Why Study Hadron Physics and the Decay Constant of Mesons?

Hluf
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Dear all;
why we study hadron physics? For instance different people calculates the decay constant of mesons using different methods and they get approximately the same result, the difference is too small. So why not people they apply the same mathematical method?
 
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To have a cross-check for the results?
In addition, it is often not clear what exactly is the easiest/most accurate method to calculate something, so several approaches are used.

why we study hadron physics?
To understand the objects we are made of. And to look for deviations from existing theories.
 
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I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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