The recent experimental measurements on $pp$ collisions at $\sqrt{s}=5.02 \,\rm TeV$ have shown a very large abundance of heavy baryon production corresponding to a ratio of $Λ_c/D^0 \sim 0.6$, about one order of magnitude larger than what measured in $e^+e^-$, $ep$ collisions and even in $pp$ collisions at LHC, but at forward rapidity. We apply for the first time to $pp$ collisions a quark coalescence plus fragmentation approach developed for $AA$ collisions, assuming the formation of Hot QCD matter at finite temperature. An approach that has correctly predicted a $Λ_c/D \sim O(1)$ in AA collisions at RHIC energy. We calculate the heavy baryon/meson ratio and the $p_T$ spectra of charmed hadrons with and without strangeness content: $D^{0}$, $D_{s}$, $Λ_{c}^{+}$, $Ξ_c$ and $Ω_c$ in $pp$ collisions at top LHC energies, finding a satisfactory result for the measured $Λ_{c}^{+}/D^0$ and the $Ξ_c/D^0$ without any specific tuning of parameters to $pp$ collisions. At variance with other approaches a coalescence approach predicts also a significant production of $Ω_c$ such that $Ω_c/D^0 \sim O(10^{-1})$ .
The statistical coalescence model for the production of open and hidden charm is considered within the canonical ensemble formulation. The data for the J/psi multiplicity in Pb+Pb collisions at 158 A GeV are used for the model prediction of the open charm yield which has not yet been measured in these reactions.
If the recently-discovered charmonium state X(3870) is a loosely-bound molecule of the charm mesons D^0 and \bar D^{*0} or \bar D^0 and D^{*0}, it can be produced in e^+ e^- annihilation at the Υ(4S) resonance by the coalescence of charm mesons produced in the decays of B^+ and B^- mesons. Remarkably, in the case of 2-body decays of the B mesons, the leading contribution to the coalescence probability depends only on hadron masses and on the width and branching fractions of the B meson. As the binding energy E_b of the molecule goes to zero, the coalescence probability scales as E_b^{1/2} log(…
The J/psi yield at midrapidity at the top RHIC (relativistic heavy ion collider) energy is calculated within the statistical coalescence model, which assumes charmonium formation at the late stage of the reaction from the charm quarks and antiquarks created earlier in hard parton collisions. The results are compared to the new PHENIX data and to predictions of the standard models, which assume formation of charmonia exclusively at the initial stage of the reaction and their subsequent suppression. Two versions of the suppression scenario are considered. One of them assumes gradual charmonium s…
We perform numerical comparison of the fragmentation mechanism of charmonium production ($g\,g\to c\,\bar{c}$ followed by $c\toψ\,c$) with the full leading order calculation ($g\,g\toψ\,c\,\bar{c}$ at $Ø (α_s^4)$). We conclude that the non-fragmentation contributions remain important up to $J/ψ$ transverse momenta about as large as 50 GeV, thus making questionable the applicability of the fragmentation approximation at smaller transverse momenta.
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…
The potential of heavy quarks as probes of the environment produced in hadronic and heavy-ion reactions is discussed. A key role is played by coalescence processes and/or resonance formation which are promising candidates to provide a comprehensive understanding of phenomena associated with reinteractions of both open and hidden heavy-quark states.
The perturbative QCD fragmentation functions can be applied phenomenologically as a model for charm and bottom quark fragmentation into heavy-light mesons. The predictions by this model on the observables $P_V$ and $\langle z \rangle$ for $D-D^*$ and $B-B^*$ systems are compared with experimental data.
