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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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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Using Isospin symmetry to find the decay width of an interaction

Say we have two decays $\Delta^+\rightarrow \pi^+n$, and $\Delta^+\rightarrow \pi^0p$. I want to show, using isospin symmetry that the probabilities for these decays is in the ratio $\tfrac{Γ(\Delta^+\...
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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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Do electrons have third component of isospin?

From what I've read, it seems like there are two types of isospin: the strong and the weak. I guess this means that leptons have no strong isospin, but they do have weak isospin. Am I right? I am a ...
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Why does the pion live in a representation of isospin SU(2) and is the mediator of the strong force generated by color SU(3)?

Why does the pion live in a representation of isospin $\rm SU(2)$ and is the mediator of the strong force generated by color $\rm SU(3)$? I somehow find strange that this is the case. Given that $\rm ...
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A question about isospin of pion and kaon

In Ch.18 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, on P.611 when discussing QCD renormalization of the weak interaction, two operators ${\cal O}^{1/2}$ and ${\...
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Clebsch-Gordan coefficient for 1x0

I'm trying to work out the combination of $|1\ 0 \rangle|0\ 0 \rangle$ (in this case they represent isospin, $|I\ I_3 \rangle$) using Clebsch-Gordan coefficients, but the table for $j_1\times j_2=1\...
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Why does the upper component of a $SU(2)$ doublet has $T^3=1/2$ and lower component $T^3=-1/2$ and not the opposite?

For a $SU(2)$ doublet, why does the upper component have $T^3=1/2$ and lower component $T^3=-1/2$? I know that this can be answered in the Standard Model by using $Q=T^3+Y/2$. But that is because we ...
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How to determine isospin $T$ (not just $T_z$) of a nuclear ground state

I’m trying to work out the total isospin and the $z$-component of the isospin for specific elements like $^{20}O$ and $^{20}F$ in the ground state. I’ve worked out the $z$-component, as I concluded ...
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What is meant by “the symmetry of an interaction”?

My understanding of a symmetry is this: apply an operation (e. g. parity inversion) to a system. If it behaves the same afterwards, it is symmetric under that operation. Now, quite often I see ...
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Two-nucleon coupling: symmetrization postulate

I have some trouble understanding isospin symmetry. If we consider a system of a proton and a neutron as two different iso-states of a nucleon and we wish to write the wave function, do we have to ...
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What are the other components of the weak isospin?

Sorry for a lazy question, I was just looking this up on the internet for a basic grasp of Standard Model. However, I couldn’t find anything on Wikipedia or just somehow managed to miss it on my ...
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Kanamori hamiltonian, rotational invariance and isospin

The Kanamori hamiltonian, if the coefficients satisfy a certain relationship, can be seen to be rotationally invariant. Its symmetry is $U(1)_C\times SU(2)_S\times SO(3)_O$ (I add the subscripts $C,S,...
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Determining conservation of isospin

I am trying to understand a worked example. The problem is to determine if all conservation laws are conserved in $$ \pi^-+n \rightarrow K^++\Lambda^0 $$ The answer says that isospin is conserved, ...
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What is the symmetry of the pion triplet ($\pi^{-}, \pi^{0}, \pi^{+}$)?

Under the entry "Isospin" in Wikipedia, it is written: The pions are assigned to the triplet (the spin-1, $\mathbf{3}$, or adjoint representation) of $SU(2)$ Why is the symmetry not $SU(3)$ since ...
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What is the symmetry of the doublet ($u$, $d$)?

The up quark $u$ and down quark $d$ form a doublet ($u$, $d$). I know that they have a SU(2) symmetry. However, they also have a U(1) symmetry because they are regarded as two states of the same type ...
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Why do we regard ($e^{-}, \nu_{e}$) as a doublet?

To my understanding, particles in a multiplet have similar properties (similar masses and so on) and slight or symmetric differences (in mass, electric charge, spin, and so on). They can be regarded ...
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What are the $\pi^1$, $\pi^2$ and $\pi^3$?

