A short review on charmed and beauty hadron production in the lepton deep inelastic scattering off proton, in proton-proton and proton-antiproton collisions at high energies is presented. It is shown that the existing theoretical and experimental information on charmed and beauty quark distributions in a proton is not satisfactory. A some procedure to study these distributions at LHC energies is suggested.
We obtain tree-level estimates of various differential branching ratios of heavy baryon decays with massive sterile neutrinos $ν_{x}$ in the final state. Heavy sterile neutrinos can be searched for in heavy baryon decays with missing mass as a signature as well as in fixed target experiments, where heavy baryon decays contribute to sterile neutrino production, with sterile neutrino decays as a signature. Generally, charmed baryons are found to be less promising than charmed mesons, in contrast to b-hadrons. In the latter case, branching ratios of beauty mesons and baryons into sterile neutrino…
We present the next-to-next-to-leading order (NNLO) QCD corrections to the decay constants for both the pseudoscalar and vector beauty-charmed mesons $B_{c}$ and $B^*_{c}$ in nonrelativistic QCD effective theory. Explicit NNLO calculation verified that the $B_c$ decay constant from pseudoscalar current is identical with the $B_c$ decay constant from axial-vector current. The NNLO result for the vector decay constant of $B^*_{c}$ meson is novel. Combined with the latest extraction of nonrelativistic QCD long-distance matrix elements of $B_c$ meson, we give the branching ratios of leptonic decay…
At hadron colliders the dominant production mechanism of $(\bar bc)$ mesons with large transverse momentum is due to parton fragmentation. We compute the rates and transverse momentum spectra for production of S-wave and P-wave $(\bar b c)$ mesons at the Tevatron via the direct fragmentation of the bottom antiquark as well as the Altarelli-Parisi induced gluon fragmentation. Since all the radially and orbitally excited $(\bar b c)$ mesons below the $BD$ flavor threshold will cascade into the pseudoscalar ground state $B_c$ through electromagnetic and/or hadronic transitions, they all contribut…
Production of charmed and beauty mesons and baryons in hadron-nucleon collisions at not very high energy is considered in the framework of the Quark-Gluon String Model. We take into account the possible corrections to the model which disappear at asymptotically high energies but could be important at comparatively low energies, essentially in the case of heavy flavour production. The case of nuclear targets is also considered and the $A$-dependence of charmed and beauty hadron yields is calculated. Predictions for the case of beauty hadron production at $\sqrt{s}$ = 39 GeV are presented.
At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and $\bar bc$ mesons in high energy $e^+e^-$ and hadronic collisions is dominated by parton fragmentation. We calculate the heavy quark fragmentation functions into the D-wave quarkonium and $\bar bc$ mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the $\bar b c$ meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation probability for a $\bar b$ antiquark to split into t…
The production of charmed and beauty hadrons in proton-proton and proton-antiproton collisions at high energies is analyzed within the modified quark-gluon string model (QGSM) including the internal motion of quarks in colliding hadrons. It is shown that using both the QGSM and NLO QCD one can describe the experimental data rather successfully in a wide region of transverse momenta. We also present some predictions for the future experiments on the beauty baryon production in $pp$ collisions at LHC energies and on the charmed meson production in ${\bar p}p$ reactions at GSI energies.
Imbalanced beauty-charmed baryons $ Ξ_{bc}^{+,0} $ are of great significance to the development of heavy flavor physics. In this work, we study the inclusive weak-annihilation decays of $Ξ_{bc}^{+,0}$ and their contributions to the $Ξ_{bc}^{+,0}$ lifetimes. For the calculation of the inclusive $Ξ_{bc}^{+,0}\to X_{cs}$ decay width where $X_{cs}$ stands for the sum of the final states with charm number +1 and strange number -1, we work in the heavy diquark effective theory which provides us with a convenient technical tool to construct the operator product expansion. The $Ξ_{bc}^{+,0}$ is consid…
With a distinctive internal structure from all established hadrons, the beauty-charmed baryons $Ξ_{bc}$ can provide us with new points of view to decipher the strong interaction. In this work, we point out that the inclusive $Ξ_{bc} \to Ξ_{cc}^{++}+X$ decay is a golden channel for the experimental discovery of $Ξ_{bc}$ at the LHC. A unique feature of this process is that the $Ξ_{cc}^{++}$ is displaced, which greatly reduces the combinatorial background. A feasibility analysis is performed on the $Ξ_{bc}^+$ search, which is expected to have a longer lifetime than $Ξ_{bc}^0$ and thus a better di…
Charmed and beauty hadrons in matter are discussed within a unitarized coupled-channel model consistent with heavy-quark spin symmetry. We analyse the formation of D-mesic states as well as the propagation of charmed and beauty hadrons in heavy-ion collisions from LHC to FAIR energies.
