The effect of an extended Cornell potential on mass spectra of heavy and heavy-light mesons is studied. The Cornell potential is extended to include quadratic potential and inverse quadratic potential. The N-radial Schrodinger equation is solved by using series method. The results for charmonium and bottomonium, and light-heavy meson masses are obtained. A comparison with other recent works is discussed. The present results are improved in comparison with other recent works and are in good agreement with experimental data.
We obtain the wave function of mesonic systems interacting via a Cornell potential by applying improved variational approach. We study Isgur-Wise function and its parameters. Then we report our calculations on the parameters of semileptonic decay of B and Bs mesons. B-->D*l$nu$ process is also investigated in this work.
Heavy quarkonia, Bc-meson, and CS-meson masses are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, and mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with oth…
The exact solution of N- dimensional radial Schrödinger equation with the generalized Cornell potential has been obtained using the Laplace transformation (LT) method. The energy eigenvalues and the corresponding wave functions for any state have been determined. The eigenvalues for some special cases of the generalized Cornell potential are obtained. The present results are applied to calculate the mass spectra of heavy quarkonium systems such as charmonium and bottomonium and the bc meson. A comparison is discussed with the experimental data and recent works. The present results are improved…
The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schrödinger equation to obtain their mass spectra using only four parameters namely quark mass ($m_c$, $m_b$) and confinement strength ($A_{c\bar c}$, $A_{b\bar b}$). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited $S$, $P$, $D$ and $F$ states. Digamma, digluon and dilepton decays of these mesons are computed usin…
Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of relativistic wave equation for the coulombic and linear components of the potential are used to derive the resonance complex-mass formula. The centered masses and total widths of the $ρ$-family resonances are calculated.
In this paper we discuss a quantity that can be derived from the hadronic spectrum - the ratio between the color hyperfine splitting of a K meson and that of a Sigma baryon. It will be shown that within the constituent quark model this ratio depends only on the ratio of contact probabilities within the hadrons. We compute this ratio assuming several phenomenological potential models, and show that the best agreement with data is obtained from the Cornell potential - Coulomb + linear. Thus the analysis of color hyperfine interactions corroborat es the preference for the Cornell potential based …
We study the scattering of J/$Ψ$-J/$Ψ$ mesons using Quadratic and Cornell potentials in our tetraquark ($c$$\bar{c}$$c$$\bar{c}$) system. The system's wavefunction in the restricted gluonic basis is written by utilizing adiabatic approximation and Hamiltonian is used via quark potential model. Resonating group technique is used to get the integral equations which are solved to get the unknown inter-cluster dependence of the total wavefunction of our tetraquark system. T-Matrix elements are calculated from the solutions and eventually the scattering cross sections are obtained using the two pot…
The typical binding energy of heavy hadron spectroscopy makes the system accessible to perturbative calculations in terms of non-relativistic QCD. Within NRQCD the predictions of heavy quarkonium energy levels rely on the accurate description of the static QCD potential $V_{\rm QCD}(r)$. Historically, heavy quarkonium spectroscopy was studied using phenomenological approaches such as the Cornell model $V_{\rm Cornell}=-κ/r+σ\, r$, which assumes a short-distance dominant Coulomb potential plus a liner rising potential that emerges at long distances. Such model works reasonably well in describin…
In the present work, we study meson systems consisting of quark-antiquark. We solve lippman-Schwinger equation numerically for heavy meson systems. We attempt to find a non-relativistic potential model through which we can solve the quark-antiquark bound state problem. The coefficients so obtained are in agreement with Martin potential coefficients. Via this method we also determine the strong coupling constant for the mesons tt, tc, and tb, which is a coefficient of Cornell potential.
In this work, we investigate the masses of a few heavy-light mesons with variational method, taking into account the two-loop effects in the static Cornell potential. Specifically, we consider two wave-function,Gaussian and Coulomb. Our analysis suggests that phenomenologically such approach is more successful in the Heavy flavoured meson sector than the stationary state perturbation theory and other approximation methods.
In the present article the mass spectrum, decay constant, weak decay widths, life time and branching fraction ratios and electromagnetic transition widths are calculated for ground and radially excited $B_c$ meson. To calculate the above properties the Schrödinger equation has been solved numerically for the potential. The potential employed consists of relativistic correction in the framework of pNRQCD, added to the Cornell potential. The calculated results are compared with available experimental and theoretical results.
