What is Isospin: Definition and 73 Discussions

In nuclear physics and particle physics, isospin (I) is a quantum number related to the up- and down quark content of the particle. More specifically, isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons.
The name of the concept contains the term spin because its quantum mechanical description is mathematically similar to that of angular momentum (in particular, in the way it couples; for example, a proton-neutron pair can be coupled either in a state of total isospin 1 or in one of 0). But unlike angular momentum it is a dimensionless quantity, and is not actually any type of spin.
Etymologically, the term was derived from isotopic spin, a confusing term to which nuclear physicists prefer isobaric spin, which is more precise in meaning. Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states. A close examination of isospin symmetry ultimately led directly to the discovery and understanding of quarks, and to the development of Yang–Mills theory. Isospin symmetry remains an important concept in particle physics.

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1. Isospin and Partons model in a pentaquark

TL;DR Summary: Given a pentaquark: (a) Determine the isospin multiplet it belongs to. (b) Calculate a kind of a Gottfried Sum Rule for this pentaquark-neutrino or -antineutrino scattering. Hello everybody, I'm having a bit of a trouble with the exercise below as it deals with a pentaquark and...
2. A The Symmetry of Antiparticle Isospin Doublets in Particle Physics

In Quarks & Leptons: An Introductory Course in Modern Particle Physics by Halzen and Martin page 42 reads: 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...
3. A For the W3 and B bosons, what is their hypercharge and isospin?

In wikipedia you can find this neat tables with the hypercharge and isospin of a ton of particles and bosons. What I want to know is: what are the values of Isospin and Hypercharge for the W3 and B bosons? Now, I know electroweak unification, don't worry about that. I know W3 and B got mixed...
4. Particle Physics- Isospin states

Hi, I have attached the question to this post. I understand on the process on getting to the answer in that you use $$\arrowvert 2, 2\rangle=\arrowvert 1,1\rangle \otimes \arrowvert 1,1\rangle$$ and apply the isospin-lowering operator to obtain $$\arrowvert 2,1 \rangle$$. Then I understand you...
5. Isospin Conservation: Calculating I3 and I

I got the I3 values for the tau(minus) to be -1, as charge is -1 and Y=0. For muon(minus) i got I3 to be -1 too using the same equation and the anti electron neutrino to have an isospin of zero (since Q=0, Y=0). This shows I3 to be conserved (which is needed for strong interaction i believe)...
6. I Isospin Operator: Act on |ud> State

How does the isospin operator I_3 act on a state |ud>, where u ist an up- and d a Down quark?
7. A G-parity - where does the minus sign come from?

Hi all, I have a question on G-parity. I know it's defined as ## G = exp(-i\pi I_{y})C ##, with ##I_y## being the second component of the isospin and ##C## is the C-parity. In other words, the G-parity should be the C-parity followed by a 180° rotation around the second axis of the isospin...
8. I Forbidden decay ##\rho^0\rightarrow \pi^0\pi^0##

Hello everybody! I have a question regarding the forbidden decay ##\rho^0 \rightarrow \pi^0\pi^0##, but it is a general doubt. My book states that one of the reasons why the decay is forbidden is Bose-Einstein statistics, the final state of two equal pions must be in an antisymmetric state...
9. I Clebsch-Gordan coefficients and their sign

Summary: Different sign in the combination of two ##\textbf{1/2}## isospins with opposite third component Hello everybody! I was doing an exercise regarding isospin and I noticed something from the Clebsch-Gordan coefficients that made me think. For example, if I consider the combination...
10. Isospin Doublet Derivation Using Clebsch-Gordan Coefficients

Homework Statement I am trying to improve my understanding of the Clebsch-Gordan coefficients. I am looking at page 5 of the following document https://courses.physics.illinois.edu/phys570/fa2013/chapter3.pdf Homework Equations I have derived the result for the I = 3/2 quadruplet but am...
11. A I need a spherically symmetric spin-dependent NN potential

First, I'll give a little background so you guys know why I've arrived at this issue. I'm writing my BSc thesis right now, and the point of the thesis is to predict the bound states of two-nucleon systems (one bound, others not) by treating the problem as a simple QM two body problem. With a...
12. I What particles have fixed weak isospin and T3?

