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.

196 questions
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What does a $\rm SU(2)$ isospin doublet really mean?

What do we really mean when we say that the neutron and proton wavefunctions together form an $\rm SU(2)$ isospin doublet? What is the significance of this? What does this transformation really doing to the wavefunctions (or fields)?
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How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content?

Title says it all: How can $\Lambda^0$ and $\Sigma^0$ both have $uds$ quark content? Doesn't this make them the same baryon?
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Why doesn't the deuterium nucleus have spin $0$?

A deuterium nucleus is composed of a proton and a neutron. Both have spin $\tfrac12$ so I would expect the deuterium to have two possible spins: $1$ for the triplet and $0$ for the singlet. But apparently deuterium always has spin $1$ and the spin…
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Phase factors under rotations of strong and weak isospin

The strong isospin raising operator changes a $d$ quark into a $u$: $$ \tau_+ \big|d\big> = \big|u\big> $$ However, for antiquarks, there is an additional phase factor: $$ \tau_+ \big|\bar u\big> = - \left|\bar d\right> $$ This phase factor is the…
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What's with the very slightly larger mass of the neutron compared to the proton?

Neutron mass: 1.008664 u Proton mass: 1.007276 u Why the discrepancy? On a related note, how does one go about measuring the mass of a neutron or proton, anyway?
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Why is there no baryon isospin singlet with spin 3/2?

All of the baryons in the spin-1/2 octet except the $\Lambda$ isospin singlet have spin-3/2 excited states in the baryon decuplet. What is it that prevents the existence of a $\Lambda^{*}$ baryon with $I=0$, $s=-1$, and $S=3/2$?
JackR
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12
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Is the neutral pion a singlet?

In Griffiths' Introduction to Elementary Particles, it is mentioned p. 179 that the $\pi^0$ is a singlet under $SU(2)$ isospin. But it is also part of the $\pi^-,\pi^0,\pi^+$ isospin triplet. How can it be both? Don't particles of a given $SU(2)$…
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Why $U(1)_Y$ hypercharge rather than $U(1)_\text{em}$ electromagnetism?

In the Standard Model we have $SU(2)_I\times U(1)_Y$, where $U(1)_Y$ is weak hypercharge and $SU(2)_I$ is the symmetry group of weak isospin. Why do we introduce $U(1)_Y$ of weak hypercharge rather than $U(1)_\text{em}$ of electromagnetism?
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$\Delta^+$ decay in GZK process

The dominant channels in the GZK process are $$p+\gamma_{\rm CMB}\to\Delta^+\to p+\pi^0,$$ $$p+\gamma_{\rm CMB}\to\Delta^+\to n+\pi^+.$$ According to the pdg, $\Delta\to N+\pi$ makes up essentially 100% of the branching ratio (BR). It doesn't,…
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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 lightest neutral meson, should have a slightly higher…
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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? Why?
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What is the cause of the minor mass difference between the proton and the neutron?

As known, the proton is from two up and a single down quark, while the neutron is from a single up and two down quarks. The down quark is a little bit more massive and the up, and so the neutron is also a little bit more massive as the proton. It…
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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 illustrated by a simple example. Consider a particular isospin…
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Why do excited states in $^4$He not decay by photon emission?

Here's a level scheme for the $^4$He nucleus (source; click image to see full size): Notice that all of the confirmed decay modes are by disintegration — emission of a neutron, proton, or deuteron. There are a few states with the right spin-parity…
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What is the symmetry of the pion triplet ($\pi^{-}, \pi^{0}, \pi^{+}$)?

Under the entry "Isospin" in Wikipedia, it states: 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 there are three particles? And in what circumstance do…
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