We solved the radial Schr"odinger equation analytically using the Exact Quantization Rule approach to obtain the energy eigenvalues with the Extended Cornell potential ECP. The present results are applied for calculating the mass spectra of heavy mesons such as charmonium cc and bottomonium bb, and heavylight mesons such as bottom-charm bc and charm-Strange cs for different quantum states. Two special cases were considered when some of the potential parameters were set to zero, resulting into Coulomb potential, and Cornell potential, respectively. The present potential provides excellent resul…
Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3γ$, $3g$ and $γgg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrödinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.
This paper aims at proving the fundamental role of a relativistic formulation for quarkonia models. We present a completely covariant description of a two-quark system interacting by the Cornell potential with a Breit term describing the hyperfine splitting. Using an appropriate procedure to calculate the Breit correction, we find heavy meson masses in excellent agreement with experimental data. Moreover, also when applied to light quarks and even taking average values of the running coupling constant, we prove that covariance properties and hyperfine splitting are sufficient to explain the li…
The quark dynamics inside light mesons, except pseudoscalar ones, can be quite well described by a spinless Salpeter equation supplemented by a Cornell interaction (possibly partly vector, partly scalar). A mass formula for these mesons can then be obtained by computing analytical approximations of the eigenvalues of the equation. We show that such a formula can be derived by combining the results of two methods: the dominantly orbital state description and the Bohr-Sommerfeld quantization approach. The predictions of the mass formula are compared with accurate solutions of the spinless Salpet…
We report some approximate analytic form of meson wave function constructed upon solving Schrodinger equation with linear plus Coulomb type Cornell potential. With this wave function, we study Isgur-Wise function and its derivatives for heavy-light mesons in the infinite heavy quark mass limit. We also explore the elastic form factors, charge radii and decay constants of pseudoscalar mesons in this QCD inspired quark model approach.
Determination of the wave-function is very essential in the calculation of static and dynamic properties like masses,decay constants of pseudo-scalar mesons and masses of vector mesons.We use Dalgarno's perturbation theory and Variation-ally Improved Perturbation Theory (VIPT) to solve Schrodinger equation in a QCD inspired potential model wuth Cornell potential,which consists linear and coulomb potential.We use both the options like Columbic parent firstly and then linear parent while using the VIPT method. Comparison of both these methods and also with experimental results are done in the ca…
We present the semileptonic decay of $B_{c}$ meson in a QCD potential model with the coulombic part of the Cornell potential $-\frac{4α_{S}}{3r}+br+c$ as perturbation. Computing the slope and curvature of Isgur Wise function in this approach, we study the pseudoscalar and vector form factors for the transition of $B_{c}$ meson to its S wave charmonium $c\bar{c}$ states. Numerical estimates of widths for the transitions of $B_{c}\rightarrow J/ψ(η_{c})lν_{l}$ are presented. The results are found to be in good agreement with other theoretical values.
We employ the variational method to study the properties such as masses, decay constants, oscillation frequency and branching ratios of leptonic decays of heavy flavour mesons with linear cum coulomb Cornell potential. Gaussian function, Coulomb wave function and Airy function are taken as the trial wave-function of variational method in this study. Our analysis suggests that Gaussian trial wave-function provides results which are in close proximity with the experimental results. We also make a comparison with the results from QCD Sum rules and lattice QCD, as well as with recent PDG data.
