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- Thread starter kerrybbarnes
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tom.stoer

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tom.stoer

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The calculation cannot be done based on first principles as even in the QCD Lagrangian neither masses nor the coupling constant is known. They are subject to renormalization ("running coupling constant"), so there are free parameters in the fundamental theory, not only for lattice gauge calculations.

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So if the masses and coupling constant you mentioned were known then the Lattice QCD method would determine the mass of the proton without any other masses? Suppose its two masses, ma and mb and one coupling constant, c. Then by running the GCD lattice mass determination for a range of these values you could determine a function for the mass of a proton Lp(ma,mb,c). If you did this for hadrons 1..n you could generate functions for each of these. Then by equating these functions to the measured values of the masses

m1 = L1(ma,mb,c)

m2 = L2(ma,mb,c)

...

mn = Ln(ma,mb,c)

You would have an overdetermined system of equations which would be a really great thing. Either they will have 0 solutions (indicating the QCD theory is wrong) 1 solution (in which case you'd have a unique determination of ma, mb and c, or an infinite number of solutions which would still mean you could use QCD to predict the value of a new hadron even though you don't know ma, mb and c directly.

I'm guessing this is all wrong but I'm trying to give you a target you can demolish. One of the things that I'm assuming is that a different Lattice QCD calculation was done for each type of hadron? Is even that part correct? Another assumption I'm making is that there are a finite number of free parameters - your comment - which I didn't understand - about "running coupling constants" makes me wonder if the situation isn't alot more complicated. But then how could two or three hadron masses fix the scale?

m1 = L1(ma,mb,c)

m2 = L2(ma,mb,c)

...

mn = Ln(ma,mb,c)

You would have an overdetermined system of equations which would be a really great thing. Either they will have 0 solutions (indicating the QCD theory is wrong) 1 solution (in which case you'd have a unique determination of ma, mb and c, or an infinite number of solutions which would still mean you could use QCD to predict the value of a new hadron even though you don't know ma, mb and c directly.

I'm guessing this is all wrong but I'm trying to give you a target you can demolish. One of the things that I'm assuming is that a different Lattice QCD calculation was done for each type of hadron? Is even that part correct? Another assumption I'm making is that there are a finite number of free parameters - your comment - which I didn't understand - about "running coupling constants" makes me wonder if the situation isn't alot more complicated. But then how could two or three hadron masses fix the scale?

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Ab-initio Determination of Light Hadron Masses

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Again - my naive assumption was that different hadrons like the proton were simulated using lattice QCD and the simulation revealed the mass of the hadron. I think from what has been said that this assumption is wrong? If so what would make it possible to actually simulate a proton directly? It seems like a desirable thing to do.

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