Heavy Quark Fragmentation Research Articles

Fully charmed tetraquarks from LHC to FCC: natural stability from fragmentation

We investigate the inclusive production of fully charmed tetraquarks, T4c(0++)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c}(0^{++})$$\\end{document} or T4c(2++)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c}(2^{++})$$\\end{document} radial excitations, in high-energy proton collisions. We build our study upon the collinear fragmentation of a single parton in a variable-flavor number scheme, suited to describe the tetraquark formation mechanism from moderate to large transverse-momentum regimes. To this extent, we derive a novel set of DGLAP-evolving collinear fragmentation functions, named TQ4Q1.0 determinations. They encode initial-scale inputs corresponding to both gluon and heavy-quark fragmentation channels, defined within the context of quark-potential and spin-physics inspired models, respectively. We work within the NLL/NLO+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {NLO}^+$$\\end{document} hybrid factorization and make use of the JETHAD numeric interface along with the symJETHAD symbolic calculation plugin. With these tools, we provide predictions for high-energy observables sensitive to T4c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{4c}$$\\end{document} plus jet emissions at center-of-mass energies ranging from 14 TeV at the LHC to the 100 TeV nominal energy of the FCC.

Nonuniversality of heavy quark hadronization in elementary high-energy collisions

It has been traditionally hypothesized that the heavy quark (charm c and bottom b) fragmentation is universal across different collision systems, based on the notion that hadronization as a soft process should occur at the characteristic nonperturbative quantum chromodynamics (QCD) scale, ΛQCD. However, this universality hypothesis has recently been challenged by the observation that the c- and b-baryon production relative to their meson counterparts in minimum bias proton-proton (pp) collisions at the CERN Large Hadron Collider (LHC) energies is significantly enhanced as compared to the electron-positron (e+e−) collisions. The conception of nonuniversality is unambiguously reinforced by the latest measurement of the charged-particle multiplicity dependence of the b-baryon–to–meson yield ratio, Λb/B, by the LHCb experiment in s=13TeVpp collisions at the LHC, evolving continuously from the saturation value in minimum bias pp collisions toward the small value in e+e− collisions as the system size gradually reduces. We address the multiplicity dependence of b-baryon production in the canonical statistical hadronization model with input b-hadron spectrum augmented with many hitherto unobserved states from quark model predictions. We demonstrate that the decreasing trend of the Λb/B toward low multiplicities can be quantitatively understood from the canonical suppression on the yield of Λb, as caused by the requirement of strict conservation of baryon number in sufficiently small systems. We have therefore proposed a plausible scenario for understanding the origin of the nonuniversality of heavy quark fragmentation in elementary collisions. Published by the American Physical Society 2024

An improved description of charm fragmentation data

We consider the fragmentation of heavy quarks into heavy-flavoured hadrons, specifically the production of charmed mesons in e+e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-$$\\end{document} collisions, at different centre-of-mass energies. We focus our attention on the ratio of moments of the D∗+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^{*+}$$\\end{document} energy spectrum measured by ALEPH and CLEO. This ratio is believed to provide us with a direct test of perturbative QCD evolution because hadronisation effects should cancel between the numerator and denominator. However, state-of-the-art calculations based on standard (final-state) collinear factorisation fail to describe the experimental data. We show that this discrepancy is considerably reduced if heavy-quark threshold effects are accounted for not only in DGLAP evolution, as it is usually done, but also in the resummed coefficient functions.

