 = 1074
cnn = 45.2

Lambda: m1 - 3cnn
Sigma: m1 + cnn - 4cns
Sigma-x: m1 + cnn + 2cns
m1 = 1269.5
cnn = 51.3
cns = 31.9

Xi: m2 + css - 4cns
Xi-x: m2 + css + 2cns
m2 + css = 1461.7
cns = 35.8

Omega: m3 + 3css

The interactions cnn and cns are fairly consistent, increasing by 6.1 and 3.9 with increasing strangeness. So I have to estimate m2 and css. Since the interactions cnn, cns, css are proportional to the product of the QCD "magnetic moments" of the quarks involved, and since (magnetic moment) ~ 1/(mass), I estimate css = 19.8. That makes m2 = 1441.9 and m3 = 1613.0

For m0, m1, m2, m3 (number = number of strange quarks), I get an approximately linear fit: 1083.17 + 180.92*n where n = 0,1,2,3. It is a fairly good fit, though I get a better fit by omitting the omega baryon: 1074.55 + 193.85*n

So each strange quark adds about 200 MeV to the mass.

 

[lpetrich]

I'll now take on magnetic moments. I'll call them g instead of mu for typographical convenience.

Proton: (1/3)*(4gu - gd)
Neutron: (1/3)*(4gd - gu)

Lambda: gs
Sigma+: (1/3)*(4gu - gs)
Sigma0: (1/3)*(2gu + 2gd - gs)
Sigma-: (1/3)*(4gd - gs)

Xi0: (1/3)*(4gs - gu)
Xi-: (1/3)*(4gs - gd)

Omega: 3gs

I start with the nucleons:
gu = 1.852
gd = -0.972
gd/gu = -1.905
That ratio is close to what the quark model predicts: -2. So I try gu = (2/3)*gn and gd = (-1/3)*gn. That gives g(proton) = gn and g(neutron) = -(2/3)*gn, giving
average of gn = 2.831

This suggests an effective quark mass of 331 MeV, with m0 - 3*(this) = 79 MeV.

For the lambda baryon, we find gs = -0.613, and scaling for charge gives 1.839.

The two charged sigmas give gn = 2.714, about right, and gs = -0.138, curiously small.

The neutral sigma has a sigma0 - lambda transition magnetic moment of (gu - gd)/sqrt(3), giving gn = 2.79, about right.

The two xis give gn = 1.798, rather small, and gs = -0.638.

The omega baryon gives gs = -0.673.

The PDG site has a review of baryon magnetic moments, with calculations of gu, gd, and gs from the proton, neutron and lambda, and calculation of all the other known baryon magnetic moments from them.

It also has a review of lattice quantum chromodynamics, the mainstream way of calculating light hadrons' masses.

 

[LordKiran]

Math hurts my squishy monkey brain.

 

[humbleman]

In another forum, I did some rather naive quark-model calculations, but rather successful ones: mathematical and geometric model for mass of proton.

Much of the thread was taken up with numerological crackpottery, and I noted that there is a well-established mainstream theory of the proton's mass: A rather technical presentation on finding the proton's mass, [hep-ex/0002035] Measurement of the Running of the Fine-Structure Constant, Current advances: The fine-structure constant, Backreaction: Asymptotic Freedom and the Coupling Constant of QCD, Theoretical Elementary Particle Physics Group @ KTH - Research Topics: Grand Unified Theories (GUTs), http://2.bp.blogspot.com/_ws8XY4ubvXg/R1qrf-HmpFI/AAAAAAAAAaY/YR29Ynif3-0/s1600-h/smmssm.jpg, [hep-ph/0012288] Beyond the Standard Model (In Search of Supersymmetry), [1006.1311] Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED, http://www.riken.go.jp/lab-www/theory/colloquium/kinoshita.pdf

The source of my numbers: Particle Data Group. Here, m is mass in MeV and mu is magnetic moment in a unit called the nuclear magneton. In ()'s, the quark content and spin.

