An-Ping Chen, Yan-Qing Ma, Hong Zhang
In this paper, we review the current status of the phenomenological study of quarkonium production in high energy collisions. After a brief introduction of several important models and effective field theories for quarkonium production, we discuss the comparisons between theoretical predictions and experimental measurements.
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We review the current theoretical situation with regard to the anomalously large cross section for exclusive J/psi + eta_c production in e^+ e^- annihilation, as measured by BELLE Collaboration.
The status of Charmonium production in photon-photon collisions is briefly reviewed. I would like to mention that although the preliminary data were obtained in experiment, the theoretical investigation is not in a compatible status.
We present the gluon-gluon and photon-gluon helicity amplitudes for color singlet and octet charmonium production in polarized and unpolarized hadron-hadron and photon-hadron collisions.
I briefly review Non-Relativistic QCD and related effective theories, and discuss applications to heavy quarkonium decay, and production in electron-positron colliders.
Within the NRQCD factorization approach the production of heavy quarkonia can be calculated in perturbative QCD in terms of a few production-process-independent NRQCD matrix elements. We test the universality of these long-distance matrix elements by comparing their values as determined from charmonium production at p pbar, e p, and e+ e- colliders, and in Z^0, Upsilon, and B decays.
In this paper initial state radiation corrections to double production of charmonium mesons on one-photon electron-positron annihilation at center of mass energy $\sqrt{s}=10.6\GeV$ are studied. It is shown, that these corrections have noticeable effect and must be taken into consideration.
The cross section value of doubly charmonium production in e+e- annihilations have been estimated at interaction energy 10.6 GeV. The quarkonium wave function shape, as well as the nonzero value of charm quark have been taken into account.
We review recent results on the production of prompt charmonium in association with a hadron jet or a prompt photon in two-photon collisions at next-to-leading order in the factorization framework of nonrelativistic quantum chromodynamics.
We review the charmonium production in $e^+e^-$ annihilation at $\sqrt{s}=10.6GeV$. NRQCD predictions for the $J/ψ$ production are compared with the recent measurements by BaBar and Belle. A NRQCD calculation for the $D$-wave charmonium production is reported to further test the color-octet mechanism and detect the $J^{PC}=2^{--}$ state. The issue of double $c \bar c$ production in $e^+e^-$ annihilation observed by Belle is also discussed.
The analyses of large transverse momentum charmonium production at the Tevatron have shown that fragmentation of gluons is an important production mechanism. We study large-$p_T$ charmonium production in $pp$ collisions at the LHC, and find that due to the copious gluon production at this energy, the gluon fragmentation contribution completely overwhelms the fusion contribution and the charm quark fragmentation contribution. Our analysis shows that for $J/ψ$ production at the LHC, there is a significant event rate even for $p_T \sim$~100~GeV. The measurement of the cross-section at such large …
We analyze the singlet $P$--wave charmonium production at $e^+ e^-$ colliders within the framework of unconstrained supersymmetry. We show that the CP--violating transitions, dominated by the gluino exchange, are typically four orders of magnitude larger than the CP--conserving ones, and former is generated by the electric dipole moment of the charm quark. Our results can be directly tested via the charmonium searches at the CLEO--c experiment.
We study the unpolarised and polarised hadro-production of charmonium in non-relativistic QCD (NRQCD) at low transverse momentum, including sufficiently higher orders in the relative velocity, $v$, so as to study the ratio of $χ_{c1}$ and $χ_{c2}$ production rates.
In statistical QCD, color deconfinement and the properties of the quark-gluon plasma determine the in-medium behavior of heavy quark bound states. In high energy nuclear collisions, charmonia probe the partonic medium produced in the early stages of the interaction. We survey the present theoretical status and provide a critical evaluation of the charmonium production measurements in experiments at the CERN-SPS and the BNL-RHIC.
