Difference between pion and rho

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Discussion Overview

The discussion centers around the differences between pions and rho mesons, particularly focusing on their quark content, spin, and mass differences. Participants explore theoretical aspects of particle physics, including the implications of spin on mass and the origins of vector mesons versus pseudoscalar mesons.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants note that pions are pseudoscalar mesons (spin 0) while rhos are vector mesons (spin 1), suggesting that this difference in spin may contribute to their mass differences.
  • There is a question about whether the mass difference between the negative pion and rho is the same as that of the positive counterparts, with some participants affirming this.
  • One participant queries the relationship between spin and mass, proposing that higher spin might correlate with greater energy and thus greater rest mass.
  • Another participant discusses the strong spin-spin force between quarks and antiquarks, indicating that this force is repulsive for spin one (rho) and attractive for spin zero (pion), which may influence mass differences.
  • There is mention of a QCD spin-spin interaction that could contribute to the mass differences, with some participants discussing the implications of electromagnetic interactions and hyperfine splitting.
  • One participant raises a point about the decay of rho mesons into pions, linking it to the repulsive nature of the interactions within the rho meson.
  • Another participant highlights the distinction between constituent quark mass and current quark mass, suggesting that this distinction is important for understanding hadron magnetic moments and mass expectations for pions.
  • There is a discussion about an approximate symmetry that affects the mass of the pion, suggesting that if current quarks were massless, the pion would also be massless.

Areas of Agreement / Disagreement

Participants express varying views on the relationship between spin and mass, the nature of interactions within mesons, and the implications of quark mass distinctions. No consensus is reached on these complex topics, and multiple competing views remain present throughout the discussion.

Contextual Notes

Participants mention unresolved mathematical steps and assumptions regarding the interactions and properties of quarks and mesons, particularly in relation to their masses and decay processes.

dsfranca
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The pion \pi+ has the same quark content as the rho\rho+, but different rest mass. Why is that? And does the same apply to the \pi- and \rho-. Will they have the same mass difference?
Thanks for your help!
 
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The pions are pseudoscalar mesons (spin 0) and the rhos are vector mesons (spin 1).

Yes the mass difference is the same for the negative pion and rho.
 
Thanks for the answer Norman, but why would a different spin result in a different mass? Is it because as they have a greater spin they will also have more energy and thus greater rest mass? Is there a way I can infere the mass of the rho knowing the masss of the pion?
 
Norman said:
The pions are pseudoscalar mesons (spin 0) and the rhos are vector mesons (spin 1).

Yes the mass difference is the same for the negative pion and rho.

How do vector mesons arise? I thought that if a field is spontaneously broken, then it must be a scalar field, or else Lorentz symmetry would be broken also?

Scalar mesons come from spontaneously breaking a scalar composite quark and antiquark field, the "quark condensate".

Where do vector mesons come from?
 
dsfranca said:
Thanks for the answer Norman, but why would a different spin result in a different mass? Is it because as they have a greater spin they will also have more energy and thus greater rest mass? Is there a way I can infere the mass of the rho knowing the masss of the pion?
There is a strong spin-spin force between the quark and the anti-quark which is repulsive for spin one and attractive for spin zero.
 
RedX said:
How do vector mesons arise? I thought that if a field is spontaneously broken, then it must be a scalar field, or else Lorentz symmetry would be broken also?

Scalar mesons come from spontaneously breaking a scalar composite quark and antiquark field, the "quark condensate".

Where do vector mesons come from?
You are talking about something other than the pseudoscalar pion and vector rho.
They are each simply described by the quark model.
 
clem said:
There is a strong spin-spin force between the quark and the anti-quark which is repulsive for spin one and attractive for spin zero.

Electromagnetic spin-spin interaction between the nucleus and the electron in a hydrogen atom is on the order of 10-6 eV (hyperfine splitting). Spin-spin interaction scales as the inverse third power of the distance. Assuming that the separation between quarks in a meson is on the order of nuclear radius, we do get a large contribution (on the order of MeV) to the difference of pi and rho masses.

But that raises another interesting question. Why is it, then, that mass difference between pi+ and rho+ is almost the same as the difference between pi0 and rho0? Spin-spin interaction is proportional to the product of magnetic momenta, and those differ significantly between an up-quark and the down-quark.

Perhaps there's also a QCD spin-spin interaction that contributes.
 
Last edited:
There is a singular QCD spin-spin interaction. That is why I used the word "strong".
 
The issue is clear to me now. This also explains why the rho quickly decays to pions, as the in the rho is repulsive. But once again I can't understand the numbers exactly, I wonder when and how I will be able to make more solid mathematical discussions on this subject!
Thank you all
 
  • #10
A couple of things are happening here.

First, yes there is a QCD magnetic force (sometimes called "chromomagnetic") which leads to a QCD hyperfine splitting. In fact, it's anything but hyperfine, as in the QCD case it's typically an order of magnitude larger than the fine structure.

Second, one has to keep straight the difference between the constituent quark mass of 300 MeV and the current quark mass of a few MeV. The reason that hadron magnetic moments aren't 50-100x larger than they are is because what matters here is the constituent quarks.

Third, the pion is funny. Normally, you'd expect the pion to weight 400 or 500 MeV, but there's an approximate symmetry at work, that drives this mass low. If the current quarks were exactly massless, the symmetry would be exact, and the pions would be massless as well.
 

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