scholarly journals Tetraquark state X(6900) and the interaction between diquark and antidiquark

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Hong-Wei Ke ◽  
Xin Han ◽  
Xiao-Hai Liu ◽  
Yan-Liang Shi
Keyword(s):  
Excited States ◽  
Bound States ◽  
Effective Interaction ◽  
Axial Vector ◽  
Bound State ◽  
Tetraquark State ◽  
Effective Coupling ◽  
Final State ◽  
Interaction Kernel ◽  
Quantum Numbers

AbstractRecently LHCb declared a new structure X(6900) in the final state di-$$J/\psi $$ J / ψ which is popularly regarded as a cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ tetraquark state. Within the Bethe–Salpeter (B–S) framework we study the possible cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound states and the interaction between diquark (cc) and antidiquark ($$\bar{c}\bar{c}$$ c ¯ c ¯ ). In this work cc ($$\bar{c}\bar{c}$$ c ¯ c ¯ ) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound state are $$0^+$$ 0 + , $$1^+$$ 1 + and $$2^+$$ 2 + . Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for the diquark and antidiquark system. Then we deduce the B–S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of X(6900) when we assign appropriate values for parameter $$\kappa $$ κ introduced in the interaction (kernel). We also briefly calculate the spectra of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ bound states. Future measurement of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ state will help us to determine the exact form of effective interaction.

ENERGY SPECTRA OF GLUINONIUM

2011 ◽  
Vol 20 (supp02) ◽  
pp. 200-209
Author(s):  
CÉSAR A. Z. VASCONCELLOS ◽  
DIMITER HADJIMICHEF ◽  
MÁRIO L. L. DA SILVA ◽  
MOISÉS RAZEIRA ◽  
ALEXANDRE MESQUITA ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Bound States ◽  
Bound State ◽  
State Equation ◽  
Relativistic Case ◽  
Light Scalar ◽  
Pseudo Scalar ◽  
Relativistic Bound States

We investigate relativistic bound states for a hypothetical light scalar gluino pair (gluinonium), in the framework of the covariant Bethe-Salpeter equation (BSE). In this paper, we derive, from the covariant BSE for a fermion-anti-fermion system, using charge conjugation, the corresponding bound-state equation for a gluino pair and we then formulate, for a static harmonic kernel, the coupled differential equations for the corresponding static Bethe-Salpeter amplitude. The steps of our approach then include a numerical solution of the Bethe-Salpeter amplitude for a two-body interaction consisting of scalar, pseudo-scalar, and four-vector components and the determination of the energy spectrum for the ground and the radially excited states of massive gluinonium. We found the energy spectrum and radial distributions of fundamental and excited states of gluinonium. The comparison of the values obtained in the extreme relativistic case with the corresponding values predicted by a harmonic oscillator potential model shows that there is good agreement between the two formulations. The predictions of the binding energy of glunionium in the non-relativistic model are however systematically higher.

scholarly journals POSSIBLE $D\bar{D}$ AND $B\bar{B}$ MOLECULAR STATES IN A CHIRAL QUARK MODEL

2012 ◽  
Vol 27 (27) ◽  
pp. 1250161 ◽  
Author(s):  
M. T. LI ◽  
W. L. WANG ◽  
Y. B. DONG ◽  
Z. Y. ZHANG
Keyword(s):  
Quark Model ◽  
Systematic Study ◽  
Bound States ◽  
Effective Interaction ◽  
Bound State ◽  
Chiral Quark Model ◽  
State Problem ◽  
Bound State Problem

We perform a systematic study of the bound state problem of [Formula: see text] and [Formula: see text] systems by using effective interaction in our chiral quark model. Our results show that both the interactions of [Formula: see text] and [Formula: see text] states are attractive, which consequently result in [Formula: see text] and [Formula: see text] bound states.

scholarly journals NONPERTURBATIVE APPROACH TO THE PROBLEM OF ANOMALOUS FB ASYMMETRY IN TOP PAIR PRODUCTION AT TEVATRON

2013 ◽  
Vol 28 (21) ◽  
pp. 1350107
Author(s):  
BORIS A. ARBUZOV ◽  
ALEXEI I. PITIKOV ◽  
IVAN V. ZAITSEV
Keyword(s):  
Pair Production ◽  
Cross Section ◽  
Production Cross Section ◽  
Bound States ◽  
Production Cross ◽  
Effective Interaction ◽  
Bound State ◽  
Satisfactory Description ◽  
Text Production ◽  
Compensation Principle

