I present a preliminary determination of the Fragmentation Functions (FFs) of unidentified charged hadrons at next-to-leading order in quantum chromodynamics. The analysis is based on hadron production cross section data in single-inclusive electron-positron annihilation. It extends a recent determination of the FFs of identified charged pions, charged kaons and protons/antiprotons performed by the NNPDF Collaboration. I illustrate the quality of the FFs determined in this analysis and show how they describe the charged hadron spectra measured in proton-(anti)proton collisions.
We present new sets of fragmentation functions for protons and inclusive charged hadrons obtained in combined NLO QCD analyses of single-inclusive hadron production in electron-positron annihilation, proton-proton collisions, and deep-inelastic lepton-proton scattering. These analyses complement previous results for pion and kaon fragmentation functions with charge and flavor discrimination. The Lagrange multiplier technique is used to assess the uncertainties in the extraction of the new sets of fragmentation functions.
We investigate the properties of interference fragmentation functions measurable from the distribution of two hadrons produced in the same jet in the current fragmentation region of a hard process. We discuss the azimuthal angular dependences in the leading order cross section of two-hadron inclusive lepton-nucleon scattering as an example how these interference fragmentation functions can be addressed separately.
Using the formalism of two-hadron fragmentation functions, we discuss single-spin asymmetries occurring in the production of two hadrons in the current region of deep inelastic scattering, with a particular emphasis on transversity measurements.
We reconsider the option of extracting the transversity distribution by using interference fragmentation functions into two leading hadrons inside the same current jet. To this end, we perform a new study of two-hadron fragmentation functions. We derive new positivity bounds on them. We expand the hadron pair system in relative partial waves, so that we can naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference between the s- and p-wave production of two mesons, as well as the production o…
We present new sets of next-to-leading order fragmentation functions describing the production of charged pions, kaons and protons from the gluon and from each of the quarks, obtained by fitting to all relevant data sets from e+ e- annihilation. The individual light quark flavour fragmentation functions are obtained phenomenologically for the first time by including in the data the light quark tagging probabilities obtained by the OPAL Collaboration.
In the hadronic decays of Z, gluon emission leads to the appearance of the longitudinal component of the fragmentation function, F_L. Measurement of F_L and the transverse component, F_T, could thus provide an insight into the gluon fragmentation function. However, hadronization corrections at low x can be significant. Here we present a method of accounting for such corrections, using the JETSET event generator as illustration.
A next-to-leading order (NLO) analysis of hadron-jet momentum correlations in p-p collisions at the LHC is carried out. We show that the inclusive charged hadron momentum distributions inside jets is a very sensitive observable which allows one to disentangle among various fragmentation function sets presently available. Correlations with identified hadrons (kaons, protons) are investigated as well.
We study the inclusive production of two hadrons in deep inelastic processes, l N ---> l h_1 h_2 X, with h_1 in the current fragmentation region (CFR) and h_2 in the target fragmentation region (TFR). Assuming a factorized scheme, the recently introduced polarized and transverse momentum dependent fracture functions couple to the transverse momentum dependent fragmentation functions. This allows the full exploration of the fracture functions for transversely polarized quarks. Some particular cases are considered.
We investigate the properties of interference fragmentation functions arising from the emission of two leading hadrons inside the same jet for semi-inclusive lepton-nucleon deep-inelastic scattering. Using an extended spectator model we give numerical estimates for the example of the fragmentation into a proton-pion pair with its invariant mass on the Roper resonance.
We apply collinear expansion to inclusive hadron production in $e^+e^-$ annihilation and derive a formalism suitable for systematic study of leading as well as higher twist contributions to fragmentation functions at the tree level. We make the calculations for hadrons with spin-0, spin-1/2 as well as spin-1 and obtain the results in terms of different components of fragmentation functions for the hadronic tensors, the differential cross section as well as hadron polarizations in different cases. The results show a number of interesting features such as the existence of transverse polarization…
I present a first determination of a set of collinear fragmentation functions of charged pions using the NNPDF methodology. The analysis is based on a wide set of single-inclusive electron-positron annihilation data, including recent measurements from $B$-factory experiments, and is performed up to next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. I discuss the results of the fits, highlighting their quality in the description of the data, their stability upon the inclusion of higher-order corrections, and their comparison to other sets of fragmentation functions.
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.