Transverse momentum-dependent heavy-quark fragmentation at next-to-leading order

The transverse momentum-dependent fragmentation functions (TMD FFs) of heavy (bottom and charm) quarks, which we recently introduced, are universal building blocks that enter predictions for a large number of observables involving final-state heavy quarks or hadrons. They enable the extension of fixed-order subtraction schemes to quasi-collinear limits, and are of particular interest in their own right as probes of the nonperturbative dynamics of hadronization. In this paper we calculate all TMD FFs involving heavy quarks and the associated TMD matrix element in heavy-quark effective theory (HQET) to next-to-leading order in the strong interaction. Our results confirm the renormalization properties, large-mass, and small-mass consistency relations predicted in our earlier work. We also derive and confirm a prediction for the large-z behavior of the heavy-quark TMD FF by extending, for the first time, the formalism of joint resummation to capture quark mass effects in heavy-quark fragmentation. Our final results in position space agree with those of a recent calculation by another group that used a highly orthogonal organization of singularities in the intermediate momentum-space steps, providing a strong independent cross check. As an immediate application, we present the complete quark mass dependence of the energy-energy correlator (EEC) in the back-to-back limit at Oαs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\alpha}_s\\right) $$\\end{document}.

Heavy quark fragmentation in e+e− collisions to NNLO+NNLL accuracy in perturbative QCD

Fragmentation of heavy quarks into heavy-flavoured hadrons receives both perturbative and non-perturbative contributions. We consider perturbative QCD corrections to heavy quark production in e+e− collisions to next-to-next-to-leading order accuracy in QCD with next-to-next-to-leading-logarithmic resummation of quasi-collinear and soft emissions. We study multiple matching schemes, and multiple regularisations of the soft resummation, and observe a significant dependence of the perturbative results on these ingredients, suggesting that NNLO+NNLL perturbative accuracy may not lead to real gains unless the interface with non-perturbative physics is properly analysed. We confirm previous evidence that D*+ experimental data from CLEO/BELLE and from LEP are not reconcilable with perturbative predictions employing standard DGLAP evolution. We extract non-perturbative contributions from e+e− experimental data for both D and B meson fragmentation. Such contributions can be used to predict heavy-quark fragmentation in other processes, e.g. DIS and proton-proton collisions.

Exotic Tetraquarks at the HL-LHC with JETHAD: A High-Energy Viewpoint

We review the semi-inclusive hadroproduction of a neutral hidden-flavor tetraquark with light and heavy quark flavor at the HL-LHC, accompanied by another heavy hadron or a light-flavored jet. We make use of the novel TQHL1.0 determinations of leading-twist fragmentation functions to describe the formation mechanism of a tetraquark state within the next-to-leading order perturbative QCD. This framework builds on the basis of a spin physics-inspired model, taken as a proxy for the lowest-scale input of the constituent heavy-quark fragmentation channel. Then, all parton-to-tetraquark fragmentation functions are consistently obtained via the above-threshold DGLAP evolution in a variable-flavor number scheme. We provide predictions for a series of differential distributions calculated by the hands of the JETHAD method, well-adapted to NLL/NLO+ hybrid-factorization studies, where the resummation of next-to-leading energy logarithms and beyond is included in the collinear picture. We provide corroborating evidence that high-energy observables sensitive to semi-inclusive tetraquark emissions at the HL-LHC exhibit a fair stability under radiative corrections, as well as MHOU studies. Our analysis constitutes a prime contact point between QCD resummations and the exotic matter.

The dynamic hadronization of charm quarks in heavy-ion collisions

The Pythia8/Angantyr model for heavy ion collisions was recently updated with a mechanism for global colour reconnection. The colour reconnection model used is QCD colour algebra inspired and enhances baryon production due to the formation of string junctions. In this paper, we present updates to the junction formation and string fragmentation mechanisms, connected to heavy quark fragmentation. This allows for the simulation of heavy quark fragmentation, using junction formation, in heavy ion collisions. The framework is validated for proton collisions, and we show results for charm baryon production in proton-lead collisions.

