Light and Heavy Mesons in The Complex Mass Scheme

International Journal of Modern Physics A, 2021

In this paper, the mass spectra of mesons with one or two heavy quarks and their diquarks partners are estimated within a nonrelativistic framework by solving Schrödinger equation with an effective potential inspired by a symmetry preserving Poincaré covariant vector–vector contact interaction model of quantum chromodynamics. Matrix Numerov method is implemented for this purpose. In our survey of mesons with heavy quarks, we fix the model parameter to the masses of groundstates and then extend our calculations for radial excitations and diquarks. The potential model used in this work gives results which are in good agreement with experimental data and other theoretical calculations.

2010

This dissertation deals with the computation of meson mass spectra in the context of quarkantiquark (q q) bound-state. Traditionally the q q bound-state problem is treated by solving the non-relativistic Schrödinger equation in position representation with a linear confining potential and a Coulomb-like attractive potential. For high energy, relativistic kinematics is I would like to thank all of those who have assisted me in this effort. I am forever thankful to my adviser, Dr. Khin Maung Maung, who taught me with great patience and helped me in many ways to complete my dissertation. He taught me with great care and helped me to understand the nature of research in the field of theoretical physics and computations. I have gained considerable amount of knowledge and experience while working under his supervision. I would like to thank my other committee members, Dr. John Norbury, Dr. Lawrence Mead, Dr. Sung Lee and Dr. Christopher Sirola, whose active support made it possible for me to complete my dissertation. I would like to thank my friend Charles Werneth with all my heart; without his active support, both academically and emotionally, it would not have been possible for me to carry on. I would like to thank my parents, Sarashi Ranjan Dhar and Manju Dhar, for their kindness, love and care. They are always very supportive. I would like to thank my brother, Tanmay Dhar, for his continuous support and care.

Physical review, 1975

Relativistic calculations of the I. = 0 energy levels of a qq pair bound by a linear potential are done both for light quarks (the p system) and heavy quarks (charmonium). The suggestion" that the)))(3105) and)))(3695) are bound states of the charmed quark 6" and its antiquark P has revived interest in dynamical calculations of the masses of the qq bound states. Detailed calculations have been done using the nonrelativistic Schrodinger equation with a linear confinement potential for the heavy (6") quarks" and for the light quarks. " For the heavy-quark calculations p posteriori justification of the nonrelativistic calculation was given e.g. by computing the expectation value of P'/m' with the Schrfidinger wave functions and finding that it is small, i.e. , the system is essentially nonrelativistic. Our relativistic calculation confirms this. The light

Physics Letters B, 1996

Quark mass ratios are expressed within the linear meson model by universal relations involving only the masses and decay constants of the flavored pseudoscalars as well as their wave function renormalization. Quantitative results are in agreement with those obtained from chiral perturbation theory, with a tendency to a somewhat higher strange quark mass.

The European Physical Journal A, 2000

Within the framework of the instantaneous Bethe-Salpeter equation, we present a detailed analysis of light meson spectra with respect to various parameterizations of confinement in Dirac space. Assuming a linearly rising quark-antiquark potential, we investigate two different spinorial forms (Dirac structures), namely 1 2 (1 I⊗1 I−γ 0 ⊗γ 0) as well as the UA(1)-invariant combination 1 2 (1 I⊗1 I−γ 5 ⊗ γ 5 − γ µ ⊗ γµ), both providing a good description of the ground state Regge trajectories up to highest observed angular momenta. Whereas the first structure is slightly prefered concerning numerous meson decay properties (see [41]), we find the UA(1)-invariant force to be much more appropriate for the description of a multitude of higher mass resonances discovered in the data of the Crystal Barrel collaboration during the last few years. Furthermore, this confinement structure has the remarkable feature to yield a linear dependence of masses on their radial excitation number. For many experimental resonances such a trajectory-like behaviour was observed by Anisovich et al. We can confirm that almost the same slope occurs for all trajectories. Adding the UA(1)-breaking instanton induced 't Hooft interaction we can compute the pseudoscalar mass splittings with both Dirac structures and for the scalar mesons a natural mechanism of flavour mixing is achieved. In the scalar sector, the two models provide completely different ground state and excitation masses, thus leading to different assignments of possibleqq states in this region. The scalar meson masses calculated with the structure 1 2 (1 I ⊗ 1 I − γ 5 ⊗ γ 5 − γ µ ⊗ γµ) are in excellent agreement with the K-matrix poles deduced from experiment by Anisovich and coworkers.

In this paper, we have calculated the masses of mesons containing t-quark and their spins' coupling coefficients. This was achieved by solving Lippmann-Schwinger equation for the quark-antiquark bound state of heavy mesons in configuration space. Heavy meson masses submitted criteria for the strong nuclear interactive potential between two quarks. We investigated the stability of a few suitable potentials and offered the best of these potentials for heavy mesons.

2001

We study Dick quark-antiquark potential (up to a color factor) $V_D(r)={-\alpha_s \over r} + gf \sqrt{N_c \over {2(N_c-1)}} \ln[exp(2mr)-1]$ in the heavy meson sector. This potential emerges from an effective dilaton-gluon coupling inspired from string theory and proves to be linearly rising at large distances which ensures quark confinement. The semi-relativistic wave equation which appears in the theory of relativistic quark-antiquark bound states is used. This equation is cast into a constituent second order Schr\"{o}dinger-like equation with the inclusion of relativistic corrections up to order $(v/c)^{2}$ in the quark speeds. The resulting equation is solved for Dick potential via the Shifted-$l$ expansion technique (SLET). The obtained results show that the spin-averaged energy levels of heavy-mesons are well explained and agree with other potential models or QCD sum rules predictions. Moreover, as a by-product, our analysis assign to the dilaton a mass around 56.9 MeV ly...

It is shown that a 25(20)% difference between the decay constants f Ds (f Bs ) and

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 Salpeter equation computed with a Lagrange-mesh calculation method.

By assuming the existence of (quasi)-linear Regge trajectories for heavy mesons, we derive new quadratic mass relations of non-Gell-Mann-Okubo type, 6M 2 (qq) + 3M 2 (cc) = 8M 2 (cq), 20M 2 (qq) + 5M 2 (bb) = 16M 2 (bq), q = n(= u, d), s which show excellent agreement with experiment. We also establish the sum rule M 2 (iī) + M 2 (jj) − 2M 2 (jī) ≈ const for any pair of flavors, (i, j).