Predictions for light charged hadron production data in the current fragmentation region of deeply inelastic scattering from the H1 and ZEUS experiments are calculated using perturbative Quantum Chromodynamics at next-to-leading order, and using fragmentation functions obtained by fitting to similar data from $e^+ e^-$ reactions. General good agreement is found when the magnitude $Q^2$ of the hard photon's virtuality is sufficiently large. The discrepancy at low $Q$ and small scaled momentum $x_p$ is reduced by incorporating mass effects of the detected hadron. By performing quark tagging, the…
We investigate the role of heavy quarks in the production of light flavored hadrons and in the determination of the corresponding non perturbative hadronization probabilities. We define a general mass variable flavor number scheme for fragmentation functions that accounts for heavy quark mass effects, and perform a global QCD analysis to an up-to-date data set including very precise Belle and BaBar results. We show that the mass dependent picture provides a much more accurate and consistent description of data.
We present a model calculation of leading order interference fragmentation functions arising from the distribution of two hadrons produced in the same jet of a fragmenting quark in a hard process. Using a simple spectator model for the mechanism of the hadronization process, for the first time we give a complete calculation and numerical estimates for the example of a proton-pion pair production with its invariant mass on the Roper resonance.
The light top-squark $\sto$ may be the lightest squark and its lifetime may be `long enough' in a kind of SUSY models which have not been ruled out yet experimentally, so colorless `supersymmetric hadrons (superhadrons)' $(\sto \bar{q})$ ($q$ is a quark except $t$-quark) may be formed as long as the light top-squark $\sto$ can be produced. Fragmentation function of $\sto$ to heavy `supersymmetric hadrons (superhadrons)' $(\sto \bar{Q})$ ($\bar{Q}=\bar{c}$ or $\bar{b}$) and the hadronic production of the superhadrons are investigated quantitatively. The fragmentation function is calculated prec…
In electron positron annihilation, changing quarks into the final hadron states is being described by fragmentation function. Based on the scaling hypothesis, this function will be independent from the center of mass energy. Gluon radiation violates the scaling feature. Transverse momentum distribution plays an important role in scaling violation of fragmentation functions. In this article, by the use of data resulted from the annihilation process of electron positron in AMY detector at 60 GeV center of mass energy, first, charged particles multiplicity distribution will be obtained and it wil…
We compute model-independently the production rates and transverse momentum spectra for the $B_c$ mesons in various spin-orbital states ($n\,^1S_0$, $n\,^3S_1$, $n\,^1P_1$, and $n\,^3P_J\,(J=0,1,2)$ ) at hadron colliders via the direct fragmentation of the bottom antiquark and via the Altarelli-Parisi-induced gluon fragmentation. Since all the radially and orbitally excited states below the $BD$ flavor threshold will decay, either electromagnetically, hadronically, or a combination of both, into the pseudoscalar ground state $1\,^1S_0$, they all contribute significantly to the inclusive $B_c$ …
Using methods of effective field theory, a systematic analysis of the fragmentation functions D_{a/H}(x,m_Q) of a hadron H containing a heavy quark Q is performed (with a=Q,Q_bar,q,q_bar,g). By integrating out pair production of virtual and real heavy quarks, the fragmentation functions are matched onto a single nonperturbative function describing the fragmentation of the heavy quark Q into the hadron H in "partially quenched" QCD. All calculable, short-distance dependence on x is extracted in this step. For x->1, the remaining fragmentation function can be matched further onto a universal fun…
We present the complete structure of the azimuthal dependences and polarization observables for two-hadron production in $e^+e^-$ annihilation processes within a transverse momentum dependent (TMD) approach adopting the helicity formalism. The leading-twist TMD fragmentation functions (TMD-FFs) for spin-1/2 hadrons are fully accounted for. The role of the polarizing FF, together with its extraction from Belle data for the transverse polarization of $Λ$'s, are discussed as well. Finally, predictions for SIDIS processes at EIC are presented.
We present a reliable estimate on the production rate of $B_c$ mesons in $1S$ and $2S$ states in the large transverse momentum region at hadronic colliders using heavy quark fragmentation functions derived within the framework of perturbative QCD. We also present the transverse momentum distribution for the $B_c$ mesons. The production rate is large enough for the $B_c$ mesons to be identified at the Tevatron. At the SSC/LHC the rate is so large that their properties can be studied in details.