Fermilab experiment E791, measuring charmed hadron production in $π^- A$ interactions at 500 GeV with high statistics, has observed a strong asymmetry between the hadroproduction cross sections for leading $D$ mesons which contain projectile valence quarks and the nonleading charmed mesons without projectile valence quarks. Such correlations of the charge of the $D$ meson with the quantum numbers of the beam hadron explicitly contradict the factorization theorem in perturbative QCD which predicts that heavy quarks hadronize through a jet fragmentation function that is independent of the initia…
The hydrodynamic (hydro) model applied to data from the relativistic heavy ion collider (RHIC) suggests that a dense QCD medium opaque to partons is formed in more-central Au-Au collisions. However, two-component spectrum analysis reveals a hard component, consistent with parton fragmentation described by pQCD, which can masquerade as "radial flow." Minimum-bias angular correlations reveal that most scattered partons survive as "minijets" even in central Au-Au collisions. Such alternative methods quantitatively describe spectrum and correlation structure via pQCD calculations. RHIC collisions …
In decays of the $Z^0$, the dominant mechanism for the direct production of charmonium states is the decay of the $Z^0$ into a charm quark or antiquark followed by its fragmentation into the charmonium state. We calculate the fragmentation functions describing the splitting of charm quarks into S-wave charmonium states to leading order in the QCD coupling constant. Leading logarithms of $M_Z/m_c$ are summed up using Altarelli-Parisi evolution equations. Our analytic result agrees with the complete leading order calculation of the rate for $Z^0 \rightarrow ψc {\bar c}$. We also use our fragment…
If the recently-discovered charmonium state X(3872) is a loosely-bound S-wave molecule of the charm mesons \bar D^0 D^{*0} or \bar D^{*0} D^0, it can be produced in B meson decay by the coalescence of charm mesons. If this coalescence mechanism dominates, the ratio of the differential rate for B^+ \to \bar D^0 D^{*0} K^+ near the \bar D^0 D^{*0} threshold and the rate for B^+ \to X K^+ is a function of the \bar D^0 D^{*0} invariant mass and hadron masses only. The identification of the X(3872) as a \bar D^0 D^{*0}/\bar D^{*0} D^0 molecule can be confirmed by observing an enhancement in the \ba…
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.
We propose a modification of the mechanism of charmed quarks fragmentation into $D$ mesons in hadronic collisions. It is shown that the distinction in valence quark distributions in the initial $π^{\pm}$ and $K^{\pm}$ mesons leads to different inclusive spectra of $D$ and $D_s$ mesons produced in $π^{\pm}$ and $K^{\pm}$ beams.
In charged current deep inelastic scattering charm is dominantly produced in scattering events on strange quarks, thereby allowing for an experimental determination of the nucleon's strange sea density. A measurement of the energy spectrum of final state charm fragments (D-mesons) determines the charm fragmentation function at spacelike scales considerably below typical e^+e^- c.m.s. energies. NLO corrections to the naive s -> c parton model production picture are important and well understood.
Fragmentation functions for heavy-light mesons, like the charmed D, D^* mesons, are proposed. They rest on next-to-leading QCD Perturbative Fragmentation Functions for heavy quarks, with the addition of a non-perturbative term describing phenomenologically the quark --> meson transition. The cross section for production of large p_T D, D^* mesons at the Tevatron is evaluated in this framework.
The observed $D^{**}$ mesons have $c\bar q$ flavor quantum numbers and spin-parity of the light degrees of freedom $s_\ell^{π_{\ell}} = 3/2^+$. In the $m_c \rightarrow \infty$ limit the spin of the charm quark is conserved and the $c \rightarrow D^{**}$ fragmentation process is characterized by the probability for the charm quark to fragment to a $D^{**}$ meson with a given helicity for the light degrees of freedom. We consider the calculated $b \rightarrow B_c^{**}$ fragmentation functions in the limit $m_c/m_b \rightarrow 0$ as a qualitative model for the $c \rightarrow D^{**}$ fragmentation…
It is well known that large nonfragmentational contributions to inclusive production of charmed particles appear at low energies. In the case of charm production in $B$-meson decays these contributions arise from the participation of the light valent quark from the $B$-meson and can be easily described phenomenologically. These contributions affect $D$-meson spectra and essentially change ratios between yields of different $D$-meson states.
We study the production of charmed hadrons with the help of ALCOR_c, the algebraic coalescence model for rehadronisation of charmed quark matter. Mesonic ratios are introduced as factors connecting various antibaryon to baryon ratios. The resulting simple relations could serve as tests of quark matter formation and coalescence type rehadronization in heavy ion collisions.
Heavy quarks are initially produced in nuclear collisions and the number is conserved during the evolution of the system. We establish a sequential coalescence model with charm conservation and apply it to charmed hadron production at RHIC and LHC energies. The charm conservation enhances the earlier formed hadrons and reduces the later formed ones, which leads to a $D_s/D^0$ enhancement and a $Λ_c/D^0$ suppression. The mass dependence of the sequential hadron formation provides us a new tool for studying the quark-gluon plasma hadronization in high energy nuclear collisions.
