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## Main Question or Discussion Point

I wonder if there are successful cases of particle mass prediction/calculation in Theoretical Particle Physics?

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I wonder if there are successful cases of particle mass prediction/calculation in Theoretical Particle Physics?

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arivero

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I think that Witten settled the question of the difference between neutron and proton mass, but I am not sure.

In the semi-empirical spirit of hadron spectroscopy, of course flavour theory got to predict masses of the SU(3) decuplet, but I am not sure of the history.

W and Z were predicted from fermi interactions and fermi constant. W was easy, Z was a bit more in dispute. But W approx 80 GeV was already in textbooks in the early seventies.

Top failed. They kept increasing the prediction until it was finally found. But in the last years previous to discovery, QFT corrections were already predicting the right range.

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arivero

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And of course, string theory got to predict the masses of high spin hadrons. Only that at that time it was not string theory yet.

Really the hadron spectrum is not very hard to control in the big picture. String-Regee theory takes care of the mass of QCD excited states. The basic states are well organised via quark model and Gellmann-etc mass formulae. Even the decay constants seem to have some reasonable organisation, as you can be on this picture of mass against decay width:

http://dftuz.unizar.es/~rivero/research/nonstrong.jpg [Broken]

Really the hadron spectrum is not very hard to control in the big picture. String-Regee theory takes care of the mass of QCD excited states. The basic states are well organised via quark model and Gellmann-etc mass formulae. Even the decay constants seem to have some reasonable organisation, as you can be on this picture of mass against decay width:

http://dftuz.unizar.es/~rivero/research/nonstrong.jpg [Broken]

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apeiron

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So pi, e, phi, etc....a set of mathematical constants....

Or physical constants like c, k, g, etc?

What is the right way to think about the choices that could be made?

- #5

arivero

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Problems for such approach are GIGO (measure how many garbage you put in and compare with the garbage, er, results, you get out) and the "law" of small integers (there are only a few of small integers, and a lot of mathematical results involving small integers, so the "birthday paradox" is bound to happen).

So pi, e, phi, etc....a set of mathematical constants....

Or physical constants like c, k, g, etc?

What is the right way to think about the choices that could be made?

- #6

tom.stoer

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W and Z in the el.-weak GSW model rely on fixing constants related to the "old" Fermi model. Low SU(3) hadrons use mainly group theoretic aspects w/o taking into account QCD. The difference is that hadrons are bound states but W and Z are (as far as we know today) elementary particles.

In the meantime lattice gauge calculations for (quenched QCD) are able to fit hadron masses within a few percent. Of course these calculations are not parameter-free.

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The mass of the hydrogen atom in terms of the mass of the electron and proton.

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Yes, something like this but for other particles. The Hydrogen is an exemplary case when knowing mThe mass of the hydrogen atom in terms of the mass of the electron and proton.

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No, I did not mean Yukawa but the Standard Model first of all. For example, a pi-meson mass, what from it is calculated? From quark masses and the strong interaction coupling constant?

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Yes, at least in principle. For instance lattice methods (including chiral extrapolation to physical quark masses) adjust the quark masses (Yukawa couplings) to the necessary amount of measured masses in the spectrum (for instance, one needs 3 hadron masses to adjust 3 quark masses) and correctly reproduce the full hadronic spectra of masses with other hadrons. Alternatively, one can attempt to calculate directly the pion mass from the Gell-Mann-Oakes-Renner relation, including some modeling for the quark condensate. The following link is the first result of "pion mass formula" from google :From quark masses and the strong interaction coupling constant?

http://arxiv.org/abs/hep-ph/9602240

(I was unaware of this particle paper before doing this search, and only use it to mention the use of Gell-Mann-Oakes-Renner relation, which is presented in nearly all QCD textbooks)

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I did not read it myself further than the abstract and I do not know whether it is worth reading. On this matter, I guess a QCD textbook would be more suited.Thanks, Humanino, I will read it.

I do not have time right now to make a decent description. Lattice QCD is merely a (non-perturbative) brute force computation of the path integral. I use "brute force" in parenthesis because quite some technical tricks are necessary to make it manageable, even with powerful supercomputers. The renormalisation amounts to taking the continuum limit, since the regulator is the lattice itself (it introduces a momentum cutoff at the lattice spacing). To compute bound state properties, one has to choose an operator with the appropriate quantum numbers and we get as a result mostly the propagator for the corresponding state.By the way, in the lattice calculations (numerical approach, I guess), what is solved? Equations for bound states? Do these calculations involve renormalizations, counter-terms?

I like this introduction to lattice QCD :

http://arxiv.org/abs/hep-lat/0506036

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tom.stoer

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Nevertheless the results are promising; a nice paper including results for hadron masses is http://de.arxiv.org/abs/0711.3091v2

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The Omega-minus particle was predicted by SU3 before it was discovered in bubble chamber pictures. See

http://www.bnl.gov/bnlweb/history/Omega-minus.asp

The Bevatron, a 6.2 GeV weak-focusing synchrotron, was built at Berkeley in the eqrly 1950's specifically to discover the anti-proton predicted by Dirac and others in the 1930's. See

http://www.lbl.gov/Science-Articles/Archive/sabl/2005/October/01-antiproton.html

Bob S

http://www.bnl.gov/bnlweb/history/Omega-minus.asp

The Bevatron, a 6.2 GeV weak-focusing synchrotron, was built at Berkeley in the eqrly 1950's specifically to discover the anti-proton predicted by Dirac and others in the 1930's. See

http://www.lbl.gov/Science-Articles/Archive/sabl/2005/October/01-antiproton.html

Bob S

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The quenched approximation was a major limitation in the past. There are several ways to include the fermion determinant. I am not sure this technical discussion is appropriate here, but I can dig references if you want. In any case, there is a popular paper on the subjectOne should mention that (as far as I know due restricted computing power) still most lattice calculations must be restricted to the "quenched approximation". That means in the path integral the fermion determinant is fixed to One = the quarks are somehow static instead of dynamic; virtual quark-antiquark loops are suppressed. So the quark content of the hadron under investigation is fixed upfront.

http://inside.hlrs.de/images/spring01_09/A8_09.jpg [Broken]

Image link : http://inside.hlrs.de/htm/Edition_01_09/article_08.html [Broken]

Original paper : Ab-initio Determination of Light Hadron Masses

See also : Colloquium on the calculationThanks to continuous progress [...] lattice QCD calculations can now be performed with[out the] neglect [of] one or more of the ingredients required for a full and controlled calculation. The five most important of those are, in the order that they will be addressed below:

- inclusion of fermion determinant
- determination of the light ground-state (Three fix the masses of u, d and s)
- Large volumes
- Controlled interpolations to physical mass
- Controlled extrapolations to the continuum

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