We consider the charmonium production in thermalized hadronic medium created in ultrarelativistic heavy ion collisions at LHC energy. The calculations for the secondary $J/ψ$ and $ψ^,$ production by $D\bar D$ annihilation are performed within a kinetic model taking into account the space-time evolution of a longitudinally and transversely expanding medium. We show that the secondary charmonium production appears almost entirely during the mixed phase and it is very sensitive to the charmonium dissociation cross section with co-moving hadrons. Within the most likely scenario for the dissociatio…
We present in this work a study of large-\pt\ charmonium production in hadronic collisions. We work in the framework of the factorization model of Bodwin Braaten and Lepage, thereby including the color octet production mechanism, and extract the values of the necessary nonperturbative parameters from a comparison with the most recent data from the Fermilab 1.8 TeV $p\bar p$ hadron collider. We extend the calculation to 630 \gev, and compare the results with data published by the UA1 Collaboration. The global agreement is satisfactory, indicating that the largest components of the production me…
We present the preliminary results of a calculation of the fragmentation contribution to charmonium production at large transverse momentum in $p\bar{p}$ colliders. The fragmentation of gluons and charm quarks is the dominant direct production mechanism for sufficiently large $p_{\perp}$. We find that for both $J/ψ$ and $ψ'$ production fragmentation dominates over the conventional gluon-gluon fusion mechanism for $p_{\perp}$ greater than about 6 GeV.} Presented at the Workshop on Physics at Current Accelerator and the Supercollider, Argonne National Laboratory, June 1993.
The production of the charmonium states in hadronic experiments is considered in NLO at the strong coupling constant. It is shown, that such an approach solves some significant problems, arising when only leading order processes are considered. In particular, in such a consideration distributions over the transverse momentum of the final charmonium can be obtained. There appears also a natural explanation to the existence of $χ_{c1}$-meson in final state, that is observed experimentally and cannot be produced in leading order processes.
The production of the charmonium states in proton-antiproton experiments is considered at the energy rates near threshold in NLO. Such a consideration allows one to obtain non zero distributions over the transverse momentum of the final charmonium and gives a natural explanation to the existence of $χ_{c1}$-meson in final state, that is observed experimentally and cannot be produced in leading order processes. The crucial role of scale parameter choice in $α_s (Q^2)$ and partonic distributions $f(x,Q^2)$ shown, and the correct choice offered.
Paired charmonium and bottomonium production in rare exclusive decays of Z boson
该研究在相对论夸克模型中研究Z玻色子衰变产生成对重夸克偶素，构建相对论振幅并计算含相对论修正的衰变宽度。
At present the color-octet mechanism is still an important and debatable part in the non-relativistic QCD(NRQCD). We find in this work that the polarized double charmonium production at the LHC may pose a stringent test on the charmonium production mechanism. Result shows that the transverse momentum($p_T$) scaling behaviors of double $J/ψ$ differential cross sections in color-singlet and -octet production mechanisms deviate distinctively from each other while $p_T$ is larger than 7 GeV. In color-octet mechanism, the two $J/ψ$s in one pair are mostly transversely polarized when $p_T\gg 2 m_c$,…
We estimate transverse spin single spin asymmetry(TSSA) in the process $e+p^\uparrow \to J/ψ+X$ using color evaporation model of charmonium production. We take into account transverse momentum dependent(TMD) evolution of Sivers function and parton distribution function and show that the there is a reduction in the asymmetry as compared to our earlier estimates wherein the $Q^2$ - evolution was implemented only through DGLAP evolution of unpolarized gluon densities.
The production of the ${}^1P_1$ charmonium state, $h_c$, at large-$p_T$ at the Tevatron is considered. The colour-octet contributions to this state are found to be dominant and give a reasonably large rate for the production of $h_c$. This should make it feasible to look for this resonance in the $J/ψ+π$ decay channel. This production rate is a prediction of NRQCD, and the observation of the $h_c$ at the Tevatron can, therefore, be used as a test of the colour-octet predictions of NRQCD.
We show that both hard perturbative and soft non-perturbative QCD effects are important in hadroproduction of charmonium. Observed $x_F$ and $p_\perp$ distributions of J/psi in fixed target experiments can be well described by our Monte Carlo model based on perturbative QCD and the Color Evaporation Model.
