Parton-hadron Duality Research Articles

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.

The fragmentation spectrum from space-time reciprocity

Analyzing the single inclusive annihilation spectrum of charged hadrons in e+e− collisions, I confront the hadronization hypothesis of local parton-hadron duality with a systematic resummation of the dependence on the small energy fraction. This resummation is based on the reciprocity between time-like and space-like splitting processes in 4 − 2ϵ-dimensions, which I extend to resum all the soft terms of the cross-section for inclusive jet production. Under the local-parton-hadron duality hypothesis, the resulting distribution of jets essentially determines the spectrum of hadrons as the jet radius goes to zero. Thus I take the resummed perturbative jet function as the non-perturbative fragmentation function with an effective infra-red coupling. I find excellent agreement with data, and comment on the mixed leading log approximation previously used to justify local parton-hadron duality.

Transverse momentum fluctuation under the Tsallis distribution at high energies

We studied the effects of the Tsallis distribution on the transverse momentum fluctuation in high energy collisions. The parton–hadron duality and the Bose–Einstein type correlation between partons were assumed. The fluctuation was calculated in the boost-invariant picture for the expectation value used in the Boltzmann–Gibbs (BG) statistics and for the expectation value used in the Tsallis nonextensive statistics. It was shown that the fluctuation is a function of [Formula: see text] which is the ratio of the inverse temperature to the correlation length. We found the following points: (1) the fluctuation depends on the form of the distribution and depends weakly on the definition of the expectation value used in the statistics, (2) the fluctuation increases as the entropic parameter value of the Tsallis distribution increases, and (3) the variation of the fluctuation as a function of the entropic parameter for the expectation value used in the BG statistics is larger than that for the expectation value used in the Tsallis nonextensive statistics in the wide range of [Formula: see text].

Fragmentation in the ϕ3 theory and the LPHD hypothesis

We present analytic solution of the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation at leading order (LO) in the [Formula: see text] theory in 6 space-time dimensions. If the [Formula: see text] model was the theory of strong interactions, the obtained solution would describe the distribution of partons in a jet. We point out that the local parton-hadron duality (LPHD) conjecture does not work in this hypothetical situation. That is, treatment of hadronisation of shower partons is essential for the description of hadron distributions in jets stemming from proton-proton (pp) collisions at [Formula: see text] TeV and from electron-positron ([Formula: see text]) annihilations at various collision energies. We use a statistical model for the description of hadronisation.

QCD test with the momentum spectra and the second binomial moment R2 using e+e− data

Experimental data on the shape of hadronic momentum spectra are compared to the context of calculations in modified leading log approximation (MLLA), under the assumption of local parton hadron duality (LPHD). Considered are the inclusive momentum spectra and charged particle distributions in the reaction e+e− → hadrons, using the experimental as well as the Monte Carlo data at center of mass energies up to 200 GeV. Values of the second binomial moment R2 obtained from the multiplicity distributions are also studied. Our results are compared with both experimental data from high and low energy e+e−, e−p, and pp experiments and QCD calculations in various theoretical approaches. In general, good agreement is found between the measurements and the corresponding QCD predictions. A quantitative check of LPHD + MLLA has been performed by extracting a value of the strong coupling constant from the corresponding distributions. Possible explanations for all these features will be presented in this paper.

Momentum distribution of charged particles in jets in dijet events and comparison to perturbative QCD predictions

Inclusive momentum distributions of charged particles are measured in dijet events. Events were produced at the AMY detector with a centre of mass energy of 60 GeV. Our results were compared, on the one hand to those obtained from other e+e−, ep as well as CDF data, and on the other hand to the perturbative QCD calculations carried out in the framework of the modified leading log approximation (MLLA) and assuming local parton–hadron duality (LPHD). A fit of the shape of the distributions yields Qeff = 263±13 MeV for the AMY data. In addition, a fit to the evolution of the peak position with dijet mass using all data from different experiments gives Qeff = 226±18 MeV. Next, αs was extracted using the shape of the distribution at the Z0 scale, with a value of 0.118 ± 0.013. This is consistent, within the statistical errors, with many accurate measurements. We conclude that it is the success of LPHD + MLLA that the extracted value of αs is correct. Possible explanations for all these features will be presented in this paper.

Hadronization scheme dependence of long-range azimuthal harmonics in high energy p + A reactions

We compare the distortion effects of three popular final-state hadronization schemes. We show how hadronization modifies the initial-state gluon correlations in high energy p + A collisions. The three models considered are (1) LPH: local parton–hadron duality, (2) CPR: collinear parton–hadron resonance independent fragmentation, and (3) LUND: color string hadronization. The strong initial-state azimuthal asymmetries are generated using the GLVB model for non-abelian gluon bremsstrahlung, assuming a saturation scale Qsat=2 GeV. Long-range elliptic and triangular harmonics for the final hadron pairs are compared based on the three hadronization schemes. Our analysis shows that the process of hadronization causes major distortions of the partonic azimuthal harmonics for transverse momenta at least up to pT=3 GeV. In particular, they appear to be greatly reduced for pT<1÷2 GeV.