Wikipedia quotes weak isospin values for some particles and not for others. Why? Is the concept of weak isospin as an observable quantity not meaningful for, for example, pions?
13. M

A Attractive strong force, isospin and hypercharges

In the electromagnetic interaction, opposite electric charges q attract each other. In the strong nuclear force, the proton p(uud) is attracted to p(uud) and the neutron n(udd), and n(udd) is attracted to p(uud) and n(udd). Both neutrons and protons have a hypercharge Y=+1, and 3rd...
14. I Do Fermi and Gamow-Teller transitions only refer to isospin

Do Fermi and Gamow-Teller transitions only refer to changes in isospin , as in beta decay and orbital electron capture
15. I What is the weak isospin of hadrons?

What are the weak isospins (T3 values) of various hadrons, including the proton, neutron, mesons, hyperons and other hadrons? How is the weak isospin calculated for any hadron? Published sources provide T3 only for fundamental fermions, that is, quarks and leptons. In the fundamental bosonic...
16. A Isospin symmetry as an ##SU(2)## symmetry

The generators for the isospin symmetry are given by $$T_{+}=|\uparrow\rangle\langle\downarrow|, \qquad T_{-}=|\downarrow\rangle\langle\uparrow|, \qquad T_{3}=\frac{1}{2}(|\uparrow\rangle\langle\uparrow|-|\downarrow\rangle\langle\downarrow|),$$ where ##|\uparrow\rangle## and...
17. I Transition matrix element and Isospin

Hi, guys. A type of problem that often appears is to find the relation between cross sections of some processes. An example would be: $$\pi _{- }+ p \rightarrow K_0 + \Sigma_0$$ $$\pi _{- }+ p \rightarrow K_+ + \Sigma_-$$ $$\pi _{+}+ p \rightarrow K_+ + \Sigma_+$$ To do this, I argue that...
18. I Quarks and isospin ladder operators

Hi, guys. This is actually a question about quantum mechanics, but since the context in which it appeared is particle physics, I'll post it here. On Thompson's book (page 227, equation (9.32)), we have $$T_+ |d\bar{u}\rangle = |u\bar{u}\rangle - |d\bar{d}\rangle$$ But I thought...
19. I Isospin conservation - an application

Hi guys! I'm trying to understand how to use the fact that the total isospin is conserved in all strong processes in the particular case (vide Griffiths, pages 118 and 119): $$p+p \rightarrow d+\pi^+$$ Griffiths first argues that the deuteron d has isospin I=0, because of experimental...
20. I Raising and lowering operators for a composite isospin SU(2)

Consider pion states composed of ##q \bar q## pairs where ##q \in \left\{u,d \right\}## transforms under an ##SU(2)## isospin flavour symmetry. These bound states transform in the tensor product ##R_1 \otimes R_2## of two representations ##(R_1, R_2)## of ##SU(2)##. Take ##R_2## as the...
21. Computing the Isospin of the Deuteron

Homework Statement The deuteron is mostly a bound state of a proton and neutron with orbital angular momentum L=0 and spin S=1. To a good approximation we can neglect the proton-neutron mass difference and electromagnetic interactions, and treat the proton and neutron as two isospin components...
22. Confused about isospin conservation in rho to pion decays

The decay \rho^0 \rightarrow \pi^- \pi^+ occurs with a probability of 100\%, whereas the decay \rho^0 \rightarrow \pi^0 \pi^0 does not occur in nature, due to isosphin conservation. I don't understand this. Looking at the Isospin and its third component ¦I,I_3\rangle we have in the first...
23. G- & Isospin Symmetry for Γ(ρ0→π0γ)

Homework Statement Show Γ(ρ0→π0γ) = Γ(ρ+→π+γ) Using G- and isospin symmetries, without exact calculating the matrix elements using additive quark model. Homework Equations L = jμAμ G = CR1802 Mif ≅ <π|jμ|ρ>eμ jμ=2/3 * (anti u)γμu - 1/3 * (andi d)γμd) The Attempt at a Solution Mif ≅...
24. Is Isospin Conversation Required In The Standard Model?

