Double charmonium production in exclusive bottomonium decays

Exclusive bottomonium decays leading to the production of charmonium pairs are considered. The respective decay widths are calculatedwithin the approach of line-cone expansion for the amplitude and nonrelativistic QCD. It is shown that the production of L _z ≠ 0 P-wave charmonium states is possible even in the leading-twist approximation. This means a violation of selection rules that require the suppression of such decays. The reason for this violation is discussed in detail.     

Open-Channel Effects on Heavy-Quarkonium Spectra: A Phenomenological Study Within a One-Open-Channel Approximation

Open-channel effects on charmonium (- and -waves) and bottomonium (-wave) spectra are investigated within a one-open-channel approximation. Mass shifts and decay widths of these states just above the threshold are obtained by taking into account a coupling between confined quarkonium states and decaying states of the open channel. The final-state interaction (FSI) between the decaying meson and antimeson plays a very important role in producing a reasonable magnitude of coupling; the FSI provides the open-channel poles (R , R ) at the appropriate positions on the complex energy plane. The result is found to be independent of the detailed form of the transition potential and the final-state interaction. Received February 12, 1997; revised August 15, 1997; accepted for publication September 25, 1997     

On the chromo-electric permittivity and Debye screening in hot QCD

We study the response functions (chromo-electric susceptibilities) for an interacting quark-gluon plasma. The interaction effects have been encoded in the effective fugacities for quasi-partons which are extracted self-consistently from the two equations of state for hot QCD. The first one is the fully perturbative O(g ⁵) EOS and the second one, which is O(g ⁶ln(1/g)) , incorporates some non-perturbative effects. We find that the response function shows large deviations from the ideal behavior. We further determine the temperature dependence of the Debye mass by fixing the effective coupling constant Q² which appears in the transport equation. We show that our formalism naturally yields the leading-order HTL expression for the Debye mass if we employ the ideal EOS. Employing the Debye mass, we estimate the dissociation temperatures for various charmonium and bottomonium bound states. These results are consistent with the current theoretical studies.     

Analysis of Vector Meson Transitions Among Heavy Quarkonium States

In this article,we study the vector meson transitions among the charmonium and bottomonium states with the heavy quark effective theory in a systematic way,and make predictions for the ratios among the vector meson decay widths of a special multiplet to another multiplet.The predictions can be confronted with the experimental data in the future.     

Heavy Quark Potential and Quarkonium Spectrum in Nonperturbative pNRQCD

The charmonium and bottomonium mass spectra are investigated systematically in potential nonrelativistic QCD with the heavy quark potential computed by lattice QCD simulations nonperturbatively. The potential consists of a static potential and relativistic corrections classified in powers of the inverse of heavy quark mass m, and the effects of the O(1/m) correction, the O(1/m ²) spin–orbit and spin–tensor corrections on the mass spectra are examined systematically. The pattern of the mass spectra is found to be in fairly good agreement with the experimental data, in which the O(1/m) correction gives an important contribution.     

Spectrum of heavy quarkonia in an instanton medium

The energy-level shift in heavy-quarkonium systems that is caused by fluctuations of vacuum gluon fields is estimated by simulating these fields by an instanton liquid. The use of the corresponding vacuum correlation function makes it possible to go beyond the dipole approximation. The width of energy levels with respect to decay to e ⁺ e ^? pairs is also given. It is shown that, both for bottomonium and for charmonium systems, an instanton medium can ensure a scale of shifts and widths of levels that is compatible with experimental data. In particular, it is indicated that a sizable logarithmic contribution at short distances is peculiar to the instanton vacuum.     

Higher <Emphasis Type="Italic">η</Emphasis><Subscript>c</Subscript>(<Emphasis Type="Italic">nS</Emphasis>) and <Emphasis Type="Italic">η</Emphasis><Subscript>b</Subscript>(<Emphasis Type="Italic">nS</Emphasis>) mesons

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using experimental data on dielectron widths. Relativistic correlations are taken into account together with the smearing of spin-spin interaction. The radius of smearing is fixed by known G/ψ−η _c(1S), ψ(2S)−η _c′(2S) splittings, which appears to be small, r _ss ≅ 0.06 fm. Nevertheless, even with such a small radius, substantial suppression of hyperfine splittings (∼50%) is observed in bottomonium. For nS b states (n = 1, 2, ..., 6), our predicted splittings (in MeV) are 28, 12, 10, 5, 6, 3. For the 3S and 4S charmonium states, the splittings 16(2) and 12(4) MeV are obtained. The text was submitted by the authors in English.     

