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Relative momentum 
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#1
Feb1014, 01:36 AM

P: 22

When we study the bound state of quarks, i.e. mesons, the relative momentum is given as; q=1/2(p_{1}p_{2}). Where p_{1} and _{2}, are momentum of quark and antiquark, 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!!! 


#2
Feb1014, 11:28 AM

Thanks
P: 1,948

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



#3
Feb1114, 02:48 AM

P: 22

Why not have a single value? For instance; q=1/2(p_{1}p_{2}), if we consider at center of mass collision for equal mass particle, i.e. p_{1}=(p,im_{1}) and p_{2}=[B]p[/B,im_{2}] then q becomes
q=1/2((p_{1}+p_{2}),i(m_{1}m_{2})) but for equal mass, p_{1}=p_{2})=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
Feb1114, 07:55 AM

Thanks
P: 1,948

Relative momentum
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
Feb2614, 01:20 AM

P: 22

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/c^{2} and mass of
d=4.1 to 5.7Mev/c^{2}. 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
Feb2614, 01:22 AM

P: 22

We know pion is the composite of up and down quarks. The mass of charged pion is 139.6 Mev/Mev/c^{2} and mass of u=1.7 to 3.0 Mev/c^{2} and mass of
d=4.1 to 5.7Mev/c^{2}. 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
Feb2714, 04:27 PM

Mentor
P: 11,601

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. 


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