View source for Physics:Hypercharge

{{Short description|Type of particle charge found in the Standard Model}}
{{Flavour quantum numbers}}
In [[Physics:Particle physics|particle physics]], the '''hypercharge''' (a portmanteau of [[Physics:Hyperon|hyperon]]ic and [[Physics:Charge|charge]]) ''Y'' of a [[Physics:Subatomic particle|particle]] is a [[Physics:Quantum number|quantum number]] conserved under the [[Physics:Strong interaction|strong interaction]]. The concept of hypercharge provides a single [[Physics:Charge|charge operator]] that accounts for properties of [[Physics:Isospin|isospin]], [[Physics:Electric charge|electric charge]], and [[Physics:Flavour (particle physics)|flavour]]. The hypercharge is useful to classify [[Physics:Hadron|hadron]]s; the similarly named [[Physics:Weak hypercharge|weak hypercharge]] has an analogous role in the [[Physics:Electroweak interaction|electroweak interaction]].

==Definition==
Hypercharge is one of two [[Physics:Quantum number|quantum number]]s of the [[Physics:Eightfold way#SU(3)|SU(3) model of hadrons]], alongside [[Physics:Isospin|isospin]]&nbsp;{{mvar|I}}{{sub|3}}. The isospin alone was sufficient for two [[Physics:Quark|quark]] flavours — namely {{subatomic particle|up quark|link=yes}} and {{subatomic particle|down quark|link=yes}} — whereas presently 6&nbsp;[[Physics:Flavour (particle physics)|flavours]] of quarks are known.

SU(3) weight diagrams (see below) are 2&nbsp;dimensional, with the coordinates referring to two quantum numbers: {{mvar|I}}{{sub|3}} (also known as {{mvar|I}}{{sub|z}}), which is the {{math|z}}&nbsp;component of isospin, and {{mvar|Y}}, which is the hypercharge (defined by [[Physics:Strangeness|strangeness]]&nbsp;{{mvar|S}}, [[Physics:Charm (quantum number)|charm]]&nbsp;{{mvar|C}}, [[Physics:Bottomness|bottomness]]&nbsp;{{mvar|B&prime;}}, [[Physics:Topness|topness]]&nbsp;{{mvar|T&prime;}}, and [[Physics:Baryon number|baryon number]]&nbsp;{{mvar|B}}). Mathematically, hypercharge is <ref>{{citation|date=2022|editor=Particle Data Group|format=PDF|language=en|title=15. Quark Model|url=https://pdg.lbl.gov/2022/reviews/rpp2022-rev-quark-model.pdf}}<!-- auto-translated by Module:CS1 translator --></ref>

:<math>Y = B + S - \frac{C - B' + T'}{3} ~. </math>

Strong interactions conserve hypercharge (and [[Physics:Weak hypercharge|weak hypercharge]]), but [[Physics:Weak interaction|weak interaction]]s do ''not''.

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

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 [[Physics:Multiplet|multiplet]]s characterized by a quantum number ''J'', which is the total [[Physics:Angular momentum|angular momentum]]. Each multiplet consists of {{nowrap|2''J'' + 1}} [[Physics: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 [[Physics: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|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
| [[Physics:Meson|Meson]]s of spin 0 form a '''nonet'''. K:&nbsp;[[Physics:Kaon|kaon]], π:&nbsp;[[Physics:Pion|pion]], η:&nbsp;[[Physics:Eta meson|eta meson]].
| Image:Baryon octet w mass.png
| The '''octet''' of light [[Physics:Spin|spin]]-{{sfrac|1|2}} baryons described in SU(3). n:&nbsp;[[Physics:Neutron|neutron]], p:&nbsp;[[Physics:Proton|proton]], Λ:&nbsp;[[Physics:Lambda baryon|Lambda baryon]], Σ:&nbsp;[[Physics:Sigma baryon|Sigma baryon]], Ξ:&nbsp;[[Physics:Xi baryon|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 [[Physics:Quark|quark]]s with a total spin of {{sfrac|3|2}} form the so-called '''baryon decuplet'''. The lower six are hyperons. ''S'':&nbsp;[[Physics:Strangeness|strangeness]], ''Q'':&nbsp;[[Physics:Electric charge|electric charge]].
}}

