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I have been trying to find an explanation for the strange quarks negative strangeness value, I understand the term strangeness predates the quark model, but I'm unsure if terminology carry over is the reason for the naming convention.

Apparently, it is also convention to give quantum numbers a positive or negative value depending on the charge of the particle. Does the strange quark's negative charge give it a negative strangeness?

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    $\begingroup$ to keep with the convention used when the kaon was discovered , en.wikipedia.org/wiki/Kaon at the quark level $\endgroup$
    – anna v
    May 8 at 13:07
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    $\begingroup$ For the same reason electrons are negatively charged: we guessed wrong which convention would be most useful. $\endgroup$
    – J.G.
    May 8 at 15:06
  • $\begingroup$ If either of you would like to write your comments up into a full answer I'd happily accept one of them. $\endgroup$
    – Connor
    May 8 at 15:23
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    $\begingroup$ A strange quark with strangeness +1 would be just what you'd expect, and therefore not strange at all :) $\endgroup$ May 9 at 4:23

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From the Wikipedia article Strangeness:

The terms strange and strangeness predate the discovery of the quark, and were adopted after its discovery in order to preserve the continuity of the phrase; strangeness of anti-particles being referred to as +1, and particles as −1 as per the original definition. For all the quark flavour quantum numbers (strangeness, charm, topness and bottomness) the convention is that the flavour charge and the electric charge of a quark have the same sign. With this, any flavour carried by a charged meson has the same sign as its charge.

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  • $\begingroup$ Sorry, I should have said I read that; I didn't find the paragraph definitive, why was +1, -1 the original definition? $\endgroup$
    – Connor
    May 8 at 15:22
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    $\begingroup$ @Connor This is the very point of the paragraph: The strangeness of the $K^-$ was assigned to be -1, same as its charge. The charm of the $D^+$ is assigned to be +1, same as its charge. $\endgroup$ May 8 at 16:04
  • $\begingroup$ @CosmasZachos Ahh, okay, that isn't clear to me from the paragraph! Probably because I don't know the history, but thank you! $\endgroup$
    – Connor
    May 8 at 18:31
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    $\begingroup$ It's all about memorable conventions. $\endgroup$ May 8 at 18:42
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The sign of additive quantum numbers is set up to a convention. Take for example the case of the electric current: we use to say in electronics that current is a positive flow of charge, that is a negative flow in the opposite direction.

Having this in mind, a subnuclear physics reason can be that the Gell-Mann & Nishijima formula that relates electric charge $Q$, strong isospin $I_3$, barionic number $B$ and strangeness $S$ (the sum of these two and all other quark numbers is called strong hypercharge, $Y$) states: $$ Q = \frac{B+S}{2} + I_3 $$ Because of this, reminding that the charge of quark strange is $-\frac{1}{3}$ we obtain the correct solution if we put $I_3 = 0$, $B = \frac{1}{3}$ and $S = -1$.

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