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A Meson Binding State Model in Two-Dimensional Space
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DOI：10.3390/particles9020055.png)
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Abstract
En 中文
In this paper, we first show that the four masses of the Upsilon binding states-namely, Y(1S) through Y(4S)-composed of bottom quarks and anti-bottom quarks follow logarithmic spacing. The correlation coefficient R between the experimental values and the straight line is 0.99997, indicating an extremely good fit. When the three peaks-Y(5S), Y(6S), and Y(7S), considered higher Upsilon binding states, as indicated in the recent Belle experiment-are added and plotted on the line of logarithmic spacing, the correlation coefficient R between the straight line and the experimental values for these seven "binding state levels" is 0.9998. If this line is extended to higher masses, an eighth peak in the cross-section is expected at a mass of (11,119 +/- 10) MeV. In other words, it is predicted that the peak in the cross-section created by Y(8S) will be found in the Belle experiment in the future. Next, we consider why meson binding states are represented by a line with logarithmic spacing. An example is the electric field generated by a charge on a two-dimensional plane; the electric field created by a charge placed on the plane is expressed as F similar to 1/r, and the potential energy is expressed as V similar to log(r). Therefore, we solve the two-dimensional Schr & ouml;dinger equation numerically under F similar to 1/r and compare the results with the three-dimensional solution. We find that differences appear in the energy levels of the J=0 eta c meson. Specifically, it is shown that the mass of the eta c meson is closer to the value obtained by solving the two-dimensional Schr & ouml;dinger equation. Based on this eta c meson series, we predict the existence of a new eta c meson with a mass of 3955 MeV.
Keywords:
logarithmic potential
meson spectroscopy
Schr & ouml
dinger equation
Numerov method
two-dimensional world