Wave-function-based characteristics of hybrid mesons

Abstract

We propose some extensions of the quark potential model to hybrids, fit them to the lattice data and use them for the purpose of calculating the masses, root mean square radii and wave functions at the origin of the conventional and hybrid charmonium mesons. We treat the ground and excited gluonic field between a quark and an antiquark as in the Born-Oppenheimer expansion, and use the shooting method to numerically solve the required Schrödinger equation for the radial wave functions; from these wave functions we calculate the mesonic properties. For masses we also check through a Crank Nichelson discretization. For hybrid charmonium mesons, we consider the exotic quantum number states with J P C = 0 +− , 1 −+ and 2 +− . We also compare our results with the experimentally observed masses and theoretically predicted results of the other models. Our results have implications for scalar form factors, energy shifts, magnetic polarizabilities, decay constants, decay widths and differential cross sections of conventional and hybrid mesons.

Decays and spectrum of bottom and bottom strange mesons

“…To this end we construct a reasonably "standard" nonrelativistic potential quark model and fit its parameters to the known B and B s mesons. The philosophy underpinning this type of modelling is the adiabatic separation of "slow" constituent quark degrees of freedom from "fast" gluonic degrees of freedom [5][6][7][8].…”

Conventional and hybrid Bc mesons in an extended potential model

“…The similar results are obtained for the charmonium and bottomonium mesons in refs. [4,20,27]. In Table 2, we compare our calculated masses of conventional B c mesons with others [5,8,9,10,16,25,26].…”

“…To describe hybrid meson in the Born-Oppenheimer (BO) approximation used in [4,18,19,20], we use the static potential V h qq (r) in place of V (r) of eq. (3):…”

“…where the values of the constants A = 3.4693 GeV, B = 1.0110 GeV, and c = 0.1745 are fixed by our earlier fit [4] to the lattice data [21]. It is shown in ref.…”

“…We suggested in ref. [4] a number of analytical expressions for this potential and then used the one which best fits the relevant lattice-generated discrete energies to find a number of dynamical implications (radii, wave functions at origin, leptonic and two photon decay widths, E1 and M 1 radiative transitions) for heavy quarkonia that can be compared with actual hard experiments. These sectors have zero net flavor and hence are eigenstates of C parity.…”