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{{Expert-subject|Physics|date=November 2008}}
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{{Flavour quantum numbers}}
 
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]].
 
== Definition ==
 
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.
 
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''&prime;), [[topness]] (''T''), and [[baryon number]] (''B'')). Mathematically, hypercharge is
 
:<math>Y = S+C+B^\prime+T+B </math>
 
and conservation of hypercharge implies a conservation of [[flavour (particle physics)|flavour]]. 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 + \frac{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 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]].
 
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>.
 
(''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.
 
{|
|-
|
[[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]]
|
[[Image:Eg2.png|250px|left|thumb|'''SU(3) weight diagram''']]
|-
|
[[Image:Eg3.png|220px|left|thumb|Note similarity with both charts on the right.]]
|
[[Image:Noneto mesônico de spin 0.png|270px|left|thumb|[[Meson]]s of spin 0 form a [[nonet]], K&nbsp;=&nbsp;[[kaon]], π&nbsp;=&nbsp;[[pion]], η&nbsp;=&nbsp;[[eta meson]]]]
|
[[Image:Baryon octet w mass.png|280px|left|thumb|The '''octet''' of light [[Spin (physics)|spin]]-1/2 baryons described in SU(3). n&nbsp;=&nbsp;[[neutron]], p&nbsp;=&nbsp;[[proton]], Λ&nbsp;=&nbsp;[[Lambda baryon]], Σ&nbsp;=&nbsp;[[Sigma baryon]], Ξ&nbsp;=&nbsp;[[Xi baryon]] ]]
|-
|
[[Image:Eg4.png|220px|left|thumb|Note similarity with chart on the right.]]
|
[[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''&nbsp;=&nbsp;[[strangeness]], ''Q''&nbsp;=&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 +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;+1/2, while neutron has ''I''<sub>3</sub>&nbsp;=&nbsp;−1/2.
* 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).
* 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.
 
== 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 (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>):
 
:<math> Y = {1 \over 3} (n_u + n_d - 2 n_s).</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 | author=Henry Semat, John R. Albright | title=Introduction to atomic and nuclear physics | publisher=Chapman and Hall | year=1984 | isbn=0-412-15670-9}}
 
[[Category:Particle physics]]
[[Category:Nuclear physics]]
[[Category:Quarks]]
[[Category:Standard Model]]
[[Category:Electroweak theory]]

Revision as of 04:13, 10 February 2014

Is actually a a strategy and often battle activation where for you must manage your different tribe and also protect it from punctures. You have to build constructions which is likely to provide protection for your current soldiers along with a person's instruction. First direct on your protection and simply after its recently been very taken treatment. You need to move forward with the criminal offense plan of action. As well as your Military facilities, you also require to keep in travel the way your group is certainly going. For instance, collecting articles as well as fostering your own tribe will be the key to good outcomes.

Secure a video game champion. These can be a lot on fun for you and then your gaming friends. You can either do this online, your own house or at a buddy's place. If you have any concerns about exactly where and how to use clash of clans cheats (Read the Full Posting), you can call us at the web page. Serve a great time snacks and get as a number of people as you can possibly involved. This is an awesome way to enjoy your game playing with companions.

Gallstones are known as your games primary forex. The Jewels are that would purchase resources along with speeding up numerous vitally important tasks. The Gallstones can also be would buy bonus items. Apart from that, this may also let the leader noticeable any undesired debris to be able to obtain a much more gems. Players has the ability to obtain Gems through constructing numerous tasks or perhaps it is using the clash of clans crack available online.

My husband and i are a group of coders that loves into play Cof. We are continuously developing Hacks to speed up Levelling easily and to benefit from more gems for clear. Without our hacks it will take you ages to reach your level.

Its important to agenda the actual apple is consistently safeguarded from association war problem because association wars are usually fought inside a improved breadth absolutely -- the following war zone. On the war region, your adapt and advance confrontation bases instead of endorsed villages; therefore, your villages resources, trophies, and absorber are never in risk.

Were you aware that some computer games are educational machines? If you know a children that likes to enjoy video games, educational choix are a fantastic generally to combine learning because of entertaining. The Web can connect you while using thousands of parents who may similar values and are more than willing that will share their reviews as well as notions with you.

So your village grows, you have to explore uncharted areas for Gold and Teak wood which are the a couple of key resources you might expect to require over start of the game ( addititionally there is almost certainly Stone resource, that your business discover later inside the type of game ). As a result of your exploration, you may very well expect to stumble to do with many islands whereby this villages happen to be held captive under BlackGuard slavery and you profit from free Gold ammenities if they are unoccupied.

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