Difference between pion and rho

[dsfranca]

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!

 

[Norman]

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.

 

[dsfranca]

Thanks for the answer Norman, but why would a different spin result in a different mass? Is it becuase 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?

 

[RedX]

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?

 

[Meir Achuz]

Thanks for the answer Norman, but why would a different spin result in a different mass? Is it becuase 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.

 

[Meir Achuz]

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.

 

[hamster143]

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.

 

[Meir Achuz]

There is a singular QCD spin-spin interaction. That is why I used the word "strong".

 

[dsfranca]

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

 

[Vanadium 50]

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.