Why Do No Stable Mesons Exist?

[jc09]

So mesons consist of two quark. I am wondering why no stable mesons exist?

 

[bcrowell]

Because they're more massive than leptons and have zero baryon number, they can decay into leptons.

 

[arivero]

Note that if the pion had the same mass that the muon, it should be stable at first order, even if the electron is massive. So mass and baryon number is not all the history, spin has a role too.

 

[tom.stoer]

Light pseudo-scalar mesons (pions, ...) can be understood as Godstone bosons generated by chiral symmetry breaking and should therefore be both stable and massless. But chiral symmetry is only an approximate symmetry b/c of small quark masses; therefore mesons are only approximately massless and approximately stable.

This does not apply to the singlet eta-prime b/c the axial U(1) symmetry is not broken spontaneously via the Goldstone mechanism but via the axial anomaly (the eta-prime is quite heavy compared to the other light mesons).

And it does not apply to heavier mesons, e.g. the vectors mesons (rho, ...)

 

[arivero]

YES Tom, it is amazing! The pion has two independent arguments to be stable, one coming from QCD via chiral symmetry breaking, and another coming from electroweak decay via the conspiracy of masses of electron, muon and pion.

 

[Parlyne]

Note that if the pion had the same mass that the muon, it should be stable at first order, even if the electron is massive. So mass and baryon number is not all the history, spin has a role too.

I don't see how you conclude this. The $\pi \rightarrow e\nu$ channel may be suppressed by the necessary electron mass insertion; but, it is non-zero at tree level, independent of the relationship between the pion and muon masses.

 

[arivero]

I don't see how you conclude this. The $\pi \rightarrow e\nu$ channel may be suppressed by the necessary electron mass insertion; but, it is non-zero at tree level, independent of the relationship between the pion and muon masses.

Indeed I said it badly; what I was thinking is that both channels, muon and pion, are strongly suppressed, that tree level into muon becomes zero if the mass of the muon is equal to the mass of the pion, and that tree level into electron becomes zero if the mass of the electron is set to zero. Is that right?

(Actually, when m_pi=m_mu, and keeping m_e at the current value, I am not sure what is greater, if the tree level into electron or the loop corrections into muon... but I ack it is not an excuse for sloopy wording)

Still, I stand amazed by the near-stability of pion, either pi- or pi0

 

[Vanadium 50]

(Actually, when m_pi=m_mu, and keeping m_e at the current value, I am not sure what is greater, if the tree level into electron or the loop corrections into muon...

Tree into electron. There is zero phase space for muonic decays in your example.

 

[arivero]

Tree into electron. There is zero phase space for muonic decays in your example.

 

[Parlyne]

Tree into electron. There is zero phase space for muonic decays in your example.

Worse. It's kinematically forbidden because of non-zero neutrino mass.