Proton (uud,1/2): m = 938.272081, mu = 2.792847351
Neutron (udd,1/2): m = 939.565413, mu = - 1.9130427
Collectively: nucleons

Delta (uuu,uud,udd,ddd,3/2): m = 1210

Lambda (uds,1/2): m = 1115.683, mu = -0.613

Sigma+ (uus,1/2): m = 1189.37, mu = 2.458
Sigma0 (uds,1/2): m = 1192.642, (from transitions, |mu| = 1.61)
Sigma- (dds,1/2): m = 1197.449, mu = -1.160
Sigma-x+ (uus,3/2): m = 1382.80
Sigma-x0 (uds,3/2): m = 1383.7
Sigma-x- (dds,3/2): m = 1387.2

Xi0 (uss,1/2): m = 1314.86, mu = -1.250
Xi- (dss,1/2): m = 1321.71, mu = -0.6507
Xi-x0 (uss,3/2) m = 1531.80
Xi-x- (dss,3/2) m = 1535.0

Omega- (sss,3/2): m = 1672.45, mu = -2.02

Averaging over the up and down quarks, the masses are:
Nucleon: 938.918747
Delta: 1210
Lambda: 1115.683
Sigma: 1193.16
Sigma-x: 1384.6
Xi: 1318.28
Xi-x: 1533.4
Omega: 1672.45

So there is a big splitting due to the QCD spin-spin interaction.

Before checking at your quark "mass", lets check your sources.

http://www.durr.itp.unibe.ch/talk_09_psi.pdf

Origin of mass: EW versus QCD phase transition

And a drawing of the silly big bang theory follows it.

This first source is discarded. A dumb theory is not base to support another theory. You support theories with facts, no with other theories, because such is idiocy.

Lets see the second source.

https://arxiv.org/abs/hep-ex/0002035

Measurement of the Running of the Fine-Structure Constant

...Bhabha scattering data recorded at \sqrt{s}=189 GeV by the L3 detector at LEP are used to measure the running of the effective fine-structure constant for spacelike momentum transfers...

That term spacelike is relativity sh*t.

https://physics.stackexchange.com/q...ghtlike-spacetime-interval-really-mean#217805

What spacelike, timelike and lightlike spacetime interval really mean?

....Suppose we have two events ... These are just mathematical definitions. What, however, is the physical intuition behind? I mean, what an interval being timelike, lightlike or spacelike means?....Spacelike separation means that there exists a reference frame where the two events occur simultaneously, but in different places....

It is time to clean up science from terms invented by followers of a false theory. This is a simple transition. Such frames of reference definitively are just illusions, and science is not based on illusions.

Second link given by you: Discarded.

Lets see if you have better luck with the third link.

https://physics.nist.gov/cuu/Constants/alpha.html

Introduction to the constants for nonexperts

....The fine-structure constant α is of dimension 1 (i.e., it is simply a number) and very nearly equal to 1/137. It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact....

...Starting in the 1980's, a new and wholly different measurement approach using the quantum Hall effect (QHE) has caused excitement ...

...According to quantum electrodynamics (QED), the relativistic quantum field theory of the interaction of charged particles and photons, an electron can emit virtual photons ...

"Relativistic quantum field theory"

Look, poor Albert passed his last years trying and trying to unify relativity with quantum until he died in 1955. He failed miserably.

So, before anything, do you know who was the one who unified both theories?

So far, no records at all in journals mention the name of such a genius who overpassed the vain intentions of poor Albert in this task.

And, by reading about your great knowledge in abstract mathematical and algebraic stuff, I can say that your topic belongs to entertainment because science is not.

I think you are trying to "impress" others who won't discuss with you because such is not their field. However, mine is research, and the first three links given by you are enough to conclude that you are having fun with abstract mathematics, but that you are not discussing science, this is for sure.

You see, before accepting what others say, as you did, one must check how verifiable are the sources. One can't fall in fanaticism when is about science.

I can see how many minds waste their capabilities by following good for nothing theories.

The attempts to make relativity as valid are so many, that relativists even target religion to spread out their theory. It is a silly rabbi who wrote his book about Genesis saying that first day of creation lasted such and such billions of years, second day such and such millions of years, and so forth, because the speed of the crated universe at it beginning... This rabbi a profound admirer of poor Albert as it is known.

It won't work.

Relativity is crap to the square, and will be found as such regardless of how many ways you try to spread out that is a valid theory.

You can make up your attempts of spreading the good for nothing theory with topics like "naive quark-model calculations", and others might agree with it, and that is fine.

My opinion -based on research about the non validity of relativity- is that the topic itself started by you is not science but pseudoscience.

So, as playing chess, you just started the game moving the horse forward. That was a great mistake.

 

[Jokodo]

Before checking at your quark "mass", lets check your sources.

http://www.durr.itp.unibe.ch/talk_09_psi.pdf



And a drawing of the silly big bang theory follows it.

