Hypercharge
From Academic Kids
Template:Flavour quantum numbers
In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness <math>\tilde B<math> and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before strong-interacting with other quarks).
- <math>(1) \qquad Y = B + S + C + \tilde B + T<math>
Originally, hypercharge only included the strangeness flavor in its definition. Do not confuse hypercharge with weak hypercharge: the first one is connected to the strong interaction, while the second appears on the electroweak interaction.
The Gell-Mann/Nishijima Law relates hypercharge with isospin and electric charge:
- <math>(2) \qquad Q = I_z + {1 \over 2} Y<math>
where Iz 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:
- <math>(3) \qquad Y = 2(Q - I_z) <math>
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
- <math>(4) \qquad Y = 2 \bar Q<math>.
which is easily derived from (3), since the hypercharge is the same for all members of a multiplet, and the average of the Iz values is 0.
Examples:
- The nucleon group (proton plus neutron) have an average charge of 1 + 0 = +1/2, so they both have hypercharge Y = 1 (baryon number B = +1, flavor charges set to 0). From Gell-Mann/Nishima Law 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 Iz of +1/2, we deduce a hypercharge of 1/3, due to its barion number (since you need 3 quarks to make a baryon, a quark has baryon number of &plusminus;1/3).
- For a strange quark, with charge −1/3, a barion number of 1/3 and strangeness of −1 we get an hypercharge Y = −1/3, so we deduce an Iz = 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 a isospin doublet.
See also
- Flavour (particle physics), baryon number and quark flavor charges: isospin, strangeness, charm, bottomness, topness
- Weak isospin, Weak hypercharge, standard modelde:Hyperladung