I found this site to give a nice explanation of isospin. Apparently, the charged pions can be described by a superposition of $\pi^1$ and $\pi^2$. Let us now consider the $\pi$'s in the ...
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What is the difference between $\Lambda$ and $\Sigma$ baryons? [duplicate]

The Lambda (uds) - 1115 MeV The Sigma (uds) - 1192 MeV Other than the 77 MeV, why are these 2 different particles? Is it the spin of 1 quark? If so, is it possible to determine which one? If not ...
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$\tau \rightarrow \rho \nu $ relation with $ \rho \rightarrow e^+ e^-$

I'm reading "Okun, Leptons and quarks.", specifically subsection 13.3 "Semihadronic decays. General remarks." Okun says "The amplitude of the $\tau \rightarrow \rho \nu $ decay is related directly to ...
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Can the reaction ${\rm n}+{\rm p} \rightarrow {\rm d} + \pi^0$ give a deuteron in excited state?

I'm trying to find the isospin quantum numbers of the deuteron on the right hand side of this equation. I know that $|\rm p\rangle = |{1\over2},{1\over2}\rangle$, $|\rm n\rangle = |{1\over2},-{1\over2}...
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Are both Gell-Mann Nishijima formulas true for the same reason?

The Gell-Mann Nishijima formula states that $$Q = I_3 + \frac{Y}{2}$$ where $Q$ is the electric charge, $I_3$ is the third component of isospin, and $Y$ is the hypercharge. This was an empirical fact ...
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What is the isospin of the photon?

As already mentioned in this Phys.SE post, the PDG booklet says that the isospin of a photon is $0,1$. Is it referring to the strong or to the weak isospin of the photon? What would be the 3rd ...
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Calculating matrix elements for quarkonium decay amplitudes

In this paper (Appendix A) several decay amplitudes are calculated. How does this work? Note that $$ |n \bar n \rangle = \frac{1}{\sqrt{2}} (| u \bar u \rangle + |d \bar d\rangle ) \\ \eta = \cos \...
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Up and down quark content of neutral pion

If isospin were a perfect symmetry, then the neutral pion would have equal $u\bar u$ and $d\bar d$ content, but since up quarks are slightly lighter than down quarks, the neutral pion, being the ...
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Does the parity operator commute with the isospin T?

I don't know if the parity operator commute with the isospin operator T for any representation, i.e., [P,T_i]=0 ? i=1,2,3.
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What is the isospin of the neutral pion?

The neutral pion, π0, should have an isospin of 0. To be certain, I am referring to the third component of isospin, $I_3$. The reason for this is very simple: I3 is an additive quantum number. The ...
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Why can a coupled wavefunction of 2 nucleons seemingly arbitrarily give two different expressions?

When looking at the Isospin representation of a proton-neutron system (with the notation $|I,I_3\rangle$), you can go from an uncoupled to a coupled representation like this: $$\textstyle|\frac{1}{2},...
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Calculation of Feynman invariant amplitude with internal global symmetry indices: trace over\and isospin

This is a complete rewriting of the older post, making more clear the problem. The issue here is to compute the $$|M|^2 =4a^2(\delta_{ad}\delta_{bc} - \frac{1}{2} \delta_{ab}\delta_{cd}) ^2 (u_{1b}^{...
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The $SU(2)$ isospin for quark v.s. anti-quark: Fix $\bar{d}=-|1/2,1/2>$?

The isospin for two quarks $u,d$, it is chosen that $$ u=|1/2,1/2>, d=|1/2,-1/2>, $$ in fundamental Rep of $SU(2)$. the anti-quarks have anti-fundamental Rep of $SU(2)$ [thus same as the ...
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Do Halzen and Martin use p and n to represent complex numbers?

In Halzen and Martin's Quarks and Leptons, on page 42, the $SU(2)$ isospin transformation represented by $e^{i\boldsymbol{\theta}\cdot\boldsymbol{\tau}/2}$ is said to act on the column represented by $...
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How nuclear force is scalar in isospin space?

In Introductory Nuclear Physics by Samuel Shaw Ming Wong (Pg. 75), it's given that nuclear force is two body in nature and scalar in isospin space. What is meant by scalar in isospin space?
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Why is the strong interaction blind to the third component of Isospin?

