A new phenomenological potential for heavy quarkonium

We suggest a new phenomenological potential for heavy quarkonium. The potential has a Lorentz vector term motivated by experimental leptonic widths for vector mesons and perturbative QCD at short distances and a Lorentz scalar term responsible for quark confinement at large distances. Using this potential we calculate the energy levels, leptonic decay widths, radiative transition rates and hadronic decay rates of the \(c\bar c, b\bar b\) and \(t\bar t\) systems. Most results agree well with the experiment.     

Continuum mixing and coupled channel effects inc\bar c andb\bar b quarkonium

We apply the unitarized quark model to heavy \(c\bar c\) and \(b\bar b\) quarkonium and study mass shifts and mixings induced by hadronic coupled channel effects. In particular, we study the two-meson continuum mixing in the quarkonium wave functions. It is found that the continuum component is 2–20% in the \(c\bar c\) and \(b\bar b\) states, measured as the squared sum of two-meson amplitudes \((D\bar D,D\bar D^ * + cc,D^ * \bar D^ * ,F\bar F,F\bar F^ * + cc,F^ * \bar F^ * for c\bar c)\) . It is the largest for states near or above the first threshold. These continuum mixings reduce the predicted radiative widths by 5–30%. The mass shifts of theP andF wave \(q\bar q\) states are similar to those ofS andD wave states previously studied. The computed resonance mixing matrices are explicitly given, enabling future calculations of relativistic effects, QCD effects, etc., to include also the coupled channel effects.     

Fine and hyperfine structures of heavy quarkonia and perturbative quantum chromodynamics

Spectroscopies of the heavy quarkonia, \(c\bar c\) , \(b\bar b\) and \(t\bar t\) , are analysed with a potential model. Relativistic effects are taken into account and spin dependent interactions are investigated in detail. We propose a flavor independent potential which has a Lorentz vector term determined by the perturbative QCD at short distances and a Lorentz scalar term confining quarks at large distances. It is stressed that the short range attenuation of the vector Coulomb potential has significant effects on the fine and hyperfine structures of the \(c\bar c\) and \(b\bar b\) systems, and also on the \(t\bar t\) level structure. We study the decay property of the \(t\bar t\) system using the calculated wave functions.     

Fine-hyperfine structures ofc\bar c andb\bar b systems in a non-relativistic Hulthen plus linear potentialsystems in a non-relativistic Hulthen plus linear potential

The heavy mesons of the charmonium and upsilon family are described in an alternative static potential model chosen in a combination of Hulthen and linear potential. We find that the quark-confining potential in the form of an equal admixture of vector and scalar parts successfully explains the fine-hyperfine structures of \(c\bar c\) and \(b\bar b\) systems in a flavour-independent manner. The leptonic decay widths of the vector mesons ofψ and γ families are calculated taking into account the Poggio-Schnitzer correction. We obtain some of the bound states of the yet-to-be observed \(t\bar t\) system for thet-quark mass ranging from 50 to 200 GeV.     

A study of a possible unified potential model

The various properties of quarkonium systems have been studies in the framework of a recently proposed potential model, which combines the asymptotic freedom at the largeQ ₂ and the multigluon effect at the lowerQ ₂ regions with the confinement at the large distance. Good agreements with experiments are found, including \(c\bar c\) and \(b\bar b\) energy levels, leptonic decay widths, and in particular the fine and hyperfine splittings. We also analyze the Lorentz structure of the confinement potential with reference to the charmonium and bottomium fine and hyperfine splittings. Our analyses conclude that almost pure scalar confinement is favored. The properties of \(t\bar t\) spectroscopies are studied over a wide range of \(M_{t\bar t}\) values (from 80 GeV to 200 GeV).     

Quark-diagram estimates ofCP violation in two-body baryonicB_d^0 - \bar B_d^0 decays

CP violation in partial-decay-rate asymmetries are examined for some two-body baryonic decays of \(B_d^0 - \bar B_d^0 \) system. We discuss two feasible experimental circumstances: the symmetrice ⁺ e ^? collisions (i) on theZ ⁰ resonance to produce incoherent \(B_d^0 \bar B_d^0 \) states, and (ii) just above the ?(4S) resonance to produceC=even \(B_d^0 \bar B_d^0 \) states. Using the quark-diagram scheme, we estimate the branching ratios of those decays, and the numbers ofb \(\bar b\) pairs needed for testing theCP-violating effects for 3σ signature. We find that the promising channels may beB _d ⁰ , \(\bar B_d^0 \to p\bar p\) , \(\Delta ^ + \bar \Delta ^ - \) , \(p\bar \Delta ^ - \) , \(\Delta ^ + \bar p\) , \(n\bar n\) , \(\Delta ^0 \bar \Delta ^0 \) , \(n\bar \Delta ^0 \) , \(\Delta ^0 \bar n\) , \(\Sigma _c^ + \bar \Sigma _c^ - \) , \(\Lambda _c^ + \bar \Lambda _c^ - \) , \(\Sigma _c^ + \bar \Lambda _c^ - \) , \(\Lambda _c^ + \bar \Sigma _c^ - \) , \(\Sigma _c^0 \bar \Sigma _c^0 \) , \(\Xi _c^0 \bar \Xi _c^0 \) , which should be interesting for experimental observation.     

