Английская Википедия:Hypercharge
Шаблон:Short description Шаблон:About Шаблон:Multiple issues Шаблон:Flavour quantum numbers In particle physics, the hypercharge (a portmanteau of hyperonic and charge) Y of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. The hypercharge is useful to classify hadrons; the similarly named weak hypercharge has an analogous role in the electroweak interaction.
Definition
Hypercharge is one of two quantum numbers of the SU(3) model of hadrons, alongside isospin Шаблон:MvarШаблон:Sub. The isospin alone was sufficient for two quark flavours — namely Шаблон:Subatomic particle and Шаблон:Subatomic particle — whereas presently 6 flavours of quarks are known.
SU(3) weight diagrams (see below) are 2 dimensional, with the coordinates referring to two quantum numbers: Шаблон:MvarШаблон:Sub (also known as Шаблон:MvarШаблон:Sub), which is the Шаблон:Math component of isospin, and Шаблон:Mvar, which is the hypercharge (defined by strangeness Шаблон:Mvar, charm Шаблон:Mvar, bottomness Шаблон:Mvar, topness Шаблон:Mvar, and baryon number Шаблон:Mvar). Mathematically, hypercharge is [1]
- <math>Y = B + S - \frac{C - B' + T'}{3} ~. </math>
Strong interactions conserve hypercharge (and weak hypercharge), but weak interactions do not.
Relation with electric charge and isospin
Шаблон:Main The Gell-Mann–Nishijima formula relates isospin and electric charge
- <math> Q = I_3 + \tfrac{1}{2}Y,</math>
where I3 is the third component of isospin and Q is the particle's charge.
Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
- <math> Y = 2 \bar Q.</math>
since the hypercharge is the same for all members of a multiplet, and the average of the I3 values is 0.
These definitions in their original form hold only for the three lightest quarks.
SU(3) model in relation to hypercharge
The SU(2) model has multiplets characterized by a quantum number J, which is the total angular momentum. Each multiplet consists of Шаблон:Nowrap substates with equally-spaced values of Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalizes the observation that certain strong baryon decays were not observed, leading to the prediction of the mass, strangeness and charge of the [[Omega baryon|Шаблон:SubatomicParticle baryon]].
The SU(3) has supermultiplets containing SU(2) multiplets. SU(3) now needs two numbers to specify all its sub-states which are denoted by λ1 and λ2.
Шаблон:Nowrap specifies the number of points in the topmost side of the hexagon while Шаблон:Nowrap specifies the number of points on the bottom side.
Examples
- The nucleon group (protons with Шаблон:Nowrap and neutrons with Шаблон:Nowrap) have an average charge of Шаблон:Sfrac, so they both have hypercharge Шаблон:Nowrap (since baryon number Шаблон:Nowrap and Шаблон:Nowrap). From the Gell-Mann–Nishijima formula we know that proton has isospin Шаблон:Nowrap while neutron has Шаблон:Nowrap
- This also works for quarks: For the up quark, with a charge of Шаблон:Sfrac, and an Шаблон:MvarШаблон:Sub of Шаблон:Sfrac, we deduce a hypercharge of Шаблон:Sfrac, due to its baryon number (since three quarks make a baryon, each quark has a baryon number of Шаблон:Sfrac).
- For a strange quark, with electric charge Шаблон:Sfrac, a baryon number of Шаблон:Sfrac, and strangeness −1, we get a hypercharge Шаблон:Nowrap so we deduce that Шаблон:Nowrap That means that a strange quark makes an isospin singlet of its own (the same happens with charm, bottom and top quarks), while up and down constitute an isospin doublet.
- All other quarks have hypercharge Шаблон:Nowrap.
Practical obsolescence
Hypercharge was a concept developed in the 1960s, to organize groups of particles in the "particle 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 strong hypercharge, Шаблон:Mvar, is the following combination of the numbers of up (Шаблон:MvarШаблон:Sub), down (Шаблон:MvarШаблон:Sub), strange (Шаблон:MvarШаблон:Sub), charm (Шаблон:MvarШаблон:Sub), top (Шаблон:MvarШаблон:Sub) and bottom (Шаблон:MvarШаблон:Sub):
- <math> Y = \tfrac{1}{3} n_\textrm{u} + \tfrac{1}{3} n_\textrm{d} - \tfrac{2}{3} n_\textrm{s} ~.</math>
In modern descriptions of hadron interaction, it has become more obvious to draw Feynman diagrams that trace through the individual constituent quarks (which are conserved) composing the interacting baryons and mesons, rather than bothering to count strong hypercharge quantum numbers. Weak hypercharge, however, remains an essential part of understanding the electroweak interaction.
References
