Mixing effects on 1S and 2S state heavy mesons in the light-front quark model

Abstract

The mass spectra and wave functions of both $1S$ and $2S$ state heavy pseudoscalar ($P$) and vector ($V$) mesons are analyzed within the light-front quark model. Important empirical constraints employed in our analysis of the mass spectra and wave functions are the experimental mass-gap relation, $\Delta M_P>\Delta M_V$, where $\Delta M_{P(V)}=M_{P(V)}^{2S}-M_{P(V)}^{1S}$ and the hierarchy of the decay constants, $f_{1S}>f_{2S}$, between $1S$ and $2S$ meson states. We maintain the orthogonality of the trial wave functions of the $1S$ and $2S$ states in our variational calculation of the Hamiltonian with the Coulomb plus confining potentials and treat the hyperfine interaction perturbatively for the heavy-heavy and heavy-light $P$ and $V$ mesons due to the nature of the heavy quark symmetry. Realizing that the empirical constraints cannot be satisfied without mixing of the $1S$ and $2S$ states, we find the lower bound of the mixing angle $\theta$ between $1S$ and $2S$ states as ${\theta }_c={\cot }^{-1}(2\sqrt{6})/2\simeq 6^{\circ }$ and obtain the optimum value of the mixing angle around $12^{\circ }$ to cover both the charm and bottom flavors of the heavy quark. The mixing effects are found to be more significant to the $2S$ state mesons than to the $1S$ state mesons. The properties of $1S$ and $2S$ state mesons including the mass spectra, decay constants, twist-2 distribution amplitudes, and electromagnetic form factors are computed. Our results are found to be in a good agreement with the available data and lattice simulations. In particular, the $2S$ state pseudoscalar $D_s$ meson is predicted to have a mass of $2600$ MeV, which is very close to the mass of the newly discovered $D_{s0}(2590{)}^{+}$ meson by the LHCb Collaboration. This supports the interpretation of the observed state as a radial excitation of the $D_s^{+}$ meson.

arXiv comment17 pages, 8 figures, 6 tables. Comments are welcome

References in corpus (51)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Semileptonic Meson Decays in the Quark Model: An Update
• Properties of heavy quarkonia and B_c mesons in the relativistic quark model
• Heavy-light meson spectroscopy and Regge trajectories in the relativistic quark model
• Update: Precision D_s decay constant from full lattice QCD using very fine lattices
• Radiative Transitions in Charmonium from Lattice QCD
• Precision tests of the J/ψ from full lattice QCD: mass, leptonic width and radiative decay rate to η_c
• Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD
• Mixing angles and electromagnetic properties of ground state pseudoscalar and vector meson nonets in the light-cone quark model
• Heavy Quarkonium in a Holographic Basis
• Decay constants and radiative decays of heavy mesons in light-front quark model
• Non-perturbatively Improved Heavy-Light Mesons: Masses and Decay Constants
• Lattice QCD and QCD Sum Rule determination of the decay constants of eta_c, J/psi and hc states
• Analysis of the masses and decay constants of the heavy-light mesons with QCD sum rules
• Quarkonium as relativistic bound state on the light front
• Distribution amplitudes and decay constants for $(\pi ,K,\rho ,K^{\ast })$ mesons in light-front quark model
• Relativistic treatment of the decay constants of light and heavy mesons
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• Decay Constants of Heavy Meson of $0^{-}$ State in Relativistic Salpeter Method
• Light-Front Quark Model Analysis of Exclusive $0^{-}$$\to$$0^{-}$ Semileptonic Heavy Meson Decays
• Vector and axial-vector couplings of D and D* mesons in 2+1 flavor Lattice QCD
• Semileptonic and radiative decays of the B_c meson in light-front quark model
• Study of orbitally excited $B$ mesons and evidence for a new $B\pi$ resonance
• Charge radii of light and heavy mesons
• Variational Analysis of Mass Spectra and Decay Constants for Ground State Pseudoscalar and Vector Mesons in Light-Front Quark Model
• Self-consistent covariant description of vector meson decay constants and chirality-even quark-antiquark distribution amplitudes up to twist-3 in the light-front quark model
• Heavy-Light Mesons on the Light Front
• Self-consistency and covariance of light-front quark models: testing via $P$, $V$ and $A$ meson decay constants, and $P\to P$ weak transition form factors
• Distribution Amplitudes of Heavy Mesons and Quarkonia on the Light Front
• Consistency of the light-front quark model with chiral symmetry in the pseudoscalar meson analysis
• Radiative transitions between $0^{-+}$ and $1^{--}$ heavy quarkonia on the light front
• Distribution amplitudes of radially-excited pi- and K-mesons
• Re-Study on the wave functions of ${\rm Y}(nS)$ states in LFQM and the radiative decays of ${\rm Y}(nS)\to {\eta }_b+\gamma$
• Mass spectra and decay properties of $D$ Meson in a relativistic Dirac formalism
• Precise measurements of the properties of the B_1(5721)^(0,+) and B_2*(5747)^(0,+) states and observation of B^(+,0) pi^(-,+) mass structures
• Observation of a new excited $D_s^{+}$ meson in $B^0\to D^{-}{D}^{+}{K}^{+}{\pi }^{-}$ decays
• Radial excitations of heavy-light mesons from QCD sum rules
• A Covariant Light-Front Model of Heavy Mesons within HQET
• Two-particle twist-3 distribution amplitudes of the pion and kaon in the light-front quark model
• Twist-2 Pseudoscalar and Vector Meson Distribution Amplitudes in Light-Front Quark Model with Exponential-type Confining Potential
• The study of leading twist light cone wave functions of 2S state charmonium mesons
• Study of quark distribution amplitudes of 1S and 2S heavy quarkonium states
• Roper-like resonances with various flavor contents and their two-pion emission decays
• The $D_{s0}(2590{)}^{+}$ as the dressed $c\bar{s}(2^1{S}_0)$ meson in a coupled-channels calculation
• Light-front wavefunctions of mesons by design
• Light-Cone Quark Model Analysis of Radially Excited Pseudoscalar and Vector Mesons
• Self-consistent light-front quark model analysis of $B\to D\ell {\nu }_{\ell }$ transition form factors
• $D_{s0}(2590)$ as a dominant $c\bar{s}$ state with a small $D^{\ast }K$ component
• Exploring the flavor content of light and heavy-light pseudoscalars
• Heavy quarkonium 2S states in light-front quark model

Cited by in corpus (14)

• The Present and Future of QCD
• Light-front wavefunctions of mesons by design
• In-medium properties of the light and heavy-light mesons in a light-front quark model
• Leading twist T-even TMDs for the spin-1 heavy vector mesons
• Pseudoscalar meson decay constants and distribution amplitudes up to twist-4 in the light-front quark model
• Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model
• Transverse and spatial structure of light to heavy pseudoscalar mesons in light-cone quark model
• Quark spin-orbit correlations in spin-0 and spin-1 mesons using the light-front quark model
• Spectroscopy of excited quarkonium states in the light-front quark model
• In-medium electromagnetic form factors of pseudoscalar mesons from the quark model
• Structure of heavy quarkonia in a strong magnetic field
• The Properties of Radially Excited Charmonia in The Light Front Quark Model
• Prospects for observing the ${\eta }_t$ $\to$ $W^{+}{W}^{-}$ decay at the HL-LHC
• Radiative Decays of Vector Mesons with Light-Cone Sum Rules