The Rubber Stamp Potential

As a last resort, we note that the ``success" of non-relativistic meson models (such as it is) is largely based on the fact that once a model is fit to one meson family, it is used to simply stamp out copies of the same mass splittings in every family.

Using = 0.1 throughout the meson spectrum should give a reasonable though inexact description of all meson levels, particularly the light mesons. The NR OGE short range potential again should also be a reasonable guide to the splittings within a level. The biggest problem not covered by this model is mixing, which is a 1/ term in the perturbative expansion. [I.e. if mixing is incorporated into a model, all other 1/ terms must also be added, including the next order OGE terms and two-gluon-exchange factors.] Mixing within a meson family is easy to spot (e.g. the and ); mixing between different isoscalar families must also be significant in this model. The (547) can, in principle, be built up of only u , d , and s quarks, but the (958) cannot. A ground state spin 0 s meson would have a mass below 700 MeV. Thus, the (958) must be considered to have a significant heavy quark content. If (958) were made of only u , d , and c quarks, it would need to have about 25 percent charm quark content; if it were composed of only s and c quarks, its c content would be about 10 percent. Both numbers are too high, but adding in a little b and/or t soon remedies the situation. [N.B. this is not a popular way of explaining the (958) mass, although the c branching ratios obviously favor a considerable content for c mesons.] Ideal mixing seems to hold outside of the ground state.

So, giving the ground state and mesons larger effective mass quarks than their and partners, using = 0.1 throughout the spectrum, and taking from the graph in the last section, we have the following light meson spectrum. (Bracketed masses refer to departures from almost-ideal-mixing among the isoscalars.)

Level	Quark spin	Meson spin	/	/		/
1S	S=0		140	135 (547)	495	643 (958)
1S	S=1		770	783	894	1020
	S=0	J=1	1260	1245 (1418)	1385	1490 (1700)
1P		J=0	980	990	1204	1316
	S=1	J=1	1254	1255	1379	1483
		J=2	1320	1290	1425	1525
2S	S=0		1246	1215 (1476)	1445	1550 (1746)
2S	S=1		1597	1575	1668	1759
	S=0	J=2	1685	1655 (1796)	1772	1860 (2020)
1D		J=1	1617	1600	1728	1817
	S=1	J=2	1683	1660	1770	1858
		J=3	1715	1680	1792	1880
	S=0	J=1	1858	1820 (1950)	1930	2010 (2150)
2P		J=0	1662	1645	1804	1888
	S=1	J=1	1854	1830	1926	2005
		J=2	1900	1855	1958	2035
3S	S=0		1843	1845 (1988)	1970	2048 (2180)
3S	S=1		2094	2040	2129	2199
	S=0	J=3	2004	1965 (2080)	2063	2138 (2260)
1F		J=2	1972	1935	2042	2118
	S=1	J=3	2003	1965	2062	2137
		J=4	2022	1980	2075	2150
			M0=612	M0=621 (841)	M0=794	M0=926 (1212)
			=-.73	=-.735	=-.729	=-.7282

Table 2:   Light Meson Spectrum