Isgur–Wise function for heavy–light mesons in theD-dimensional potential model

Abstract

This letter reports some improvement of the formalism and analysis of our very recent work [1] on the studies of Isgur-Wise function for heavy-light mesons following higher dimensional string inspired potential model.

A higher dimensional potential model approach in the study of the Isgur–Wise function for heavy–light mesons

“…This Nambu-Goto potential in higher dimension is analogous to the linear plus Coulombic type Cornell potential in 3 + 1 dimensional QCD. Earlier, we have developed similar formalism considering Lüscher term as parent in perturbation technique [53]. However, physical basis of string potential model supports the fact that the linear confinement term as the main contributing part in inter-quark potential and Lüscher's term arises in this potential as a first order correction to the linear confinement term σr [13].…”

Effective string theory inspired potential and meson masses in higher dimension

“…The meson wave function within string inspired potential model considering Lüscher (− γ r ) term as parent and linear term (σr) as perturbation (with µ 0 = 0)has been reported in [17,18] as:…”

“…The surface element in D spatial dimension is DC D r D−1 dr, where the explicit expression of the terms C D has been stated in section 2.1. As the wave function in this case contains Airy's infinite polynomial series, we calculate < H > through numerical integration using the following integrals: (27) In this case, with Airy's function involved in the wave function, simpler equations like (13)(14)(15)(16)(17)(18)(19)(20)(21)(22) in the large D limit are not possible as we follow numerical integration to evaluate terms < H 1 >, < H 2 >, < H 3 >.…”

“…However, in our analysis, for simplification, we have worked with fixed value of σ and increasing values of dimension parameter D in γ to explore the variation of meson masses. With this potential based on effective string theory for flux tube, recently we have developed meson wave function in higher dimension, by solving Schrodinger wave equation in higher dimension [15,16] following quantum mechanical perturbation technique for both the cases -(a) Lüscher term as parent(unperturbed term) with linear term as perturbation [17,18] and (b) linear term as parent (unperturbed term) with Lüscher term as perturbation [19]. In this letter, we report ground state masses of heavy-light mesons in higher dimension making use of these wave functions.…”

A Potential Model Approach in the Study of Static and Dynamic Properties of Heavy-Light Quark-Antiquark Systems

“…In this paper, we propose a simpler form of analytic solution of Schrodinger equation with Cornell potential. Our earlier work with Cornell potential using perturbation technique [15][16][17]72,73], considering its linear confinement term as parent, we have found that Airy's infinite polynomial function appears in the solution for wave function. Based upon our past study, here we construct the analytic form of the meson wave function for linear plus Coulombic potential in terms of Airy's function.…”