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     

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.     

Spectroscopy and decay properties of charmonium

The mass spectra of charmonium are investigated using a Coulomb plus linear(Cornell)potential.Gaussian wave functions in position space as well as in momentum space are employed to calculate the expectation values of potential and kinetic energy respectively.Various experimental states(X(4660)(5~3S_1),X(3872)(2~3P_1),X(3900)(2~1P_1),X(3915)(2~3P_0)and X(4274)(3~3P_1)etc.)are assigned as charmonium states.We also study the Regge trajectories,pseudoscalar and vector decay constants,electric and magnetic dipole transition rates,and annihilation decay widths for charmonium states.     

Non-perturbative contribution to the thrust distribution in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

We re-evaluate the non-perturbative contribution to the thrust distribution in e ⁺ e ⁻→ hadrons, in the light of the latest experimental data and the recent NNLO perturbative calculation of this quantity. By extending the calculation to NNLO+NLL accuracy, we perform the most detailed study to date of the effects of non-perturbative physics on this observable. In particular, we investigate how well a model based on a low-scale QCD effective coupling can account for such effects. We find that the difference between the improved perturbative distribution and the experimental data is consistent with a 1/Q-dependent non-perturbative shift in the distribution, as predicted by the effective coupling model. Best fit values of α _s (91.2 GeV)=0.1164_−0.0026^+0.0028 and α ₀(2 GeV)=0.59±0.03 are obtained with χ ²/d.o.f.=1.09. This is consistent with NLO+NLL results but the quality of fit is improved. The agreement in α ₀ is non-trivial because a part of the 1/Q-dependent contribution (the infrared renormalon) is included in the NNLO perturbative correction. Address after 1 October 2008: Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK.     

What do we really know about cold nuclear matter effects?

The measurement of charmonium suppression in relativistic heavy ion collisions is posited to be an unambiguous probe of the properties of the strongly interacting quark gluon plasma (sQGP). In hot and dense QCD matter Debye color screening prevents charm and anti-charm quark pairs from forming J/ψ mesons if the screening radius is smaller than the binding radius. However, one must have a clear understanding of the expected suppression in normal density QCD matter before interpreting any additional anomalous suppression. The PHENIX experiment has measured J/ψ production from colliding proton + proton and deuteron + gold beams at 200 GeV from the relativistic heavy ion collider (RHIC). The deuteron + gold data can be compared to the proton + proton baseline in order to establish the typical suppression in cold nuclear matter (CNM). For PHENIX, a suppression of J/ψ in cold nuclear matter is observed as one goes forward in rapidity (in the deuteron-going direction), corresponding to a region more sensitive to initial state low-x gluons in the gold nucleus. These results can be convoluted with the nuclear-environment-modified parton distribution functions, extracted from deep inelastic scattering (DIS) and Drell-Yan (DY) data, in order to estimate the J/ψ break up cross section in cold nuclear matter. One can also use a data driven method that does not rely on the assumption of the production mechanism, or PDF parameterization, to extrapolate to the heavy ion collision case. At this time both the predictions for CNM effect suppression in heavy ion collisions are somewhat ambiguous. Future results using the data acquired by the PHENIX experiment in run-6 (p + p) and run-8 (d + Au) will be vital for our understanding. These data, which are in the process of being analyzed, will provide a needed improvement in the statistical and systematic precision of constraints for CNM effects. These constraints must be improved in order to make firm conclusions concerning additional hot nuclear matter charmonium suppression in the sQGP.     

