Relativistic effects and the constituent quark model of heavy quarkonia

Charmonium \(c\bar c\) and bottomonium \(b\bar b\) are investigated in the framework of a constituent quark model. A scalar confining and a one-gluon exchange (OGE) potential are used in a nonrelativistic reduction to order (p/m)². Therefore the model includes spin dependent as well as spin independent terms. Their influence on the meson mass spectra and decay widths is analysed. We find that the experimental spectra can be reproduced by using a full model as well as by using a reduced version neglecting the spin independent terms. For both versions we calculate leptonic and radiative decay widths including relativistic corrections for the current operators. We find that for leptonic decays inclusion of all terms of the OGE potential gives better results than the non-relativistic formulas. For radiative transitions relativistic corrections are important.     

Mass spectra and leptonic decay widths of heavy quarkonia

A nonrelativistic Hamiltonian with plausible spin dependent corrections is proposed for the quarkonia below their respective strong decay thresholds. With only six free parameters this model reproduces the nine known masses of the bottomonia within about 1 MeV, the six known masses of the charmonia within a few MeV and the five known leptonic decay widths of the states within about 20%. The model is then used to predict the masses of the remaining 43 qu arkonia (some of them for the first time) and of the leptonic decay widths of the two states. Comparison with some other models is made. Received: 17 June 1997     

Decay rates and electromagnetic transitions of heavy quarkonia

The electromagnetic radiative transition widths for heavy quarkonia,as well as digamma and digluon decay widths,are computed in the framework of the extended harmonic confinement model(ERHM) and Coulomb plus power potential(CPP_v) with varying potential index v.The outcome is compared with the values obtained from other theoretical models and experimental results.While the mass spectra,digamma and digluon widths from ERHM as well as CPP_(v=1) are in good agreement with experimental data,the electromagnetic transition widths span over a wide range for the potential models considered here making it difficult to prefer a particular model over the others because of the lack of experimental data for most transition widths.     

Comment on the hadronic decay of excited heavy quarkonia

We make comments on [1], and provide partial wave analysis to the decays of excited heavy S-wave quarkonia into the basic quarkonia state plus . It is revealed that there exist contributions of D-wave transition in , and by using the data-fitting results in [1]. A possible experimental method to measure the D-wave directly is discussed. Received: 14 May 1998 / Published online: 21 September 1998     

Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

We calculate the dynamical relativistic corrections, originating from radiative one-gluon exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of light-front dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J = 1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in , even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potentials to describe these decays are described. Received: 6 December 2001 / Published online: 5 April 2002     

Photon polarization in the two-photon decay of heavy hydrogen-like ions

We have applied the density matrix and second-order perturbation theory in order to re-analyze the two-photon decay of hydrogen-like ions for the polarization of emitted light. Special attention is paid to the linear polarization of one of the photons, while the spin state of the second photon is supposed to be unobserved. For such an “angle-polarization” correlation of the two photons we investigate the contributions that arise from non electric-dipole terms in the expansion of the electron-photon interaction. Detailed calculations are performed for the 2s_1/2 →1s_1/2 and 3d_5/2 →1s_1/2 transitions in neutral hydrogen as well as in hydrogen-like uranium.     

Direct decays of heavy quarkonia

The branching ratios are evaluated of the ψ (3770) and (4S) decays into ππ, , ωπ⁰, ωη, ωη ′, π, η, η′, , . They arise due to the transition through the real intermediate states and , respectively. It is shown that some branching ratios exceed the three-gluon one by an order of magnitude. The rates of the decays ,

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and are evaluated also. τ-C and B factories coul be good tools for studying all decays mentioned.     

Radiative corrections in heavy quarkonia

We investigate radiative corrections in heavy quarkonia and calculate relativistic corrections which are not taken into account in earlier papers. It appears that these terms cannot be neglected as compared to the usually calculated radiative corrections and lead to a considerable contribution to the level splittings.     

Relations between inclusive decay rates of heavy baryons

The dependence of inclusive weak decay rates of heavy hadrons on the flavors of spectator light quarks is revisited with application to decays of charmed and b hyperons. It is pointed out that the differences in the semileptonic decay rates, the differences in the Cabibbo-suppressed decay rates of the charmed hyperons, and the splitting of the total decay rates of the b hyperons are all related to the differences in the lifetimes of the charmed hyperons independently of poor knowledge of hadronic matrix elements. The approximations used in these relations are the applicability of the expansion in the inverse of the charmed quark mass and the flavor SU(3) symmetry.     

Relativistic effects in quarkonia decays with axion production

In the framework of the potential approach it is shown that relativistic effects connected with the relative motion of quarks in quarkonia lead to a strong decrease in the values of the ratios Br(ψ→aγ)/Br(ψ→μ⁺μ⁻) and B Br(ϒ→aγ)/Br(ϒ→μ⁺μ⁻), predicted by the nonrelativistic quark model. This does not allow to exclude already unambiguously the existence of a long-lived axion on the basis of available experimental data on these decays.     

Hadronic decays of excited heavy quarkonia

We construct an effective Lagrangian for the hadronic decays of a heavy excited s-wave-spin-one quarkonium Ψ′ into a lower s-wave-spin-one state Ψ. We show that reasonable fits to the measured invariant mass spectra in the charmonium and bottomonium systems can be obtained within this framework. The mass dependence of the various terms in the Lagrangian is discussed on the basis of a quark model.     

Heavy quark potential and quarkonia dissociation rates

Quenched lattice data for the interaction (in terms of heavy quark free energies) in the color-singlet channel at finite temperatures are fitted and used within the non-relativistic Schrödinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is demonstrated that a temperature dependent gluon mass has an essential influence on the heavy quarkonia dissociation, but that this process alone is insufficient to describe the heavy quarkonia dissociation rates.Arrival of the final proofs: 8 July 2005PACS: 12.38.Gc, 12.38.Mh, 14.40.GxD. Blaschke: Present address: GSI mbH, 64291 Darmstadt, Germany