Hypercharge

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Flavour in particle physics v • d • e
Flavour quantum numbers: Lepton number: L Baryon number: B Strangeness: S Charm: C Bottomness: B' Topness: T Isospin: I_z or I Weak isospin: T_z Electric charge: Q Combinations: Hypercharge: Y Y=2(Q-I_z) Y=B+S+C+B'+T Weak hypercharge: Y_W Y_W=2(Q-T_z) Y_W=B−L Related topics: CPT symmetry CKM matrix CP symmetry Chirality

In particle physics, the hypercharge (represented by Y) of a particle is related to the strong interaction, and it should not be confused with similarly named weak hypercharge, which has an analogous role in the electroweak interaction.

[edit] Electric Charge and Hypercharge

The Gell-Mann–Nishijima formula relates hypercharge with isospin and electric charge:

$(1) \qquad Q = I_z + {1 \over 2} Y$

where I_z is the third component of isospin and Q is the particle's charge. This allow us to express the hypercharge in terms of isospin and charge:

$(2) \qquad Y = 2(Q - I_z)$

Isospin creates multiplets of particles whose average charge is related to the hypercharge by:

$(3) \qquad Y = 2 \bar Q$ .

which is easily derived from (2), since the hypercharge is the same for all members of a multiplet, and the average of the I_z values is 0.

Examples:

The nucleon group (proton plus neutron) have an average charge of (1 + 0)/2 = +1/2, so they both have hypercharge Y = 1 (baryon number B = +1, flavor charges set to 0). From the Gell-Mann–Nishijima formula we know that proton has isospin +1 - 1/2 = +1/2, while neutron is the 0 − 1/2 = −1/2.
This also works for quarks: for the up quark, with a charge of +2/3, and an I_z of +1/2, we deduce a hypercharge of 1/3, due to its baryon number (since you need 3 quarks to make a baryon, a quark has baryon number of ±1/3).
For a strange quark, with charge −1/3, a baryon number of 1/3 and strangeness of −1 we get a hypercharge Y = −1/3, so we deduce an I_z = 0. That means that a strange quark makes a singlet of its own (same happens with charm, bottom and top quarks), while up and down constitute an isospin doublet.

[edit] Practical Obsolescence

Hypercharge was a concept developed in the mid-to-late 1900's, to organize groups of particles in the "subatomic zoo" and to develop ad-hoc conservation laws based on their observed transformations. With the advent of the quark model, it is now obvious that hypercharge Y, is merely half the difference between the number of up quarks ( $n u$ ) less the number of down quarks ( $n d$ ):

$(4) \qquad Y = {1 \over 2} (n_u - n_d)$

In modern descriptions of hadron interaction, it has become more obvious to draw Feynman diagrams that trace through individual quarks composing the interacting baryons and mesons, rather than counting hypercharge quantum numbers. Weak hypercharge, however, remains of practical use in various theories of the electroweak interaction.