Calculations of heavy quark and charmonium hadroproduction are presented in the k_t-factorization approach. The resulting differential cross sections are compared to experimental values and NLO collinear predictions. The application of the full effective Fadin-Lipatov quark-antiquark- production-vertex has an important influence on the results and in particular leads to a strong suppression of certain color octet contributions which are related to the outstanding problem of the production of polarized J/Psi.
It is shown that the nuclear shadowing of charmonium due to the modification of the nuclear parton distribution is similar in the factorization approach based on non relativistic QCD and in the color evaporation model. In the first model, a separate study of the color octet and color singlet contributions to the yields of the various charmonium states as well as the contributions of these states to the total $J/Ψ$ production is performed. It is found a clear $x_F$ dependence of these contributions which can reproduce experimental data for moderate $x_F$.
The color evaporation model simply states that charmonium production is described by the same dynamics as $D \bar D$ production, {\em i.e.}, by the formation of a colored $c \bar c$ pair. Its color happens to be bleached by soft final-state interactions. We show that the model gives a complete picture of charmonium production including low-energy production by proton, photon and antiproton beams, and high-energy production at the Tevatron and HERA. Our analysis includes the first next-to-leading-order calculation in the color evaporation model.
We calculate the D-wave charmonium production in $e^+e^-$ annihilation at BELLE and BABAR at $\sqrt{s}=10.6$ GeV using the nonrelativistic QCD factorization formalism, including color singlet and color octet contributions. We analyze the contributions of various processes for $δ_J(J=1,2)$ production. We find that both the color singlet and color octet channels may give substantial contributions, and the production rates are estimated to be $σ(δ_1)\simeq 0.043-0.16pb$ and $σ(δ_2)\simeq 0.094-0.29pb$, which, however, are very sensitive to the choice of the color octet matrix elements of the D-wa…
In this paper the production of excited vector and pseudoscalar charmonium mesons in $\epem$ annihilation is analyzed in the framework of light cone. In particular the cross sections $\epem \to ψ(2S)η_c(1S), ψ(1S)η_c(2S),ψ(2S)η_c(2S)$ have been calculated. It is shown, that contrary to NRQCD the cross sections calculated in the framework of light cone agree with experimental data.
In this paper we study inclusive production of vector charmonium states $J/ψ$ or $ψ(2S)$ in two-photon $\epem$-annihilation at $\sqrt s=10.6 \rm GeV$ using color-singlet model. Analytic expressions for differential cross sections, numerical values of total cross sections and plots of different distributions are presented. These distributions differ significantly from the one-photon case so these modes can be easily separated.
Charmonium production at SPS and FAIR energies
应用Remler形式论研究重离子碰撞中重子丰富物质对粲偶素产生和解离的影响，并在PHSD框架下实现。
We calculate the double charmonium production cross section within the framework of $4\times 4$ Bethe-Salpeter Equation in the electron-positron annihilation, at center of mass energy $\sqrt{s}= 10.6$GeV, that proceeds through the exchange of a single virtual photon. In this calculation, we make use of the full Dirac structure of 4D BS wave functions of these charmonia, with the incorporation of all the Dirac covariants (both leading and sub-leading). The calculated cross-sections for the double charmonium productions for final states, ($J/Ψ, η_c$); ($Ψ',η_c$) ; ($J/Ψ, η_c'$); and ($Ψ',η_c'$) …
The color-evaporation model quantitatively describes all data on photoproduction and hadroproduction of charmonium. Although the model is in part nonperturbative, the associated parameters can for instance be determined from the charmonium photoproduction data. At this point its predictions for the prompt production of $ψ$'s at the $Z$ pole are made with no free parameters. We show here that this approach successfully describes all data on the production of prompt $ψ$'s in $Z$ decays.