Forward hadron productions in high energyppcollisions from a Monte-Carlo generator for color glass condensate

We develop a Monte Carlo event generator based on the combination of a parton production formula including the effects of parton saturation (called the DHJ formula) and a hadronization process due to the Lund string fragmentation model. This event generator is designed for the description of hadron productions at forward rapidities and in a wide transverse momentum range in high-energy proton-proton collisions. We analyze transverse momentum spectra of charged hadrons as well as identified particles, including pion, kaon, and (anti)proton at RHIC energy and ultraforward neutral pion spectra from the LHCf experiment. We compare our results to those obtained in other models based on parton-hadron duality and fragmentation functions.

Centrality and transverse momentum dependencies of minijets and hadrons in Au-Au collisions

In the study of hadron production in Au-Au collisions at RHIC minijets play an important role in generating shower partons in the intermediate \ppt\ region. Momentum degradation of the hard and semihard partons as they traverse the inhomogeneous medium at various azimuthal angles results in a complicated convolution of geometrical, nuclear and dynamical factors that cannot usually be described in a transparent way. In this work a compact formula is found that represents the inclusive distributions of minijets of any parton type at the surface of the medium for any collision centrality. They take into account the contributions from all initiating partons created at any point in the medium. By comparing with the case of no energy loss, a ratio has been determined that is analogous to the nuclear modification factor for minijets. Phenomenological reality of such distributions is examined by calculating the hadronization of the minijets in the recombination model. Good fits of the data on pion, kaon and proton production throughout the intermediate \ppt\ region have been obtained by adjusting the parameters controlling the magnitude of the thermal partons and the degradation rates of the semihard partons. The result gives support to the minijet spectra at any centrality on the one hand, and the hadronization procedure used on the other. An important property made manifest in this study is that quarks and gluons must not lose energy in the same way because the partons form mesons and baryons differently by recombination and the momenta of quarks and gluons must be degraded at different rates in order to reproduce the experimental pion and proton spectra. This is a feature that renders invalid the notion of parton-hadron duality or other hadronization schemes based on similar ideas.

Extraction of [formula omitted] from deep inelastic scattering at large x

We present an analysis of the role of the running coupling constant at the intersection of perturbative and non-perturbative QCD. Although the approaches that have been considered so far in these two regimes appear to be complementary to each other, a unified description might be derived through the definition of the effective coupling, as they both provide ways of analyzing its freezing at low values of the scale. We extract the effective coupling from all available experimental data on the unpolarized structure function of the proton, F2p, at large values of Bjorken x, including the resonance region. We suggest that parton–hadron duality observed in this region can be explained if non-perturbative effects are included in the coupling constant. The outcome of our analysis is a smooth transition from perturbative to non-perturbative QCD physics, embodied in the running of the coupling constant at intermediate scales.

EXPLICIT MODEL REALIZING PARTON–HADRON DUALITY

We present a model that realizes both resonance-Regge (Veneziano) and parton–hadron (Bloom–Gilman) duality. We first review the features of the Veneziano model and we discuss how parton–hadron duality appears in the Bloom–Gilman model. Then we review limitations of the Veneziano model, namely that the zero-width resonances in the Veneziano model violate unitarity and Mandelstam analyticity. We discuss how such problems are alleviated in models that construct dual amplitudes with Mandelstam analyticity (so-called DAMA models). We then introduce a modified DAMA model, and we discuss its properties. We present a pedagogical model for dual amplitudes and we construct the nucleon structure function F2(x, Q2). We explicitly show that the resulting structure function realizes both Veneziano and Bloom–Gilman duality.

Light-cone QCD plasma

We deduce the maximum-entropy state of partons created in proton-proton and nucleus-nucleus collisions. This state is characterized by a distribution function $n(x,{p}_{\ensuremath{\perp}})$ depending on the light-cone fraction $x$ and the transverse momentum ${p}_{\ensuremath{\perp}}$ of forward or backward particles, respectively. The mean transverse momentum $⟨{p}_{\ensuremath{\perp}}⟩$ determines the single parameter of the maximum entropy distribution which is constrained by the sum of all light-cone momentum fractions being unity. The total multiplicity is related to the transverse area of the colliding Lorentz-contracted hadrons. Assuming parton-hadron duality, we can compare the model to data from RHIC and LHC.

Three-particle correlations in QCD jets and beyond

In this paper, we present a detailed study of three-particle correlations in quark and gluon jets. We give theoretical results for this observable in the double logarithmic approximation and the modified leading logarithmic approximation. In both resummation schemes, we use the formalism of the generating functional and solve the evolution equations analytically from the steepest descent evaluation of the one-particle distribution. In addition, in this paper we include predictions beyond the limiting spectrum approximation and study this observable near the hump of the single inclusive distribution. We thus provide a further test of the local parton hadron duality and make predictions for the LHC. The computation of higher rank correlators is presented in the double logarithmic approximation and shown to be rather cumbersome.

