18 votes
Accepted

$SU(3)_F$ flavour symmetry and $SU(2)$ isospin symmetry

Both SU(3) flavor and SU(2) isospin are approximate symmetries of the Standard Model at low energies. Consider physics below the proton mass, where we can talk about the pions and kaons that are the ...
Henry Deith's user avatar
  • 1,116
16 votes
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How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content?

The isospin is different. $I=0$ for the $\Lambda^0$ and $I=1$ for the $\Sigma^{0}$. This makes the $\Lambda^0$ an isospin singlet state but the $\Sigma^0$ is part of an isospin triplet. There are ...
ProfRob's user avatar
  • 131k
13 votes
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What makes the number of neutrons the number of proton similar?

You probably know that the electrons in atoms occupy a series of energy levels, the $1s$, $2s$, $2p$, etc orbitals. Although the structure of nuclei is complicated, basically the same idea applies to ...
John Rennie's user avatar
11 votes
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Why $U(1)_Y$ hypercharge rather than $U(1)_\text{em}$ electromagnetism?

Short answer: to accurately model reality. Long answer: The weak interaction has several peculiar properties: The $W$ bosons are vector bosons (so the weak theory is likely a gauge theory) The $W$ ...
Luke Pritchett's user avatar
11 votes
Accepted

What is the symmetry of the pion triplet ($\pi^{-}, \pi^{0}, \pi^{+}$)?

$\newcommand{\BK}[3]{\left|{#1},{#2}\right\rangle_{#3}} \newcommand{\BKB}[3]{\mathbf{\left|{#1},{#2}\right\rangle_{\boldsymbol{#3}}}} \newcommand{\FR}[2]{{\textstyle \frac{#1}{#2}}} \...
Frobenius's user avatar
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10 votes

Why is there no baryon isospin singlet with spin 3/2?

Symmetry and statistics. The quarks being fermions dictate a fully antisymmetric wavefunction of the three constituents of the baryon. The color wavefunction is antisymmetric, so the combined spin&...
Cosmas Zachos's user avatar
10 votes
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Why is there no baryon isospin singlet with spin 3/2?

First, the neutron $n$ and the proton $p$ don't have "excited counterparts" in the decuplet, either, do they? Now, the two multiplets are completely different. One has eight $SU(3)_{\rm flavor}$ ...
Luboš Motl's user avatar
8 votes

Isospin conservation for total isospin or third component of isospin?

The third component of isospin is isomorphic to electric charge, which is (so far as we know) an exact symmetry in all systems. The total isospin is an approximate symmetry of the strong nuclear ...
rob's user avatar
  • 89.9k
7 votes

How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content?

how can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content? Doesn't this make them the same baryon? Well, the basic difference which started their group classification is that $\Lambda$ has a ...
anna v's user avatar
  • 234k
7 votes

How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content?

To start 3 quarks u,d,s form an irreducible representation for the SU(3) group. Now $\mathbf{3\times 3\times 3} = \mathbf{10+8+8+1}$ for the SU(3) group. The first irreducible representation 10 has 10 ...
Siddharth Dhanpal's user avatar
7 votes

How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content?

A similar question is the following. How can $\pi^0$ and $\eta$ in the $SU(3)_F$ meson octet both have the same $SU(3)_F$ flavor content? One could answer that this is because $\pi^0$ is part of ...
Qmechanic's user avatar
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7 votes
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Why is neutron slightly heavier than the proton?

There is an easy partial answer to the question. The proton is (uud) and the neutron is (udd). The up quark is 2.2MeV and the down quark is 4.7MeV. So there is a 2.5MeV mass increase with the neutron. ...
Lawrence B. Crowell's user avatar
6 votes

Motivation for isospin

Quite generally in quantum mechanics, we know that whenever we have a set of states which are degeneratein energy (or mass) there is no unique way of specifying the states: any linear combination of ...
Mass's user avatar
  • 2,020
6 votes

What is the third component of the isospin, $I_3$?

The proton and neutron are the two projections of the nucleon on the third axis of the isospin operator, like "spin up" and "spin down" are the two projections of angular momentum on your favorite ...
rob's user avatar
  • 89.9k
6 votes

Motivation for the $\text{SU}_f(3)$ flavour symmetry of Gell-Mann and why did it work?

Some history Is it because three more quarks $(c,b,t)$ were not discovered at that time? People even didn't know about quarks when Gell-Mann was discovering his "eightfold way" (and long-long ...
Name YYY's user avatar
  • 8,821
6 votes
Accepted

What does it mean if an intertwiner respects a group action?

