Study of Heavy Mesons using Effective Theories and Potential Model

Abstract

The work presented in the thesis is carried out to investigate recently observed heavy mesons using heavy quark effective theory and phenomenological potential model. Since the momentous discovery of heavy quarks, namely the charm (c) and bottom (b) quarks, there has been a notable and focused interest in investigating the properties of heavy hadrons. Different experimental facilities like LHCb, BABAR, BESIII, FOCUS, SLAC, Belle, CDF, etc., have been on a discovery spree for stimulating the spectrum of heavy mesons. Consequently, it becomes essential to employ appropriate theoretical methodologies in order to attain a profound comprehension of these mesons. Several theoretical models, such as the Heavy Quark Effective Theory (HQET), potential models, lattice Quantum Chromodynamics (QCD), and QCD sum rules, are present in the literature for the in-depth exploration of these heavy mesons. In the past few years, HQET has emerged out as a successful model for studying the properties of heavy-light mesons. In this thesis, we intend to study the basic properties like masses, strong decays, branching ratios, and splittings for the newly observed heavy-light mesons in both the charm and bottom sectors. By this study, we will be able to fill the charm and bottom spectra up to F-wave and P-wave mesons for radial quantum numbers n = 2 and n = 3, respectively. Also, to understand quark-antiquark interactions and their dynamics, we have explored bottomonia in the framework of the phenomenological potential model. This thesis is organized into six chapters, a transient outline of which is given below: • Chapter 1 gives a brief discussion of theoretical and experimental aspects related to the study of bound states of quarks, which interact through the exchange of gluons. Here, we have categorized bound state hadrons into two primary groups: Baryons, which are composed of qqq structure, and mesons, having qq¯ configuration. The primary focus of this thesis is on the investigation of mesons, particularly heavy mesons, which come in low-energy regimes. For high-energy interactions, the strong coupling constant is small; thus, perturbative techniques are a viable option, while, the inclusion of heavy quarks invokes low-energy interactions, thus treated non-perturbatively. We conduct a brief review of various non-perturbative approaches commonly found in the 8 literature, such as potential models, lattice QCD, effective theories, and QCD sum rules. The major focus is given to effective field theories. Unlike other phenomenological models, these theories construct Lagrangian based on QCD symmetries, and interaction terms are organized systematically by some expansion parameters. We particularly highlight the fundamental concepts behind effective theories, with a specific focus on heavy quark effective theory and potential model. The heavy quark effective theory explored two essential symmetries in QCD: one in the limit of infinite heavy quark mass (mQ → ∞, where Q = c, b) and the other in the chiral limit of light quark masses (mq → 0, where q = u, d, s). The potential models are based on the concept that potential can describe the interaction of quarks and antiquarks. Although interquark interaction is a non-abelian and non-linear theory, it is complicated and still poorly understood. But, with the help of the potential model, we can grasp interquark interaction to some extent. Some of the potential models are mentioned and discussed in this chapter. • In Chapter 2, we give details of the HQET framework used in the thesis to study the heavy-light charm and bottom mesons. We start by exploring the concept of heavy quark SU(2NH) spin and flavor symmetry, which serve as the origin of heavy quark effective theory. We present a general notation nLslJ P for any heavy-light state for its quantum numbers. In particular, J P notations for the S-wave ground state and low-lying excited P-wave states are mentioned. We also define how the static nature of the heavy quark, classifies the states into doublets, which are represented by some covariant effective fields like Ha, Sa, T µ a , etc. We proceed to write the effective general Lagrangian for heavy-light system in the inverse powers of 1/mQ, by embodying the heavy quark symmetry in the QCD Lagrangian. This results in the modification of the QCD Feynman rules in the limit mQ → ∞. The leading order term of this Lagrangian will preserve the heavy quark symmetries while the higher orders will break these symmetries. This chapter also provides a short introduction to the chiral perturbation theory, which describes the low-energy interactions between the higher excited heavy-light charm and bottom mesons and their ground state S-wave mesons by the emission of goldstone bosons 9 π, η, K. Effective chiral Lagrangians at the leading order describing the interactions among different doublets help in calculating the two-body strong decay widths. The strong decay widths formulae dependent on the initial and final meson masses, their strong coupling constants, pion decay constant, energy scale Λ, mass, and momentum of light pseudo-scalar mesons are listed in this chapter. • In Chapter 3, by exploring heavy quark effective theory (HQET), we use theoretical available data for bottom mesons to analyze the masses and decays for n = 3 charm mesons. Then, mass results of n = 3 charm meson are used as input to calculate masses of n = 3 bottom mesons. For a better understanding of bottom mesons, we further extend mass calculations for Fwave states. From the predicted masses, we studied ground state strong decay modes in terms of couplings. Comparing the decays with available total decay widths, we provide upper bounds on the associated couplings. We also plot Regge trajectories for our predicted data in planes (J, M2 ) and (nr, M2 ) and estimated higher masses (n = 4) by fixing Regge slopes and intercepts. These Regge trajectories and branching ratio are used to clarify D∗ 2 (3000) state’s J P as 1 3F2 state. In addition to this, values of coupling constants g˜HH, ≈ gHH, ≈ gSH, ≈ gT H are estimated with heavy quark symmetry by using Pearson chi-square test with multivariate normal distribution. • In Chapter 4, we have employed HQET to give the spin-parity quantum numbers for recently observed bottom strange states BsJ (6063) and BsJ (6114) by LHCb collaborations. By exploring flavour independent parameters ∆ (c) F = ∆ (b) F and λ (c) F = λ (b) F appearing in HQET Lagrangian, we calculated masses of experimentally missing bottom strange meson states 2S, 1P, 1D. The parameter ∆F appears in HQET Lagrangian and gives the spin averaged mass splitting between excited state doublets (F) and ground state doublets (H). Another parameter λF comes from first-order corrections in HQET Lagrangian and gives hyperfine splittings. We have also analyzed these bottom strange masses by taking 1/mQ corrections which lead modifications of parameter terms as ∆ (b) F = ∆(c) F + δ∆F and λ (b) F = λ (c) F δλF . Further, we have analyzed their two-body decays, couplings, and branching ratios via the emission of 10 light pseudoscalar mesons. Based on predicted masses and decay widths, we tentatively identified the states BsJ (6063) as 2 3S1 and BsJ (6114) as 1 3D1. Our predictions may provide crucial information for future experimental studies. • In Chapter 5, we comprehensively explore bottomonia mass spectra and their decay properties by solving the non-relativistic Schrodinger wave equation numerically with approximate quark-antiquark potential form. We also incorporate spin-dependent terms - spin-spin, spin-orbit, and tensor terms to remove mass degeneracy and to obtain excited states (nS, nP, nD, nF, n = 1, 2, 3, 4, 5) mass spectra. By using Van Royen - Weisskopf formula, we investigate leptonic decay constants, di-leptonic, di-gamma, tri-gamma, di-gluon decay widths and also incorporate first-order radiative corrections. We also computed radiative transition widths, which give a better insight into the non-perturbative aspects of QCD. The present results for mass spectroscopy and decay properties are in tune with available experimental values and other theoretical prediction • Chapter 6, summarizes the work carried out in this thesis. A brief account of the results obtained and the conclusion so drawn is discussed, and a possible extension of this work from a future perspective is outlined.