The production of charmed and beauty baryons in proton-proton collisions at high energies is analyzed within the modified quark-gluon string model. We present some predictions for the experiments on the forward beauty baryon production in pp collisions at LHC energies. This analysis allows us to find useful information on the Regge trajectories of the heavy (b barb) mesons and the sea beauty quark distributions in the proton.
A number of ways are reviewed in which the study of charmed particles can answer corresponding questions about particles containing $b$ quarks. Topics include the properties of resonances, the magnitude of decay constants, the size of spin-dependent effects, and the hierarchy of lifetime differences.
We present hadron-level predictions from the Monte-Carlo generator CASCADE and numerical calculations of beauty quark and quarkonium production in the framework of the kt-factorization approach for LHC energies. Our predictions are compared with the CMS experimental data.
The production of charmed and beauty hadrons in proton-proton collisions at high energies are analyzed within the modified quark-gluon string model (QGSM) including the internal motion of quarks in colliding hadrons. We present some predictions for the future experiments on the beauty baryon production in $pp$ collisions at LHC energies. This analysis allows us to find interesting information on the Regge trajectories of the heavy (b{\bar b}) mesons and the sea beauty quark distributions in the proton.
The possibility of beauty baryon polarization measurement by cascade decay angular distribution analysis in the channel Lambda0 J/psi --> p pi- l+ l- is demonstrated. The error analysis shows that in the proposed LHC experiment ATLAS at the luminosity $10^{4} pb^{-1}$ the polarization can be measured with the statistical precision better than $δ=0.010$ for Lambda_b0 and $δ=0.17$ for Xi_b0.
The yield of doubly charmed baryons with excited heavy diquark in $S$ wave and $P$ wave states has been estimated at LHC energies. The observation possibility of such baryons is discussed.
We present predictions for the inclusive production of charmed hadrons at the CERN LHC in the general-mass variable-flavor-number scheme at next-to-leading order. Detailed numerical results are compared to data where available, or presented in a way to ease future comparisons with experimental results. We also point out that measurements at large rapidity have the potential to pin down models of intrinsic charm.
This note will be part of Chapter 6.5 of the ALICE Physics Performance Report (PPR), "ALICE Physics: Charm and Beauty", where the capabilities of ALICE for the detection of open heavy flavour particles will be described. We define here the present ALICE baseline for what concerns the heavy flavour production cross sections at LHC and the kinematical distributions of the heavy quark pairs. We start by qualitatively assessing the Bjorken x regimes accessible with charm and beauty measurements at LHC with ALICE (Section 1). In Section 2 we report the most recent results (and the uncertainties) of…
We extend Voloshin's recent analysis of charmed and beauty hyperon decays based on SU(3) symmetry and heavy quark effective theory, by introducing a rather moderate model-dependence, in order to obtain more predictive power, e.g. the values of lifetimes of the (Λ_{b},Ξ_{b}) hyperon triplet and the lifetime of Ω_{b}. In this way we obtain an improvement of the ratio τ(Λ_{b})/τ(B_{d}^{0}) \sim 0.9 and the hierarchy of lifetimes τ(Λ_{b}) \simeq τ(Ξ_{b}^{0}) < τ(Ξ_{b}^{-}) < τ(Ω_{b}) with lifetimes of Ξ_{b}^{-} and Ω_{b} exceeding the lifetime of Λ_{b} by 22% and 35%, respectively.
