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Questions tagged [isospin-symmetry]

Isospin is a symmetry in nuclear physics under the interchange of neutrons and protons. The strong nuclear force conserves isospin, but the symmetry is broken by the electromagnetic force, which only operates between protons.

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Why is isospin utilized in determining the branching fraction of $K_1(1270)\to K\pi\pi$ final states?

The branching fraction of $\mathcal{B}_{K_1 \rightarrow K^{+} \pi^{+}\pi^{-}}$ is determined by $$\mathcal{B}_{K_1 \rightarrow K^{+} \pi^{+}\pi^{-}}=\frac{1}{3} \times \mathcal{B}_{K_1 \rightarrow K \...
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Relation between parity and symmetry for deuteron

I am currently reading the book Física Nuclear y de Partículas by Antonio Ferrer Soria. In this book the following claim is made (this is at translationn from the Spanish): The wave function of ...
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Isospin and quark composition of neutral pion

We have that the neutral pion has quark composition given by: $$\pi^0=\frac{u\bar{u}-d\bar{d}}{\sqrt{2}}$$ I want to justify this. This can be deduced by reasoning with isospin. We know that: $$|\pi^0\...
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Isospin doublet and quark content from contraction of quarks

Let's introduce a quark $SU(2)$ doublet. We are in the $m_u \approx m_d$ limit. So we have $$ q = \begin{pmatrix} u\\ d \end{pmatrix}. $$ Then we can construct the Nucleonic field $$ N := q q q = \...
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Allowed Isospin states of two nucleons

I have a question on my Quantum Mechanics homework where we consider protons and neutrons to be manifestations of the same particle -- a nucleon. We think of the proton as the "isospin up state&...
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Two nucleons system with total isospin quantum number $T = 1$

I am confused with the resolution of this question: A system of two nucleons is in a state with a total isospin quantum number $T = 1$. What are the possible values for the total spin quantum number $...
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Question about the wavefunctions of a system of non-identical fermions

If one interchanges two identical fermions in the wavefunction of a $N$-particle system, the total wavefunction changes by a sign i.e., the total wavefunction should be antisymmetric under the ...
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Mass of different isospin baryons

Why are the masses of baryons (of same quark content) with different isospin, different? - Is there a physical intuition/explanation to this? Does higher isospin baryons always higher mass than lower ...
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$\Sigma^0$ baryon decay

I’ve seen it stated that the sigma baryon $\Sigma^0$ only decays to $\Lambda^0 \gamma$, and then $\Lambda^0$ decays to $p\pi^{-}$ or $n\pi^0$. I understand that the weak interaction conserves weak ...
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Nonconservation of hypercharge in Higgs decay

From Wikipedia, Higgs boson has hypercharge of +1 and isospin of -1/2. W bosons have hypercharge 0 and isospin +-1. Now Higgs boson can decay into 2 W bosons of opposite electric charge. No matter how ...
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Why not put the anti-quarks in the conjugate representation?

The isospin doublet consisting of $u$ and $d$-quark is defined as $$ \begin{pmatrix} u\\ d \end{pmatrix}. \tag{1} $$ But the isospin doublet consisting of the antiquarks, $\bar{u}$ and $\bar{d}$, is ...
Solidification's user avatar
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Why does isospin symmetry survive chiral symmetry breaking?

In QCD there is a breaking of chiral symmetry such that, for the lightest quarks only, we have $$\langle \overline{u} u \rangle = \langle \overline{d} d \rangle = \mathrm{const.}$$ where the constant ...
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Why can't $uus$ and $uds$ quark content have $I = 1$ Isospin?

Well, I know the isospin singlet with $I=0$ and isospin triplet with $I = 1$. But for $I = 0$, why it must be $uds$ quark content rather than other assembly like $uus$ or $dds$? $ud$ can have $I = 0$ ...
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If isospin is only approximately conserved by strong interaction, why do we never see isospin violation?

Due to the mass difference between the $u$-quark and the $d$-quark, SU(2) isospin symmetry is only an approximate symmetry (even in a universe devoid of weak and EM interactions). This suggests to me ...
Solidification's user avatar
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Non-leptonic weak decay with $|\Delta T=3/2|$ suppression (from "Inward bound" Pais' book)

In Abraham Pais' "Inward Bound" book at page 564 it is mentioned that if we describe the weak interactions with the usual current-current interaction (including Cabibbo angle) we still do ...
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Why Lambda Baryon and Sigma Baryon unequal sum isospin with "really" isospin?

For information isospin for $u$-quark = 1/2, isospin for $d$-quark = -1/2 and isospin for $s$-quark = 0. Lambda Baryon consists $uds$ quarks,therefore sum isospin 1/2-1/2+0=0, It true. But sum isospin ...
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What is a fermion doublet exactly?