Mixings and CP violations of theB^0 - \bar B^0 system in the four-generation model

We study the mixings and CP violations in the \(B^0 - \bar B^0 \) system together with the \(K^0 - \bar K^0 \) one in the four-generation model, taking into account the ARGUS data for the \(B_d^0 - \bar B_d^0 \) mixing. We take typical six cases of the mixing hierarchy and search for the allowed regions of three phases in the 4×4KM matrix. The CP violating parameter ? _K in the \(K^0 - \bar K^0 \) system gives a severe constraint for the phases, and the smaller mixing than that in the three-generation model is predicted for the \(B_s^0 - \bar B_s^0 \) system. The asymmetry parameters for the two-body non-leptonic decays of theB ⁰ and \(\bar B^0 \) mesons are also predicted.     

TheN\bar N and ππ decay modes of baryonium

A non-relativistic quark model is used to calculate the decay widths of baryonium states to \(N\bar N,N\bar \Delta \) , \(N\bar N,N\bar \Delta \) and \(\Delta \bar \Delta \) . Large widths are found and used to estimate the \(\bar pp\) and \(\bar pn\) elastic cross-sections. The couplings of baryonium states to two identical mesons are also investigated.     

The process\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma as an alternative to\pi ^0 \to v\bar v

The process \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) is investigated as an alternative to \(\pi ^0 \to v\bar v\) . It is shown that the experimental bound on the branching fraction for missing energy (in the form of \(\lambda _\gamma \bar \lambda _\gamma \) and/or \(v\bar v\) ) may be understood in terms of \(\pi ^0 \to \lambda _\gamma \bar \lambda _\gamma \) for the kinematically allowed photino mass, if the squark mass is >8 GeV.     

Perturbative QCD coherence ine + e − annihilation

We study the pattern of soft parton radiation in the hard annihilation processes \(e^ + e^ - \to q\bar q\gamma \) and \(e^ + e^ - \to q\bar qg\) by explicit evaluation of the cross sections for \(e^ + e^ - \to q\bar q\gamma g\) and \(e^ + e^ - \to q\bar qgg + q\bar qq\bar q\) taken care of correct normalization. We find the coherence effects as observed experimentally and discuss why these effects are not present in the usual models based onO(α _s ² ) perturbation theory with subsequent independent fragmentation.     

Multi-quark structure ofU(3.1)

We interpret the recently observedU(3.1) mesons with the \(\Lambda \bar p\) + pions decays as the bound state of \(\Lambda ,\bar p\) andX ₀(1480). TheX ₀(1480) is a mesonium with \(Q^2 \bar Q^2 \) structures observed in γγ reactions and \(\bar pn\) annihilations. With this interpretation, we can understand its decay modes. Furthermore, we predict the ratio of \(\sigma (\Lambda \bar p\pi ^ + \pi ^ - )/\sigma (\Lambda \bar p\pi ^ + \pi ^ + )\) to be ?3.1 for centrally produced events and that the width of \(U^ - (\Lambda \bar p\pi ^ + \pi ^ - )\) to be greater than that of \(U^ + (\Lambda \bar p\pi ^ + \pi ^ + )\) . Both predictions seem to be in reasonable accord with the available data. We call for the detection of the \(\Lambda \bar p\pi ^ - \pi ^ - \) mode to verify the present interpretation.     

Mass mixing,CP violation and left-right symmetry for heavy neutral mesons

We investigate \(M^0 - \bar M^0 \) mixing and CP violation in the minimal left-right symmetric gauge model with spontaneous P and CP violation. The dominant contributions to the mixing amplitude including QCD corrections are calculated explicitly for \(B^0 - \bar B^0 \) . While the amount of mixing is not much changed with respect to the standard model leftright symmetry can give rise to significantly larger CP violation in the \(B_s^0 - \bar B_s^0 \) system (up to two orders of magnitude for the dilepton charge asymmetry). Sizable CP violating effects require that the left-right contribution to theK _L K _S mass difference has the same sign as the standard model contribution. We also comment on \(D^0 - \bar D^0 \) mixing including a careful discussion of the standard model prediction for the short distance part.     