We propose the characterization of fragmentation functions by the energy fraction x, a hadron takes away from the energy of the jet measured in the frame co-moving with the jet. Besides, we propose the usage of the jet mass as the fragmentation scale Q. We show that these two Lorentz-invariant variables emerge naturally in a microcanonical ensemble with conserved fourmomentum. Then, we construct a statistical hadronisation model, in which, two features of the hadronic final states in various high-energy reactions (power law spectra and negative-binomial multiplicity distributions) can be conne…
In the fragmentation of a color flux tube in high-energy $pp$ collisions or $e^+$-$e^-$ annihilations, the production of $q$-$\bar q$ pairs along a color flux tube precedes the fragmentation of the tube. The local conservation laws in the production of these $q$-$\bar q$ pairs will lead to the correlations of adjacently produced hadrons. As a consequence, the fragmentation of a flux tube will yield a many-hadron correlation in the form of a chain of hadrons ordered in rapidity, with adjacent hadrons correlated in charges, flavor contents, and azimuthal angles. It will also lead to a two-hadron…
We calculate the spin density matrix of the hadron $h$ created via quark fragmentation in the process $e^-e^+ \to q\bar q \to h + X$. In the case of $h=Λ$ the experimental data could possibly elucidate the problem of $s$-quark contribution to the spin of the $Λ$-hyperon, to be compared with the case of the proton (``spin crisis''). Generally we find that for hadrons with spin 1/2 the parton description, using only probabilities, works much better than for vector particles, since in the former case the non diagonal matrix elements of the hadron spin density matrix are suppressed by a small fact…
By expanding functions of parton fragmentation into a heavy hadron in the inverse of the heavy quark mass $m_Q$ we attempt to factorize them into perturbative- and nonperturbative parts. In our approach the nonperturbative parts can be defined as matrix elements in heavy quark effective theory, the shape of the functions is predicted by perturbative QCD. In this work we neglect effect at order of $m_Q^{-2}$ and calculate the perturbative parts at one-loop level for heavy quark- and gluon fragmentation. We compare our results from leading log approximation with experimental results from $e^+e^-…
We present an analytical next-to-leading order QCD calculation of the partonic cross sections for the process $pp\rightarrow ({\text{jet}} \,h)X$, for which a specific hadron is observed inside a fully reconstructed jet. In order to obtain the analytical results, we assume the jet to be relatively narrow. We show that the results can be cast into a simple and systematic form based on suitable universal jet functions for the process. We confirm the validity of our calculation by comparing to previous results in the literature for which the next-to-leading order cross section was treated entirel…
We present the systematic results for three dimensional fragmentation functions defined via the quark-quark correlator for hadrons with spin 0, 1/2 and 1 respectively. These results are presented in terms of a spin independent part, a vector polarization dependent part and a tensor polarization dependent part. For spin 0 hadrons, only the spin independent part is needed, for spin 1/2 hadron, the polarization independent and vector polarization dependent parts are present, while for spin 1 hadrons, all the three parts exist. We discuss the general properties of these fragmentation functions and…
We review the description of inclusive single unpolarized light hadron production using fragmentation functions in the framework of the factorization theorem. We summarize the factorization of quantities into perturbatively calculable quantities and these universal fragmentation functions, and then discuss some improvements beyond the standard fixed order approach. We discuss the extraction of fragmentation functions for light charged and neutral hadrons using these theoretical tools through global fits to experimental data from reactions at various colliders, in particular from accurate e+e- …
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 compare recent experimental results for one-particle-inclusive processes in deeply inelastic scattering at HERA with theoretical predictions in next-to-leading-order QCD perturbation theory, and study the factorization scale dependence of cross sections and charged multiplicities. In the future, for the HERA machine running at design luminosity, scaling violations of fragmentation functions permit the measurement of the strong coupling constant. We estimate the size of the statistical error of $α_s$ that can be achieved, and study the theoretical error due to the various parton density para…
We investigate the properties of interference fragmentation functions arising from the emission of two leading hadrons inside the same jet for inclusive lepton-nucleon deep-inelastic scattering. Using an extended spectator model for the mechanism of the hadronization, we give a complete calculation and numerical estimates for the examples of a proton-pion pair produced with invariant mass on the Roper resonance, and of two pions produced with invariant mass close to the $ρ$ mass. We discuss azimuthal angular dependence of the leading order cross section to point up favourable conditions for ex…
We present nonperturbative fragmentation functions (FFs) for bottom-flavored ($B$) hadrons both at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the $\overline{\mathrm{MS}}$ factorization scheme with five massless quark flavors. They are determined by fitting all available experimental data of inclusive single $B$-hadron production in $e^+e^-$ annihilation, from the ALEPH, DELPHI, and OPAL Collaborations at CERN LEP1 and the SLD Collaboration at SLAC SLC. The uncertainties in these FFs as well as in the corresponding observables are estimated using t…
The forward-backward asymmetry is an important measurable quantity which can enable independent determination of the neutral-current couplings of fermions. In this paper, we extend the definition of the asymmetry from the partonic level to the hadronic level by calculating this asymmetry of the hadron pair in the semi-inclusive electron position annihilation process. Semi-inclusive implies that a back-to-back jet is also measured in addition to the hadron pair. Due to the limitation of the factorization theorem, we calculate this process up to leading order twist-4 level by applying the collin…
We compute the contributions due to gluon and heavy-quark fragmentation to quarkonium production at large transverse momentum in $\bar p p$ and $p p$ collisions. For inclusive $J/ψ$ production, there is a large contribution from the $g \rightarrow χ_c$ fragmentation. At large $p_T$, this is comparable to the conventional charmonium model prediction via gluon fusion at the ISR and dominates over the latter at the Tevatron energy. This may help to explain, at least partly, the large $J/ψ$ production cross-section recently observed by the CDF experiment. However, the fragmentation contribution to…
We analyse LEP and PETRA data on single inclusive charged hadron cross-sections to establish new sets of Next-to-Leading order Fragmentation Functions. Data on hadro-production of large-$p_{\bot}$ hadrons are also used to constrain the gluon Fragmentation Function. We carry out a critical comparison with other NLO parametrizations.
The dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation, that is the splitting of a high energy parton into a hadronic state and other partons. We review the present schemes to calculate the heavy quark fragmentation functions (FFs) and drive an exact analytical expression of FF which includes most of the kinematical and dynamical properties of the process. Using the perturbative QCD, we calculate the FF for c-quark to split into S-wave D-meson to leading order in the QCD coupling constant. Our result is compared with the current well-known pheno…
Light charged hadron production data in the current fragmentation region at HERA are calculated using next-to-leading order perturbative calculations and fragmentation functions obtained from similar data from e+ e- reactions. General good agreement is found at large photon virtuality Q^2 and intermediate momentum fraction x_p, consistent with fragmentation function universality. The description of the small x_p and Q^2 region is improved by incorporating hadron mass effects.
Factorizing the cross section for single hadron production in $e^+e^-$ annihilations, differential in $z_h$, $P_T$ and thrust, is a highly non trivial task. We have devised a factorization scheme that allows us to recast the $e^+e^- \to hX$ cross section in the convolution of a perturbatively calculable coefficient and a universal Transverse Momentum Dependent (TMD) Fragmentation Function (FF). The predictions obtained from our NLO-NLL perturbative computation, together with a simple ansatz to model the non-perturbative part of the TMD, are applied to the experimental measurements of the BELLE…
We propose a new procedure for parton-to-hadron fragmentation in proton-proton collisions. The hadronization is considered in the parton-parton center-of-mass system and hadrons are assumed to be emitted in the direction of outgoing partons in that frame and then their four-momenta are transformed to the overall center-of-mass system using relevant Lorentz transformations and appropriate distributions are constructed. For heavy hadron production the energy-momentum condition is imposed. In many cases our procedure disagrees with the commonly used rule that rapidity of produced hadron is the sa…
It is shown that the azimuthal dependence of the distribution of hadrons in a quark jet is a probe of the transverse spin of the quark initiating the jet. This results in a new spin-dependent fragmentation function that acts at the twist-2 level. One example of a process where it contributes is semi-inclusive deeply inelastic scattering with a transversely polarized nucleon target but with an {\em unpolarized} electron beam. This process is treated in detail. Another process is the cross section for singly polarized hadron-hadron scattering when two high $p_{\perp}$ hadrons are measured in the…
In the literature it is assumed that the parton to hadron fragmentation function cannot be studied by using the lattice QCD method because of the sum over the (unobserved) outgoing hadronic states. However, in this paper we find that since the hadron formation from the partons can be studied by using the lattice QCD method, the parton to hadron fragmentation function can be studied by using the lattice QCD method by using the LSZ reduction formula for the partonic processes.
