Relative Momentum of Quarks in Mesons at Center of Mass Frame

[Hluf]

When we study the bound state of quarks, i.e. mesons, the relative momentum is given as; q=1/2(p₁-p₂). Where p₁ and ₂, are momentum of quark and anti-quark, respectively.My question is, what is the value of q at center of mass frame? For example, P=(0,iM), at center of mass frame, where P is the momentum of meson.
Thank you, for your suggestions!

 

[dauto]

There isn't one single value. There is a distribution function of values.

 

[Hluf]

Why not have a single value? For instance; q=1/2(p₁-p₂), if we consider at center of mass collision for equal mass particle, i.e. p₁=(p,im₁) and p₂=-p[/B,im₂] then q becomes
q=1/2((p₁+p₂),i(m₁-m₂))
but for equal mass, p₁=p₂)=p
where p is a vector
q=1/2(2p,0)⇔q=(p,0)→why not this, the value of q at center of mass frame?

 

[dauto]

You're assuming that there is nothing else inside the meson besides its valence quarks. In fact the quarks are immersed in a soup of virtual quarks and gluons. The energy and momenta of these virtual particles must be included in the description of the meson.

 

[Hluf]

Mass of pion meson

We know pion is the composite of up and down quarks. The mass of charged pion is 139.6 Mev/^c and mass of u=1.7 to 3.0 Mev/c² and mass of
d=4.1 to 5.7Mev/c². From these we see that the mass of single quark greater than the mass of the pion. This is my question, why? Any one voluntary answer my question, Thanks!

 

[Hluf]

Mass of pion meson

We know pion is the composite of up and down quarks. The mass of charged pion is 139.6 Mev/Mev/c² and mass of u=1.7 to 3.0 Mev/c² and mass of
d=4.1 to 5.7Mev/c². From these we see that the mass of single quark greater than the mass of the pion. This is my question, why? Any one voluntary answer my question, Thanks!

 

[mfb]

Most of the mass of the light hadrons (and the pion is a light hadron) comes from binding energy - or, as an alternative picture, the kinetic energy of the real and virtual particles inside.
Those quarks don't have a fixed momentum, they have a very broad distribution, given by the parton distribution functions.

 

[Bill_K]

We know pion is the composite of up and down quarks. The mass of charged pion is 139.6 Mev/Mev/c² and mass of u=1.7 to 3.0 Mev/c² and mass of d=4.1 to 5.7Mev/c². From these we see that the mass of single quark greater than the mass of the pion. This is my question, why? Any one voluntary answer my question, Thanks!

I think you dropped a decimal point. 5 MeV plus 5 MeV is not greater than 139 MeV.