We study the production of charmed hadrons $D^{0}$ and $Λ_c^+$ in relativistic heavy-ion collisions using an improved quark coalescence model. In particular, we extend the usual coalescence model by letting a produced hadron to have the same velocity as the center-of-mass velocity of coalesced constituent quarks during hadronization to take into account the effect of collective flow in produced quark-gluon plasma. This results in a shift of charmed resonances of higher masses to larger transverse momenta ($p_T^{}$). Requiring all charm quarks of very low $p_T^{}$ to be converted to hadrons via…
The production of the excited charmed baryon doublet $Λ_c^*$ via fragmentation is studied. An analysis of the subsequent hadronic decays of the doublet within the framework of heavy hadron chiral perturbation theory produces expressions for both the angular distribution of the decay products and the polarization of the final state heavy baryon in terms of various nonperturbative fragmentation parameters. Future experimental investigation of this system will determine these parameters. In addition, recent experimental results are shown to fix one of the parameters in the heavy hadron chiral Lag…
The asymmetry of $D^-$ and $D^+$ meson production in $π^-N$ scattering observed by the E791 experiment is a typical phenomenon known as the leading particle effect in charm hadroproducton. We show that the phenomenon can be explained by the effect of light quark fragmentation into charmed hadrons (LQF). Meanwhile, the size of the LQF effect is estimated from data of the E791 experiment. A comparison is made with the estimate of the LQF effect from prompt like-sign dimuon rate in neutrino experiments. The influence of the LQF effect on the measurement of nucleon strange distribution asymmetry f…
We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a $D$ meson with a certain momentum fraction, in the Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the NJL model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of $D$ meson production at CLEO, we further match the above FF to that in …
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 consider the production of electroweak $Z$ or $W^\pm$ bosons associated with $J/ψ$ mesons at the LHC conditions. Our attention is focused on new partonic subprocesses which yet have never been considered in the literature, namely, the charmed or strange quark excitation subprocesses followed by the charmed quark fragmentation $c\to J/ψ+c$. Additionally we take into account the effects of multiple quark and gluon radiation in the initial and final states. We find that the contributions from the new mechanisms are important and significantly reduce the gap between the theoretical and experime…
The cross section for the photoproduction of large-p_T J/psi mesons at HERA is calculated at next-to-leading order, adopting a perturbative approach to describe the fragmentation of charm quarks and gluons into J/psi mesons. We treat the charm quark according to the massless factorization scheme, where it is assumed to be one of the active flavours inside the proton and the resolved photon. We present inclusive distributions in transverse momentum and rapidity, including the contributions due to direct and resolved photons. The importance of the colour-octet components of the J/psi wave functi…
Quarkonium production at a given large p_T is dominated by parton fragmentation: a parton which is produced with transverse momentum p_T/z fragments into a quarkonium state which carries a fraction z of the parton momentum. Since parton production cross sections fall steeply with p_T, high z fragmentation is favored. However, quantum number constraints may require the emission of gluons in the fragmentation process, and this softens the z dependence of the fragmentation function. We discuss the possibility that higher- order processes may enhance the large z part of fragmentation functions and…
The production of particles with double, triple and hidden charm in heavy ion collisions is studied in the framework of the statistical coalescence model. According to the postulates of the model, the charm quark-antiquark pairs are created at the initial stage of a heavy ion reaction in hard parton collisions. The amount of charm is assumed to be unchanged at later stages. The charm (anti)quarks are distributed among different hadron species at hadronization according to the laws of statistical physics. Several approaches to the statistical treatment of charm hadronization are considered. The…
We compute the contributions to large-$p_T$ $J/ψ$ production at HERA coming from fragmentation of gluons and charm quarks. We find that the charm quark fragmentation contribution dominates over the direct production of $J/ψ$ via photon-gluon fusion at large-$p_T$, while the gluon fragmentation is negligibly small over the whole range of $p_T$. An experimental study of $p_T$ distributions of $J/ψ$ at HERA will provide a direct probe of the charm quark fragmentation functions.
The next-to-leading open charm production in $γp$ collisions is calculated within the Perturbative Fragmentation Functions formalism, to allow resummation of $\as\log(\pt^2/m^2)$ terms. In the large $\pt$ region $(\pt > m)$ the result is consistent with the fixed order NLO calculation, small discrepancies being found for very large $\pt$ and at the edge of phase space. The two approaches differ in the definition and the relative contribution of the direct and resolved terms, but essentially agree on their sum. The resummation is found to lead to a reduced sensitivity to the choice of the renor…
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 fragmentation fractions of c and b quarks into the weakly decaying charmed hadrons D0, D+, D_s+ and Lambda_c+, and into the charmed vector meson D*+ have been derived from the LEP measurements and averaged. The c quark fragmentation fractions represent probabilities to hadronise as a given charmed hadron, while the b quark fragmentation fractions are defined as sums of probabilities to hadronise as a particular charmed hadron or its antiparticle.
