Bounds on the Slope and Curvature of Isgur-Wise Function in a QCD-Inspired Quark Model

Abstract

The quantum chromodynamics-inspired potential model pursued by us earlier has been recently modified to incorporate an additional factor 'c' in the linear cum Coulomb potential. While it felicitates the inclusion of standard confinement parameter b = 0.183 GeV 2 unlike in previous work, it still falls short of explaining the Isgur-Wise function for the B mesons without ad hoc adjustment of the strong coupling constant. In this work, we determine the factor 'c' from the experimental values of decay constants and masses and show that the reality constraint on 'c' yields bounds on the strong coupling constant as well as on slope and curvature of Isgur-Wise function allowing more flexibility to the model.

RMS and charge radii in a potential model

“…This important point was overlooked in earlier publications [7,8,9] of the subject, but the present work takes into account this.…”

“…For potential (7), we can make four choices: Choice-I:− 4αs 3r as parent and br+c as perturbation Choice-II:br as parent and − 4αs 3r + c as perturbation Choice-III:− 4αs 3r + c as parent and br as perturbation and Choice-IV: br+c as parent and − 4αs 3r as perturbation It is well known in quantum mechanics that a constant term 'c' in the potential can at best shift the energy scale, but should not perturb the wave function. This important point was overlooked in earlier publications [7,8,9] of the subject, but the present work takes into account this.…”

“…We have applied the perturbatively compatible approach to the QCD potential model studied earlier [7,8,9,24,27] and computed the upper and lower bounds of the RMS radii of heavy light mesons. The theoretical prediction of bound for cc meson is shown in table-3 .…”

“…In this spirit a QCD potential model has been pursued for the two choices in seperation in ref. [7,8,9] by considering the Dalgarno's method [10,11] of perturbation. The results include static and dynamical properties of heavy flavored mesons, like their form factors, masses, decay constants as well as Isgur wise function.…”