We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulae for the energy spectra which closely approximate numerical exact calculations performed with the Schrodinger or the spinless Salpeter equations. The Bohr-Sommerfeld quantization procedure can also be used to calculate other observables such as r.m.s. radius or wave function at the origin. Asymptotic dependence of these observables on quantum numbers are also obtained in the case of potentials which behave asymptotically as a power-law…
We derive and analyze the confinement potential of the Cornell type within the framework of the generalized Soft Wall holographic model that includes a parameter controlling the intercept of the linear Regge spectrum. In the phenomenology of Regge trajectories, this parameter is very important for the quantitative description of experimental data. Our analysis shows that the ''linear plus Coulomb'' confinement potential obtained in the scalar channel is quantitatively consistent with the phenomenology and lattice simulations while the agreement in the vector channel is qualitative only. This r…
In this paper, we study the finite temperature-dependent Schrödinger equation by using the Nikiforov-Uvarov method. We consider the sum of the Cornell, inverse quadratic, and harmonic-type potential as the potential part of the radial Schrödinger equation. Analytical expressions for the energy eigenvalues and the radial wave function are presented. Application of the results for the heavy quarkonia and $B_c$ meson masses are good agreement with the current experimental data except for zero angular momentum quantum numbers. Numerical results for the temperature dependence indicates a different …
The N-dimensional radial Schrodinger equation with an extended Cornell potential is solved. The analytical exact iteration method is applied. The energy eigenvalues are calculated in the N-dimensional space. The charmonium meson, the bottomonium meson and the bc meson masses are calculated in the N-dimensional space. The special cases are obtained from the general case. The study of the effect of dimensionality number is studied. The mean value of the radius and the mean square velocity of charmonium meson, bottomonium meson, and bc meson are calculated. The present results are improved in com…
The Dalgarno's method of perturbation is used to solve the Schrodinger's equation with the Cornell potential $V(r)=-\frac{4α_s}{3r}+br+c$. The short range and long range effect of the potential is incorporated in the same wave function by using two scales $r^S$ and $r^L$ as an integration limit. The results for bounds on r.m.s. radii of various heavy flavored mesons are reported. We have also showed the relation between r.m.s. and charge radius of mesons.
Along the years, the Cornell Model has been extraordinarily successful in describing hadronic phenomenology, in particular in physical situations for which an effective theory of the strong interactions such as NRQCD cannot be applied. As a consequence of its achievements, a relevant question is whether its model parameters can somehow be related to fundamental constants of QCD. We shall give a first answer in this article by comparing the predictions of both approaches. Building on results from a previous study on heavy meson spectroscopy, we calibrate the Cornell model employing NRQCD predic…
The interquark static potential for heavy mesons described by a massive One Gluon Exchange interaction obtained from the propagator of the truncated Dyson-Schwinger equations does not reproduced the expected Cornell potential. I show that no formulation based on a finite propagator will lead to confinement of quenched QCD. I propose a mechanism based on a singular nonperturbative coupling constant which has the virtue of giving rise to a finite gluon propagator and (almost) linear confinement. The mechanism can be slightly modified to produce the screened potentials of unquenched QCD.
Thermodynamics properties of heavy mesons are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the quadratic potential plus the inverse of quadratic potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The obtained results are applied for calculating the mass of spectra of charmonium, bottomonium, bc, and cs mesons. The thermodynamics properties of heavy quarkonia such as, the mean energy, specific heat, free energy,…
Based on the numeric solution of a system of coupled channels for vector mesons ($S$- and $D$-waves mixing) and for tensor mesons ($P$- and $F$-waves mixing) mass spectrum and wave functions of a family of vector mesons $q\bar{q}$ in triplet states are obtained. The calculations are performed using a well known Cornell potential with a mixed Lorentz-structure of the confinement term. The spin-dependent part of the potential is taken from the Breit-Fermi approach. The effect of singular terms of potential is considered in the framework of the perturbation theory and by a configuration interacti…
The Feynman--Hellmann theorem is used to show that vector meson energy eigenvalues are monotonically decreasing functions of the reduced masses of their constituent quarks. The experimental meson masses are used to put constraints on the values of quark masses and to predict the masses of some as yet undiscovered mesons. The mass of the $B_c^*$ meson is predicted to be $6320\pm 10$ MeV, and, with less precision, the masses of a number of excited vector mesons are also predicted.
The contributions of one-loop diagrams with dynamical vector mesons to masses and decay constants of pseudoscalar mesons are determined. Hereby, a relativistic Lagrangian for both the pseudoscalar-meson octet and the vector-meson nonet is used. The vector mesons are given in the antisymmetric tensor representation. Both the differences between static and dynamical vector mesons and the differences between calculations with and without vector mesons are studied as functions of the light quark mass.
We estimate the ground state masses of the heavy hybrid mesons using a phenomenological QCD-type potential. 0^{- -},1^{- -},0^{- +},1^{- +} and 0^{+ -} J^{PC} states are considered.
We use the 1/N_c method to estimate electromagnetic contributions to vector meson masses and mixings. We identify several new sources of rho-omega mixing coming from short-distance effects. We comment on the extraction of quark masses from the vector meson masses. We also present a simple group theoretical discussion of the electromagnetic mass differences.