We elaborate the inclusive production of single heavy-flavored hadrons in e^+e^- annihilation at next-to-leading order in the general-mass variable-flavor-number scheme. In this framework, we determine non-perturbative fragmentation functions for D^0, D^+, and D^{*+} mesons by fitting experimental data from the Belle, CLEO, ALEPH, and OPAL Collaborations, taking dominant electroweak corrections due to photonic initial-state radiation into account. We assess the significance of finite-mass effects through comparisons with a similar analysis in the zero-mass variable-flavor-number scheme. Under …
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…
We present results of a phase space coalescence approach within the UrQMD transport and -hybrid model for a very wide range of beam energies from SIS to LHC. The coalescence model is able to qualitatively describe the whole range of experimental data with a fixed set of parameters. Some systematic deviations are observed for very low beam energies where the role of feed down from heavier nuclei and multi-fragmentation becomes relevant. The coalescence results are mostly very close to the thermal model fits. However, both the coalescence approach as well as thermal fits are struggling to simult…
In Phys. Rev. D 58, 014014 (1998) and 71, 094013 (2005), we determined non-perturbative D^0, D^+, D^{*+}, D_s^+, and Lambda_c^+ fragmentation functions, both at leading and next-to-leading order in the MS-bar factorization scheme, by fitting e^+e^- data taken by the OPAL Collaboration at CERN LEP1. The starting points for the evolution in the factorization scale mu were taken to be mu_0 = 2m_Q, where Q = c,b. For the reader's convenience, in this Addendum, we repeat this analysis for mu_0 = m_Q, where the flavor thresholds of modern sets of parton density functions are located.
We calculate the process-independent fragmentation functions for a $\bar b$ antiquark to fragment into longitudinally and transversely polarized $B_c^*$ ($^3S_1$) mesons to leading order in the QCD strong coupling constant. In the special case of equal quark mass we recover previous results for the fragmentation of $c\to ψ$ and $b\toΥ$. Various spin asymmetry parameters are defined as measures of the relative population of the longitudinally and transversely polarized vector meson states. In the heavy quark mass limit $m_b \to \infty$ our polarized fragmentation functions obey heavy quark spin…
We calculate the leading order QCD fragmentation functions for the production of $P$-wave charmed beauty mesons. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wavefunction at the origin and a second parameter related to the probability for a $(\bar b c)$ heavy quark pair that is produced in a color-octet $S$-wave state to form a color-singlet $P$-wave bound state. The four $2P$ states and those $3P$ states which lie below the $BD$ flavor threshold eventually all decay into the $1S$ ground state $B_c$ through hadronic cascades or by emittin…
We have refined a model for charm fragmentation at hadron colliders. This model can also be applied to the photoproduction of charm. We investigate the effect of fragmentation on the distribution of produced charm quarks. The drag effect is seen to produce charm hadrons that are shifted in rapidity in the direction of the beam remnant. We also study the importance of different production mechanisms such as charm in the photon and from parton showers.
