Relative Momentum of Quarks in Mesons at Center of Mass Frame

In summary, the value of q at the center of mass frame is not a single value, but a distribution function of values that takes into account the virtual particles and binding energy within the meson. This explains why the mass of a single quark is not greater than the mass of the pion.
  • #1
Hluf
22
0
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!
 
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  • #2
There isn't one single value. There is a distribution function of values.
 
  • #3
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
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
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
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!
 
  • #7
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
Hluf said:
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.
 

1. What is the concept of relative momentum in mesons at the center of mass frame?

The relative momentum of quarks in mesons at the center of mass frame refers to the momentum of quarks with respect to the center of mass of the meson. In particle physics, the center of mass frame is a reference frame in which the total momentum of a system is zero. In this frame, the momentum of each individual particle can be described as its relative momentum to the center of mass.

2. How is the relative momentum of quarks in mesons at the center of mass frame calculated?

The relative momentum of quarks in mesons at the center of mass frame is calculated using the momentum conservation equation: Σp = 0, where Σp is the total momentum of the system. This equation takes into account the momentum of each individual quark and their respective masses.

3. What is the significance of studying the relative momentum of quarks in mesons at the center of mass frame?

Studying the relative momentum of quarks in mesons at the center of mass frame provides valuable information about the internal structure and dynamics of mesons. It can also help in understanding the strong interaction between quarks and the formation of bound states of particles such as mesons.

4. Can the relative momentum of quarks in mesons at the center of mass frame be measured experimentally?

Yes, the relative momentum of quarks in mesons at the center of mass frame can be measured experimentally using various high-energy particle accelerators. These experiments involve colliding particles at high speeds and analyzing the resulting particles and their momenta.

5. Are there any other factors that can affect the relative momentum of quarks in mesons at the center of mass frame?

Yes, there are other factors that can affect the relative momentum of quarks in mesons at the center of mass frame. These include the spin and charge of the quarks, as well as the energy and momentum of the particles involved in the collision. These factors must be taken into account when calculating and interpreting the relative momentum of quarks in mesons.

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