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hypercharge

 
Dictionary: hy·per·charge   ('pər-chärj') pronunciation
n. (Symbol Y)
A quantum number equal to twice the average electric charge of a particle multiplet or, equivalently, to the sum of the strangeness and the baryon number.


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Sci-Tech Encyclopedia: Hypercharge
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A quantized attribute, analogous to electric charge, introduced in the classification of a subset of elementary particles—the so-called baryons—including the proton and neutron as its lightest members. As far as is known, electric charge is absolutely conserved in all physical processes. Hypercharge was introduced to formalize the observation that certain decay modes of baryons expected to proceed by means of the strong nuclear force simply were not observed. See also Electric charge.

Unlike electric charge, however, the postulated hypercharge was found not to be conserved absolutely; the weak nuclear interactions do not conserve hypercharge—and indeed can change hypercharge by ±1 or 0 units.

When the known baryons are classified according to their electric charge and their hypercharge, they naturally group into octets in the scheme first proposed by M. Gell-Mann and K. Nishijima. The quarks, hypothesized as the fundamental building blocks of matter, must have fractional hypercharge as well as electrical charge; the simplest quark model suggests values of 1/3 and 2/3, respectively. See also Baryon; Elementary particle; Quantum mechanics; Quarks; Unitary symmetry.


Wikipedia: Hypercharge
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Flavour in particle physics
Flavour quantum numbers:

Combinations:

  • Hypercharge: Y
    • Y = (B + S + C + B′ + T)
    • Y = 2 (QI3)
  • Weak hypercharge: YW
    • YW = 2 (QT3)
    • X + 2YW = 5 (BL)

Flavour mixing

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 into a single charge.

Contents

Definition

Hypercharge in particle physics is a quantum number relating the strong interactions of the Special Unitary of a 3x3 matrix algebraic structure or SU(3) model. Isospin is defined in the SU(2) model while the SU(3) model defines hypercharge.

SU(3) weight diagrams (see below) are 2 dimensional with the coordinates referring to two quantum numbers, Iz, which is the z-component of isospin and Y, which is the hypercharge (the sum of strangeness (S), charm (C), bottomness (B′), topness (T), and baryon number (B)). Mathematically, hypercharge is

Y =  S+C+B^\prime+T+B

and conservation of hypercharge implies a conservation of flavours. Strong interactions conserve hypercharge, but weak interactions do not.

Relation with Electric charge and Isospin

The Gell-Mann–Nishijima formula relates isospin and electric charge

(1) \qquad Q = I_3 + \frac{1}{2}Y,

where I3 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:

(3) \qquad Y = 2 \bar Q.

Since the hypercharge is the same for all members of a multiplet, and the average of the I3 values is 0.

SU(3) model in relation to hypercharge

The SU(2) model has multiplets characterized by a quantum number J, which is the total angular momentum. Each multiplet consists of 2J + 1 substates with equally spaced values of Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalises the observation that certain strong baryon decay were not observed leading to the prediction of the mass, strangeness and charge of the Ω 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 λ1 and λ2.

1 + 1) specifies the number of points in the topmost side of the hexagon while (λ2 + 1) specifies the number of points on the bottom side.

SU(3) weight diagram, where Y is Hypercharge and I3 is the third component of isospin
SU(3) weight diagram
Note similarity with both charts on the right.
Mesons of spin 0 form a nonet
The octet of light spin-1/2 baryons described in SU(3). n=neutron, p=proton, Λ, Σ and Ξ are hyperons
Note similarity with chart on the right.
A combination of three u, d or s-quarks with a total spin of 3/2 form the so-called baryon decuplet. The lower six are hyperons. S=Strangeness, Q= Electric charge

Examples

  • The nucleon group (protons with Q = +1 and neutrons 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 I3 = +1/2, while neutron has I3 = −1/2.
  • This also works for quarks: for the up quark, with a charge of +2/3, and an I3 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 I3 = 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 "subatomic 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, down and strange quarks (nu) , (nd), (ns):

(4) \qquad Y = {1 \over 3} (n_u + n_d - 2 n_s).

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

See also

References

  • Henry Semat, John R. Albright (1984). Introduction to atomic and nuclear physics. Chapman and Hall. ISBN 0-412-15670-9. 

 
 

 

Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
Sci-Tech Encyclopedia. McGraw-Hill Encyclopedia of Science and Technology. Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Hypercharge" Read more