On heavy-flavour jets with Soft Drop

We study hadronic jets that are tagged as heavy-flavoured, i.e. they contain either beauty or charm. In particular, we consider heavy-flavour jets that have been groomed with the Soft Drop algorithm. In order to achieve a deeper understanding of these objects, we apply resummed perturbation theory to jets initiated by a massive quark and we perform analytic calculations for two variables that characterise Soft Drop jets, namely the opening angle and the momentum fraction of the splitting that passes Soft Drop. We compare our findings to Monte Carlo simulations. Furthermore, we investigate the correlation between the Soft Drop energy fraction and alternative observables that aim to probe heavy-quark fragmentation functions.

Recent Findings from Heavy-Flavor Angular Correlation Measurements in Hadronic Collisions

The study of angular correlations of heavy-flavor particles in hadronic collisions can provide crucial insight into the heavy quark production, showering, and hadronization processes. The comparison with model predictions allows us to discriminate among different approaches for heavy quark production and hadronization, as well as different treatments of the underlying event employed by the models to reproduce correlation observables. In ultra-relativistic heavy-ion collisions, where a deconfined state of matter, the quark–gluon plasma (QGP), is created, heavy-flavor correlations can shed light on the modification of the heavy quark fragmentation due to the interaction between charm and beauty quarks with the QGP constituents, as well as characterize their energy loss processes while traversing the medium. Insight into the possible emergence of collective-like mechanisms in smaller systems, resembling those observed in heavy-ion collisions, can also be obtained by performing correlation studies in high-multiplicity proton–proton and proton–nucleus collisions. In this review, the most recent and relevant measurements of heavy-flavor correlations performed in all collision systems at the LHC and RHIC will be presented, and the new understandings that they provide will be discussed.

Probing parton propagation in heavy-ion collisions with ALICE heavy-flavour measurements

Heavy quarks (charm and beauty) are valuable probes for investigating the properties of the quark–gluon plasma (QGP) formed in ultra-relativistic heavy-ion collisions, as they are mainly produced through hard-scattering processes prior to the formation of the QGP, and their number is conserved during the subsequent QGP evolution. Measurements of the nuclear modification factor RAA of charm and beauty hadrons allow us to characterise the in-medium energy loss of heavy quarks while traversing the QGP. Information on their diffusion and degree of participation in the collective motion of the medium can be obtained by measuring the elliptic-flow coefficient v2 of heavy-flavour particles. Complementary insights into heavy-quark fragmentation and energy redistribution can be obtained by measuring angular correlations involving heavy-flavour particles. In this contribution, the recently published results on the non-prompt v2 coefficient of D0 mesons are presented, comparing them with those of other particle species in Pb–Pb collisions at √SNN = 5.02 TeV. Additionally, we report the recent findings on the RAA of prompt D mesons and Λc+ baryons in Pb–Pb collisions at the same energy. Furthermore, we discuss the new Pb–Pb results on angular correlations between heavy-flavour decay electrons and charged particles in the same collision system.

Heavy quark fragmentation function in two-dimensional QCD in Nc→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c\\rightarrow \\infty $$\\end{document} limit

We carry out a comprehensive study of the quark-to-meson fragmentation function in the ’t Hooft model, i.e., the two-dimensional quantum chromodynamics (QCD) in Nc→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_c\\rightarrow \\infty $$\\end{document} limit, following the operator definition pioneered by Collins and Soper. We apply the Hamiltonian approach as well as the diagrammatic approach to construct the functional form of the quark-to-meson fragmentation function in terms of the meson’s light-cone wave function. For the sake of comparison, we also investigate the heavy quark fragmentation into quarkonium in two-dimensional QCD within the framework of the nonrelativistic QCD (NRQCD) factorization, at the lowest order in quark velocity. In the heavy quark limit, the quark fragmentation function obtained from the ab initio method agrees well, both analytically and numerically, with that obtained from the NRQCD approach. This agreement might be regarded as a nontrivial justification for the validity of both field-theoretical approaches to compute the heavy quark fragmentation function.