A factorization theorem for $P$-wave quarkonium production, recently derived by Bodwin, Braaten, Yuan and Lepage, is applied to $Υ\to χ_{cJ} + X$, where $χ_{cJ}$ labels the ${}^3 P_J$ charmonium states. The widths for $χ_{cJ}$ production through color-singlet $P$-wave and color-octet $S$-wave $c \bar c$ subprocesses are computed each to leading order in $α_s$. Experimental data on $Υ\to J / ψ+ X$ is used to obtain an upper bound on a nonperturbative parameter (related to the probability for color-octet $S$-wave $c \bar c$ hadronization into $P$-wave charmonium) that enters into the factorizati…
The production cross sections of $J/ψ~η_b$, $Υ\;η_c$ pairs in a single boson $e^+e^-$ annihilation have been studied in a wide range of energies, which will be achieved at future $e^+e^-$ colliders. The main color singlet contributions to the production processes are taken into account, including the one loop QCD contribution.
We present an analysis of the existing data on charmonium hadro-production based on non-relativistic QCD (NRQCD) calculations at the next-to-leading order (NLO). All the data on J/psi and psi' production in fixed-target experiments and on pp collisions at low energy are included. We find that the amount of color octet contribution needed to describe the data is about 1/10 of that found at the Tevatron.
The calculation of D-wave charmonium prodution rates in B meson deacys under the NRQCD factorization formalism is presented. We find that inclusion of the color-octet contributions permits us to detect the D-wave charmonium states in B decays at present experimental facilities. The same amount signals of 2^{--} D-wave state as that of ψ' could be observed at LEP and CESR. We also predict the relative production rates for four D-wave states are δ^c:δ^c_1: δ^c_2:δ^c_3=2.5:3:5:7, where δ^c, δ^c_1, δ^c_2, δ^c_3 represent respectively the 2^{-+}, 1^{--}, 2^{--}, 3^{--} states.
New evaluation of the relativistic effects in the double production of $S$-wave charmonium states is performed on the basis of perturbative QCD and the relativistic quark model. The main improvement consists in the exact account of properties of the relativistic meson wave functions. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $\sqrt{s}$ up to the second order. The exact relativistic treatment of the wave functions makes all such second order terms convergent, th…
Charmonium production in association with a forward or backward pion in nucleon-antinucleon annihilation is one of the most promising reaction to access nucleon-to-pion transition distribution amplitudes (TDAs) at PANDA. We briefly review the description of this reaction in terms of πN TDAs within the collinear factorization approach and present the first results of dedicated feasibility studies for the PANDA experimental setup.
We study charmonium production at high-energy colliders (Tevatron, HERA, and LEP2) in the framework of the k_T-factorization approach and the factorization formalism of non-relativistic quantum chromodynamics at leading order in the strong-coupling constant alpha_s and the relative velocity v. The transverse-momentum distributions of direct and prompt J/psi-meson production measured at the Fermilab Tevatron are fitted to obtain the non-perturbative long-distance matrix elements for different choices of unintegrated gluon distribution functions in the proton. Using the matrix elements thus obta…
Production of metastable charmonium states more massive than the $ψ(3685)$ is expected in models and could be the source of up to $50\%$ of the $ψ$ observed at large $p_T$ at the Tevatron.Narrow $2^{-+},2^{--} c\bar{c}$ are predicted at around 3.8GeV and radially excited $2^3P_{1,2}$ may also have suppressed hadronic widths making these states potentially extra sources of $ψ(3685)$. Colour octet components are believed to dominate $ψ$ production at the Tevatron which suggests that hybrid charmonium production may also be prominent. Estimates of hybrid production rates and branching ratios into…
Recent measurements of the Belle Collaboration of the exclusive production of two charmonia in the $e^+e^-$ annihilation differ substantially from theoretical predictions. Recently it was suggested that a significant part of this discrepancy can be explained by the process $e^2e^- --> 2J/psi$ and value for its cross-section was published. In this paper it is shown, that these results are incorrect and the values for the cross-sections of the production of different vector charmonia are presented.
