Relative Momentum of Quarks in Mesons at Center of Mass Frame

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Discussion Overview

The discussion revolves around the relative momentum of quarks in mesons, particularly in the context of the center of mass frame. Participants explore the implications of quark momentum distributions, the composition of mesons, and the relationship between quark masses and meson mass.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant asks for the value of relative momentum q at the center of mass frame, suggesting a specific calculation based on the momenta of quark and anti-quark.
  • Another participant counters that there is not a single value for q, but rather a distribution function of values.
  • A different participant challenges the assumption of a single value by providing a calculation that leads to a specific expression for q in the center of mass frame, questioning why this value isn't accepted.
  • One participant introduces the concept that mesons are not just composed of valence quarks, but also include virtual quarks and gluons, which must be considered in the momentum description.
  • Several participants raise questions about the mass of pions, noting that the mass of individual quarks appears greater than the mass of the pion itself, and seek explanations for this discrepancy.
  • Another participant suggests that the mass of light hadrons, including pions, primarily arises from binding energy and kinetic energy of particles inside, indicating that quarks have a broad momentum distribution.
  • One participant points out a potential error in the mass comparison, suggesting that the sum of quark masses does not exceed the mass of the pion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of quark momentum in mesons and the implications of quark mass versus meson mass. There is no consensus on the value of relative momentum q or the reasons behind the mass discrepancies.

Contextual Notes

Participants highlight the complexity of meson structure, including the influence of virtual particles and binding energy, which complicates straightforward calculations and assumptions about momentum and mass.

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

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