Relative momentum

  1. 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!!!
     
  2. jcsd
  3. There isn't one single value. There is a distribution function of values.
     
  4. 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?
     
  5. 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.
     
  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/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!!!
     
  7. 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!!!
     
  8. mfb

    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.
     
  9. Bill_K

    Bill_K 4,157
    Science Advisor

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