Using the operator product expansion and nonrelativistic QCD we study the production of charmonium hybrids in B decays. We express the decay rate in terms of a few matrix elements which eventually will be fixed by experimental measurements or calculated on the lattice. While the Fock state expansion is problematic for hybrids, the operator product expansion still provides a model independent framework for phenomenological calculations of hybrid production and decay. We then use a simple flux tube model to estimate the branching ratio B -> psi_g+X, where psi_g is a J^{PC}=0^{+-} hybrid, the lar…
At existing and planned neutrino factories (high energy and high intensity neutrino beam facilities) precision studies of QCD in neutrino-nucleon interactions are a realistic opportunity. We investigate charmonium production in fixed target neutrino experiments. We find that $J/ψ$ production in neutrino-nucleon collision is dominated by the color octet $^3S_1$ NRQCD matrix element in a neutral current process, which is not accessible in photo or leptoproduction. Neutrino experiments at a future Muon Collider will acquire sufficient event rate to accurately measure color octet matrix element co…
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to inclusive processes $W^+\to J/ψ(η_c)+c+\bar{s}+X$ and $W^+\to B_c(B_c^{*})+b+\bar{s}+X$ in the framework of nonrelativistic QCD (NRQCD) factorization formalism. Result indicates that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are greatly reduced. The charmonium and $B_c$ meson yielding rates at the Large Hadron Collider (LHC) are given.
Hard and soft QCD dynamics are both important in charmonium hadroproduction, as presented here through a next-to-leading order QCD matrix element calculation combined with the colour evaporation model. Observed $x_F$ and $p_\perp$ distributions of $J/ψ$ in hadroproduction are reproduced. Quite similar results can also be obtained with a Monte Carlo event generator where \ccbar pairs are instead produced through leading order matrix elements and the parton shower approximation of higher order processes. The soft dynamics may alternatively be described by the soft colour interaction model. We al…
In this invited presentation I review some recent developments in the theory of charmonium that appear likely to be of importance for future experimental studies in this field. The specific areas considered are double charmonium production, LQCD studies of charmonium, recent results for hadron loops, c-cbar production cross sections at PANDA, charm molecules, and two recent developments, "charmiscelleny".
Rare decay process of the Higgs boson into a pair of $J/Ψ$ and $Υ$ particles is studied within perturbative Standard Model and relativistic quark model. The relativistic corrections connected with the relative motion of quarks are calculated in the production amplitude and the wave functions of the bound states. Numerical values of the decay widths of the Higgs boson are obtained, which can be used for comparison with experimental data.
We propose the study of unpolarized transverse momentum dependent gluon parton distributions as well as the effect of linearly polarized gluons on transverse momentum and rapidity distributions of $J/ψ$ and $Υ$ production within the framework of transverse momentum dependent factorization employing color evaporation model (CEM) in unpolarized proton-proton collision. We estimate the transverse momentum and rapidity distributions of $J/ψ$ and $Υ$ at LHCb, RHIC and AFTER energies using TMD evolution formalism.
This paper is devoted to the leading twist exclusive bottomonia decays with double charmonium in the final state. Using models of the twist-2 charmonia distribution amplitudes the widths of these decays are calculated within light cone formalism. In addition, the processes under consideration are studied within nonrelativistic QCD. In our analysis we have found that the production of some of the $P$-wave charmonia mesons with $L_z \neq 0$ is allowed already at the leading twist approximation. This means that the selection rules which predict the suppression of such decays are violated. The mec…
The CDF preliminary analysis on polarized charmonium production at moderate transverse momentum, $p_T \sim 4 - 20$ GeV, severely challenges the color octet model (COM), which predicts quarkonium to be transversely polarized with increasing $p_T$. Based on this data, we analyze the compatibility of the Tevatron and the photoproduction at HERA in the context of the COM. Due to the uncertainty on the extraction of non-relativistic QCD (NRQCD) matrix elements and a lack of complete next-to-leading order calculations, one cannot completely rule out the COM. Nonetheless, both collider experiments se…
We calculate the direct production rate of $J/ψ$ in top quark decays. The color-octet $J/ψ$ production via $t\rightarrow W^+ b J/ψ$ is shown to have a large branching ratio of order $1.5\times 10^{-4}$, which is over an order of magnitude higher than that of the color-singlet $J/ψ$ production via $t\rightarrow W^+ b J/ψ~g~g $ or $t\rightarrow W^+ b~χ_{cJ}~g$ followed by $χ_{cJ}\rightarrow J/ψ~γ$. This result can be used as a powerful tool to test the importance of the color-octet mechanism in heavy quarkonium production.
