How is weak isospin/hypercharge calculated?

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SUMMARY

The calculation of weak isospin (T3) and weak hypercharge (YW) is defined by the equation YW = 2(Q-T3), where Q represents electric charge. Weak isospin is assigned to left-handed chirality leptons and quarks, distinguishing charge states within each generation. The formula for weak isospin is T3 = Q + L/2 - B/2, incorporating lepton number (L) and baryon number (B). A comprehensive table detailing weak isospin and weak hypercharge for various particles is available in the Wikipedia article on weak hypercharge.

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  • Understanding of weak isospin and weak hypercharge concepts
  • Familiarity with particle physics terminology
  • Knowledge of electric charge, lepton number, and baryon number
  • Basic grasp of chirality in particle physics
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  • Research the derivation of weak isospin and weak hypercharge equations
  • Study the role of chirality in particle physics
  • Examine the relationship between lepton number and baryon number in particle interactions
  • Review the Wikipedia article on weak hypercharge for detailed particle tables
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Particle physicists, students studying the Standard Model, and anyone interested in the properties of leptons and quarks will benefit from this discussion.

Harry235435
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I am familiar with the following equation which relates weak isospin (T3) and weak hypercharge (YW):
YW = 2(Q-T3)
(Where Q is electric charge)
However, while this can be used to calculate YW from T3 and vice versa, how do you calculate each of these properties individually, without using the other?
 
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Weak isospin is assigned to the usual (left-handed chirality) leptons and quarks in such a way as to distinguish the two different charge states in each generation, in the same way that normal isospin distinguishes the up and down quarks. I think that for those particles T3 = Q + L/2 - B/2 where Q is the charge, L is the lepton number and B is the baryon number.

There's a table of weak isospin and weak hypercharge for those particles in the Wikipedia article on weak hypercharge.
 
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