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…
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 present a detailed analysis of the use of heavy quark fragmentation into heavy hadrons for testing the heavy quark effective theory through comparison of the measured fragmentation parameters of the $c$ and $b$ quarks. Our analysis is entirely model independent. We interpret the known perturbative evolution in a way useful for exploiting heavy quark symmetry at low energy. We first show consistency with perturbative QCD scaling for measurements done solely with $c$ quarks. We then apply the perturbative analysis and the heavy quark expansion to relate measurements from ARGUS and LEP. We pla…
The gluon fragmentation function of $g \to h_c$ at leading order of strong coupling constant $α_s$ and typical velocity $v$ is calculated in the framework of NRQCD, of which the contributions from both color-singlet and -octet processes are taken into account and hence the result is infrared safe. It is found that the fragmentation probability of a high energy virtual gluon to split into $h_c$ is about $7.1\times 10^{-7}$. The analytic fragmentation function presented in this work can be employed to the study of $h_c$ production in large transverse momentum at hadron colliders, such as Large H…
We study the azimuthal modulations of dihadron fragmentation functions (DiFFs) of a transversely polarised quark using an NJL-jet based model that incorporates the Collins effect for single hadron emission. The DiFFs are extracted as Monte Carlo (MC) averages of corresponding multiplicities using their probabilistic interpretation. To simplify the model and highlight the possible mechanisms that create this modulation, we choose the elementary Collins function to be proportional to the elementary unpolarised fragmentation and a constant probability ($P_{SF}$) for the quark to flip its spin aft…
We review recent progress in the development of an approach valid to any order which unifies the fixed-order DGLAP evolution of fragmentation functions at large x with soft-gluon logarithmic resummation at small x. At leading order, this approach, implemented with the Double Logarithmic Approximation, reproduces exactly the Modified Leading Logarithm Approximation, but it is more complete due to the degrees of freedom given to the quark sector and the inclusion of the fixed-order terms. We find that data from the largest x values to the peak region can be better fitted than with other approach…
We propose the formulation of a dihadron fragmentation function in terms of parton matrix elements. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order (LO) in e+ e- annihilation is shown to factorize into a short distance parton cross section and the long distance dihadron fragmentation function. We also derive the DGLAP evolution equation of this function at leading log. The evolution equation for the non-singlet quark fragmentation function is solved numerically with a simple ansatz for the init…
Semi-inclusive deep inelastic scattering of polarized leptons off hadrons enables one to measure the antisymmetric part of the hadron tensor. For unpolarized hadrons this piece is odd under time reversal. In deep inelastic scattering it shows up as a $\langle \sin ϕ\rangle$ asymmetry for the produced hadrons. This asymmetry can be expressed as the product of a twist-three "hadron $\rightarrow$ quark" distribution function and a time reversal odd twist-two "quark $\rightarrow$ hadron" fragmentation function. This fragmentation function can only be measured for nonzero transverse momenta of the …
We consider dihadron fragmentation functions, describing the fragmentation of a parton in two unpolarized hadrons, and in particular extended dihadron fragmentation functions, explicitly dependent on the invariant mass, $M_h$, of the hadron pair. We first rederive the known results on $M_h$-integrated functions using Jet Calculus techniques, and then we present the evolution equations for extended dihadron fragmentation functions. Our results are relevant for the analysis of experimental measurements of two-particle-inclusive processes at different energies.
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…
We present new sets of pion, kaon, proton and inclusive charged hadron fragmentation functions obtained in NLO combined analyses of single-inclusive hadron production in electron-positron annihilation, proton-proton collisions, and deep-inelastic lepton-proton scattering with either particles identified in the final state. At variance with all previous fits, the present analyses take into account data where hadrons of different electrical charge are identified, which allow to discriminate quark from anti-quark fragmentation functions.
Motivated by the excellent agreement between next-to-leading-order pQCD calculations and the inclusive jet spectra measured by CDF, we cross-check PYTHIA fragmentation functions. The convolution of the measured jet spectra with unmodified PYTHIA fragmentation functions results in reasonable agreement with the PYTHIA charged particle spectrum over the entire p_T range of interest, while there is a sizable disagreement with the measured charged particle spectrum above p_T=30 GeV/c. In an attempt to understand the source of this discrepancy, we introduce a number of increasingly different toy-mod…
We discuss the properties of fragmentation functions arising from the interference of two leading hadrons produced inside the same jet in the current fragmentation region of a hard process. For the case of semi-inclusive Deep Inelastic Scattering (DIS), a proper folding of the cross section, integrated over the azimuthal position of the detected hadrons, produces a factorized form that allows for the extraction of the quark transversity distribution at leading twist. Using an extended spectator model, explicit calculations are shown for the hadron pair being two pions with invariant mass insid…
We give a general overview of the role and interpretation of fragmentation functions in hard processes. Transverse momentum dependence gives rise to time-reversal odd fragmentation functions contributing at leading order. Final state interactions are necessary to have non-zero time reversal odd functions. We present a model calculation for the special case of interference fragmentation functions in two-hadron inclusive lepton hadron scattering.
A combined analysis of the polarization vector of the Lambda baryons produced in DIS processes may give a relevant insight of the hadronization process which governs the transition from partons to physical hadrons and precise indications on the mechanisms of $spin$ transfer from partons to hadrons. We give here a short review of some interesting results.