Formation of charmonium states in heavy-ion collisions and thermalization of charm

We examine the possibility to utilize in-medium charmonium formation in heavy-ion interactions at collider energy as a probe of the properties of the medium. This is possible because the formation process involves recombination of charm quarks which imprints a signal on the resulting normalized transverse momentum distribution containing information about the momentum distribution of the quarks. We have contrasted the transverse momentum spectra of J/ψ, characterized by 〈p _T ²〉, which result from the formation process in which the charm quark distributions are taken at opposite limits with regard to thermalization in the medium. The first uses charm quark distributions unchanged from their initial production in a pQCD process, appropriate if their interaction with the medium is negligible. The second uses charm quark distributions which are in complete thermal equilibrium with the transversely expanding medium, appropriate if a very strong interaction between charm quarks and medium exists. We find that the resulting 〈p _T ²〉 of the formed J/ψ should allow one to differentiate between these extremes, and that this differentiation is not sensitive to variations in the detailed dynamics of in-medium formation. We include a comparison of predictions of this model with preliminary PHENIX measurements, which indicates compatibility with a substantial fraction of in-medium formation.     

The ωDD vertex in a sum rule approach

The study of charmonium dissociation in heavy ion collisions is generally performed in the framework of effective Lagrangians with meson exchange. Some studies are also developed with the intention of calculate form factors and coupling constants related with charmed and light mesons. These quantities are important in the evaluation of charmonium cross sections. In this Letter we present a calculation of the ωDD vertex that is a possible interaction vertex in some meson-exchange models spread in the literature. We used the standard method of QCD sum rules in order to obtain the vertex form factor as a function of the transferred momentum. Our results are compatible with the value of this vertex form factor (at zero momentum transfer) obtained in the vector-meson dominance model.     

Analysis of the Radiative Decays Among the Charmonium States

In this article, we study the radiative decays among the charmonium states with the heavy quark effective theory, and make predictions for the ratios among the radiative decay widths of an special multiplet to another multiplet. The predictions can be confronted with the experimental data in the future and put additional constraints in identifying the X, Y, Z charmonium-like mesons.     

Markovian MC simulation of QCD evolution at NLO level with minimum <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>

We present two Monte Carlo algorithms of the Markovian type which solve the modified QCD evolution equations at NLO level. The modifications with respect to the standard DGLAP evolution concern the argument of the strong coupling constant, α _S. We first analyze the z-dependent argument and then the k _T -dependent one. The evolution time variable is identified with the rapidity. The two algorithms are tested to 0.05% precision level. We find that the NLO corrections in the evolution of the parton momentum distributions with k _T -dependent coupling constant are of the order of 10 to 20%, and in the small-x region even up to 30%, with respect to the LO contributions. The project is partly supported by the EU grant MTKD-CT-2004-510126, realized in a partnership with the CERN Physics Department and by the Polish Ministry of Science and Information Society Technologies grant No. 620/E-77/6.PR UE/DIE 188/2005-2008.     

A Partial Width Calculation of OZI-Allowed Charmonium Decays in a Coupled Channel Framework

Okubo–Zweig–Iizuka-allowed partial decay widths, masses, and total decay width of charmonium states are studied in a nonrelativistic coupled-channel framework based on microscopic effective quark interactions. With the help of the complex scale transformation, the coupled channel equation is easily solved under the proper boundary condition for resonances. The obtained result as a whole is very successful and encouraging for the traditional charmonium states including ψ(4040) whose features of mass and partial decay widths have been argued historically. The coupling mechanisms of these states are investigated by reducing artificially the channel coupling strengths little by little and finally turning the coupling off. The situations turn out to be quite different from what we would have naively supposed. Other solutions than the traditional charmonium states were obatined at the same time. Some of them are discussed in relation with new particles observed recently.     

Charmonium States in QCD-Inspired Quark Potential Model Using Gaussian Expansion Method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22?%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of J/ψ and ψ′ are alleviated. This work also provides an inspection and suggestion for the possible cc? states among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as M(2¹ D ₂)?= 4164.9 MeV and M(3³ P ₂)?= 4352.4 MeV, which strongly favor the J ^PC ?=?2^?+, 2⁺⁺ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.