A new experimental result from BESIII finds that there is isospin violation in the decays of J/Psi mesons in a path involving scalar mesons (with a narrow width in tension with world averages) and notes that a previous experiment found isospin violation in another decay chain...
25. Why do proton and neutron form isospin doublet? I3 or I?

As far as I understand, ##I_{3}##, the component of isospin in a certain direction is additive, but ##I## is to be treated as a vector sum, is this correct? So, ##I_{3}=1/2## for ##u## quark, ##I_{3}=-1/2 ## for ##d## quark. Adding ##I_{3}## then for a proton we find ##I_{3}=1/2## and for a...
26. Weak Isospin, Chirality and Helicity

Could someone please help me to understand the difference between the concepts of Weak Isospin, Chirality and Helicity. In particular, I have the following questions to which I was unable to find answers so far: 1. Since both spin direction and momentum are vectors, would not their apparent...
27. Decomposed Isospin: Proj. Operator Tech. to Obtain Eq.(1)

How to use the standard techniques of projection operators to obtain the equation (1) by the first formula? Thanks
28. Help with Heisenberg's "isospin" Hamiltonian

I'm having some trouble grasping the meaning of the exchange term in the Hamiltonian Heisenberg gives in his classic 1932 paper (the one typically given as the first to describe nucleons via a spin-like degree of freedom; NOTE: I realize this isn't the same as what is today called isospin, but...
29. Isospin breaking, charge symmetry and charge indepedence

Hi, I'm just getting a little confused with all the definitions here and I need some confirmation on what I say is correct or not; Isospin symmetry: The property that an interaction is independent of the T_3 value? Isospin breaking: The property that it is dependent on T_3 ? Charge symmetry...
30. Exchange symmetry when isospin is concerned?

As far as I know identical fermions are antisymmetric under exchange. Identical bosons are symmetric under exchange. Is this fact blurred when we consider isospin? Considering the wavefunction of a proton-neutron system; \psi = \psi_{space} \psi_{spin} \psi_{isospin} I'm told this needs...
31. How Do Spin, Isospin, and Charges Interact in Particle Physics?

Recently, I was thinking about spin and isospin. It's been a while since I've dealt with particle physics, so my knowledge may be a bit rusty. In the Standard Model, we have three interactions with associated coupling constants e, gw and gs. A particle may have three different charges Qe, Qw...
32. Is weak isospin conserved by all interactions?

Hi people: I keep reading one day that weak isospin is exactly conserved by all interactions; other days that sometimes weak isospin is *not* conserved. Can anyone clear this one up?!
33. Why is weak nuclear bosons carry the isospin charge?

The leptons and hadrons carry the weak isospin charge. What allows the weak bosons do carry the charge? Is it because they have a mass?
34. Is the Proton-Electron Theory Disproved by Experimental Evidence?

Hi, I read Georgi's Lie algebras in Particle Physics 2nd chap5 and have two questions. 1) In the beginning he mentioned Heisenberg regarded neutron is composed as proton and electron, the force between nucleons are exchanging electrons. My question is, what is the experimental evidence...
35. Particle Phys.; Isospin conservation for cross sections of scattering

Homework Statement What relations can you derive from isospin conservation for the cross sections of the following scattering processes: K^{+} + p → K^{+} + p K^{+} + n → K^{0} + p K^{0} + n → K^{0} + n The Attempt at a Solution I do not really have my own solution as I've...
36. Isospin and quark model, why isospin is not considered in quark model

Homework Statement why the isospin wave function was not considered in quark model? only the others (flavour, color, space, spin) are considered? Homework Equations The Attempt at a Solution
37. Isospin Asymmetry in Nuclear Matter

