Running coupling constant and masses in QCD, the meson spectrum

Abstract

Abstract. In line with some previous works, we study in this paper the meson spectrum in the framework of a second order quark-antiquark Bethe-Salpeter formalism which includes confinement. An analytic one loop running coupling constant α s (Q), as proposed by Shirkov and Sovlovtsov, is used in the calculations. As for the quark masses, the case of a purely phenomenological running mass for the light quarks in terms of the c. m. momentum is further investigated. Alternatively a more fundamental expression m P (Q) is introduced for light and strange quarks, combining renormalization group and analyticity requirements with an approximate solution of the Dyson-Schwinger equation. The use of such running coupling constant and masses turns out to be essential for a correct reproduction of the the light pseudoscalar mesons.

Regge trajectories for the mesons consisting of different quarks

“…In Ref. [27], the authors obtained a first principal Bethe-Salpeter equation, and then reduced it to the eigenvalue equation for the square mass operator [26][27][28][29][30] by means of a three dimensional reduction…”

“…As applying the formula (1) to fit the bottomonia and charmonia, the results are excellent. In the present work, we use the quadratic form of the spinless Salpeter-type equation (QSSE) [26][27][28][29][30][31][32][33] to discuss the Regge trajectories for the mesons consisting of different quarks. We find that the obtained formula can be written in the same form as the Regge trajectories in Eq.…”

Hadronic contributions to electroweak observables within DPT

“…is the one-loop perturbative running coupling, and HLMNT'11 [66] JS'11 [67] DHMZ'11(τ) [68] DHMZ'11(e) [68] This work stands for the one-loop infrared enhanced analytic running coupling [62,63], which was independently rediscovered in Refs. [64,65]. The perturbative approximation of Π(q 2 ) (14) contains infrared unphysical singularities, that makes it inapplicable at low energies.…”

Single transverse spin asymmetries in semi-inclusive deep inelastic scattering in a spin-1 diquark model

“…For the sake of comparison as well as a deeper understanding of the role of coupling constant we have also calculated the asymmetry by replacing the fixed coupling constant (α 1 ) by running coupling constants where higher order contributions, particularly the closed quark loops, can be taken into account. We take an analytic one-loop running coupling constant as proposed by the Shirkov and Sovlovstov [49][50][51]…”

“…However, for Λ 2 QCD = Q 2 , an nonphysical singularity existed which contradicted some analytical properties and had to be modified in the infrared region. Therefore, the above said coupling constant was modified [49][50][51] such that it remains finite at Λ 2 QCD = Q 2 and is given by…”