S-wave heavy pentaquark production in direct fragmentation of heavy quark

Study of exotic hadrons with configurations beyond the naive quark model has attracted a lot of interests in recent years. Due to their complicated configuration many theoretical models have been designed for describing their structure. Understanding the production mechanism of exotic hadrons could be helpful to find out their inner structure and to test the theory of QCD as well. It is well-known that the dominant production mechanism for conventional heavy hadrons with large transverse momentum is fragmentation so as this mechanism could also be extended to heavy pentaquarks production. This work is a first effort to study the direct fragmentation of heavy quarks into ground state heavy pentaquarks in leading order of perturbative QCD. Considering the picture of compact pentaquark states, through the Suzuki approach we will compute the fragmentation function of heavy quarks into S-wave heavy pentaquarks. The production cross section of heavy pentaquarks through pair annihilation will also be estimated at lowest order of perturbative QCD.

Dead cone effect in charm and bottom quark jets

The evolution of a heavy quark initiated jet is mainly ruled by gluon bremsstrahlung. As a consequence of the dead-cone effect, this radiation is suppressed in the forward direction at angles smaller than that proportional to the heavy quark mass MQ, i.e. Θ0=MQ/EQ at energy EQ of the primary quark. In this paper, we unveil this effect in charm and bottom quark jets using DELPHI and OPAL data from Z0 boson decays in e+e− annihilation at center of mass energy 91.2 GeV. The analysis of the reconstructed heavy quark fragmentation function in momentum space shows the strong suppression of hadrons at high momenta in such events compared to light quark fragmentation by a factor ≲1/10. The amount of this suppression is well reproduced by perturbative QCD (pQCD) within the Modified Leading Logarithmic Aproximation and the compact scheme of Local Parton Hadron Duality (MLLA-LPHD). As a new result, we obtain an almost perfect agreement between the light quark fragmentation functions expected at W0∝MQ from DELPHI and OPAL data with Pythia8 and shed light on the reasons for the existence of the ultra-soft gluon excess at small momentum fraction in comparison with pQCD predictions.

Transverse momentum distributions of heavy hadrons and polarized heavy quarks

We initiate the study of transverse momentum-dependent (TMD) fragmentation functions for heavy quarks, demonstrate their factorization in terms of novel nonperturbative matrix elements in heavy-quark effective theory (HQET), and prove new TMD sum rules that arise from heavy-quark spin symmetry. We discuss the phenomenology of heavy-quark TMD FFs at B factories and find that the Collins effect, in contrast to claims in the literature, is not parametrically suppressed by the heavy-quark mass. We further calculate all TMD parton distribution functions for the production of heavy quarks from polarized gluons within the nucleon and use our results to demonstrate the potential of the future EIC to resolve TMD heavy-quark fragmentation in semi-inclusive DIS, complementing the planned EIC program to use heavy quarks as probes of gluon distributions.

Unconventional Mechanisms of Heavy Quark Fragmentation

Heavy and light quarks produced in high-pT partonic collisions radiate differently. Heavy quarks regenerate their color field, stripped-off in the hard reaction, much faster than the light ones and radiate a significantly smaller fraction of the initial quark energy. This peculiar feature of heavy-quark jets leads to a specific shape of the fragmentation functions observed in e+e− annihilation. Differently from light flavors, the heavy quark fragmentation function strongly peaks at large fractional momentum z, i.e., the produced heavy–light mesons, B or D, carry the main fraction of the jet momentum. This is a clear evidence of the dead-cone effect, and of a short production time of a heavy–light mesons. Contrary to propagation of a small qq¯ dipole, which survives in the medium due to color transparency, a heavy–light Qq¯ dipole promptly expands to a large size. Such a big dipole has no chance to remain intact in a dense medium produced in relativistic heavy ion collisions. On the other hand, a breakup of such a dipole does not affect much the production rate of Qq¯ mesons, differently from the case of light qq¯ meson production.