Hi all what is meant isospin asymmetry for nuclear matter ? thanks alot
38. Isospin decomposition of K->ππ decay

I'm studying the decay K->ππ and I have some doubts on the isospin decomposition. We know that the state (\pi\pi) can have total isospin 0 or 2. Now, if we remember that in the isospin representation we have |\pi^+\langle=|1,1\langle, |\pi^0\rangle=|1,0\rangle and |\pi^-\rangle=|1,-1\rangle...
39. Exploring Isospin: Understanding its Role in the Strong Force

What exactly is isospin and what does it have to do with the strong force?
40. Isospin should be I=1, I think.

Homework Statement a) η decays into two photons, but not three. Through which interaction does the decay occur. What is C(η)? b) ρ0 decays into \pi^{+}\pi^{-} but \eta^0 does not. Why is that? c) \omega decays through electromagnetic interaction into \pi^0\gamma. C(\omega)? d) b_1(1235)...
41. Is Isospin Conserved in Particle Interactions?

Homework Statement Hey I just want to clarify something. In particle physics, isospin is a flavor quantum number. Is it isospin or the z component of isospin which is conserved in particle interactions Homework Equations electron neutrino + proton -> electron pion+ + proton The...
42. What is the isospin of the Higgs particle

I had always assumed that the simplest possible standard model Higgs particle had isospin 0, but when I tried to verify this assumption I read some conflicting opinions (not to mention discussions about more complicated Higgs mechanisms). I also read conflicting views about the conservation of...
43. Isospin: how serious must I take it? Superposition of proton and neutron?

Hello, So I'm reading about isospin in Griffith's Introduction to Elementary Particles, but the concept seems rather fishy, and I'm not quite sure what to make out of it. For example, if p and n (proton and neutron) are seen as different states of the same system, then what does...
44. What is isospin (and spin) really

My question is simple, though the answer is probably not. What is isospin? (Here, I refer to the strong isospin introduced by Cassen and Condon). From the algebra it is clear that there are analogies to be drawn with the intrinsic spin that arises in angular momentum conservation, but how far...
45. A problem related to isospin

I am reading Griffiths' introduction to elementary particles and I am confused about problem 4.33a in that book. It says that given there is no isotope of hydrogen of weight 4, nor of lithium of weight 4, what can we say about the isospin of an alpha particle? Thanks in advance!
46. Dimension of electric charge, hypercharge and isospin

For SU(2) the three represented gauge fields are A_\mu^1, A_\mu^2 and A_\mu^3 and for U(1) the gauge field is B_\mu. The A_\mu^3 and B_\mu are electrically neutral. The photon \gamma and Z particle are combinations of these. My interest is the dimensions of the following parameters...
47. How do you calculate the strong isospin of nucleons?

First post, so hi everyone. I have been banging my head against this question for a little while now. I've found two methods that appear to give the same result, but am not quite happy with what I've done: Homework Statement Calculate the strong isospin components of both tritium (3H)...
48. How can particles undergo EM interactions *and* have definite strong isospin?

I am deeply confused about the following and I'd really appreciate it if anyone could help! Consider a charged hadron such as a proton. Amongst the state-independent properties that define a proton are strong isospin Iz=1/2 and charge Q=e. Now, the total Hamiltonian for a proton is Hs...
49. Exploring Isospin Symmetry in Particle Physics

Hello! I have difficulty trying with the interpretation of: (\frac{1}{2}) \otimes (\frac{1}{2}) \otimes (\frac{1}{2}) = (\frac{3}{2}) \otimes (\frac{1}{2}) \otimes (\frac{1}{2}) If I´m right this is the SU(2) irrep for isospin but what does this mean? Proton = Neutron?
50. Conservation of weak hypercharge and isospin

So I've been playing around with different electroweak lagrangians (sourceless, higgsless, unbroken, broken, etc), and finding the equations of motion for them. Everything looks about right, but the issue I'm having is when you add in the masses of the weak bosons(no higgs though).This breaks...