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| {{Expert-subject|Physics|date=November 2008}}
| | Hello and welcome. My name is Figures Wunder. Doing ceramics is what her family members and her appreciate. Minnesota has usually been his home but his spouse wants them to move. My working day job is a meter reader.<br><br>My homepage :: [http://Shortener.us/dietfooddelivery78594 diet meal delivery] |
| {{Flavour quantum numbers}}
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| In [[particle physics]], the '''hypercharge''' ''Y'' of a particle is related to the [[strong interaction]], and is distinct from the similarly named [[weak hypercharge]], which has an analogous role in the [[electroweak interaction]]. The concept of hypercharge combines and unifies [[isospin]] and [[flavour (particle physics)|flavour]] into a single [[charge (physics)|charge]].
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| == Definition ==
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| Hypercharge in particle physics is a [[quantum number]] relating the [[strong interaction]]s of the [[SU(3)|SU(3) model]]. [[Isospin]] is defined in the [[SU(2)]] model while the SU(3) model defines hypercharge.
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| SU(3) [[weight diagram]]s (see below) are 2 dimensional with the coordinates referring to two quantum numbers, ''I''<sub>z</sub>, which is the z-component of isospin and ''Y'', which is the hypercharge (the sum of [[strangeness]] (''S''), [[charm (quantum number)|charm]] (''C''), [[bottomness]] (''B''′), [[topness]] (''T''), and [[baryon number]] (''B'')). Mathematically, hypercharge is
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| :<math>Y = S+C+B^\prime+T+B </math>
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| and conservation of hypercharge implies a conservation of [[flavour (particle physics)|flavour]]. Strong interactions conserve hypercharge, but weak interactions do not.
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| == Relation with Electric charge and Isospin ==
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| {{Main|Gell-Mann–Nishijima formula}}
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| The [[Gell-Mann–Nishijima formula]] relates isospin and [[electric charge]]
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| :<math> Q = I_3 + \frac{1}{2}Y,</math>
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| where ''I''<sub>3</sub> is the third component of isospin and ''Q'' is the particle's charge.
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| Isospin creates multiplets of particles whose average charge is related to the hypercharge by:
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| :<math> Y = 2 \bar Q.</math>
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| since the hypercharge is the same for all members of a multiplet, and the average of the ''I''<sub>3</sub> values is 0.
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| == SU(3) model in relation to hypercharge ==
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| The SU(2) model has [[multiplet]]s characterized by a quantum number ''J'', which is the total [[angular momentum]]. Each multiplet consists of 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 formalises 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]].
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| The SU(3) has ''supermultiplets'' containing SU(2) multiplets. SU(3) now needs 2 numbers to specify all its sub-states which are denoted by ''λ''<sub>1</sub> and ''λ''<sub>2</sub>.
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| (''λ''<sub>1</sub> + 1) specifies the number of points in the topmost side of the [[hexagon]] while (''λ''<sub>2</sub> + 1) specifies the number of points on the bottom side.
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| {|
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| [[Image:Eg1.png|220px|left|thumb|'''SU(3) weight diagram''', where ''Y'' is Hypercharge and ''I''<sub>3</sub> is the third component of isospin]]
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| [[Image:Eg2.png|250px|left|thumb|'''SU(3) weight diagram''']]
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| [[Image:Eg3.png|220px|left|thumb|Note similarity with both charts on the right.]]
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| [[Image:Noneto mesônico de spin 0.png|270px|left|thumb|[[Meson]]s of spin 0 form a [[nonet]], K = [[kaon]], π = [[pion]], η = [[eta meson]]]]
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| [[Image:Baryon octet w mass.png|280px|left|thumb|The '''octet''' of light [[Spin (physics)|spin]]-1/2 baryons described in SU(3). n = [[neutron]], p = [[proton]], Λ = [[Lambda baryon]], Σ = [[Sigma baryon]], Ξ = [[Xi baryon]] ]]
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| [[Image:Eg4.png|220px|left|thumb|Note similarity with chart on the right.]]
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| [[Image:Baryon decuplet w mass.png|290px|left|thumb|A combination of three u, d or s-[[quark]]s with a total spin of 3/2 form the so-called '''baryon decuplet'''. The lower six are hyperons. ''S'' = [[strangeness]], ''Q'' = [[electric charge]]]]
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| |}
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| == Examples ==
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| * The [[nucleon]] group ([[proton]]s with ''Q'' = +1 and [[neutron]]s with ''Q'' = 0) have an average charge of +1/2, so they both have hypercharge ''Y'' = 1 (baryon number ''B'' = +1, ''S'' = ''C'' = ''B''′ = ''T'' = 0). From the Gell-Mann–Nishijima formula we know that proton has isospin ''I''<sub>3</sub> = +1/2, while neutron has ''I''<sub>3</sub> = −1/2.
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| * This also works for [[quark]]s: for the ''up'' quark, with a charge of +2/3, and an ''I''<sub>3</sub> 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).
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| * For a ''strange'' quark, with charge −1/3, a baryon number of 1/3 and [[strangeness]] of −1 we get a hypercharge ''Y'' = −2/3, so we deduce an ''I''<sub>3</sub> = 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.
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| == Practical obsolescence ==
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| 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 (if one only includes the up, down and strange quarks out of the total 6 quarks in the Standard Model), hypercharge ''Y'' is the following combination of the numbers of [[up quark|up]] (''n''<sub>u</sub>), [[down quark|down]] (''n''<sub>d</sub>), and [[strange quark]]s(''n''<sub>s</sub>):
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| :<math> Y = {1 \over 3} (n_u + n_d - 2 n_s).</math>
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| 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]].
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| == References ==
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| * {{cite book | author=Henry Semat, John R. Albright | title=Introduction to atomic and nuclear physics | publisher=Chapman and Hall | year=1984 | isbn=0-412-15670-9}}
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| [[Category:Particle physics]]
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| [[Category:Nuclear physics]]
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| [[Category:Quarks]]
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| [[Category:Standard Model]]
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| [[Category:Electroweak theory]]
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Hello and welcome. My name is Figures Wunder. Doing ceramics is what her family members and her appreciate. Minnesota has usually been his home but his spouse wants them to move. My working day job is a meter reader.
My homepage :: diet meal delivery