Neutron and the proton have different values of $I_3$, the third component of the Isospin. Yet the strong interaction cannot distinguish between them. Why is this so? I can't understand this. The ...
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$SU(3)_F$ flavour symmetry and $SU(2)$ isospin symmetry

There is an approximate $SU(3)_F$ flavour symmetry that exists at the quark level between $u$, $d$ and $s$ quarks. But we often talk about an approximate isospin $SU(2)$ between up and down quark only?...
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Where does $SU(2)$ isospin symmetry come from?

Where does $SU(2)$ isospin symmetry come from? Strong (nuclear) interaction does not distinguish between neutrons and protons. I know that neutron and proton form an Isopin $SU(2)$ doublet. But I have ...
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Isospin, cross section

I need to find the ration of cross sections for the following two reactions: $$\rm p + d\rightarrow He^3 + \pi^0$$ and $$\rm p+d\rightarrow H^3 + \pi ^+.$$ Since the cross section for a reaction $\...
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Proof of the G-Parity Relation $G=(-1)^IC$

As stated in the question title, I am trying to prove the relation (pg. 144 of Griffiths' Introduction to Elementary Particle' or pg. 126 on Riazuddin's 'High Energy Physics') concerning the ...
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Applying ladder operators to Isospin states for quarks

I'm having trouble finding the isospin representation of the meson isospin triplet $|\rho\rangle$. Starting from the $|\rho^+\rangle$ meson $|u^\uparrow\bar d^\uparrow\rangle$ (where the arrows ...
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From isospin of nucleons to hadrons

To my understanding, isospin was introduced for nucleons (neutrons and protons) because of their similar properties. When it was found out that they are made up of quarks, naturally the quarks could ...
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States of $^{18}$O using nuclear shell model

Using the nuclear shell model it can be proved that in the external shell $1d_{5/2}$ of $^{18}$O there are two neutrons. Thus, by composition of angular momentum, the possible states of the nucleus ...
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Two particle state for $T = 0$

A state of T=1 could be imagined as two protons or two neutrons or else half the time first particle proton second a neutron and other half time vice-versa but how would one imagine a T=0 state? Just ...
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What makes the number of neutrons the number of proton similar?

In basic chemistry, we are taught that an atom has roughly the same number of neutrons and number of protons, this doesn't seems to hold for larger atoms, but it is always roughly proportional (i.e. ...
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Can sea quarks change the (iso)spin of a hadron?

A hadron is made up of valance quarks ($qqq$ in the case of baryons and $q\bar q$ in the case of mesons) and sea quarks ($q\bar q$ pairs). Since all internal quantum numbers of quarks and anti-quarks ...
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Why are there both scalar and vector mesons?

I understand that the term "vector meson" denotes a meson particle (composite particle with a quark and an antiquark) which transforms as a vector under the Lorentz group. Since both the quark and the ...
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Hypercharge and Isospin as additive quantum numbers in $SU(3)$ flavour symmetry

I am studying the $SU(3)$ flavour symmetry and I'm reading that we use the fact that hypercharge and isospin are additive quantum numbers in order to decompose the tensor products of the fundamental ...
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What does it mean if an intertwiner respects a group action?

This is more of A maths question however it cropped up when I was researching isospin so I think it belongs here. I am wondering what exactly is meant by 'respects' and how it works in the context of ...
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Ratio of partial widths for $\pi^- p \rightarrow \pi^0 n$ reaction

Reaction $$\pi^- p \rightarrow \pi^0 n$$ has a peak due to $\Delta$ resonance, which has a mass 1232 MeV and $\Gamma$ = 120 MeV. The partial widths are $\Gamma_i = 40$ MeV and $\Gamma_f = 80$ MeV. I ...
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What is the branching fraction of the $\Delta^0$?

I've been looking for a literature value and can't find one, even from the PDG. Does anyone know where I could find the branching fractions for the $\Delta^0$ decay modes, specifically $\Delta^0 \...