Three-particle correlations in QCD parton showers

Three-particle correlations in quark and gluon jets are computed for the first time in perturbative QCD. We give results in the double logarithmic approximation and the modified leading logarithmic approximation. In both resummation schemes, we use the formalism of the generating functional and solve the evolution equations analytically from the steepest descent evaluation of the one-particle distribution. We thus provide a further test of the local parton hadron duality and make predictions for the LHC.

Transversity form factors of the pion in chiral quark models

The transversity form factors of the pion, involving matrix elements of bilocal tensor currents, are evaluated in chiral quark models, both in the local Nambu--Jona-Lasinio with the Pauli-Villars regularization, as well as in nonlocal models involving momentum-dependent quark mass. After suitable QCD evolution the agreement with recent lattice calculations is very good, in accordance to the fact that the spontaneously broken chiral symmetry governs the dynamics of the pion. Meson dominance of form factors with expected meson masses also works properly, conforming to the parton-hadron duality in the considered process.

Scaled momentum distributions of charged particles in dijet photoproduction at HERA

The scaled momentum distributions of charged particles in jets have been measured for dijet photoproduction with the ZEUS detector at HERA using an integrated luminosity of 359 pb-1. The distributions are compared to predictions based on perturbative QCD carried out in the framework of the modified leading-logarithmic approximation (MLLA) and assuming local parton-hadron duality (LPHD). The universal MLLA scale, Lambda_eff, and the LPHD parameter, kappa^ch, are extracted.

NA60 results on thermal dimuons

The NA60 experiment at the CERN SPS has measured muon pairs with unprecedented precision in 158 A GeV In–In collisions. A strong excess of pairs above the known sources is observed in the whole mass region 0.2<M<2.6 GeV. The mass spectrum for M<1 GeV is consistent with a dominant contribution from π + π −→ρ→μ + μ − annihilation. The associated ρ spectral function shows a strong broadening, but essentially no shift in mass. For M>1 GeV, the excess is found to be prompt, not due to enhanced charm production, with pronounced differences to Drell–Yan pairs. The slope parameter T eff associated with the transverse momentum spectra rises with mass up to the ρ, followed by a sudden decline above. The rise for M<1 GeV is consistent with radial flow of a hadronic emission source. The seeming absence of significant flow for M>1 GeV and its relation to parton–hadron duality is discussed in detail, suggesting a dominantly partonic emission source in this region. A comparison of the data to the present status of theoretical modeling is also contained. The accumulated empirical evidence, including also a Planck-like shape of the mass spectra at low p T and the lack of polarization, is consistent with a global interpretation of the excess dimuons as thermal radiation. We conclude with first results on ω in-medium effects.

Elliptic flow of gluon matter in ultrarelativistic heavy-ion collisions

Employing a perturbative QCD based parton cascade we calculate the elliptic flow ${v}_{2}$ and its transverse momentum dependence ${v}_{2}({p}_{T})$ for the gluon matter created in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV. To make comparisons with the experimental data at the BNL Relativistic Heavy Ion Collider (RHIC), parton-hadron duality is assumed. We find that whereas the integrated ${v}_{2}$ matches the experimental data, the gluon (or pion) ${v}_{2}({p}_{T})$ is about 20--50% smaller than the experimental data. Hadronization via gluon fragmentation and quark recombination seems to be the key to explaining the necessary jump of ${v}_{2}({p}_{T})$ from the partonic to the hadronic phase. We also show that the elliptic flow values moderately depend on the chosen freezeout condition, which will thus constrain the shear viscosity to the entropy density ratio of the quark gluon plasma created at RHIC.

Pion electromagnetic form factor, perturbative QCD, and large-NcRegge models

We present a construction of the pion electromagnetic form factor where the transition from large-N{sub c} Regge vector-meson dominance models with infinitely many resonances to perturbative QCD is built in explicitly. The construction is based on an appropriate assignment of residues to the Regge poles, which fulfills the constraints of the parton-hadron duality and perturbative QCD. The model contains a slowly falling off nonperturbative contribution, which dominates over the perturbative QCD radiative corrections for the experimentally accessible momenta. The leading order and next-to-leading order calculations show a converging pattern that describes the available data within uncertainties, while the onset of asymptotic QCD takes place at extremely high momenta Q{approx}10{sup 3}-10{sup 4} GeV. The method can be straightforwardly extended to study other form factors where the perturbative QCD result is available.

Two-particle momentum correlations in jets produced inpp¯collisions ats=1.96 TeV

We present the first measurement of two-particle momentum correlations in jets produced in $p\bar p$ collisions at $\sqrt{s}=1.96$ TeV. Results are obtained for charged particles within a restricted cone with an opening angle of 0.5 radians around the jet axis and for events with dijet masses between 66 and 563 GeV/c$^{2}$. A comparison of the experimental data to theoretical predictions obtained for partons within the framework of resummed perturbative QCD in the next-to-leading log approximation (NLLA) shows that the parton momentum correlations survive the hadronization stage of jet fragmentation, giving further support to the hypothesis of local parton-hadron duality. The extracted value of the NLLA parton shower cutoff scale $Q_\mathit{eff}$ set equal to $\Lambda_\mathit{QCD}$ is found to be $(1.4^{+0.9}_{-0.7})\times 100$ MeV.