Azimuthal correlations of heavy-flavor hadron decay electrons with charged particles in pp and p–Pb collisions at pmb {sqrt{s_{mathrm{{NN}}}}} = 5.02 TeV

The azimuthal (Delta varphi ) correlation distributions between heavy-flavor decay electrons and associated charged particles are measured in pp and p–Pb collisions at sqrt{s_{mathrm{{NN}}}} = 5.02 TeV. Results are reported for electrons with transverse momentum 4<p_{textrm{T}}<16textrm{GeV}/c and pseudorapidity |eta |<0.6. The associated charged particles are selected with transverse momentum 1<p_{textrm{T}}<7textrm{GeV}/c, and relative pseudorapidity separation with the leading electron |Delta eta | < 1. The correlation measurements are performed to study and characterize the fragmentation and hadronization of heavy quarks. The correlation structures are fitted with a constant and two von Mises functions to obtain the baseline and the near- and away-side peaks, respectively. The results from p–Pb collisions are compared with those from pp collisions to study the effects of cold nuclear matter. In the measured trigger electron and associated particle kinematic regions, the two collision systems give consistent results. The Delta varphi distribution and the peak observables in pp and p–Pb collisions are compared with calculations from various Monte Carlo event generators.

Observation of the dead cone effect in charm and bottom quark jets and its QCD explanation

The production of a heavy quark is accompanied by gluon bremsstrahlung which is suppressed at small angles $\Theta\lesssim M_Q/E$ for mass $M_Q$ and high energy $E$ according to perturbative Quantum Chromo Dynamics (QCD) (``dead cone effect''). As particles at small angles typically have large momenta, the heavy quark mass also causes a suppression of high momentum particles. In this paper, we studied this effect in c- and b-quark events using data from Z boson decays in $e^+e^-$ annihilation. The heavy quark fragmentation function for charged particles is reconstructed in the momentum fraction variable $x$ or $\xi=\ln(1/x)$ by removing the decays of the heavy quark hadrons. Indeed, we find an increasing suppression of particles with rising $x$ down to a fraction of $\lesssim 1/10$ for particles with $x\gtrsim0.2$ in b-quark and $x\gtrsim0.4$ in c-quark jets in comparison to light quark fragmentation. The sensitivity to the dead cone effect in the present momentum analysis is considerably increased in comparison to the recently presented angular analysis. This amount of suppression and the differences between c- and b-quark fragmentation are in good quantitative agreement with the expectations based on perturbative QCD within the Modified Leading Logarithmic Approximation (MLLA) in the central kinematic region. The data also support a two parameter description in the MLLA of these phenomena (``Limiting Spectrum''). The sensitivity of these measurements to the heavy quark mass is investigated.

Recent heavy-flavour measurements with ALICE

In this contribution, an overview on the latest results of the ALICE Collaboration on the production of heavy-flavour hadrons in pp and Pb–Pb collision systems will be presented. Due to their large masses, heavy quarks are produced on shorter time scales than the typical QGP formation time, thus they participate to the system evolution and interact with the medium constituents making the heavy-flavour quarks a perfect probe to investigate the QGP properties. Heavy-flavour production measurements in pp collisions are a needed reference for Pb–Pb studies, to study the hadronization mechanisms in small colliding systems and to test perturbative QCD calculations at the LHC energies. The results presented report charm and beauty cross section measurements with an unprecedented precision down to very low momentum. In addition, results on heavy-flavour production highlight the non-universality of heavy-quark fragmentation fractions among different collision systems and energy scales.

Selected Results in Heavy-Quark Fragmentation

I review a few selected topics concerning heavy-quark fragmentation, taking particular care about bottom- and charm-quark production in e+e− annihilation and the inclusion of non-perturbative corrections. In particular, I discuss the recent developments of calculations carried out in the framework of perturbative fragmentation functions and the perspective to extend them to other processes and higher accuracy. Special attention is paid to the use of an effective strong coupling constant to model hadronization effects.

Heavy quark jet production near threshold

In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1 − z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJR ∼ m and EJR » m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJR/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.