Strong chiral symmetry (SSB?)

In summary, the chiral symmetry breakdown is determined for the vector/axial current by comparing the mass difference between the pion+ and pion0 for the vector current and the pion and f0 meson for the axial current. This is because, if chiral isospin were conserved, we would expect to find groups of particles with the same mass related to each other by chiral isospin rotations. However, the presence of the heavier f0 meson compared to the pions indicates that chiral isospin rotations must be spontaneously broken.
  • #1
ChrisVer
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Why is the chiral symmetry breakdown determined for the vector/axial current as:

[itex] V = \frac{m_{π^{+}}-m_{π^{0}}}{m_{π^{0}}+m_{π^{+}}}\approx 0.01 [/itex]
[itex] A= \frac{m_{π^{+}}-m_{f^{0}}}{m_{f^{0}}+m_{π^{+}}}\approx 1[/itex]
?
why do we choose the difference between the pion+ (~140MeV) and pion0 (~135MeV) for the vector current or the difference between the pion(~140MeV) and the f0 meson (~900MeV) for the axial? Also why take that formulas for those asymmetries?
 
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  • #2
If a symmetry is not spontaneously broken, then we expect to find groups of particles with the same mass that are related to each other by that symmetry. For example, the lightest three mesons are the three pions. They all have approximately same mass--##V## in your post is small--and they are related to each other by isospin rotations. This is because isospin is conserved to pretty good accuracy.

If the chiral version of isospin were conserved, we would expect to find groups of particles with the same mass related to each other by chiral isospin rotations. Chiral transformations, among other things, transform pseudoscalars into scalars. So we would expect there to be some scalar meson degenerate with the pions, which are pseudoscalars. There's no such meson; the ##f_0## is one of the lightest scalar mesons and it is much heavier than the pions, as the large value of ##A## in your post shows. So chiral isospin rotations must be spontaneously broken.
 

1. What is chiral symmetry and how does it relate to strong interactions?

Chiral symmetry is a fundamental symmetry in physics that describes how particles behave differently based on their handedness or chirality. In the context of strong interactions, chiral symmetry refers to the symmetries of the strong force between quarks and gluons. It plays a crucial role in our understanding of how these particles interact and form the structure of matter.

2. What is the significance of strong chiral symmetry breaking (SSB)?

Strong chiral symmetry breaking is a phenomenon in which the chiral symmetry of the strong force is spontaneously broken at high energies. This results in the generation of mass for certain particles, such as the quarks, which would otherwise be massless. SSB is a crucial concept in the Standard Model of particle physics and helps explain why certain particles have mass.

3. How does strong chiral symmetry breaking affect the behavior of particles?

Strong chiral symmetry breaking leads to the formation of bound states of quarks, such as protons and neutrons, which make up the nuclei of atoms. It also plays a role in the behavior of particles in high-energy collisions, such as those that occur in particle accelerators. Understanding the effects of SSB is crucial for accurately predicting the behavior of subatomic particles.

4. Can strong chiral symmetry breaking be observed in experiments?

Yes, strong chiral symmetry breaking has been observed in experiments, particularly in studies of the strong interactions using particle accelerators. It has also been observed indirectly through various experimental evidence, such as the mass of the proton and neutron and their interactions with other particles.

5. How does strong chiral symmetry breaking impact our understanding of the universe?

SSB is a key concept in the Standard Model of particle physics, which is the most comprehensive theory we have for understanding the fundamental particles and forces of the universe. By studying SSB, we gain a deeper understanding of how particles interact and form the structures we see in the universe, such as atoms and galaxies.

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