Measurements of the polarization of $\jp$ produced in pion-nucleus collisions are in disagreement with leading twist QCD prediction where $\jp$ is observed to have negligible polarization whereas theory predicts substantial polarization. We argue that this discrepancy cannot be due to poorly known structure functions nor the relative production rates of $\jp$ and $χ_J$. The disagreement between theory and experiment suggests important higher twist corrections, as has earlier been surmised from the anomalous non-factorized nuclear $A$-dependence of the $\jp$ cross section.
Charmonium production in the TMD factorization using the Improved Color Evaporation Model
本文基于TMD框架的软胶子重求和方法与改进型色蒸发模型研究质子-质子碰撞中非极化J/ψ产生，发现强子化参数F^{J/ψ}的能量依赖性，并给出SPD NICA实验运动学下的J/ψ产生预测。
We suggest searching for excited charmonium states in $e^+e^-$ annihilation via double charmonium production at $\sqrt{s}=10.6$ GeV with $B$ factories, based on a more complete leading order calculation including both QCD and QED contributions for various processes. In particular, for the C=+ states, the $χ_{c0}(nP)$ (n=2,3) and $η_c(mS)$ (m=3,4) may have appreciable potentials to be observed; while for the C=- states, the $η_ch_c$ production and especially the $χ_{c1}h_c$ production might provide opportunities for observing the $h_c$ with higher statistics in the future. A brief discussion fo…
$J/ψ$ production cross section considering the contributions of both color-singlet and color-octet $c\bar c$ channels is calculated. The result is used to study the suppression of $J/ψ$ in nuclear collisions. With absorption cross sections for $(c \bar c)_8$ $σ_{abs}^8\simeq 11mb $ and $(c \bar c)_1$ $σ_{abs}^1\simeq 0mb $ the p-A and A-B data except for Pb-Pb can be explained. Possible explanations of additional suppression in Pb-Pb are discussed.
We compare the color-evaporation model (CEM) and nonrelativistic QCD (NRQCD) factorization predictions for inclusive quarkonium production. Using the NRQCD factorization formulas for quarkonium production and for perturbative QQ-bar production, we deduce relationships that are implied by the CEM between the nonperturbative NRQCD matrix elements that appear in the factorization formula for quarkonium production. These relationships are at odds with the phenomenological values of the matrix elements that have been extracted from the Tevatron data for charmonium production at large transverse mom…
We study the possibility to probe the unpolarized and linearly polarized transverse momentum- dependent gluon distributions in unpolarized pp collision in charmonium and bottomonium produc- tion, employing non-relativistic QCD (NRQCD) based color octet model within transverse momentum dependent (TMD) factorization framework. The transverse momentum (p T ) and rapidity distributions of J/ψ and Υ(1S) at LHCb, RHIC and AFTER energies are estimated. Significant modulations in transverse momentum spectrum of quarkonium in the low p T region is obtained when contributions of linearly polarized gluon…
In this paper the processes $e^+ e^- \to J/ΨJ/Ψ, J/Ψψ', ψ' ψ'$ are considered in the framework of light cone formalism. An important distinction of this approach in comparison to the approaches used in other papers is that relativistic and leading logarithmic radiative corrections to the cross section can be easily resummed within light cone formalism. In this paper the effect of this resummation is studied. It is shown that this effect is important especially for the production of higher charmonium mesons. The predicted cross sections are in agreement with the upper bounds set by Belle collab…
The dominance of chi_0 in the data for e+e- to psi + chi_J(c\bar{c}) is shown to violate OZI factorization. Single gluon exchange gives a non-factorizing effective S.L interaction that generates a large scalar production amplitude. This also has observable effects near threshold in e+e- to D*D_J, where enhancements of D*D_0 and DD_1 channels are predicted. Further tests and implications are discussed.
In this paper we summarize our recent results for low energy associated charmonium production cross sections, using 1) crossing symmetry, and 2) an explicit hadronic model. These predictions are of relevance to the planned charmonium and charmonium hybrid production experiment PANDA at GSI.
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