Isospin in the context of "Sigma baryon"

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⭐ Core Definition: Isospin

In nuclear physics and particle physics, isospin ( I ) is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin.Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons.

The name of the concept contains the term spin because its quantum mechanical description is mathematically similar to that of angular momentum (in particular, in the way it couples; for example, a proton–neutron pair can be coupled either in a state of total isospin 1 or in one of 0). But unlike angular momentum, it is a dimensionless quantity and is not actually any type of spin.

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👉 Isospin in the context of Sigma baryon

The sigma baryons are a family of subatomic hadron particles which have two quarks from the first flavour generation (up and / or down quarks), and a third quark from a higher flavour generation, in a combination where the wavefunction sign remains constant when any two quark flavours are swapped. They are thus baryons, with total isospin of 1, and can either be neutral or have an elementary charge of +2, +1, 0, or −1. They are closely related to the lambda baryons, which differ only in the wavefunction's behaviour upon flavour exchange.

The third quark can hence be either a strange (symbols Σ
, Σ
, Σ
), a charm (symbols Σ
c
, Σ
c
, Σ
c
), a bottom (symbols Σ
b
, Σ
b
, Σ
b
) or a top (symbols Σ
t
, Σ
t
, Σ
t
) quark. However, the top sigmas are expected to never be observed, since the Standard Model predicts the mean lifetime of top quarks to be roughly 5×10 s. This is about 20 times shorter than the timescale for strong interactions, and therefore it does not form hadrons.

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Isospin in the context of Strange quark

The strange quark or s quark (from its symbol, s) is the third lightest of all quarks, a type of elementary particle. Strange quarks are found in subatomic particles called hadrons. Examples of hadrons containing strange quarks include kaons (K), strange D mesons (D
s
), sigma baryons (Σ), and other strange particles.

According to the IUPAP, the symbol s is the official name, while "strange" is to be considered only as a mnemonic. The name sideways has also been used because the s quark (but also the other three remaining quarks) has an I3 value of 0 while the u ("up") and d ("down") quarks have values of +1/2 and −1/2 respectively.

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Isospin in the context of Hypercharge

In particle physics, the hypercharge (a portmanteau of hyperonic and charge) Y of a particle is a quantum number conserved under the strong interaction. The concept of hypercharge provides a single charge operator that accounts for properties of isospin, electric charge, and flavour. The hypercharge is useful to classify hadrons; the similarly named weak hypercharge has an analogous role in the electroweak interaction.

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Isospin in the context of Weak isospin

In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the W
bosons; particles with zero weak isospin do not.Weak isospin is a construct parallel to the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I, with the third component written as T3 or I3 . T3 is more important than T; typically "weak isospin" is used as short form of the proper term "3rd component of weak isospin". It can be understood as the eigenvalue of a charge operator.

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Isospin in the context of Exotic meson

In particle physics, exotic mesons are mesons that have quantum numbers not possible in the quark model; some proposals for non-standard quark model mesons could be:

All exotic mesons are classed as mesons because they are hadrons and carry zero baryon number. Of these, glueballs must be flavor singlets – that is, must have zero isospin, strangeness, charm, bottomness, and topness. Like all particle states, exotic mesons are specified by the quantum numbers which label representations of the Poincaré symmetry, q.e., by the mass (enclosed in parentheses), and by J, where J is the angular momentum, P is the intrinsic parity, and C is the charge conjugation parity; One also often specifies the isospin I of the meson. Typically, every quark model meson comes in SU(3) flavor nonet: an octet and an associated flavor singlet. A glueball shows up as an extra (supernumerary) particle outside the nonet.

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Isospin in the context of Rho meson

In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as ρ
, ρ
and ρ
. Along with pions and omega mesons, the rho meson carries the nuclear force within the atomic nucleus. After the octet consisting of the pions, kaons, and eta meson, the rho mesons are the lightest strongly interacting particle, with a mass of about 775 MeV for all three states.

The rho mesons have a very short lifetime and their decay width is about 145 MeV; because that is large compared with the mass, the resonance width measurably deviates from a Breit–Wigner form. The principal decay route of the rho mesons is to a pair of pions with a branching rate of 99.9% (however, all neutral pions is forbidden).

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