Usually when one says a function $f$ respects a group action, they mean that $f$ and the group action commute. To be specific, let $g\in G$, $f: X \rightarrow Y$, and the group action of $G$ on $X$ ...
Aaron's user avatar
  • 2,889
6 votes

What makes the number of neutrons the number of proton similar?

A phenomenological model can be described in terms of the liquid drop model and semi-empirical mass formula. This ascribes a nucleus a binding energy of $$B(A,Z) = a_v A - a_s A^{2/3} - a_c Z^2A^{-1/...
ProfRob's user avatar
  • 131k
6 votes
Accepted

Where does $SU(2)$ isospin symmetry come from?

DomDoe's answer is the historical answer, but I suspect that mithusengupta123 may really be asking something like: Given our understanding of the Standard Model of particle physics, how is it that ...
Henry Deith's user avatar
  • 1,116
6 votes

Is there a law stating why a quark never decays weakly into a quark of the same weak-isospin ($T_3$)?

The law is called: "There are no flavor-changing neutral currents", given the association of $T_3$ with electric charge—the hyper charge remaining invariant, naturally. At tree level, it ...
Cosmas Zachos's user avatar
5 votes
Accepted

What electric charges do the $SU(2)$ weak isospin bosons carry?

$W^1,W^2$ do not have well defined electric charge. They are not charge eigenstates: $$ \begin{aligned} Q|W^1\rangle&=+i|W^2\rangle\\ Q|W^2\rangle&=-i|W^1\rangle \end{aligned} $$ On the other ...
AccidentalFourierTransform's user avatar
5 votes
Accepted

(Iso)spin coupling of three particles

OK, I'll get to the answer with insouciance that would make Paul Gordan turn in his grave, and only then, separately, I'll dismiss your dilemma by summary reassurance via the Racah recouping ...
Cosmas Zachos's user avatar
5 votes

Why $U(1)_Y$ hypercharge rather than $U(1)_\text{em}$ electromagnetism?

Detailed answer The thing is that you cannot really force in an a priori interpretation of the gauge group with which you extend your existing theory. You can only decide on the symmetries of your ...
jrekier's user avatar
  • 278
5 votes
Accepted

What is the branching fraction of the $\Delta^0$?

Except for small electromagnetic decay branching ratios like $\Delta\to N\gamma$, essentially 100% of the branching ratio of the $\Delta$ is to $N\pi$ final states. This is just kinematics. The only ...
Thomas's user avatar
  • 18.7k
5 votes
Accepted

The $SU(2)$ isospin for quark v.s. anti-quark: Fix $\bar{d}=-|1/2,1/2>$?

If you start from the quarks transforming under fundamental representation of $SU(2)$ $$\psi'_i = U_{ij}\psi_j$$ and complex conjugate both sides, you get $${\psi'}_i^* = U_{ij}^* \psi_j^*$$ ...
Bruce Lee's user avatar
  • 5,237
5 votes
Accepted

Why do we regard ($e^{-}, \nu_{e}$) as a doublet?

You are contrasting the Weak interactions to the Strong interactions, where the breaking is spontaneous (and large) as contrasted to explicit (and small), respectively. ($e^{-}, \nu_{e}$) are a ...
Cosmas Zachos's user avatar
5 votes

Isospin for Antiparticles

I do not understand what the issue is, however. What do they mean by "we want... to transform in exactly the same way"? Didn't they just show that they do transform in exactly the same way? ...
Cosmas Zachos's user avatar
4 votes

Up/Down Quark Color and Isospin

The strong interaction works with colored gluons. The up and down quarks have the same type of color couplings--nothing about their color couplings can recognize whether they are up or down, they are ...
Cosmas Zachos's user avatar
4 votes
Accepted

Construction of interaction Lagrangian invariant under isospin $SU(2)$ transformations

Let's account for isospin through the dimensionalities of the multiplets, which best count states, so the isospinor fermion is a doublet, 2, and the isovector scalar is a triplet, 3, the adjoint. So, ...
Cosmas Zachos's user avatar
4 votes
Accepted

States of $^{18}$O using nuclear shell model

You (your professor) have selected a case, where $^{16}O$ is magic nucleus and it works as a core for the games of orbitals above and it is much easier to put strong statements like it can be proved ...
jaromrax's user avatar
  • 1,984

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