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Natural Science Forum / Physics / Particle Physics / October 2004mass of bound system
Hello, I seem to miss a quite fundamental point concerning the mass of a bound system. When I ask people what makes the mass of the proton, I always get vague answers as: E=mc2, mass is equivalent to energy, ... and I always have the feeling that they haven't understood it either. Does anybody have a good way of explaining why a bound system of massless quarks can give a very massive particle, and why increasing the kinetic energy (or orbital angular momentum) of the system will increase its mass? Thanks a lot in advance! Pedro > Hello, > [quoted text clipped - 9 lines] > Thanks a lot in advance! > Pedro The quarks are not massless. Indeed, in the search for the Higgs boson, the decay modes of the Higgs are calculated on the assumption that the coupling to the final particle-antiparticle pair is proportional to the mass of the particle/antiparticle. Note that the heavier quarks are expected to be stronger Higgs signals than lighter quarks. However, you may be confusing two different definition of quark masses -- so-called "current quark" and "constituent quark" masses. To understand the difference between these will take more time than I'm willing to expend at the moment. PD > Hello, > [quoted text clipped - 9 lines] > Thanks a lot in advance! > Pedro The quarks are not massless. Indeed, in the search for the Higgs boson, the decay modes of the Higgs are calculated on the assumption that the coupling to the final particle-antiparticle pair is proportional to the mass of the particle/antiparticle. Note that the heavier quarks are expected to be stronger Higgs signals than lighter quarks. However, you may be confusing two different definition of quark masses -- so-called "current quark" and "constituent quark" masses. To understand the difference between these will take more time than I'm willing to expend at the moment. PD I may just be talking out of my a.s, but it is rarely assumed that a particle has a mass of zero, even if no reasonable number has been achieved to the claim the mass of said particle. I suppose, for the sake of arguing, that if quarks were massless, that even virtual particles that do not meet the "requirements" of relativity attribute some energy to space -- there is no such thing as a system with no energy, but there is such a thing as a system with the lowest possible energy. If massless particles come together, I suppose it is a feasible concept that energy is created, as long as we are assuming it is in a holistic system. Thanks Paul, for your help. But the Higgs mechanism is not what I meant. What I heard was that, assuming only QCD with massless quarks, one can calculate the proton mass with a precision of a few percent. So the proton mass must somehow be possible to be explained just by energy-mass-equivalence in connection with kinetic and potential energy. A good example would also be quarkonium spectra. You won't be able to explain the mass differences in the spectra just with constituent quark masses. Somehow the different orbital angular momentum or radial excitation must account for the mass differences. But somehow I have the feeling that I haven't REALLY understood it. Does somebody have a nice intuitive picture for how a different energy level gives a different mass? Pedro > Thanks Paul, for your help. But the Higgs mechanism is not what I > meant. What I heard was that, assuming only QCD with massless quarks, [quoted text clipped - 10 lines] > > Pedro First of all, I'm not sure where you would have heard that assuming massless quarks and QCD you can calculate the proton mass. You need to point more specifically. Now, there are some lattice gauge calculations that are attempting to do something similar, but there are a LOT of caveats and artifacts associated with those methods. Secondly, indeed angular momentum and radial excitations (in, say, a bag model) can account for energy differences, in much the same way that different electron angular momenta in a multi-electron atom can account for differences in electron binding energy. And binding energy does result in the mass of the collection being LOWER than the mass of the separate parts, not HIGHER. PD Hi, I am not referring to any specific calculations, and I just want to understand this intuitively. OK, maybe we could assume that there is a potential between two quarks just as you learn it in course books about particle physics, something like V(r) = -a/r + kr, and we could assume that this could be explained by QCD by applying some calculational method (even if this is a too naive assumption). It seems to me that what I am having problems with is Einstein's equivalence between mass and energy. OK, if r goes to 0, then the quarks are free and the combined system has mass 0. At some non-0 values of r we then get bound states with higher energy. How can I now see with some (microscopic) picture, that this bound system gained inertia, ie mass? Thank you, Pedro > Hi, > [quoted text clipped - 11 lines] > see with some (microscopic) picture, that this bound system gained > inertia, ie mass? You're mixing too many half-baked notions together unfortunately. Asymptotic freedom does not correspond well enough to objects at r=0 in a classical potential for it to make much sense. But if you want, think of it this way: The quarks are tied together with rubber bands (this is the nature of gluon exchange). This is unlike electromagnetic interaction, which gets weaker as distance increases. Here, the further quarks are separated, the more energy is occupied in potential energy. Separating the particles far enough puts enough energy into the "rubber band" that new quark-antiquark pairs can be created out of the energy. I suspect you've heard this description before. Does it help? PD Hi Paul, thanks for the clarification of my naive picture. Things became already much clearer and I am now sure what I do not understand: Einstein's equivalence between mass and energy, how eg two quark fields that couple with the gluon field in a way that you get a bound state actually gain mass. Somehow I was believing that a similar intuitive picture exists like for the coupling of a quark to the Higgs field. But it seems that such a picture does not exist, or at least I haven't heard of any. Or could one just say that gaining energy for the two-quark system means that there are many quark-gluon interactions and the two-quark system drags itself through the gluon field, ie gets scattered around and therefore the effective speed is less than in the massless case? Would that be correct? Best regards, Pedro > Hi Paul, > [quoted text clipped - 15 lines] > Best regards, > Pedro No, the mechanism for the Higgs coupling producing mass is actually something that is difficult to describe conceptually. It is NOT a binding energy analog. It is more like "drag" through a surrounding field. PD > Hi Paul, > [quoted text clipped - 15 lines] > Best regards, > Pedro Read Leon Lederman's popular book, "The God Particle". It's all about this. |
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