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Bob_for_short
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I wonder if there are successful cases of particle mass prediction/calculation in Theoretical Particle Physics?
apeiron said:What kind of quantities or constants would it be most natural for particles masses to depend on when people are doing "particle numerology"?
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?
Count Iblis said:The mass of the hydrogen atom in terms of the mass of the electron and proton.
humanino said:It appears that we can calculate all known masses given the parameters of the standard model. I thought the OP was about Yukawa couplings.
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 :Bob_for_short said:From quark masses and the strong interaction coupling constant?
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.Bob_for_short said: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.Bob_for_short said: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?
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 subjecttom.stoer said:One 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.
Thanks 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
Particle mass prediction in theoretical physics is the process of using mathematical models and theories to predict the mass of particles, such as subatomic particles or elementary particles. It is an important area of study in theoretical physics as it helps us understand the fundamental building blocks of the universe.
Particle mass prediction is achieved through complex calculations and simulations using mathematical equations and theories, such as the Standard Model of particle physics. These calculations take into account various factors, such as the interaction between particles and the effects of fundamental forces, to predict the mass of a particle.
One of the most famous and successful examples of particle mass prediction is the prediction of the existence and mass of the Higgs boson, which was later confirmed by experiments at the Large Hadron Collider. Other successful predictions include the masses of the top quark and charm quark, as well as the masses of various mesons and baryons.
One of the biggest challenges in particle mass prediction is the complexity of the calculations and simulations involved. These predictions also often require advanced mathematical and computational techniques, making it a challenging field for scientists. Additionally, there is still much we do not know about the fundamental laws of physics, which can make predictions less accurate.
Particle mass prediction is crucial in helping us understand the fundamental laws and building blocks of the universe. By accurately predicting the mass of particles, we can gain insights into the behavior and interactions of these particles, leading to a deeper understanding of the universe and its origins.