The recent successes of the SM do not weaken the arguments in favour of New Physics residing at the TeV scale. Finding and identifying it represents the prime challenge for a generation of high energy physicists. To differentiate between different scenarios of New Physics we need to analyze their impact on flavour dynamics. A continuing comprehensive program of heavy flavour studies instrumentalizing the high sensitivity of \cp analyses is intrinsically connected to LHC's core mission. In B decays we can typically expect no more than moderate deviations from SM predictions. $B_s$ transitions p…
We investigate the $σ$ and $ρ$ coupling constants for the $DD$ and $D^*D^*$ interactions, based on correlated $2π$ exchange in the $DD$ and $D^*D^*$ interactions. Starting from the $D\bar{D}\to ππ$ and $D^*\bar{D}^*\to ππ$ amplitudes derived in the pseudophysical region ($4m_π^2\le t \le 52m_π^2$) with the $S$- and $P$-wave $2π$ correlations considered, we obtain the spectral functions for the $DD\to DD$ and $D^*D^*\to D^*D^*$ amplitude with correlated $S$- and $P$-wave $2π$ exchanges. Using the pole approximation, we estimate the $DDσ$, $DDρ$, $D^*D^*σ$, and $D^*D^*ρ$ coupling constants. We e…
We present hadron-level predictions from the Monte Carlo generator Cascade and parton level calculations of open b quark, b-flavored hadron and inclusive b-jet production in the framework of the kt-factorization QCD approach for the LHC energies. The unintegrated gluon densities in a proton are determined using the CCFM evolution equation and the Kimber-Martin-Ryskin (KMR) prescription. Our predictions are compared with the first data taken by the CMS and LHCb collaborations at 7 TeV. We study the theoretical uncertainties of our calculations and investigate the effects coming from parton show…
Our community has to apply {\em non}-perturbative QCD on different levels of flavor dynamics in strange, charm \& beauty hadrons and even for top quarks. We need {\em consistent} parameterization of the CKM matrix and describe weak decays of beauty hadrons with {\em many-body} final states. It is crucial to use the {\em Wilsonian} OPE as much as possible and discuss "duality" in the worlds of quarks and hadrons. The pole mass of heavy quarks is {\em not} well-defined on the {\em non}-perturbative level -- i.e., it is {\em not} Borel summable in total QCD. We need a novel team to combine the st…
The $B_c ^+$ family of $(c\bar{b})$ mesons with beauty and charm is of special interest among heavy quarkonium systems. The $B_c ^+$ mesons are intermediate between $(c\bar{c})$ and $(b\bar{b})$ states both in mass and size, so many features of the $(c\bar{b})$ spectrum can be inferred from what we know of the charmonium and bottomonium systems. The unequal quark masses mean that the dynamics may be richer than a simple interpolation would imply, in part because the charmed quark moves faster in $B_c$ than in the $J/ψ$. Close examination of the $B_c ^+$ spectrum can test our understanding of t…
Comparing the expected spectroscopy in the relativistic quark model and the predicted strong decays in the $^3P_0$ model employing the realistic wave functions from the relativistic quark model with the measured properties of the LHCb and BaBar charmed states, we find that the masses and strong decays of these charmed states can be reasonably explained in the conventional $q\bar{q}$ picture, and therefore suggest that the $D(2550)$/$D_J(2580)$, $D^*(2600)$/$D^*_J(2650)$, $D(2750)$/$D_J(2740)$, $D^*(2760)$/$D^*_J(2760)$, $D_J(3000)$, and $D^*_J(3000)$ can be identified as the $D(2^1S_0)$, $D(2^…
We predict the spectrum of the four $1S$ and eight $1P$ nonstrange and strange states in the beauty meson family in the context of effective field theory. By the union of heavy quark effective theory and chiral perturbation theory, the mass formalisms for the heavy-light mesons are defined. Our analysis uses mass expressions involving, for the first time, the full leading self-energy corrections and leading power corrections to the heavy quark and chiral limits. The counterterms present in these expressions are fitted using available experimental and theoretical information on the charmed meso…
The effective theory for heavy quarks has additional symmetries with respect to QCD, which relate charm and beauty hadron masses. Assuming the spectrum of charmed particles, we predicted in a previous work the masses of some beauty particles. The predictions of the Lambda_b mass, M(Lambda_b)=5630 MeV, and of the B_s mass, M(B_s)=5379 MeV, are in agreement with present experimental data. We continue this work using recent experimental data on charm hadron masses. The results are: M(Sigma_b)=5822+-6 MeV, M(Sigma_b*)-M(Sigma_b)=33+-3 MeV, M(Omega_b)=6080+-7 MeV, M(Omega_b*)-M(Omega_b)=32+-3 MeV, …
We present predictions for the inclusive productions of the D meson originating from bottom hadrons at the CERN LHC in the general-mass variable-flavour-number scheme at next-to-leading order. We present results using two methods to describe the transition for $b\rightarrow D$: a two-step transition $b\rightarrow B \rightarrow D$, based on the $b\rightarrow B$ fragmentation functions and the spectra for $B\rightarrow D$ as measured by CLEO and a one-step transition based on the fragmentation functions for $b\rightarrow D$. The results of both approaches are compared.