I am trying to prove that the Weinberg operator is the only dimension-5 operator that can be constructed out of Standard Model fields. To that end, I've tried to write up all the dimension-5 operators ...
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Can the weak isospin of elementary particles be measured experimentally or is it penciled into the Standard Model?

The chart below from Wikipedia lists the weak isospins of all elementary particles. It states that right-handed matter particles and left-handed anti-matter particles have a weak isospin of 0. Is ...
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If an $SU (2)$ isospin transformation converts a proton to a neutron, how does a pion transform under the same transformation?

I read in a particle physics note that if an $SU(2)$ isospin transformation makes $p\rightarrow n$ then under the same transformation pions go like $\pi^+ \rightarrow\pi^-$. I'm assuming that this ...
Aravind Madhavan's user avatar
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Can I still use the table of Clebsh-Gordan coefficients if isospin isn't conserved, to calculate the branching ratio?

the title is basically everything. For example, the interaction $\Lambda^0 \rightarrow \Sigma^+ + \pi^-$ or $\Lambda^0 \rightarrow \Sigma^0 + \pi^0$. Isospin isn't conserved but the interaction is ...
Double_you's user avatar
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Meaning of $SU(n)$ and $SO(n)$ symmetry groups in particle physics

I am currently self studying introductory particle physics using An Introduction to Elementary Particles by David J. Griffiths. I was reading Chapter 4 of this textbook which deals with the topic of ...
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Isospin multiplet for a given pentaquark

Considering the pentaquark $P = (uudt\bar{c})$, with orbital angular momentum $L = 0$, and assuming a space-spin wavefunction that corresponds to the maximum-J state, I want to know the isospin ...
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Spin and isospin

Considering, for example, the baryon octet, we have then that for $L = 0$, $J = 1/2$, as it is made of spin-1/2 particles. Hence, the isospin $I = 1/2$ and so, some of the wavefunctions of the octet ...
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Isospin at Vertices

I want to calculate the isospin factors at each vertex for the diagram below. For me the problem is, it depends on the direction of the $\pi_0$ direction, which it shouldn't. For the left vertex, I ...
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Confusion on states in level scheme in the popular deuteron isospin and spin explanation

I'm having trouble understanding a specific part of the classic deuteron example when introducing Isospin. I have seen this exact example in multiple lectures and textbooks (recently "Nuclear ...
Heschoscho's user avatar
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The isospin of pions

In the thesis(Page:53), the author defined three pion bases, namely, $$ |\pi^{1}\rangle = |1, 1\rangle, \quad |\pi^{0}\rangle=|1,0\rangle, \quad |\pi^{-1}\rangle=|1, -1\rangle. $$ Here, the first ...
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On the quark composition of baryons

Baryons are made of three quarks, in the form $\vert qqq \rangle$. If we consider just the isospin doublet $u$ and $d$, there are 8 total possibilities: Now, the first 4 are respectively $\Delta^{++}...
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Can we derive the formula $Q=I_3+\frac{1}{2}(B+S)$ instead of accepting it as an empirical relation?

The electric charge of a quark or lepton, $Q$, is related to the third component of the weak Isospin $T_3$ and weak hypercharge $Y$ according to the formula $$Q=T_3+\frac{Y_W}{2}.\tag{1}$$ This, in a ...
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Finding $\Sigma$ wavefunctions from proton wavefunction. Any operator which can achieve this?

Knowing the isospin part of the wavefunction of the proton, it is possible to find that of the neutron by applying the isospin lowering operator $I_-$ which sits horizontally to the left of the proton ...
Solidification's user avatar
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Is there a law stating why a quark never decays weakly into a quark of the same weak-isospin ($T_3$)?

So I read multiple articles on weak isospin and one of them stated that "a quark never decays weakly into a quark of the same $T_3$". If this is true, can someone please explain what law ...
Jungwoon Song's user avatar
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Deriving isospin factors in phenomenological pion nucleon nucleon interactions

Preface One commonly finds this interaction Lagrangian in phenomenology (ignoring constants): $$\mathscr{L} \propto \bar\psi \gamma^5\gamma^\mu \vec\tau\psi \cdot \partial_\mu \vec\pi \tag{1}$$ ...
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Unfamiliar notations about $\pi\pi\rightarrow\pi\pi$ scattering amplitudes in Weinberg’s QFT?

I’m reading section 19.5 of Weinberg’s second volume of QFT, and confused about some notations. In that chapter, he introduce the non linear sigma model as an low energy effective theory of 2-flavor ...
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What is the difference between isospin, weak isospin, hypercharge, weak hypercharge and the isospin third component $I_{3}$?