In terms of an effective chiral theory of mesons it is shown quantitatively that in the limit of $m_{q}=0$, the masses of $ρ$, $ω$, $K^{*}(892)$, $m_ϕ$, $a_{1}$, $f_{1}(1286)$, $K_{1}(1400)$, and $f_{1}(1510)$ mesons originate from dynamical chiral symmetry breaking.
Considering the Cornell potential $V(r)=-\frac{4α_s}{3r}+br+c$, we have revisited the Dalgarno's method of perturbation by incorporating two scales $r^{short}$ and $r^{long}$ as integration limit so that the perturbative procedure can be improved in a potential model. With the improved version of the wave function the ground state masses of the heavy-light mesons $ D, D_s, B, B_s$ and $B_c $ are computed. The slopes and curvatures of the form factors of semi-leptonic decays of heavy-light mesons in both HQET limit and finite mass limit are calculated and compared with the available data.
Employing $U(3)_L\times U(3)_R$ chiral field theory, we find that Dashen's theorem, which holds for pseudoscalar mesons, can be generalized to the sector of axial-vector mesons, however, fails for vector mesons.
It is shown that the empirical rule that the masses of the stable mesons and baryons of the gamma-branch are integer multiples of the mass of the pi0 meson with a maximal deviation of 3.3% holds also for the meson and baryon resonances, regardless whether the spin of the particles is 0 or 1/2. It is also shown that the masses of the particles with weak decay are integer multiples of the mass of the charged mesons times a common factor 0.853.
We report the masses of $B$ and $D$ sectors heavy-flavoured mesons obtained by using our recently developed meson wave function employing potential model approach with linear confinement term in potential as parent in the perturbation method. As the wave-function involves infinite Airy's polynomial series, in carrying out the mass calculation, to avoid divergences, we have introduced some cut-off parameter for inter-quark separation. Our results for ground state masses of heavy-flavoured $B$ and $D$ sector mesons are reasonably closer to the PDG masses.
We focus on the chiral and heavy quark mass expansion of mesons masses and decay constants. We propose a light-front QCD formalism for the evaluation of these quantities, consistent with chiral perturbation theory and heavy quark effective theory.
Using a previously derived QCD effective hamiltonian we find the masses of heavy quarkonia states. Non perturbative effects are included through temperature dependent gluonic condensates. We find that even a moderate change in these condensates in a hot hadronic environment (below the deconfining transition) is sufficient to significantly change the heavy meson masses.
Spectrum, radii, radial wave functions at origin, decay constants and momentum widths for radial and orbital excited $B_c$ mesons are derived within non-relativistic quark model framework through finding numerical solution of the Schrodinger equation by shooting method. Masses of orbitally excited states are derived with a more simpler method that is developed by combining the uncertainty and variational principles. Masses of $B_c$ mesons are also calculated by using Momentum widths. Besides calculations, theoretical results are compared with the experimental observations which have implicatio…
We calculate the masses and decay constants of the light tensor mesons with quantum numbers $J^P =2^+$ in the framework of the QCD sum rules in the standard model. The non-perturbative contributions up to dimension-$5$ as important terms of the operator product expansion are considered.
We extend the three-flavor linear sigma model with (axial-)vector mesons to four flavors. We compute the masses of (pseudo)scalar and (axial-)vector mesons including open and hidden charmed mesons as well as weak decay constants. The results are in good agreement with experimental data.
Trigonometric Rosen-Morse Potential is employed as a mesonic potential interaction. The extended Nikiforov-Uvarov method is used to solve the N-radial Fractional Schrodinger equation analytically. Using the generalized fractional derivative, the energy eigenvalues are obtained in the fractional form. The current findings are used to calculate the masses of mesons such as charmonium, bottomonium, and heavy-light mesons. The current findings are superior to those of other recent studies and show good agreement with experimental data as a result, the fractional parameter is crucial in optimizing …
A recent renormalization group analysis of the effective light-cone Hamiltonian yields 5 flavor masses and 2 mass shifts as free parameters. These are determined in the present note and used to calculate the masses of all 30 physical mesons (The topped mesons have been omitted). The agreement between experiment and theoretical estimate is quite satisfactory over the whole dynamical range, from the lightest pseudo-scalar mesons like the pion up to the heaviest vector mesons like the upsilon. Evidence for an additive quark model is given and for how the concept of isospin is realized in a gauge …