With the acceleration of lead nuclei in the LHC, heavy-ion physics will enter a new energy domain. One of the main novelties introduced by the 30-fold energy-jump from RHIC to the LHC is the abundant heavy-quark production. After discussing a few examples of physics issues that can be addressed using heavy quarks, we present a selection of results on the expected experimental capability of ALICE, the dedicated heavy-ion experiment at the LHC, in the open-heavy-flavour sector.
The phenomenological analysis of the LHC data on transverse momentum spectrum and elliptic flow of $J/ψ$ and D mesons in PbPb collisions at center-of-mass energy 2.76 TeV per nucleon pair is presented. The charmed meson production pattern in PbPb collisions may be reproduced by two-component model HYDJET++ including thermal and non-thermal components. The significant part of D-mesons is found to be in a kinetic equilibrium with the created medium, while $J/ψ$-mesons are not.
Tree-level $b$ decays play a critical role in characterising the quark flavour sector, and exposing possible effects of physics beyond the Standard Model. These proceedings cover recent results from the LHCb experiment on semileptonic $b$ baryon decays, $\mathcal{R}(D^{\ast-})$ using three-prong hadronic $τ$ decays, $CP$ observables in $B^- \to D^{(\ast)}h^-$ decays, and an updated combination on the CKM angle $γ$.
Invited "News & Views" for the journal, SCIENCE CHINA: Physics, Mechanics & Astronomy, on a recently new search for the doubly charmed baryon $Ξ_{cc}^+$ at the LHC, which is done by the LHCb Collaboration, arXiv:1909.12273.
We present a detailed discussion on the doubly charmed baryon $Ξ_{cc}$ production at the RHIC and LHC via the proton-nucleus ($p$-N) and nucleus-nucleus (N-N) collision modes. The extrinsic charm mechanism via the subprocesses $g+c\to (cc)[n]+\bar{c}$ and $c+c\to (cc)[n]+g$ together with the gluon-gluon fusion mechanism via the subprocess $g+g\to(cc)[n]+\bar{c}+\bar{c}$ have been taken into consideration, where the intermediate diquark is in $[n]=[^1S_0]_{\bf 6}$-state or $[^3S_1]_{\bar{\bf 3}}$-state, respectively. Total and differential cross sections have been discussed under various collis…
The LHCb collaboration has recently performed a first measurement of the angular production asymmetry in the distribution of beauty quarks and anti-quarks at a hadron collider. We calculate the corresponding standard model prediction for this asymmetry at fixed-order in perturbation theory. Our results show good agreement with the data, which is provided differentially for three bins in the invariant mass of the $b \bar b$ system. We also present similar predictions for both beauty-quark and charm-quark final states within the LHCb acceptance for a collision energy of $\sqrt{s} = 13 \, {\rm Te…
We study the enhanced production of $Λ_c$ charmed baryons relative to that of charmed $D^0$ mesons in proton-proton collisions at LHC energies. We simulated collision events with the enhanced color-reconnection model in PYTHIA 8 MC generator and propose measurements based on the comparative use of different event-activity classifiers to identify the source of the charmed-baryon enhancement. We demonstrate that in this enhanced color-reconnection scenario the excess production is primarily linked to the underlying event and not to the production of high-momentum jets.
