User talk:Vectorboson

welcome! Count Iblis (talk) 23:44, 1 May 2008 (UTC)

"LIST OF BARYONS" SECTION UNDER CONSTRUCTION:

Relation between isospin and up and down quark content

The third component of isospin for the up quark is 1⁄2; for the down quark it is - 1⁄2; and it is zero for the other quarks. The third component of isospin for a baryon is simply the sum of that of its quarks. Different baryons that have the same constituent quarks are distinguishable by their other characteristics (like spin).

Particles of isospin 3⁄2 can only be made by a mixture of three u and d quarks.
The four
Δ
s are:

Δ⁺⁺
(uuu) with Iz = 3⁄2

Δ⁺
(uud) with Iz = 1⁄2

Δ⁰
(udd) with Iz = - 1⁄2

Δ⁻
(ddd) with Iz = - 3⁄2

Particles of isospin 1 are made of one c, s, or b quark together with two u quarks or two d quarks or a u and a d quark.
The nine
Σ
s are:

Σ⁺
(uus),
Σ⁰
(uds),
Σ⁺
(dds), with Iz being +1, 0, -1 respectively

Σ⁺⁺
_c (uuc),
Σ⁺
_c (udc),
Σ⁰
_c (ddc), with Iz being +1, 0, -1 respectively

Σ⁺
_b (uub),
Σ⁰
_b (udb),
Σ⁻
_b (ddb) with Iz being +1, 0, -1 respectively

Particles of isospin 1⁄2 can be made of two u quarks and one d quark, or two d quarks and one u quark.
The two
N
s are:

p⁺
(uud),
n⁰
(udd)

They can also be made of a combination of two c, s, or b quarks together with one u or d quark.
The twelve
Ξ
s are:

Ξ⁰
(uss),
Ξ⁻
(dss),

Ξ⁺
_c (usc),
Ξ⁰
_c (dsc),

Ξ⁺⁺
_cc (ucc),
Ξ⁺
_cc (dcc),

Ξ⁰
_b (usb),
Ξ⁻
_b (dsb),

Ξ⁺
_cb (ucb),
Ξ⁰
_cb (dcb),

Ξ⁰
_bb (ubb),
Ξ⁻
_bb (dbb)

Particles of isospin 0 can be made of one u and one d quark plus one c, s, or b.
The three
Λ
s are:

Λ⁰
(uds),

Λ⁺
_c (udc),

Λ⁰
_b (udb)

Isospin 0 baryons can also be made of no u or d quarks at all.
The ten
Ω
s are:

Ω⁻
(sss),
Ω⁰
_c (ssc),
Ω⁺
_cc (scc),
Ω⁻
_b (ssb),
Ω⁰
_cb (scb),
Ω⁻
_bb (sbb)

Ω⁺⁺
_ccc (ccc},
Ω⁺
_ccb (ccb),
Ω⁰
_cbb (cbb),

Ω⁻
_bbb (bbb)

Rules for making baryons

With my old rules, I could make every baryons out there with no extra baryons. The rules were quarks of the same flavor must have their isospin aligned, and quarks of different flavor can, but need not, have their isospin aligned. See Talk:List of baryons#List Progress Overview for the list of particles and their corresponding isospin values it gave me.

Now if I go with the PDG rules; that I and I_z are additive numbers and that I = 1⁄2 for u and d quarks and that I_z = 1⁄2 for u and −1⁄2 for d, then I can't account for nucleons (can't get isospin 1⁄2 with three u or d quarks, and Lambda's (can't get isospin 0 with a u and d quark).

So what am I missing? [[::User:Headbomb|Headbomb]] ([[::User talk:Headbomb|talk]] · [[::Special:Contributions/Headbomb|contribs]]) 13:32, 3 May 2008 (UTC)

First, I-spin is NOT additive, I_z IS additive-- so forget about I-spin for a minute and concentrate on I_z. When constructing composite particles, I_z is the additive quantum number. A proton has two up quarks and one down quark -- the I_z values add to 1/2. The neutron had two down quarks and one up quark-- the I_z values add to -1/2. I-spin doesn't have a direction in real space, so I-spin CANNOT "align" as can spin.

Lambda's have one up and one down quark (total I_z = 0) plus another quark with I_z = 0 -- total lambda I_z then = 0.

Did that help?--Vectorboson (talk) 01:01, 4 May 2008 (UTC)