**Use quantum mechanical calculational methods of atomic energy levels and calculate the mesonic mass**

Bound states of the positronium can be calculated according to quantum mechanical laws. To do this, one should consider the mass of each charged particle and the strength of the charge as given parameters.

Mesons are bound state of quark and antiquark. The aim of this research topic is to find out if a simple model based on the assumption that the dynamics of the strong force, that binds the quark to the antiquark, is like the dynamics of the electromagnetic force of the positronium.

To do this, one should use several free parameters e.g. the mass of the *u,d,s* quarks of a Dirac-like equation of two elementary fermions and the strength of the strong charge. Assume that the mass *M(u) = M(d)* and ignore electromagnetic effects and the mass difference between members of the same isospin multiplet. Use quantum mechanical laws and calculate the energy of the quark-antiquark bound states, which are (approximately) the experimentally known mass of mesons. Ignore mesons that are not made of *u,d,s* quarks.

The proton contains additional quark-antiquark pairs [1,2] and every hadron, including meson, has additional quark-antiquark pairs. For the simplicity of the calculation, you may ignore this effect.

Advice: Begin with mesons that contain no s quark – namely, I=1 mesons.

#### References

[1] D. H. Perkins, Introduction to High Energy Physics, (Addison-Wesley, Menlo Park CA, 1987).

[2] M. Alberg, *Prog. Part. Nucl. Phys.* **61**, 140 (2008).