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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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 ...
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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 ...
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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 ...
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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. ?
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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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Why the isospin structure of the two-nucleon force falls into the four different classes?

According to this article Nuclear forces from chiral effective field theory the isospin structure of the two-nucleon force falls into the four different classes according to the $$ \begin{array}{ll} \...
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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 ...
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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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Mixing of $\gamma$ and $Z^{0}$ boson: Isospin?

In our lecture, we had for the Lagrange density of the $\gamma$ and the $Z^{0}$ boson: $$\mathcal L = -\sum_{\psi = e_{L}, e_{R}, \nu_{L}, \nu_{R}}\bar{\psi}\gamma^{\mu}\left( gT^{3}W_{\mu}^{3} + g'\...
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Measuring conserved charges of gauge bosons with conserved charge operators

In QED we don't care about this because the photons carry no charge and so it is no problem that the conserved charge operator: $$Q=\int\psi^{\dagger}\psi \ d^{3}x$$ That ends up consisting of number ...
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Relative cross section rates using isospin

There is a step in a solved problem I am not able to make sense of. Such problem finds the relative cross-section rates for the two following reactions using isospin formalism: \begin{equation*} R= \...
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Pion pion state: why wave function has to be symmetric?

For a $\pi^+$ $\pi^-$ state, why does the wave function have to be symmetric? For example, in the isospin state $|I=1,I_3=0\rangle = \frac{1}{\sqrt{2}}(\pi^+ \pi^- -\pi^- \pi^+)$, the angular momentum ...
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Is isospin magnitude $I$ conserved? [duplicate]

Here is a table of isospin conservation in certain reactions. It is often loosely stated that 'isospin is always conserved in strong interactions', but it is never clear whether they mean total ...
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Do Clebsch Gordan Coefficients add to one when squared for adding 3 isospin states?

I've been calculating the possible isospin states for $\pi^0\pi^+\pi^-$ state and get this as my final answer after referencing the Clebsch Gordan Coefficients table: $$\frac{1}{\sqrt{10}}|30\rangle+\...
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Wave function of a proton and a neutron with and without isospin

Suppose I have a proton and a neutron in an external harmonic oscillator potential well. Let us first neglect all interactions between the two: since they are distinguishable particles I conclude ...
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Hadrons as tensors of flavor symmetry even though flavor symmetry is broken?

I will briefly summarize what I know and then ask my questions. If you spot mistakes in my summary, please tell me. The idea of flavor symmetry is that massless QCD is invariant under SU(6) ...
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Scattering in pion-proton-neutron theory with isospin conservation

I am following Sidney Coleman's lecture of Quantum Field Theory. In ch 24.3 (starting from page 516) he discussed how to use isospin concept to consider the scattering of one nucleon and one pion. I ...
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Isospin and Clebsch Gordan coefficients [closed]

If I have to combine 2 spin $\frac{1}{2}$ particles I do with Clebsch Gordan coefficients so that for example $|{\frac{1}{2},\frac{1}{2}}\rangle|{\frac{1}{2},\frac{-1}{2}}\rangle=\frac{1}{\sqrt{2}}(|{...
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Are this isospin eigenstate same energy states?

Let's consider a system of two nucleons (protons and neutrons). $\hat T$ is the total isospin operator and $\hat T_3$ it's projection on the axis. The eigenstate are: singlet state: $|0,0\rangle$ ...
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Relation between isospin invariance and charge independence

I don't know if this question is better suited for this forum or math.stackexchange.com. I come from a mathematical background and I'm struggling to understand a passage in Lipkin's book "Lie groups ...
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Deuteron nucleus, what is the wavefunction (including isospin)?

What is the exact form of the wavefunction of the deuteron nucleus. Without electrons. Only neutron and proton combined to a total wavefunction. In the ket-notation I have something like this: $| \...
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Nuclear force behavior

I am confused about when the nuclear force is attractive and when not. Based on deuteron (the book I am following is Wong), we see that we can't have bound state with isospin T=1 (otherwise we would ...
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How to determine the isospin of a pair of nucleons?

While I was reading from the book of Brussaard on shell-model applications in nuclear spectroscopy, he mentioned that isospin of a neutron-neutron pair couple to $T=1$. On the other hand, if it was ...
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What's the definition of $\bar\psi$ in QCD?

This is a two part question. What is the definition of $\bar\psi$ in QCD? In QED I know that $\bar\psi=\psi^\dagger\gamma^0$, but in QCD we also have flavor and/or color space. In particular, I'm ...
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How to formulate with a tensor multiplication method $2\otimes 2\otimes 2$ in $SU(2)$ group?

In $SU(2)$ we can write $2\otimes 2=3\oplus 1$ or \begin{equation} q_iq^j=\left(q_iq^j-\frac{1}{2}\delta^i_jq^kq_k\right)+\frac{1}{2}\delta^i_jq^kq_k, \end{equation} where $q_i$ is a $SU(2)$ doublet, ...
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Expanding isospin symmetry to $SU(3)$ flavor symmetry for Baryon octet diagram

Let's consider about the Baryon octet diagram. We can identify the isospin $I_3$ symmetry by noticing the mirror symmetry with respect to the $I_3$, i.e. x-axis. However, how can we expand this into $...
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Highest and Lowest $SU(3)_F$ states

For the finite dimensional $(p,q)$-irreducible representation of $SU(3)_F$, we can label the states as $\mid T_3,Y\rangle$. Where $T_3$ is the third component of isospin and $Y$ is the hypercharge. ...
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Isovector Representation of $SU(2)$

In Electroweak Interactions by Renton (page 407) there is the calculation of matrix elements for electromagnetic interactions/weak interactions involving nuclei: A point of confusion for me is the ...
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Isospin and $\Delta$ Production

Edited to add new information I have seen the relation between cross sections postulated: \begin{align} \sigma(\nu+p\to\mu^- + \Delta^{++})=9\sigma(\nu+n\to\mu^- + \Delta^{+}) \end{align} Motivated ...
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Experimental proof for isospin conservation of strong interaction

I am having a surprisingly hard time to find direct experimental results for the (approx.) conservation of isospin in strong interactions. The canonical examples seem to be $\omega \! \to 3\pi^0$ and $...
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Pions and $SU(2)$ representation

I was reading about the pion ($\pi$) SU(2) representation and stumbled upon an expression for the isospin operator, $$ I_i=\epsilon_{ijk}\int d^3x\phi_j \dot\phi_k=-i\int d^3x \dot{\phi}^T t_i \phi ,...
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An invariant of the gauge group $G$ that is totally symmetric with three indices in the adjoint representation

In Ch.19 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.680 the property of a quantity $$\mathcal{A}^{abc}=\mathrm{tr}\left[t^a\{t^b,t^c\}\right]\tag{19.132}$$ ...
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What is the effect of isospin on the proton or neutron alone, i.e. not in a doublet?

So I start with a proton $p$. I extend my "physical" space by means of the internal degree of freedom of isospin, so that I know write $p$ in a higher dimensional space: $$ p = \left( \begin{array}{...
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Why is neutron slightly heavier than the proton? [duplicate]

With latest knowledge of QCD, is there any explanation for why the neutron is slightly heavier than the proton? Can it be boiled down to a simple formula?
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When is $Q= B/2 + I_3$ true in particle physics?

I have seen stated that for unflavoured quarks, the relation between baryon number, electric charge and third component of isospin can be written as $Q= B/2 + I_3$. However, I have also seen this ...
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