Solving Schrödinger Wave Equation for the Charmonium Spectrum Using Artificial Neural Networks

Table 1

Comparison of our calculated masses of ground and radially excited states of charmonium mesons using an artificial neural network with other predicted theoretical and experimental results.

	Meson				Our calculated mass using an artificial neural network (GeV)	Theoretical mass [53] using the shooting method (GeV)	Theoretical mass [54] with NR potential model (GeV)	Exp. mass (GeV) [55]
1S		0	0	0	2.98101	2.9816	2.982
		0	1	1	3.0953	3.08999	3.090
2S		0	0	0	3.63890	3.6303	3.630
		0	1	1	3.68611	3.6718	3.672
3S		0	0	0	4.0430	4.0432	4.043	—
		0	1	1	4.04000	4.0716	4.072	[54]
4S		0	0	0	4.38400	4.3837	4.384	—
		0	1	1	4.41500	4.4061	4.406	[54]
1P		1	0	1	3.5255	3.5156	3.516
		1	1	0	3.4149	3.4233	3.424
		1	1	1	3.51070	3.5005	3.505
		1	1	2	3.5583	3.5490	3.556
2P		1	0	1	3.9344	3.9336	3.934	—
		1	1	0	3.8519	3.8715	3.852	—
		1	1	1	3.9256	3.9203	3.925	—
		1	1	2	3.9272	3.9648	3.972
3P		1	0	1	4.279	4.2793	4.279	—
		1	1	0	4.202	4.2295	4.202	—
		1	1	1	4.26695	4.2663	4.271	—
		1	1	2	4.3171	4.3093	4.317	—
4P		1	0	1	4.58500	4.5851	—	—
		1	1	0	4.5425	4.5424	—	—
		1	1	1	4.57201	4.5720	—	—
		1	1	2	4.6141	4.6141	—	—
1D		2	0	2	3.799001	3.7994	3.799	—
		2	1	1	3.7699	3.7805	3.785	[54]
		2	1	2	3.8000	3.8002	3.800	—
		2	1	3	3.8060	3.8053	3.806	—
2D		2	0	2	4.1580	4.1576	4.158	—
		2	1	1	4.1590	4.1363	4.142	[54]
		2	1	2	4.158	4.1580	4.158	—
		2	1	3	4.167	4.1655	4.167	—
3D		2	0	2	4.4718	4.4718	—	—
		2	1	1	4.4492	4.4492	—	—
		2	1	2	4.4704	4.4719	—	—
		2	1	3	4.4816	4.4810	—	—
4D		2	0	2	4.7562	4.7574	—	—
		2	1	1	4.73388	4.7339	—	—
		2	1	2	4.7573	4.7573	—	—
		2	1	3	4.7675	4.7675	—	—
1F		3	0	3	4.0252	4.0256	4.026	—
		3	1	2	4.283	4.0283	4.029	—
		3	1	3	4.02871	4.0287	4.029	—
		3	1	4	4.0216	4.0212	4.021	—
2F		3	0	3	4.34993	4.3499	4.350	—
		3	1	2	4.34631	4.3494	4.351	—
		3	1	3	4.3522	4.3522	4.352	—
		3	1	4	4.3449	4.3476	4.348	—
3F		3	0	3	4.64292	4.6429	—	—
		3	1	2	4.64031	4.6403	—	—
		3	1	3	4.64493	4.6448	—	—
		3	1	4	4.6422	4.6422	—	—
4F		3	0	3	4.91371	4.9137	—	—
		3	1	2	4.90957	4.9095	—	—
		3	1	3	4.91535	4.9153	—	—
		3	1	4	4.91409	4.9141	—	—