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Register a new userWave functions and annihilation widths of heavy quarkonia
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Janakiben Jagadishchandra Patel
Publication date
2020
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English
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Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into $gammagamma$, $gg$, $3gamma$, $3g$ and $gamma gg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrodinger wave function at zero quark-antiquark separation.
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We calculate the annihilation decay rates of the $^3D_2(2^{--})$ and $^3D_3(3^{--})$ charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. The wave functions of states with quantum numbers $J^{PC}=2^{--}$ and $3^{--}$ are constructed. By solving the corresponding instantaneous Bethe-Salpeter equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the $3g$ channel are as follows: $Gamma_{^3D_2(cbar c)rightarrow ggg} = 9.24$ keV, $Gamma_{^3D_3(cbar c)rightarrow ggg}=25.0$ keV, $Gamma_{^3D_2(bbar b)rightarrow ggg}= 1.87$ keV, and $Gamma_{^3D_3(bbar b)rightarrow ggg}= 0.815$ keV.
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In this work, we revise the conventional description of J/Psi(1S), Y(1S), Psi(2S) and Y(2S) elastic photo- and electroproduction off a nucleon target within the color dipole picture and carefully study various sources of theoretical uncertainties in calculations of the corresponding electroproduction cross sections. For this purpose, we test the corresponding predictions using a bulk of available dipole cross section parametrisations obtained from deep inelastic scattering data at HERA. Specifically, we provide the detailed analysis of the energy and hard-scale dependencies of quarkonia yields employing the comprehensive treatment of the quarkonia wave functions in the Schroedinger equation based approach for a set of available c-bar{c} and b-bar{b} interquark interaction potentials. Besides, we quantify the effect of Melosh spin rotation, the Q^2-dependence of the diffractive slope and an uncertainty due to charm and bottom quark mass variations.
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