The processes of D^{(*)}-mesons and Λ_c-baryons production in e^+e^--annihilation at 10.58 GeV and 91.18 GeV energies are concerned. At the 10.58 GeV energy the production of charmed particles via the B-mesons decays is also concerned. Scaling violation of the fragmentation functions is calculated at the NLL-accuracy. Nonperturbative fragmentation functions are retrieved from the experimental data of B-factories and are approximated by simple analytic expressions. It is proved, that the difference between nonperturbative fragmentation functions of mesons and baryons can be easily explained by …
H1 Collaboration recently observed the charmed pentaquark. In this short note, we point out that the dominant production mechanism for pentaquark consisting of a heavy quark is heavy quark fragmentation. We obtain a crude estimate on the fragmentation probability for charm quark into Theta_c^0, based on the known fragmentation probabilities of charm quark into mesons and baryons: f(c-bar --> Theta_c^0) =~ (2-7) x 10^{-3}. Similarly, we also obtain the fragmentation probability for bottom quark into Theta_b^+: f(b-bar --> Theta_b^+) =~ (5-20) x 10^{-3}. We also estimate the prospect of observin…
We discuss charm $D^0 D^0$ meson-meson pair production in the forward rapidity region related to the LHCb experimental studies at $\sqrt{s}$ = 7 TeV. We consider double-parton scattering mechanisms of double $c \bar c$ production and subsequent standard $cc \to D^{0}D^{0}$ scale-independent hadronization as well as new double $g$ and mixed $g c\bar c $ production mechanisms with $gg \to D^{0}D^{0}$ and $gc \to D^{0}D^{0}$ scale-dependent hadronization. The new scenario with gluon fragmentation components results also in a new single-parton scattering mechanism of $gg$ production which is also …
We calculate the fragmentation function for charm quark into J/psi at the QCD next-to-leading-order (NLO) and find that the produced J/psi is of larger momentum fraction than it is at the leading-order. Based on the fragmentation function and partonic processes calculated at the NLO, the transverse momentum distribution on J/psi hadroproduction associated with a charm c (or \bar{c}) jet are predicted. We find that the distribution is enhanced by a factor of 2.0--3.3 at the NLO as p_t increased from 10 GeV to 100 GeV and it is measurable at the LHC with charm tagger. The measurement at the LHC …
We use a recently proposed non-perturbative model, based on an effective strong coupling constant and free from tunable parameters, to study c-flavoured hadron production in e+e- annihilation. Charm-quark production is described in the framework of perturbative fragmentation functions, with NLO coefficient functions, NLL non-singlet DGLAP evolution and NNLL large-x resummation. We model hadronization effects by means of the effective coupling constant in the NNLO approximation and compare our results with experimental data taken at the Z0 pole and at the Upsilon(4S) resonance. We find that, wi…
Recent results on physics in the charm energy region are reviewed. (1) The new data and puzzles in exclusive hadronic decays of $J/ψ$ and $ψ'$ give new challenges to the theory of hadronic decays. (2) With the new observation for $ξ(2230)$ and $f_0(1500)$ in $J/ψ$ radiative decays and other experiments, the situation in searching for glueballs is encouraging, but theoretical uncertainties related to the properties of glueballs still remain and need to be further reduced. (3) For the prompt production of charmonium at large transverse momentum, gluon and quark fragmentations dominate over leadi…
I present the main aspects of open charm production in $π^-\p$ collisions in the context of the Lund String Fragmentation Model as implemented in the Monte Carlo program PYTHIA. The emphasis is on the transition from large to small strings and the dependence on model parameters. A modified version is presented and compared with experimental results both on asymmetries, single-charm spectra and correlations.
A study of elliptic flow of open charm mesons, $D^0$ and $D_S ^\pm$ using quark coalescence as a mechanism of hadronization of heavy quarks implemented in conjunction with A Multi Phase Transport (AMPT) model has been presented. We have studied the transverse momentum dependence of the elliptic flow parameter at mid-rapidity ($|y|$ $<$ 1.0) for Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV (RHIC) and Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV (LHC) for different values of partonic interaction cross-section and QCD coupling constant. We have compared our calculations with the experimentally…
We study charm particle production in hadron-hadron collisions. After calculating perturbatively the charm quark differential cross section, we study the hadronization mechanisms. It is shown that recombination is the key to understand the so called Leading Particle Effect in charm meson production. For charm baryon production, however, leading particle effects are due to a combination of contributions coming from both, the recombination and the fragmentation mechanisms. We compare our calculations to experimental data on charm hadron production in $π^- N$ and $p N$ interactions from several e…
We perform an analysis of semi-inclusive production of charm (D-mesons) in neutral current (NC) and charged current (CC) deep inelastic scattering (DIS) at full O(alpha_s^1). Our calculation is based on the heavy quark scheme developed by Aivazis, Collins, Olness and Tung (ACOT) where we include an O(alpha_s^1) calculation of quark scattering contributions for general masses and couplings. We review the relevant massive formulae and subtraction terms and discuss their massless limits. We show how the charm fragmentation function can be measured in CC DIS and we investigate whether the charm pr…
In a coalescence plus independent fragmentation approach we calculate the $p_T$ spectra of the main hadrons: $π, K, p, \bar p, Λ, ϕ$ in a wide range of transverse momentum from low $p_T$ up to about 10 GeV. The approach in its main features was developed several years ago at RHIC energy. Augmenting the model with the inclusion of some more main resonance decays, we show that the approach correctly predicts the evolution of the $p_T$ spectra from RHIC to LHC energy and in particular the baryon-to-meson ratios $p/π,\bar p/π,Λ/K$ that reach a value of the order of unit at $p_T \sim 3\, \rm GeV$. …
