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 and taking into account the self-energy and string corrections. Due to the flattening effect both slopes, $\beta_n$ of the radial and $\beta_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $\beta_n=1.30(5)$~GeV$^2$ being larger than $ \beta_l=0.95(5)$~GeV. The self-energy correction provides the linearity of RT and remains important up to very high excitations; the string correction decreases the slope of the orbital RT, while the intercept $\beta_0=0.51(1)~ $GeV$^2$ is equal to the squared centroid mass of $\rho(1S)$. If the universal gluon-exchanged potential without fitting parameters and screening function, as in heavy quarkonia, is taken, then the slope of the radial RT decreases, $\beta_n=1.15(8)$~GeV$^2$, and its value coincides with the slope of the orbital RT, $\beta_l=1.08(8)$~GeV$^2$ within theoretical errors, producing the universal RT.
Highlights
The spectroscopy of light mesons refers to the field where nonperturbative QCD dominates and the Regge trajectories (RT), both orbital and radial, appear to be the most explicit manifestation of nonperturbative effects
It is known that the leading RT in the ðM2; JÞ-plane has a linear behavior with the slope βJðexpÞ 1⁄4 2πσ 1⁄4 1.13ð1Þ GeV2, which corresponds to the value of the string tension σ 1⁄4 0.180ð2Þ GeV2 in the string models [1,2], and precisely this σ has been used in the realistic potential model with linear confining potential (CP)
The simplest way to show the structure of the RTs is to determine the light meson spectrum in a purely linear CP and consider other interactions as a perturbation; in this case the mass Mcog is defined by analytical expressions
Summary
The spectroscopy of light mesons refers to the field where nonperturbative QCD dominates and the Regge trajectories (RT), both orbital and radial, appear to be the most explicit manifestation of nonperturbative effects. We pay special attention to the negative correction produced by the self-energy (SE) term [28], whose magnitude remains large, δSE ∼ −300 MeV, even for high excitations of light mesons; being proportional to 1=MðnlÞ, it maintains linearity of the RT. The contributions from the GE potential to the masses of excited states are not large, ≲90 MeV, the GE correction is very important, decreasing all parameters of the RTs. The masses can be calculated in two ways: either solving Eq (7) with the potential V0ðrÞ 1⁄4 VCðrÞ þ VGE, or considering VGEðrÞ as a perturbation. If for all states with a given l the numbers b2n 1⁄4 b are equal, the radial RT reduces to the radial RT, introduced in Ref. [5]: Mðn; lÞ2 1⁄4 M2g þ bn; ðl fixedÞ; ð18Þ where Mgðn 1⁄4 0; lÞ is the mass of the ground state
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
