Is there a vibration energy term associated with mesons?

[Pedro de la Torre]

Hello, I am learning about solutions of the Schrödinger equation including the term of rotational energy (i.e. L^2 /2I, in its quantized form) and I was wondering if there should be another quantum term describing vibrational states of hadrons or any other composite subatomic particle, in analogy to what happens with molecules.
In my mind, thinking, for example, in a pion, I imagine a couple of quarks joint by a non-rigid string and both quarks rotating around its center. In addition to this rotation, they will have a vibration (like in a spring) whose frequency must matter in the total energy of the particle or its interaction with other particles.
Could anyone tell me if this is used or not and, if possible, some literature to read about?
Thanks in advance!

 

[azntoon]

As far as I am aware, there is no accepted model of hadrons that includes vibrational energy. Hadrons are made up of quarks, which interact via the strong nuclear force, and so any vibration or rotational energy would be very hard to calculate. However, some theoretical models have been proposed which include vibrational energy. In particular, the string-flip model suggests that the quarks can flip their orientation while travelling along a string, resulting in a vibrational energy associated with the hadron. There have also been some studies of hadronic vibrations using lattice QCD simulations. If you are looking for more information on these topics, I suggest you start by doing a literature search for "hadronic vibrations" and "string-flip model".