Charmed nuclei and exotic charmed meson production at CBM@FAIR and ALICE@LHC
Suranaree University of Technology（素叻他尼理工大学）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心有限公司）；Frankfurt Institute for Advanced Studies（法兰克福高级研究所）；Institut für Kernphysik, Goethe-Universität Frankfurt（法兰克福歌德大学核物理研究所）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；Department of Physics, University of Houston（休斯顿大学物理系）
We present our results on open beauty production in proton-nucleus collisions for the recent LHC $p$Pb run at $\sqrt{s_{NN}}$=5 TeV. We have analysed the effect of the modification of the gluon PDFs in nucleus at the level of the nuclear modification factor. Because of the absence of measurement in $pp$ collisions at the same energy, we also propose the study of the forward-to-backward yield ratio in which the unknown proton-proton yield cancel. Our results are compared with the data obtained by LHCb collaboration and show a good agreement.
All the available experimental information on open charm and beauty mesons is used to classify the observed states in heavy quark doublets. The masses of some of the still unobserved states are predicted, in particular in the beauty sector. Adopting an effective Lagrangian approach based on the heavy quark and chiral symmetry, individual decay rates and ratios of branching fractions are computed, with results useful to assign the quantum numbers to recently observed charmed states which still need to be properly classified. Implications and predictions for the corresponding beauty mesons are p…
We discuss hadroproduction of open charmed mesons ($D^0$, $D^{\pm}$, $D^{\pm}_{S}$) at the LHC energy $\sqrt{s} = 7$ TeV. The cross section for inclusive production of $c \bar c$ pairs is calculated within the $k_{\perp}$-factorization (or high-energy factorization) approach which effectively includes higher-order corrections. Results of the $k_{\perp}$-factorization approach are compared to NLO parton model predictions. The hadronization of charm quarks is included with the help of the Peterson fragmentation functions. Inclusive differential distributions in (pseudo)rapidity and transverse mo…
The recent discovery, by the LHCb collaboration, of the $Ξ_{cc}^{++}$ doubly charmed baryon, has renewed interest in the spectroscopy of doubly heavy hadrons. Experimentally, however, searches for such states appear highly challenging. The reconstructed final states tend to involve multiple heavy flavoured (beauty or charm) hadrons, so the yield for any exclusive decay mode will be suppressed to unobservably low levels by the product of several branching fractions, each of which is typically $10^{-3}$--$10^{-2}$. Noting that decays of double beauty hadrons are the only possible source of $B_c^…
The present paper is based on the assumption that heavy quarks bound states exist in the Standard Model (SM). Considering New Bound States (NBS) of top-anti-top quarks (named T-balls) we have shown that: 1) there exists the scalar 1S-bound state of 6t+6\bar t; 2) the forces which bind the top-quarks are very strong and almost completely compensate the mass of the twelve top-anti-top-quarks in the scalar NBS; 3) such strong forces are produced by the Higgs-top-quarks interaction with a large value of the top-quark Yukawa coupling constant g_t\simeq 1. Theory also predicts the existence of the N…
Important goals of RHIC and LHC experiments with ion beams include the creation and study of new forms of matter, such as the Quark Gluon Plasma. Heavy quark production and attenuation will provide unique tomographic probes of that matter. We predict the suppression pattern of open charm and beauty in $Au+Au$ collisions at RHIC and LHC energies based on the DGLV formalism of radiative energy loss. A cancelation between effects due to the $\sqrt{s}$ energy dependence of the high $p_T$ slope and heavy quark energy loss is predicted to lead to surprising similarity of heavy quark suppression at R…
We give the explicit wave functions of the $qqqq\bar{q}$ components of the C=+1, J=1/2 charmed baryons, $Σ_{c}$, $Λ_{c}$ and $Ξ_{c}^{a}$, and calculate the magnetic moments by adding the 5q components contributions, and we also compute the magnetic moments of the $Σ_{b}$ and $Σ_{b}^{*}$ baryons. The influence of the additional light and strange $q\bar{q}$ pairs is investigated. It's obvious that the constituent quark masses of the charm and beauty quarks are much heavier than that of the light and strange quarks, consequently, the hidden flavor contributions to the baryons magnetic moments may…
