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# Relating Quarkonium Wave Functions at the Origin

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### Abstract

Within the context of nonrelativistic potential models, we obtain several formulas (with varying degrees of rigor) relating the wave functions at the origin of the $$c{\bar c}$$, $$b{\bar c}$$ and $$b{\bar b}$$ S-wave quarkonium systems. One of our main results is a model-independent relation which seems to hold to within 3% for any reasonable choice of interquark potential and any choice of radial quantum number -- namely, $${|\Psi_{b{\bar c}}(0)|^2 \simeq |\Psi_{c{\bar c}}(0)|^{1.3}|\Psi_{b{\bar b}}(0)|^{0.7}}$$ (the exponents are motivated in the text). One of the physical consequences of this result is the following relationship between heavy meson masses which we expect to hold at about the 10% level: $${M_{B_c^*}-M_{B_c}\simeq (0.7)(M_{J/\psi} -M_{\eta_c})^{0.65}(M_{\Upsilon}-M_{\eta_b})^{0.35}}$$.

### Most cited references6

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### Charmonium: Comparison with experiment

(1980)
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### Quarkonia and quantum chromodynamics

(1981)
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### Quarkonium Wave Functions at the Origin

(1995)
We tabulate values of the radial Schr\"{o}dinger wave function or its first nonvanishing derivative at zero quark-antiquark separation, for $$c\bar{c}$$, $$c\bar{b}$$, and $$b\bar{b}$$ levels that lie below, or just above, flavor threshold. These quantities are essential inputs for evaluating production cross sections for quarkonium states.
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### Author and article information

###### Journal
31 October 1996
10.1016/S0370-2693(96)01514-6
hep-ph/9610547
UICHEP-TH/96-16
Phys.Lett. B393 (1997) 155-160
TEX, 9 pages, requires harvmac
hep-ph

High energy & Particle physics