View source for Hypercharge

{{about|a quantum number of hadrons|similar number in electroweak theory|weak hypercharge}}
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{{Flavour quantum numbers}}
In [[particle physics]], the '''hypercharge''' (a portmanteau of [[hyperon|hyperonic]] and [[charge (physics)|charge]]) ''Y'' of a [[subatomic particle|particle]] is a [[quantum number]] conserved under the [[strong interaction]]. The concept of hypercharge combines and unifies{{how|date=July 2019}} [[isospin]] and [[flavour (particle physics)|flavour]] into a single [[charge (physics)|charge operator]]. The hypercharge is useful to classify [[hadron]]s; the similarly named [[weak hypercharge]] has an analogous role in the [[electroweak interaction]].

==Definition==
Hypercharge is one of two [[quantum number]]s of the [[Eightfold way (physics) #SU(3)|SU(3) model of hadrons]], alongside [[isospin]]&nbsp;''I''<sub>3</sub>. The isospin alone is sufficient for two [[quark]] flavours—namely, {{subatomic particle|up quark|link=yes}} and {{subatomic particle|down quark|link=yes}}—whereas presently six flavours of quarks are known.

SU(3) [[weight diagram]]s (see below) are 2-dimensional with the coordinates referring to two quantum numbers, ''I''<sub>3</sub> (also known as ''I<sub>z</sub>''), which is the ''z''-component of isospin and ''Y'', which is the hypercharge (the sum of [[strangeness]]&nbsp;''S'', [[charm (quantum number)|charm]]&nbsp;''C'', [[bottomness]]&nbsp;''B''&prime;, [[topness]]&nbsp;''T'', and [[baryon number]]&nbsp;''B''). Mathematically, hypercharge is

:<math>Y = S+C+B^\prime+T+B. </math>

Strong interactions conserve hypercharge, but weak interactions do not.

==Relation with electric charge and isospin==
{{Main|Gell-Mann–Nishijima formula}}
The [[Gell-Mann–Nishijima formula]] relates isospin and [[electric charge]]

:<math> Q = I_3 + \tfrac{1}{2}Y,</math>

where ''I''<sub>3</sub> 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 ''I''<sub>3</sub> values is 0.

==SU(3) model in relation to hypercharge==
The SU(2) model has [[multiplet]]s characterized by a quantum number ''J'', which is the total [[angular momentum]]. Each multiplet consists of {{nowrap|2''J'' + 1}} [[Quantum state|substates]] with equally-spaced values of ''J<sub>z</sub>'', 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|{{SubatomicParticle|Omega-}} 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 ''λ''<sub>1</sub> and ''λ''<sub>2</sub>.

{{nowrap|(''λ''<sub>1</sub> + 1)}} specifies the number of points in the topmost side of the [[hexagon]] while {{nowrap|(''λ''<sub>2</sub> + 1)}} specifies the number of points on the bottom side.

{{gallery
| width=290
| Image:Eg1.png
| '''SU(3) singlet weight diagram''', where ''Y'' is hypercharge and ''I''<sub>3</sub> is the third component of isospin.
| Image:Eg2.png
| '''SU(3) triplet weight diagram'''
| Image:Eg3.png
| '''SU(3) septet, octet, and nonet weight diagram''' Note similarity with both charts on the right. The number used to describe the weight diagram depends on whether the particle(s) occupying the center of the diagram have one, two, or three distinct names.
| Image:Noneto mesônico de spin 0.png
| [[Meson]]s of spin 0 form a '''nonet'''. K:&nbsp;[[kaon]], π:&nbsp;[[pion]], η:&nbsp;[[eta meson]].
| Image:Baryon octet w mass.png
| The '''octet''' of light [[Spin (physics)|spin]]-{{sfrac|1|2}} baryons described in SU(3). n:&nbsp;[[neutron]], p:&nbsp;[[proton]], Λ:&nbsp;[[Lambda baryon]], Σ:&nbsp;[[Sigma baryon]], Ξ:&nbsp;[[Xi baryon]].
| Image:Eg4.png
| '''SU(3) decuplet weight diagram''' Note similarity with chart on the right.
| Image:Baryon decuplet w mass.png
| A combination of three up, down or strange [[quark]]s with a total spin of {{sfrac|3|2}} form the so-called '''baryon decuplet'''. The lower six are hyperons. ''S'':&nbsp;[[strangeness]], ''Q'':&nbsp;[[electric charge]].
}}

==Examples==
*The [[nucleon]] group ([[proton]]s with ''Q''&nbsp;=&nbsp;+1 and [[neutron]]s with ''Q''&nbsp;=&nbsp;0) have an average charge of +{{sfrac|1|2}}, so they both have hypercharge ''Y''&nbsp;=&nbsp;1 (baryon number ''B''&nbsp;=&nbsp;+1, ''S''&nbsp;=&nbsp;''C''&nbsp;=&nbsp;''B''&prime;&nbsp;=&nbsp;''T''&nbsp;=&nbsp;0). From the Gell-Mann–Nishijima formula we know that proton has isospin ''I''<sub>3</sub>&nbsp;=&nbsp;+{{sfrac|1|2}}, while neutron has ''I''<sub>3</sub>&nbsp;=&nbsp;−{{sfrac|1|2}}.
*This also works for [[quark]]s: for the ''up'' quark, with a charge of +{{sfrac|2|3}}, and an ''I''<sub>3</sub> of +{{sfrac|1|2}}, we deduce a hypercharge of {{sfrac|1|3}}, due to its baryon number (since three quarks make a baryon, a quark has a baryon number of {{sfrac|1|3}}).
*For a ''strange'' quark, with charge −{{sfrac|1|3}}, a baryon number of {{sfrac|1|3}} and [[strangeness]] of −1 we get a hypercharge ''Y'' = −{{sfrac|2|3}}, so we deduce an ''I''<sub>3</sub>&nbsp;=&nbsp;0. That means that a ''strange'' quark makes an isospin singlet of its own (same happens with ''charm'', ''bottom'' and ''top'' quarks), while ''up'' and ''down'' constitute an isospin doublet.

==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 hypercharge ''Y'' is the following combination of the numbers of [[up quark|up]] (''n''<sub>u</sub>), [[down quark|down]] (''n''<sub>d</sub>), [[strange quark|strange]] (''n''<sub>s</sub>), [[charm quark|charm]] (''n''<sub>c</sub>), [[top quark|top]] (''n''<sub>t</sub>) and [[bottom quark|bottom]] (''n''<sub>b</sub>):

:<math> Y = \tfrac13 \left(n_u + n_d - 2 n_s + 4 n_c - 2 n_b + 4 n_t\right).</math>

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

==References==
*{{cite book | first1=Henry |last1=Semat |first2=John R. |last2=Albright | title=Introduction to Atomic and Nuclear Physics | publisher=Chapman and Hall | year=1984 | isbn=978-0-412-15670-0}}

[[Category:Particle physics]]
[[Category:Nuclear physics]]
[[Category:Quarks]]
[[Category:Standard Model]]
[[Category:Electroweak theory]]

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