# Relative momentum

1. ### Hluf

22
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.

2. ### dauto

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

3. ### Hluf

22
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?

4. ### 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.

5. ### Hluf

22
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!!!

6. ### Hluf

22
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!!!

### Staff: Mentor

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.

8. ### Bill_K

4,157
I think you dropped a decimal point. 5 MeV plus 5 MeV is not greater than 139 MeV.