Effective potential for local composite operators and the problem of factorization of multi-field condensates

A new formulation of effective potential for local composite operators is given. The two-fermion condensate \(\langle \bar \Psi \Psi \rangle \) and four-fermion condensate \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) are calculated simultaneously in the Gross-Neveu model up to next-to-the-leading order in 1/N expansion. It is shown that factorization \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle = C_1 \langle \bar \Psi \Psi \rangle ^2 \) holds only in theN→∞ limit and the non-factorized part of \(\langle \bar \Psi \Psi \bar \Psi \Psi \rangle \) contributed by the order-1/N terms is comparable to \(C_1 \langle \bar \Psi \Psi \rangle ^2 \) when takingN=3.     

The 3 gluon decay of quarkonium

We discuss the process $$e^ + e^ - \to Q\bar Q \to 3gluons \to 3jets$$ with attention to the kinematics and observability of the jets. We also show how to check the gluon spin through jet or hadron angular distributions. Gluon flavor can be checked by looking for quantum number correlations between opposite jets. We predict that correlations exist off resonance for \(e^ + e^ - \to q\bar q\) , but not on resonance for \(Q\bar Q \to 3g\) .     

B \bar B widths of the diquoniums based on quark potential model

A detailed and systematic study is carried out of the \(B\bar B(N\bar N, N\bar \Delta , \Delta \bar \Delta )\) widths of the “True” (colour \(3 \times \bar 3\) ) diquoniums making use of the quark pair creation model supplemented by the idea of a quark-quark potential. The widths, which continue to be of the order of 10 MeV, help confirm our hypothesis of avoiding the need for the “Mock” (colour \(6 \times \bar 6\) ) diquoniums to explain the narrow width resonances observed in the production experiments. Another outcome concerns the criterion to select out the dominant ones among the numerous diquonium trajectories. It is proposed to replace the one based on “peripherality” withR～1/m _π with another more natural one based on the width pattern itself.     

Duality ine + e − annihilation

With the help of a relativistic generalization of the formula for the leptonic width of quarkonium in the semiclassical approximation it is shown that for any confinement potential nonsingular at the origin the sum of total cross sections for the production of the heavy quarkonium states \((Q\bar Q)_n\) with masses \(M_n \leqq \sqrt s\) ine ⁺ e ^?-annihilation is equal to the cross section at givens for the production of the free quark-antiquark pair \(Q\bar Q\) . We obtain also a family of dual sum rules for quarkonium which are in agreement with the available experimental data on charmonium and beautionium within experimental errors.     

Coherence ofu\bar u andd\bar d final states: Possible influence onZ 0 decay width ande + e − annihilation cross section

The decay width of theZ ⁰ associated with its coupling tou andd quarks is usually expressed as the incoherent sum of the widths into \(u\bar u\) and \(d\bar d\) final states, \(\Gamma (u\bar u) + \Gamma (d\bar d)\) . We examine a specific correction to this estimate arising from the coherence of the \(u\bar u\) and \(d\bar d\) systems, dictated by isospin symmetry. The decay width is written in the alternative form Γ(G=+1)+Γ(G=?1), which recognises that final hadronic states can be classified according to even and odd G-parity. Assuming that states withG=+1(?1) evolve from configurations containing even (odd) numbers ofG=?1 systems, and considering various multiplicity distributions for such systems, small corrections are obtained relative to the conventional estimate. A similar analysis applied to the cross section for \(e^ + e^ - \to u\bar u, d\bar d\) yields small energy-dependent corrections to the parameter R.     

Flavor annihilation and the decaysD s →K 0 * K

We have studied \(D_s^ + \to K_0^{* + } \bar K^0\) and \(D_s^ + \to \bar K_0^{*0} K^ +\) decays in the factorization of the hadron currents approximation. The spectator model leads the decays have different but negligible branching ratios. We show, however, that the inclusion of annihilation contribution can enhance the branching ratios. We predict that \(B(D_s^ + \to \bar K_0^{*0} K^ + )\) and \(B(D_s^ + \to K_0^{* + } \bar K^0 )\) could be around 2%.     

Compositness effects in toponium physics

We study the effects of composite quarks and leptons in toponium physics. Introducing two kinds of non-standard four fermion effective couplings involving top quarks, we compute their influence on \(\theta (t\bar t)\) widths, on cross-sections and asymmetries for \(e^ + e^ - \to \theta \to l\bar l\) , \(q\bar q\) and single quark decay modes. New bounds on four quark contact terms can be inferred at the energies of LEP I and SLC.