This first source is discarded. A dumb theory is not base to support another theory. You support theories with facts, no with other theories, because such is idiocy.

Lets see the second source.

https://arxiv.org/abs/hep-ex/0002035

Measurement of the Running of the Fine-Structure Constant

...Bhabha scattering data recorded at \sqrt{s}=189 GeV by the L3 detector at LEP are used to measure the running of the effective fine-structure constant for spacelike momentum transfers...

That term spacelike is relativity sh*t.

https://physics.stackexchange.com/q...ghtlike-spacetime-interval-really-mean#217805

What spacelike, timelike and lightlike spacetime interval really mean?

....Suppose we have two events ... These are just mathematical definitions. What, however, is the physical intuition behind? I mean, what an interval being timelike, lightlike or spacelike means?....Spacelike separation means that there exists a reference frame where the two events occur simultaneously, but in different places....

It is time to clean up science from terms invented by followers of a false theory. This is a simple transition. Such frames of reference definitively are just illusions, and science is not based on illusions.

Second link given by you: Discarded.

Lets see if you have better luck with the third link.

https://physics.nist.gov/cuu/Constants/alpha.html

Introduction to the constants for nonexperts

....The fine-structure constant α is of dimension 1 (i.e., it is simply a number) and very nearly equal to 1/137. It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact....

...Starting in the 1980's, a new and wholly different measurement approach using the quantum Hall effect (QHE) has caused excitement ...

...According to quantum electrodynamics (QED), the relativistic quantum field theory of the interaction of charged particles and photons, an electron can emit virtual photons ...

"Relativistic quantum field theory"

Look, poor Albert passed his last years trying and trying to unify relativity with quantum until he died in 1955. He failed miserably.

So, before anything, do you know who was the one who unified both theories?

So far, no records at all in journals mention the name of such a genius who overpassed the vain intentions of poor Albert in this task.

And, by reading about your great knowledge in abstract mathematical and algebraic stuff, I can say that your topic belongs to entertainment because science is not.

I think you are trying to "impress" others who won't discuss with you because such is not their field. However, mine is research, and the first three links given by you are enough to conclude that you are having fun with abstract mathematics, but that you are not discussing science, this is for sure.

You see, before accepting what others say, as you did, one must check how verifiable are the sources. One can't fall in fanaticism when is about science.

I can see how many minds waste their capabilities by following good for nothing theories.

The attempts to make relativity as valid are so many, that relativists even target religion to spread out their theory. It is a silly rabbi who wrote his book about Genesis saying that first day of creation lasted such and such billions of years, second day such and such millions of years, and so forth, because the speed of the crated universe at it beginning... This rabbi a profound admirer of poor Albert as it is known.

It won't work.

Relativity is crap to the square, and will be found as such regardless of how many ways you try to spread out that is a valid theory.

You can make up your attempts of spreading the good for nothing theory with topics like "naive quark-model calculations", and others might agree with it, and that is fine.

My opinion -based on research about the non validity of relativity- is that the topic itself started by you is not science but pseudoscience.

So, as playing chess, you just started the game moving the horse forward. That was a great mistake.

man, you could really use some humility.

 

[Elixir]

man, you could really use some humility.

Why?
I mean, you have to admit - this is one very very special brand of TEH STOOPID.
You can't really blame someone who is too stupid to have any idea how stupid they are.

 

[lpetrich]

And a drawing of the silly big bang theory follows it.

Why do you consider the Big Bang "silly"? What do you consider more plausible and why?

You support theories with facts, no with other theories, because such is idiocy.

Why do you think that our values of quark masses are derived from Big Bang theorizing?

That term spacelike is relativity sh*t.

Why do you dismiss relativity?

"Relativistic quantum field theory"

Look, poor Albert passed his last years trying and trying to unify relativity with quantum until he died in 1955. He failed miserably.

No he didn't. He tried to find a theory that unifies gravity with electromagnetism, and he failed. It was all in the classical limit with no quantum mechanics. But while he was working on that, some other physicists were working a relativistic quantum field theory of photons and electrons -- quantum electrodynamics. It was a great success, and it was later extended to other particles and other interactions, giving the Standard Model of particle physics.

So, as playing chess, you just started the game moving the horse forward. That was a great mistake.

There is a chess opening that involves exactly that first move: the Reti Opening.

