In this work, we assume two different potentials for the initial and final heavy quarkonia and the intermediary hybrid states. The most popular potential form for the study of heavy quarkonia is the Cornell potential [11] V(r)= -κ/r + b r (2.13)
Usually many authors prefer α_s (r) instead of κ. The relation between them is κ=(4α_s (r))/3 and α_s (r) can treated as constant for bb ̅ and cc ̅ quarkonia. It may be more reasonable to choose a modified Cornell potential which includes the spin-related term [12], the modified potential is V(r)= -κ/r + b r+V_s (r)+V_0 …show more content…
[12] it was set to be zero, but fix it by fitting the spectra of heavy …show more content…
(Nosheen paper : higher hybrid charmonia in an ext pot model )
3.7 Characteristics of Hybrid Charmonium Mesons
We use the following quark anti-quark effective potential for the conventional meson [17]
V_(qq ̅ ) (r)= -(4α_s (r))/3r + b r+〖(32πα_s (r))/(9m_c^2 )(σ/√π)〗^3 e^(-σ^2 r^2 ) 〖□S〗_c .□(〖□( S)〗_c ̅ )+1/(m_c^2 ) [((2α_s)/r^3 -b/2r)L.S+(4α_s)/r^3 T]
L.S=[J(J+1)-L(L+1)-S(S+1)]/2
To describe the hybrid meson in BO approximation, we used the static potential V_(qq ̅)^h in place of V_(qq ̅)^h
V_(qq ̅)^h (r)=V_(qq ̅ ) (r)+V_g (r)
Where V_g (r) is the gluonic potential whose functional form varies with the level of gluonic excitation. This potential and the corresponding gluonic states are labeled by the magnitude of the projection of total angular momentum of gluons onto quark anti-quark (Λ=0,1,2… corresponding to Greek letters Σ,Π,Δ….) and the behavior of projection under the combined operation of spatial inversion and charge conjugation. In the present work we study the hybrid in which the gluons are in the first excitation state Λ=1 this state is represented by label Π_u. Radial differential equation for the hybrid mesons is given
Usually many authors prefer α_s (r) instead of κ. The relation between them is κ=(4α_s (r))/3 and α_s (r) can treated as constant for bb ̅ and cc ̅ quarkonia. It may be more reasonable to choose a modified Cornell potential which includes the spin-related term [12], the modified potential is V(r)= -κ/r + b r+V_s (r)+V_0 …show more content…
[12] it was set to be zero, but fix it by fitting the spectra of heavy …show more content…
(Nosheen paper : higher hybrid charmonia in an ext pot model )
3.7 Characteristics of Hybrid Charmonium Mesons
We use the following quark anti-quark effective potential for the conventional meson [17]
V_(qq ̅ ) (r)= -(4α_s (r))/3r + b r+〖(32πα_s (r))/(9m_c^2 )(σ/√π)〗^3 e^(-σ^2 r^2 ) 〖□S〗_c .□(〖□( S)〗_c ̅ )+1/(m_c^2 ) [((2α_s)/r^3 -b/2r)L.S+(4α_s)/r^3 T]
L.S=[J(J+1)-L(L+1)-S(S+1)]/2
To describe the hybrid meson in BO approximation, we used the static potential V_(qq ̅)^h in place of V_(qq ̅)^h
V_(qq ̅)^h (r)=V_(qq ̅ ) (r)+V_g (r)
Where V_g (r) is the gluonic potential whose functional form varies with the level of gluonic excitation. This potential and the corresponding gluonic states are labeled by the magnitude of the projection of total angular momentum of gluons onto quark anti-quark (Λ=0,1,2… corresponding to Greek letters Σ,Π,Δ….) and the behavior of projection under the combined operation of spatial inversion and charge conjugation. In the present work we study the hybrid in which the gluons are in the first excitation state Λ=1 this state is represented by label Π_u. Radial differential equation for the hybrid mesons is given