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I'm fairly new to quantum mechanics, and I was looking up some basic information about the weak force and it's interactions. I found this equation of weak hypercharge on Wikipedia and quoted a few other places.

https://en.wikipedia.org/wiki/Flavour_(particle_physics)

Hypercharge = $Y = B + S + C + B′ + T$

Here:

B is the Baryon number which is always 1/3 for quarks.

S = strangeness which is a function of the number of strange and anti-strange quarks.

C = charm which is a function of the number of charm and anti-charm quarks.

B' = bottomness which is a function of the number of bottom and anti-bottom quarks.

T = topness which, as you might expect, is a function of the number of top and anti-top quarks.

For me, noticeably absent are the $up$ and $down$ quarks. If the Baryon number is always $1/3$ for quarks no information about the type of quark should influence it (I think). I suppose that if I were to describe the hypercharge of an $up$ or $down$ quark, I might set all parameters except B to zero; in which case the Hypercharge would be $1/3$. However, this would mean that the $up$ and $down$ quarks have different hypercharges from all the other quarks. Which intuitively seems strange. Why isn't hypercharge a function of "up-ness" and "down-ness" in addition to all the other parameters?

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What you quote there is not the equation for weak hypercharge, but for strong hypercharge, a concept from the early days when we didn't understand how all those particles were formed from quarks. Yes, the quarks do not possess the same strong hypercharge, strong hypercharge is a rather arbitrary (but conserved) combination of the quark numbers that was designed before we knew those numbers ("strangeness", "bottomness", etc.) really were quark numbers.

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  • $\begingroup$ I see. I thought that the equation seemed a bit ad-hoc. Thanks for clearing it up! $\endgroup$ – user2944352 May 31 '16 at 4:54

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