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 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 ...
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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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Clebsch-Gordon coefficients for isospin transformations
I'm trying to understand a paper in which the author uses the nuclear matrix elements from beta decay to arrive at the matrix elements for neutral-current neutrino-nucleus excitation. The author ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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