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.     

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.     

Evidence for hybrid mesonsQ\bar QG

We point out that the recent CESR data on γ(5 S) and γ(6 S) show evidence for \(b\bar b\) and \(b\bar bg\) mixing. We show that ψ(4159) and ψ(4030) are not2D and 3S, \(c\bar c\) states but mixtures of 3S, \(c\bar c\) and \(c\bar cg\) states. We show various ways to find further evidence for hybrid states experimentally.     

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.     

Charged hadron multiplicities in high energy\bar v_\mu n and\bar v_\mu pinteractions

Charged hadron multiplicity distributions in \(\bar v_\mu n\) and \(\bar v_\mu p\) interactions in the energy range \(5< E_{\bar v}< 150GeV\) GeV are presented. They are obtained from about \(6000\bar v_\mu \) charged current events produced in BEBC filled with deuterium. Multiplicity moments are studied as a function of the invariant mass of the hadronic systemW. Results on multiplicity distributions in the forward and backward directions in the hadronic c.m.s. are presented and discussed within the framework of the quark parton model. Values for the average charge of the forward jet are also determined and compared with other experimental data.     

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.     

Spectroscopy ofQ\bar Qg hybrid mesons

Hybrid mesons composed of a quark, an antiquark, and a gluon are studied in the case of heavy quarks. Their masses are calculated with the potential model which can interpret heavy quarkonium spectroscopy. The ground state of the hybrid mesons \(c\bar cg\) and \(b\bar bg\) is found to be almost spherically symmetric, whereas that of \(t\bar tg\) is two-centered as anH ₂ ⁺ molecule. The \(b\bar bg\left[ {t\bar tg} \right]\) ground state turns out to have a mass below the \(B\bar B\left[ {T\bar T} \right]\) threshold. The excited states contain 0^??, 1^?+ exotic states and 1^?? states which may be examined bye ⁺ e ^? colliders.     

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.     

QCD calculation ofB \to \pi l\bar v_l and the matrix element |V bu|

Using QCD sum rules for a two-point function involving beauty vector currents, together with current algebra-PCAC sum rules, we estimate the hadronic matrix element in \(B \to \pi l\bar v_l \) . We find \(\Gamma \left( {\bar {\rm B}^0 \to \pi ^ + l\bar v_l } \right) = \left( {1.45 \pm 0.59} \right) \times 10^{13} \left| {V_{bu} } \right|^2 s^{ - 1} \) . As a byproduct, the vector current contribution to the decay \(B \to \rho l\bar v_l \) is also estimated.     

Thep - \bar p decays ofP-wave quarkonium and the helicity characteristics of massless QCD

We consider the exclusive \(p - \bar p\) decays of the quarkoniumP-states. Due to the helicity conservation of massless QCD the \(p - \bar p\) mode is forbidden in this limit for the¹ P ₁ and the³ P ₀ states. The angular distributions for the decays of the remaining states in the cascade \(^3 S\prime _1 \to \gamma ^3 P_J \to \gamma p\bar p\) are specific to QCD and can serve as a test of the theory. The same is true of the formation process \(p\bar p \to ^3 P_J \to ^3 S_1 \gamma \) . In lowest order QCD we obtain overall branching ratios for charmonium of the order of 10^?4.     

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.     

Second order QCD corrections toq\bar q-anihilation into a lepton pair at large transverse momentum

The \(\mathcal{O}{\text{(}}\alpha _{\text{s}}^{\text{2}} )\) correction is presented to \(q\bar q\) -annihilation into a lepton pair at large transverse momentum. I calculate the corresponding hadron cross section difference \(\frac{{d\sigma }}{{d^4 q}}(p\bar p - pp) \to e^ + e^ - + x(q\) is the momentum of the lepton pair system). The correction to this cross section difference is found to be large. This essentially agrees with recently published results by Ellis, Martinelli and Petronzio. Two improtant approximations are used: the invariant mass of the two-gluon-system is put to zero, and only valence-valence quark scattering is considered.     

Study of theJ/\Psi \to p\bar p\gamma and\Upsilon /(1S) \to p\bar p\gamma decays as possible tests of the proton wave function

Considering the proton either as a three-quark state with its wave function fulfilling QCD sum rules or as a quark-diquark state with wave function parametrizations that are shown to fitG _M ^P , we study the possibility of discriminating between these two competing pictures by comparing their respective predictions for \(J/\Psi \to p\bar p\gamma \) and \(\Upsilon (1S) \to p\bar p\gamma \) decays. ForJ/Ψ decay, thep \(\bar p\) invariantmass distributions derived from either model are found to be of about the same magnitude, but neither of them is able by itself to reproduce present-day data. Differences between the two pictures may eventually show up in the case of Υ(1S) decay, but the predicted counting rates are small. We also consider some other possible production mechanisms for \(p\bar p\gamma \) final states.     

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.     

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.     

Suggestion for Einstein-Podolsky-Rosen experiments using reactions likee^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p

Since weakly decaying particles are their own polarimeters, reactions like \(\eta _c \to \Lambda \bar \Lambda , \psi \to \Lambda \bar \Lambda ,e^ + e^ - \to \mu ^ + \mu ^ -\) , etc. are interesting for testing the non-locality of quantum mechanical predictions. Although such reactions, in principle, do not exclude all classes of hidden variable theories, they can be used to complement current experiments with external polarimeters. The reaction \(\eta _c \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^{ + - } \bar p\) is conceptually the simplest and most useful as agedanken experiment, although it has not yet been seen experimentally. The reaction \(e^ + e^ - \to \Lambda \bar \Lambda \to \pi ^ - p\pi ^ + \bar p\) near threshold or at the φ resonance can be used for essentially the same test. This is feasible with presently available data and would be the first EPR experiment involving weak interactions.     

N\bar N resonance and the corrections to the Goldberger-Treiman relationresonance and the corrections to the Goldberger-Treiman relation

The relevance of the recent experimental observation of possible bound and resonant states in \(N\bar N\) scattering to the Goldberger-Treiman (GT) relation is examined. It is pointed out that anS-wave resonance in \(N\bar N\) scattering goes a long way towards accounting for the corrections to the GT relations. Values of the mass and width of the resonance capable of giving a reasonable fit for the GT relation are presented.     

B^0 - \bar B^0 mixing within and beyond the standard model

The standard model with three fermion families is found to be compatible with the Argus observation of a relatively large amount of \(B_{^d }^0 - \bar B_d^0 \) mixing provided that the top quark is rather heavy. From an analysis of the existing information on mixing angles, and of the constraints imposed by the kaon system, in particular by the ε parameter, we conclude that almost certainlym _t <45 GeV and probablym _t >90 GeV. In view of the Argus result the standard model unambiguously leads to the prediction of a nearly maximal amount of \(B_{^s }^0 - \bar B_s^0 \) mixing. Apart from the rather obvious case of a fourth family of quarks, most “minimal” extensions of the standard model preserve the prediction of a large \(B_{^s }^0 - \bar B_s^0 \) mixing. We discuss \(B^0 - \bar B^0 \) mixing in minimal supersymmetric models compatible with the UA1 lower bounds on gluino and squark masses. Contributions from charged Higgs exchange in the box diagrams are also discussed. While supersymmetry (although marginally) and charged Higgses can lead to an appreciable enhancement of \(B^0 - \bar B^0 \) mixing, minimal left-right symmetric models actually predict a modest suppression of the effect with respect to the standard model.     

DecayB \to Dl\bar v from QCD sum rules

\(B \to Dl\bar v\) form factor is calculated using 3-point QCD sum rules.