These terms crop up all the time in particle physics but I am confused as to what the difference is. I have read that hypercharge is the third component of isospin. This wikipedia page differentiates ...
spacexyz's user avatar
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On $\Delta^{+}$ particle decay

Using isospin notation $$ \Delta^+=\left|\frac 3 2,\frac 1 2\right\rangle=\frac{1}{\!\sqrt{3}}\bigg(|duu\rangle+|udu\rangle+|uud\rangle\!\bigg) $$ It is known all of the $\Delta$ baryons with mass ...
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On the properties of $\Delta$ baryons

Considering the up and down quarks as an isospin doublet $|I, I_z\rangle$ $$ u=\left | \frac 1 2, \frac 1 2 \right\rangle, \qquad d=\left | \frac 1 2, - \frac 1 2 \right\rangle $$ their bound states ...
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If isospin is conserved in a given strong interaction, can we say that the interaction is certainly allowed?

If isospin is conserved in a given strong interaction, can we say that it is certainly allowed and it's not needed to check other conservation rules like baryon number, electric charge etc. ?
Detective W.'s user avatar
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Determination of isospin probabilities

I have the following problem: If $| I I_3 \rangle = \alpha |1/2,-1/2 \rangle |1,1\rangle + \beta |1/2,1/2 \rangle |1,0\rangle $, are the isospin and the third component of the isospin, calculate $\...
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Isospin for Antiparticles

In Quarks & Leptons: An Introductory Course in Modern Particle Physics by Halzen and Martin page 42 reads: The construction of antiparticle isospin multiplets requires care. It is well ...
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Why do isospin representations need to be eigenstates of rotations?

In a previous question I asked about the cartesian components of isospin, i.e. $\pi_1$, $\pi_2$, and $\pi_3$ and why only the $\pi^\pm$ and $\pi^0$ fields are physical. The answer states that The &...
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Interpretation of $T_1$ & $T_2$ operators in Isospin

In isospin, the $T_3$ operator corresponds to whether a particle has "up" isospin, or "down" isospin, but what do the $T_1$ & $T_2$ operators correspond to then? I know we can ...
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How to calculate the strong isospin of an interaction?

I am given the following interaction : $$pp \rightarrow H K^+ K^+ $$ In order for this interaction to happen the charge value, strong isospin, strangeness and baryon number must be the same on both ...
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Gell-Mann—Okubo formula

How was the Gell-Mann—Okubo formula $$ M = a_0 + a_1 Y + a_2 \left[ I \left( I + 1 \right)-\frac{1}{4} Y^2 \right] $$ rewritten using isospin and strangeness to this formula? $$\frac{N + \Xi}{2} = \...
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Why are Delta baryons called "Delta isobars"?

A lot of people seem to call the $\Delta$ baryon "Delta isobar", however there is no mention of "isobar" on its Wikipedia page. Am I missing something? Why do people use the term &...
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How would the "belt trick" analogy of a pion look like?

Since the (charged) pion has a spin of 0, this by itself would suggest that it has spherical symmetry. However, because if it's non-zero iso-spin property it does not have spherical symmetry (is this ...
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Isospin Triplet and Spin Singlet Relationship

Why does the isospin triplet correspond to a spin singlet when observing a nuclei? Similarly, why is a isospin singlet correspond to a spin triplet for the same system? Is there a physical meaning to ...
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Question about calculating isospin couplings

So say we have the following interaction: $$ \Sigma_c^+ \rightarrow \Lambda_c^+ + \pi^0 $$ And say that we want to find out the quark composition of $\Sigma_c^+$ through inspection of the isospins ...
Aidan Daly's user avatar
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Does isospin symmetry between different multiplets arise from flavour symmetry?

Initially we were introduced to isospin as a way of abusing the approximate symmetry of the strong force, e.g. we would define an $I=\frac{1}{2}$ group of $p$ with $I_3 = +\frac{1}{2}$ and $n$ with $...
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Conservation of isospin

Our particles course has two contradicting descriptions of how isospin must be conserved in strong interactions (assuming a perfect sitution with only the strong interaction so isospin symmetry is ...
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$SU(2)$ isospin invariance of the nucleon-pion system

I'm reading "Dynamics of the Standard Model,Cambridge monographs on particle physics, nuclear physics and cosmology" and in page 10 it says that the response of an individual pion component ...
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Higgs U(1) charge and the isospin operators

So if the higgs field $h=(h^+,h^0)$ is at its vev (up to a gauge choice) with $\langle h\rangle =\frac{1}{\sqrt{2}}(0,v)$, then in turn you can show $$I_{1}\langle h\rangle=\frac{\sigma_1}{2}\langle h\...
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