 

[repoman]

Are you saying that atomic nucleons have a statistical chance (superposition of states) of having strange quarks inside?

I typed this

can nucleons have strange quarks

into google and got some hits.

There is a lot of jargon to parse for me being so rusty in general science and never having looked at these details...

What is really mindblowing is that despite having a whirling mass of virtual particles that all protons and neutrons have the same mass. Also the exchange of particles between nucleons is interesting.

on a time average basis protons and neutrons have a constant mass, what about for very small amounts of time? How much larger or smaller a mass do they have? Especially neutrons which decay.

 

[lpetrich]

Hadrons have "sea quarks" in them as well as "valence quarks", what one sees from outside. Sea quarks are quark-antiquark pairs that come and go. Thus, nucleons have some strange quarks in them, with an equal number of strange antiquarks alongside them.

As to measuring a particle's mass, if one measures it over time T, then the maximum precision that one can do so is h/(c^2*T) where h is Planck's constant and c the speed of light in a vacuum. So measured values will be somewhat "fuzzy". This is from the uncertainty principle, and that, in turn, is a consequence of the wave nature of matter.

But particles' masses and energy levels and other such features are well-defined quantities, without such fuzziness.

There are further issues, but I'd have to teach a whole course in quantum mechanics to cover them.

 

[lpetrich]

The nucleon quark content from lattice QCD - 0.pdf

Lattice QCD? That is a way of solving the equations of quantum chromodynamics, the theory of the strong interaction. The simplest way of starting with such equations was first worked out for electromagnetism as quantum electrodynamics (QED). One starts with free-particle states and one adds interactions as perturbations. For QED, the small parameter is the fine-structure constant, essentially the square of the elementary charge. It is 1/137, which is small enough to permit a solution as a series in it: c0 + c1*FSC + c2*FSC^2 + c3*FSC^3 + ...

That has been very successfully done for the electron's extra magnetic moment -- it has about 1/1000 more than the lowest-order prediction.

The effective value of the FSC increases with interaction energy from low-energy 1/137 to about 1/128 near 90 GeV, the mass of the Z particle.

But QCD has a great difficulty. Its counterpart of the FSC is about 0.1 at the Z particle's mass, but at a light hadron's mass, around a GeV, it is around 1, and it is difficult to calculate c0 + c1 + c2 + c3 + ... where the c's get very complicated to calculate very quickly.

So that's led to lattice gauge theory, and lattice QCD more specifically. It involves finding the values of all the particle fields at each point in a 4D hypercubical lattice -- and repeatedly doing so while making them obey the equations of motion. To get good results, one must go through a *lot* of field configurations, and that has required some very big computers.

But that effort has paid off. [0906.3599] Ab-initio Determination of Light Hadron Masses (2009) describes calculations of the masses of some light hadrons to within a few percent. [1406.4088] Ab initio calculation of the neutron-proton mass difference (2014) is more recent. Electromagnetic effects give the proton about 1 MeV more mass than the neutron, but the up quark is lighter than the down quark, and that gives the neutron about 2.5 MeV of mass, giving the observed neutron-proton mass difference of 1.3 MeV.

 

[lpetrich]

There is a kind of crackpottery that consists of finding elementary-particle constants by doing lots of mathematical manipulation, typically without presenting any motivation of it. Some favorite targets are the fine structure constant and the electron-proton mass ratio.

But neither of those quantities can reasonably be called fundamental, even in the Standard Model.

 

[Kharakov]

Math hurts my squishy monkey brain.

It's math without English translations that "hurts" your brain (it's like reading a Russian novel using a dictionary, if you've never read Russian before).

It's a closed language, and while mathematicians claim Euler's conventions are the most convenient, they create a quantum obfuscation barrier.... which allows some of them to get further ahead in certain branches of the field, since they can build on the work of others.




Loren- You wrote something on Lisi's theory (in the past), right?

 

[lpetrich]

I don't recall having written anything on Garrett Lisi's E8 Grand Unification Theory (GUT).

But I have written other stuff on GUT's, like in "Brahman Particle" - not "God Particle"

 

[Kharakov]

link's broken (yours): http://showthread.php/?12182-quot-Brahman-Particle-quot-not-quot-God-Particle-quot

good:

https://talkfreethought.org/showthr...hman-Particle-quot-not-quot-God-Particle-quot

 

[lpetrich]

Oops. Thanx. "Brahman Particle" - not "God Particle"