==Examples==
* The [[Physics:Nucleon|nucleon]] group ([[Physics:Proton|proton]]s with {{nowrap| {{mvar|Q}} {{=}} +1 }} and [[Physics:Neutron|neutron]]s with {{nowrap| {{mvar|Q}} {{=}} 0 }}) have an average charge of {{sfrac|+|1|2}}, so they both have hypercharge {{nowrap| {{mvar|Y}} {{=}} 1 }} (since baryon number {{nowrap| {{mvar|B}} {{=}} +1 ,}} and {{nowrap|1= {{mvar|S}} = {{mvar|C}} = {{mvar|B&prime;}} = {{mvar|T&prime;}} = 0 }}). From the Gell-Mann–Nishijima formula we know that proton has isospin {{nowrap| {{mvar|I}}{{sub|3}} {{=}} {{sfrac|+|1|2}} ,}} while neutron has {{nowrap| {{mvar|I}}{{sub|3}} {{=}} {{sfrac|−|1|2}} .}}
* This also works for [[Physics:Quark|quark]]s: For the ''up'' quark, with a charge of {{sfrac|+|2|3}}, and an {{mvar|I}}{{sub|3}} of {{sfrac|+|1|2}}, we deduce a hypercharge of {{sfrac|1|3}}, due to its baryon number (since three quarks make a baryon, each quark has a baryon number of {{sfrac|+|1|3}}).
* For a ''strange'' quark, with electric charge {{sfrac|−|1|3}}, a baryon number of {{sfrac|+|1|3}}, and [[Physics:Strangeness|strangeness]] −1, we get a hypercharge {{nowrap| {{mvar|Y}} {{=}} {{sfrac|−|2|3}} ,}} so we deduce that {{nowrap| {{mvar|I}}{{sub|3}} {{=}} 0 .}} 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 {{nowrap| {{mvar|Y}} {{=}} 0 }}.

==Practical obsolescence==
Hypercharge was a concept developed in the 1960s, to organize groups of particles in the ''"[[Physics:Particle zoo|particle zoo]]"'' and to develop ''ad hoc'' conservation laws based on their observed transformations. With the advent of the [[Physics:Quark model|quark model]], it is now obvious that strong hypercharge, {{mvar|Y}}, is the following combination of the numbers of [[Physics:Up quark|up]]&nbsp;({{mvar|n}}{{sub|u}}), [[Physics:Down quark|down]]&nbsp;({{mvar|n}}{{sub|d}}), [[Physics:Strange quark|strange]]&nbsp;({{mvar|n}}{{sub|s}}), [[Physics:Charm quark|charm]]&nbsp;({{mvar|n}}{{sub|c}}), [[Physics:Top quark|top]]&nbsp;({{mvar|n}}{{sub|t}}) and [[Physics:Bottom quark|bottom]]&nbsp;({{mvar|n}}{{sub|b}}):

:<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 [[Physics:Hadron|hadron]] interaction, it has become more obvious to draw [[Physics:Feynman diagram|Feynman diagram]]s that trace through the individual constituent quarks (which are conserved) composing the interacting [[Physics:Baryon|baryon]]s and [[Physics:Meson|meson]]s, rather than bothering to count strong hypercharge quantum numbers. ''[[Physics:Weak hypercharge|Weak hypercharge]]'', however, remains an essential part of understanding the [[Physics:Electroweak interaction|electroweak interaction]].

==References==
{{Reflist}}
*{{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:Nuclear physics]]
[[Category:Quarks]]
[[Category:Standard Model]]
[[Category:Electroweak theory]]

he:היפרמטען

{{Sourceattribution|Hypercharge}}