We apply Bogoliubov compensation principle to the problem of forward–backward asymmetry in [Formula: see text] production at TEVATRON. The nontrivial solution of compensation equation for anomalous four-fermion effective interaction of doublets of heavy and light quarks leads to possibility of existence of [Formula: see text] vector bound states (resonance). The coupling of the bound state to [Formula: see text], u pair is calculated. With this result we obtain satisfactory description of totality of data on the effect of FB asymmetry including slope of effect dependence on invariant [Formula: see text] mass. Predictions for the resonance mass and production cross-section at LHC are presented.

scholarly journals Goldstonic pseudoscalar mesons in Bethe–Salpeter-inspired setting

2018 ◽  
Vol 33 (08) ◽  
pp. 1850047 ◽  
Author(s):  
Wolfgang Lucha ◽  
Franz F. Schöberl
Keyword(s):  
Effective Interaction ◽  
Bound State ◽  
State Equation ◽  
Interaction Kernel ◽  
Zero Mass ◽  
Pseudoscalar Mesons

For a two-particle bound-state equation closer to its Bethe–Salpeter origins than Salpeter’s equation, with effective interaction kernel deliberately forged such as to ensure, in the limit of zero mass of the bound-state constituents, the vanishing of the arising bound-state mass, we scrutinize the emerging features of the lightest pseudoscalar mesons for their agreement with the behavior predicted by a generalization of the Gell-Mann–Oakes–Renner relation.

scholarly journals Determination of the possible quantum numbers for the newly observed Ξb(6227)0 state

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
K. Azizi ◽  
Y. Sarac ◽  
H. Sundu
Keyword(s):  
Experimental Data ◽  
Excited State ◽  
Excited States ◽  
Light Cone ◽  
Sum Rules ◽  
Lhcb Collaboration ◽  
Coupling Constants ◽  
Final State ◽  
Quantum Numbers

Abstract The LHCb Collaboration recently reported the observation of a new excited bottom baryon Ξb(6227)0 and announced an improvement in the measurements related to the previously observed Ξb(6227)− state. We conduct an analysis for Ξb(6227)0 state considering it as isospin partner of the Ξb(6227)− resonance and possibly 1P or 2S excited state with spin J = $$ \frac{3}{2} $$ 3 2 . The corresponding masses for both possibilities have consistent results with the experimental data, indicating that only with the mass sum rules, one can not make exact decision on the nature and quantum numbers of this state. To go further, the decays of these possible excited states to $$ {\Xi}_b^{-}{\pi}^{+} $$ Ξ b − π + final state are also considered and the relevant strong coupling constants are extracted from the light cone sum rules. The obtained decay width values support the possibility of Ξb(6227)0 to be the 1P excited state of Ξb(5945)0 baryon.

Quantum field theory of bound states IV. Relativistic theory of the excited states of hydrogen

1953 ◽  
Vol 219 (1139) ◽  
pp. 516-526 ◽  
Keyword(s):  
Excited States ◽  
Lamb Shift ◽  
Bound States ◽  
Bound State ◽  
Crossing Over ◽  
Quantum Field ◽  
Coupled Equations ◽  
First Approximation ◽  
Single Integral ◽  
The Difference

When allowance is made for the instability of the excited states of hydrogen it is necessary to replace the equation of Salpeter & Bethe (1951) by a set of coupled integral equations for representatives of the state vector. These representatives correspond to an electron-proton bound state and also to the electron and proton with any number of photons present. The coupled equations can be reduced to a single integral equation, which gives the electronproton bound state as an eigenstate of a modified propagator. The modified propagator is related to the two-body propagator of Salpeter & Bethe. The difference between the first approximation to the modified propagator and the first approximation to the two-body compound propagator (Eden 1952, 1953) can be represented by a displacement of its singularity in total energy-momentum space. This displacement gives in a relativistic form all the relevant contributions to the Lamb shift to this order; these include the contribution from low-energy transverse photons crossing over an arbitrary number of longitudinal photons; previously this term has always been deduced by physical arguments and obtained by non-relativistic methods (Bethe 1947; Salpeter 1952). The displacement of the singularity also gives decay coefficients to this order in the charge. The method can readily be extended to higher approximations.

scholarly journals A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

2016 ◽  
Vol 10 ◽  
pp. 8-22
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Star Product ◽  
Three Dimensional ◽  
Spin Symmetry ◽  
Hamiltonian Operator ◽  
Bound State ◽  
Exact Bound ◽  
Quantum Numbers ◽  
Quantum Symmetries

New exact bound state solutions of the deformed radial upper and lower components of Dirac equation and corresponding Hermitian anisotropic Hamiltonian operator are studied for the modified Kratzer-Fues potential (m.k.f.) potential by using Bopp’s shift method instead to solving deformed Dirac equation with star product. The corrections of energy eigenvalues are obtained by applying standard perturbation theory for interactions in one-electron atoms. Moreover, the obtained corrections of energies are depended on two infinitesimal parameters (θ,χ), which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (j=l±1/1,s=±1/2,landm) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended quantum symmetries (NC: 3D-RS).

