Dynamics of the quark-antiquark interaction and the universality of Regge trajectories

Abstract

The dynamical picture of a quark-antiquark interaction in light mesons, which provides linearity of radial and orbital Regge trajectories (RT), is studied with the use of the relativistic string Hamiltonian with flattened confining potential (CP) and taking into account three negative corrections: the gluon-exchanged, the self-energy, and the string corrections. Due to the flattening effect the radial slope βn and the orbital slope β l of the Regge trajectories decrease by ∼ 30% as compared to those in linear CP, while the string correction decreases only the orbital slope by the value ∼ 10%. The self-energy correction is very important and has large magnitude, ∼ −300 MeV for high excitations. It also provides the linearity of the RT, built for the centroid squared masses, and gives the small value of the intercept, β0 = 0.50(1) GeV 2 , equal to the squared centroid mass of ρ(1S). If the universal gluon-exchanged potential without fitting parameters and screening function, as in heavy quarkonia, is taken, then the radial slope, βn = 1.15(9) GeV 2 (l = 0), and the orbital slope, β l = 1.03(9) GeV 2 , have close values and the RT can be considered as approximately universal.

The Regge Trajectories and Leptonic Widths of the Vector $$\varvec{s}\bar{\varvec{s}}$$ Mesons

“…From Table 1 one can see that the masses, defined by the ERT with m s = 125 MeV and m s = 180 MeV, coincide within ∼ 10 MeV accuracy for φ(1S) and φ(2S) and differ only by ∼ 20 MeV for the higher 3S and 4S excitations, although their intercepts and the radial slopes are different. Notice that for a smaller m s = 125 MeV the values of the intercept and the radial slope are practically equal to those for light mesons [12,[20][21][22], while for m s = 180 MeV they are closer to the values in heavy quarkonia [17].…”

“…First, we consider the φ(n 3 S 1 ) radial trajectory, which needs special consideration since its radial slope is larger than that of the ERT for the states with l = 0 [17]; this effect is seen in the RT of light mesons [9][10][11][12][18][19][20][21], as well as in heavy quarkonia [17]. The reason why the radial slope is larger in the S-wave mesons is explained by the stronger gluon-exchange (GE) interaction in the states with l = 0 than in those with l = 0 [22]. The radial ERT of φ(nS) can be presented as,…”

“…To define the leptonic widths of the φ(1020), φ(1680), φ(1 3 D 1 ), φ(2 3 D 1 ) their wave functions (w.f.s) are calculated, using the relativistic string Hamiltonian (RSH) [18,19,22,27,28] without fitting parameters, where the centroid mass M cog (nl) is defined by the eigenvalues M 0 (nl) of the equation,…”

“…and by two negative corrections, the self-energy and the string corrections [18,19,22,29,30]. Here m s = 180 MeV and the potential V 0 (r ) is taken as the sum of the confining potential and the gluon-exchange (GE) term, V GE = − 4α V (r ) 3r , with the parameters from Ref.…”

“…Here m s = 180 MeV and the potential V 0 (r ) is taken as the sum of the confining potential and the gluon-exchange (GE) term, V GE = − 4α V (r ) 3r , with the parameters from Ref. [22]. Since the ground states have relatively small sizes, their dynamics is defined by the linear CP, V c (r ) = σ r = 0.18 r GeV, while for high excitations, which have large sizes, a flattened CP…”