Hypercharge

From Academic Kids

Template:Flavour quantum numbers

In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness <math>\tilde B<math> and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before strong-interacting with other quarks).

<math>(1) \qquad Y = B + S + C + \tilde B + T<math>

Originally, hypercharge only included the strangeness flavor in its definition. Do not confuse hypercharge with weak hypercharge: the first one is connected to the strong interaction, while the second appears on the electroweak interaction.

The Gell-Mann/Nishijima Law relates hypercharge with isospin and electric charge:

<math>(2) \qquad Q = I_z + {1 \over 2} Y<math>

where Iz is the third component of isospin and Q is the particle's charge. This allow us to express the hypercharge in terms of isospin and charge:

<math>(3) \qquad Y = 2(Q - I_z) <math>

Isospin creates multiplets of particles whose average charge is related to the hypercharge by:

<math>(4) \qquad Y = 2 \bar Q<math>.

which is easily derived from (3), since the hypercharge is the same for all members of a multiplet, and the average of the Iz values is 0.

Examples:

  • The nucleon group (proton plus neutron) have an average charge of 1 + 0 = +1/2, so they both have hypercharge Y = 1 (baryon number B = +1, flavor charges set to 0). From Gell-Mann/Nishima Law we know that proton has isospin +1 - 1/2 = +1/2, while neutron is the 0 − 1/2 = −1/2.
  • This also works for quarks: for the up quark, with a charge of +2/3, and an Iz of +1/2, we deduce a hypercharge of 1/3, due to its barion number (since you need 3 quarks to make a baryon, a quark has baryon number of &plusminus;1/3).
  • For a strange quark, with charge −1/3, a barion number of 1/3 and strangeness of −1 we get an hypercharge Y = −1/3, so we deduce an Iz = 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 a isospin doublet.

See also

Navigation

Academic Kids Menu

  • Art and Cultures
    • Art (http://www.academickids.com/encyclopedia/index.php/Art)
    • Architecture (http://www.academickids.com/encyclopedia/index.php/Architecture)
    • Cultures (http://www.academickids.com/encyclopedia/index.php/Cultures)
    • Music (http://www.academickids.com/encyclopedia/index.php/Music)
    • Musical Instruments (http://academickids.com/encyclopedia/index.php/List_of_musical_instruments)
  • Biographies (http://www.academickids.com/encyclopedia/index.php/Biographies)
  • Clipart (http://www.academickids.com/encyclopedia/index.php/Clipart)
  • Geography (http://www.academickids.com/encyclopedia/index.php/Geography)
    • Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
    • Maps (http://www.academickids.com/encyclopedia/index.php/Maps)
    • Flags (http://www.academickids.com/encyclopedia/index.php/Flags)
    • Continents (http://www.academickids.com/encyclopedia/index.php/Continents)
  • History (http://www.academickids.com/encyclopedia/index.php/History)
    • Ancient Civilizations (http://www.academickids.com/encyclopedia/index.php/Ancient_Civilizations)
    • Industrial Revolution (http://www.academickids.com/encyclopedia/index.php/Industrial_Revolution)
    • Middle Ages (http://www.academickids.com/encyclopedia/index.php/Middle_Ages)
    • Prehistory (http://www.academickids.com/encyclopedia/index.php/Prehistory)
    • Renaissance (http://www.academickids.com/encyclopedia/index.php/Renaissance)
    • Timelines (http://www.academickids.com/encyclopedia/index.php/Timelines)
    • United States (http://www.academickids.com/encyclopedia/index.php/United_States)
    • Wars (http://www.academickids.com/encyclopedia/index.php/Wars)
    • World History (http://www.academickids.com/encyclopedia/index.php/History_of_the_world)
  • Human Body (http://www.academickids.com/encyclopedia/index.php/Human_Body)
  • Mathematics (http://www.academickids.com/encyclopedia/index.php/Mathematics)
  • Reference (http://www.academickids.com/encyclopedia/index.php/Reference)
  • Science (http://www.academickids.com/encyclopedia/index.php/Science)
    • Animals (http://www.academickids.com/encyclopedia/index.php/Animals)
    • Aviation (http://www.academickids.com/encyclopedia/index.php/Aviation)
    • Dinosaurs (http://www.academickids.com/encyclopedia/index.php/Dinosaurs)
    • Earth (http://www.academickids.com/encyclopedia/index.php/Earth)
    • Inventions (http://www.academickids.com/encyclopedia/index.php/Inventions)
    • Physical Science (http://www.academickids.com/encyclopedia/index.php/Physical_Science)
    • Plants (http://www.academickids.com/encyclopedia/index.php/Plants)
    • Scientists (http://www.academickids.com/encyclopedia/index.php/Scientists)
  • Social Studies (http://www.academickids.com/encyclopedia/index.php/Social_Studies)
    • Anthropology (http://www.academickids.com/encyclopedia/index.php/Anthropology)
    • Economics (http://www.academickids.com/encyclopedia/index.php/Economics)
    • Government (http://www.academickids.com/encyclopedia/index.php/Government)
    • Religion (http://www.academickids.com/encyclopedia/index.php/Religion)
    • Holidays (http://www.academickids.com/encyclopedia/index.php/Holidays)
  • Space and Astronomy
    • Solar System (http://www.academickids.com/encyclopedia/index.php/Solar_System)
    • Planets (http://www.academickids.com/encyclopedia/index.php/Planets)
  • Sports (http://www.academickids.com/encyclopedia/index.php/Sports)
  • Timelines (http://www.academickids.com/encyclopedia/index.php/Timelines)
  • Weather (http://www.academickids.com/encyclopedia/index.php/Weather)
  • US States (http://www.academickids.com/encyclopedia/index.php/US_States)

Information

  • Home Page (http://academickids.com/encyclopedia/index.php)
  • Contact Us (http://www.academickids.com/encyclopedia/index.php/Contactus)

  • Clip Art (http://classroomclipart.com)
Toolbox
Personal tools