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ribbie
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Can someone give a list of all the pure numbers that relate to elementary particles (such as the fine-structure constant)? How many such numbers are there? Is it likely that more will be discovered?
Thanks
Thanks
ribbie said:Can someone give a list of all the pure numbers that relate to elementary particles (such as the fine-structure constant)? How many such numbers are there? Is it likely that more will be discovered?
Thanks
the_house said:Like maverick_starstrider, I'm not sure what exactly you mean by pure numbers, but let's assume you mean free parameters in the standard model of particle physics.
See the table http://en.wikipedia.org/wiki/Standard_Model#Construction_of_the_Standard_Model_Lagrangian"
Besides the fine structure constant that you mention, there are 2 more coupling constants, making a total of 3. Then there are masses for all of the fermions, making 12 total (the neutrino masses aren't in the wikipedia table, since the original "standard model" had massless neutrinos, but now we know they have mass.) Then there are 3 CKM mixing angles and 1 phase, plus 3 neutrino mixing angles and a corresponding phase. There's also a possible QCD vacuum angle, as well as extra parameters for the Higgs mechanism (according to the wikipedia page, there are 2 parameters for a standard model Higgs).
If you prefer dimensionless numbers, you can just take all of the dimensionfull quantities above and divide them by Lambda_QCD.
the_house said:Thanks for the corrections. You're right on all counts.
I was on the right track at least, though, right? :)
Parlyne said:Definitely the right track. Some of this is just a matter of convention or history. For instance, the fact that people usually cite the fine structure constant and the Weinberg angle rather than the SU(2)_L and U(1)_Y coupling constants.
PhilDSP said:Can you recommend a good resource that clearly explains the theory relating the Fine Structure Constant and Weinberg angle to the SU(2)_L and U(1)_Y coupling constants?
And in general, a resource that shows what factors of geometry and groups are necessary to arrive at the Standard Model?
Pure numbers are related to elementary particles through various physical constants and equations that describe the behavior and properties of particles. These numbers represent fundamental quantities such as mass, charge, and energy that are inherent to particles and help us understand their interactions.
Yes, pure numbers can be used to predict the existence of new elementary particles by analyzing patterns and relationships between known particles and their corresponding numerical values. These predictions are then verified through experiments and observations.
There is no definite answer to this question as the number of pure numbers that relate to elementary particles depends on the specific physical phenomenon or property being studied. However, there are a significant number of important pure numbers that have been identified and studied by scientists.
Not all elementary particles have a corresponding pure number, as some particles may have similar properties and behaviors that can be described by the same numerical value. Additionally, there may be particles whose properties are not fully understood or described by current theories, making it difficult to assign a pure number to them.
Pure numbers play a crucial role in our understanding of elementary particles by providing a quantitative framework for describing their properties and interactions. They allow us to make predictions, perform calculations, and test theories, ultimately leading to a deeper understanding of the fundamental building blocks of the universe.