Expectation Values of Quasibound States: Nuclear Quadrupole Coupling Constants of BH in the X1 Σ+ and B1 Σ+ States

1998 ◽  
Vol 63 (9) ◽  
pp. 1309-1320
Author(s):  
Michal Juřek ◽  
Vladimír Špirko ◽  
Wolfgang P. Kraemer
Keyword(s):  
Bound States ◽  
Bound State ◽  
Coupling Constants ◽  
Electric Field Gradients ◽  
Expectation Values ◽  
Field Gradients ◽  
Quantum Numbers ◽  
Quadrupole Coupling ◽  
Vibrational Levels ◽  
Nuclear Quadrupole

The 10B and 11B nuclear quadrupole coupling constants of the bound and quasibound rotation-vibrational levels of BH in the ground X~1Σ+ and double-minimum excited B~1Σ+ electronic states are evaluated using ab initio calculated potentials and electric field gradients. The predicted expectation values of the resonance states are found to be smooth continuations of those of the bound states, but their dependence on the rotational and vibrational quantum numbers differs from the standard Dunham-type polynomial dependences obtained for bound state constants.

scholarly journals CONFORMAL MAPPING, POWER CORRECTIONS, AND THE QCD BOUND STATE SPECTRUM

1998 ◽  
Vol 13 (22) ◽  
pp. 3929-3952
Author(s):  
H. F. JONES ◽  
A. RITZ ◽  
I. L. SOLOVTSOV
Keyword(s):  
Conformal Mapping ◽  
Axial Vector ◽  
Bound State ◽  
Mass Splitting ◽  
Operator Product ◽  
Convergence Properties ◽  
Vacuum Condensate ◽  
Effective Coupling ◽  
Power Corrections ◽  
Bound State Spectrum

We analyze the heavy quark bound state spectrum using an order-dependent conformal mapping to re-sum the peturbative expansion for current correlators. The procedure consists of two main steps. Firstly, the Borel plane structure of the truncated perturbative expression is modified to ensure consistency with the operator product expansion. This is analogous to a resummation of infrared renormalon chains. Secondly, this perturbative expansion is conformally mapped to a new series with improved convergence properties. This approach may be shown to induce power corrections consistent with existing condensates, and the resulting expansion may be ordered in powers of an infrared-analytic effective coupling. The technique is then applied to [Formula: see text] and [Formula: see text] sum rules without any explicit introduction of vacuum condensate parameters. Ground state masses for the vector, axial–vector and A′ channels are well reproduced, while results for the scalar–pseudoscalar mass splitting are less impressive.

scholarly journals The Morbid Equation of Quantum Numbers

2021 ◽  
Author(s):  
XD Dongfang
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Bound States ◽  
Valence Electron ◽  
Coulomb Field ◽  
Bound State ◽  
Quantum Model ◽  
Conservation Of Energy ◽  
Quantum Numbers ◽  
The Law

The quantum model of valence electron generation orbital penetration of alkali metal elements with unique stable structure is investigated. The electric field outside the atomic kernel is usually expressed by the Coulomb field of the point charge mode, and the composite electric field in atomic kernel can be equivalent to the electric field inside the sphere with uniform charge distribution or other electric fields without divergence point. The exact solutions of two Schrödinger equations for the bound state of the Coulomb field outside the atom and the binding state of the equivalent field inside the atom determine two different quantization energy formulas respectively. Here we show that the atomic kernel surface is the only common zero potential surface that can be selected. When the orbital penetration occurs, the law of conservation of energy requires that the energy level formulas of the two bound states must have corresponding quantum numbers to make them equal. As a result, there is no solution to the quantum number equation, indicating that the two quantum states of the valence electron are incompatible. This irreconcilable contradiction shows that the quantized energy of quantum mechanics cannot absolutely satisfy the law of conservation of energy.

Sign in / Sign up

Export Citation Format

Share Document