Using a statistical approach in the framework of non-covariant perturbation theory the distributions for light and charmed quarks in the hadron have been derived, taking into account the mass of the charmed quark. The parameters of the model have been extracted from the comparison with NA3 data on hadroproduction of J/psi particles. A reanalysis of the EMC data on charm production in muon-nucleon scattering has been performed. It has been found in comparison with the conventional source of charmed quarks from photon-gluon fusion, that the EMC data indicate the presence of an additional contrib…
In a coalescence plus fragmentation approach we calculate the heavy baryon/meson ratio and the $p_T$ spectra of charmed hadrons $D^{0}$, $D_{s}$ and $Λ_{c}^{+}$ in a wide range of transverse momentum from low $p_T$ up to about 10 GeV and discuss their ratios from RHIC to LHC energies without any change of the coalescence parameters. We have included the contribution from decays of heavy hadron resonances and also the one due to fragmentation of heavy quarks which do not undergo the coalescence process. The coalescence process is tuned to have all charm quarks hadronizing in the $p_T\rightarrow…
Anomalous b --> s transitions from LHCb data may suggest a new massive gauge boson Z' that couples to the left-handed b --> s current, which in turn implies a coupling to the t --> c current. In this paper, we study flavor-changing neutral current (FCNC) decays of the top quark induced by a Z' boson, namely t --> c Z', based on a model of the gauged L_mu - L_tau symmetry (the difference between the muon and tauon numbers) with vector-like quarks, which was introduced to explain the anomalous LHCb data. We illustrate that searching for t --> c Z' via Z' --> mu^+ mu^- with LHC Run 1 data can alr…
The production of $D$-mesons in high-energy $pp$ collisions at the LHC kinematic regime is analyzed with the dipole approach in the momentum representation. We present predictions for the $D$-meson differential cross section in terms of the transverse momentum and rapidity distributions taking into account the nonlinear behavior of the QCD dynamics. Comparison between our results and the corresponding experimental measurements reported by the ALICE and LHCb Collaborations in different rapidity bins is performed. We show that the $D$-meson production in the high energy limit can be properly add…
The preasymptotic effects originating from the four-quark operators are disentangled from the other contributions by considering appropriate combinations of inclusive decay rates. Under the assumption of the isospin and heavy-quark symmetry, a set of relations connecting charmed and beauty decays is obtained without invoking specific models. The results are compared with other approaches and confronted with experiment.
Based on the color-spin interaction in diquarks, we argue that charmed multiquark hadrons are likely to exist. Because of the appreciable number of charm quarks produced in central nucleus-nucleus collisions at ultrarelativistic energies, production of charmed multiquark hadrons is expected to be enhanced in these collisions. Using both the quark coalescence model and the statistical hadronization model, we estimate the yield of charmed tetraquark meson $T_{cc}$ and pentaquark baryon $Θ_{cs}$ in heavy ion collisions at RHIC and LHC. We further discuss the decay modes of these charmed exotic ha…
We perform a quantitative analysis of the decays of $cc\bar c\bar c$ tetraquarks with $J^{PC}=0^{++}, 2^{++}$ into 4 muons and into hidden- and open-charm mesons and estimate, for the first time, the fully charmed tetraquark decay width. The calculated cross section upper limit is $\sim 40$ fb for the 4 muons channel, and $\sim 28$ nb for the $D^{(*)} \bar D^{(*)} \to eμ$ channel. On the basis of our results, with the present sensitivity LHCb should detect both signals, for $0^{++}$ and $2^{++}$ fully-charmed tetraquarks.
We calculate the angular distribution spectra between beauty ($B$) and anti-beauty ($\bar B$) mesons in proton-proton collisions in the leading order approximation of the parton Reggeization approach consistently merged with the next-to-leading order corrections from the emission of additional hard gluon. To describe b-quark hadronization we use the universal scale-depended parton-to-meson fragmentation functions extracted from the world $e^+e^-$ annihilation data. We have obtained good agreement between our predictions and data from the CMS Collaboration at the energy $\sqrt{S}=7$ TeV for $B …
We compare results of exact calculations of single parton scattering (SPS) and double parton scattering (DPS) for production of $c \bar c c \bar c$ and for $D$ meson correlations. The SPS calculations are performed in collinear approximation with exact matrix element for $g g \to c \bar c c \bar c$ and $q \bar q \to c \bar c c \bar c$ subprocesses. It is shown that the contribution of gluon-gluon subprocess is about factor 50 larger than that for quark-antiquark annihilation. The new results are compared with results of previous calculation with the approximate matrix element for $g g \to c \b…
