Quark Fragmentation Research Articles

Role of Cahn and Sivers effects in deep inelastic scattering

The role of intrinsic $\bfk_\perp$ in inclusive and semi-inclusive Deep Inelastic Scattering processes ($\ell p \to \ell h X$) is studied with exact kinematics within QCD parton model at leading order; the dependence of the unpolarized cross section on the azimuthal angle between the leptonic and the hadron production planes (Cahn effect) is compared with data and used to estimate the average values of $k_\perp$ both in quark distribution and fragmentation functions. The resulting picture is applied to the description of the weighted single spin asymmetry $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ recently measured by the HERMES collaboration at DESY; this allows to extract some simple models for the quark Sivers functions. These are compared with the Sivers functions which succeed in describing the data on transverse single spin asymmetries in $\pup p \to \pi X$ processes; the two sets of functions are not inconsistent. The extracted Sivers functions give predictions for the COMPASS measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent preliminary data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed and found to be small. Predictions for $A_{UT}^{\sin(\phi_K - \phi_S)}$ for kaon production at HERMES are also given.

RECENT HERMES RESULTS ON MESON PRODUCTION

An overview is given of selected recent HERMES results involving hadron production. Topics including transversity, hard exclusive production of pion pairs, observation of the Θ+ pentaquark state and quark fragmentation in nuclei will be presented.

High pT hadron–hadron correlations

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 and singlet quark fragmentation function and the gluon fragmentation function are solved numerically with the initial condition taken from event generators. Modifications to the dihadron fragmentation function from higher twist corrections in DIS off nuclei are computed. Results are presented for the cases of physical interest.

Fragmentation production of triply heavy baryons at the CERN LHC

The triply heavy baryons in the standard model formed in direct $c$ and $b$ quark fragmentation are the $\Omega_{ccc}$, $\Omega_{ccb}$, $\Omega_{cbb}$ and $\Omega_{bbb}$ baryons. We calculate their fragmentation functions in leading order of perturbative QCD. The universal fragmentation probabilities fall within the range of $10^{-5}-10^{-7}$.We also evaluate their cross section at the LHC ($\sqrt{s}=14$ TeV) using next-to-leading order matrix elements for heavy quark-antiquark pair production. We present the differential cross sections as functions of the transverse momentum as well as the total cross sections. They range from a few nb to a few pb.

RECENT HERMES RESULTS ON MESON PRODUCTION

An overview is given of selected recent HERMES results involving meson production. Topics including single and double spin asymmetries in semi-inclusive and exclusive meson production, hard exclusive production of pion pairs and quark fragmentation in nuclei will be presented.

Fragmentation in [formula omitted] processes

I study bottom quark fragmentation in the Standard Model Higgs decay H → b b ¯ , within the framework of perturbative fragmentation functions. I resum large collinear logarithms ln ( m H 2 / m b 2 ) in the next-to-leading logarithmic (NLL) approximation, using the DGLAP evolution equations. Soft contributions to the MS ¯ coefficient function and to the initial condition of the perturbative fragmentation function are resummed to NLL accuracy as well. The implementation of collinear and soft resummation has a relevant impact on the b energy spectrum, which exhibits a milder dependence on factorization and renormalization scales and on the Higgs mass. I present some predictions on the energy distribution of b-flavoured hadrons in Higgs decay, making use of data from LEP and SLD experiments to fit a few hadronization models. I also compare the phenomenological results yielded by a few processes recently provided with NLL collinear and soft resummations.

Scaling violations of quark and gluon jet fragmentation functionsin ${\rm e^ + e^-}$ annihilations at $\sqrt s = 91.2$ and 183-209 GeV

Flavour inclusive, udsc and b fragmentation functions in unbiased jets, and flavour inclusive, udsc, b and gluon fragmentation functions in biased jets are measured in e+e- annihilations from data collected at centre-of-mass energies of 91.2, and 183-209 GeV with the OPAL detector at LEP. The unbiased jets are defined by hemispheres of inclusive hadronic events, while the biased jet measurements are based on three-jet events selected with jet algorithms. Several methods are employed to extract the fragmentation functions over a wide range of scales. Possible biases are studied in the results are obtained. The fragmentation functions are compared to results from lower energy e+e- experiments and with earlier LEP measurements and are found to be consistent. Scaling violations are observed and are found to be stronger for the fragmentation functions of gluon jets than for those of quarks. The measured fragmentation functions are compared to three recent theoretical next-to-leading order calculations and to the predictions of three Monte Carlo event generators. While the Monte Carlo models are in good agreement with the data, the theoretical predictions fail to describe the full set of results, in particular the b and gluon jet measurements.

Dihadron fragmentation function and its evolution

Dihadron fragmentation functions and their evolution are studied in the process of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. Under the collinear factorization approximation and facilitated by the cut-vertex technique, the two hadron inclusive cross section at leading order is shown to factorize into a short distance parton cross section and a long distance dihadron fragmentation function. We provide the definition of such a dihadron fragmentation function in terms of parton matrix elements and derive its Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation at leading log. The evolution equation for the nonsinglet quark fragmentation function is solved numerically with a simple ansatz for the initial condition and results are presented for cases of physical interest.

Dihadron fragmentation functions and high pT hadron–hadron correlations

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 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 initial condition and results are presented for cases of physical interest.

A note on charmed and bottomed pentaquark production by fragmentation

H1 Collaboration recently observed the charmed pentaquark. In this short Letter, 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 Θc0, based on the known fragmentation probabilities of charm quark into mesons and baryons: f(c¯→Θc0)≃(2–7)×10−3. Similarly, we also obtain the fragmentation probability for bottom quark into Θb+: f(b¯→Θb+)≃(5–20)×10−3. We also estimate the prospect of observing Θc0 and Θb+ at HERA, LEP, and Tevatron.

SINGLE SPIN ASYMMETRIES FOR LOW ENERGY π±'S AND FOR ρ MESONS AT RHIC ENERGIES

The production asymmetry of both π and ρ mesons in the reaction p↑p→hX is calculated in a two-component model in which hadrons are produced by a nonperturbative recombination process and by fragmentation of quarks in the final state. Thomas precession in the recombination mechanism seems to be responsible of the single spin asymmetry. We obtain a good description of experimental data. Predictions of single spin asymmetries for ρ production at RHIC energies are presented.

New formalism for QCD parton showers

We present a new formalism for parton shower simulation of QCD jets, which incorporates the following features: invariance under boosts along jet axes, improved treatment of heavy quark fragmentation, angular-ordered evolution with soft gluon coherence, more accurate soft gluon angular distributions, and better coverage of phase space. It is implemented in the new HERWIG++ event generator.

Quark fragmentation to π±, π0, K±, p and [formula omitted] in the nuclear environment

The influence of the nuclear medium on lepto-production of hadrons was studied in the HERMES experiment at DESY in semi-inclusive deep-inelastic scattering of 27.6 GeV positrons off deuterium, nitrogen and krypton targets. The differential multiplicity for krypton relative to that of deuterium has been measured for the first time for various identified hadrons (π+, π−, π0, K+, K−, p and p̄) as a function of the virtual photon energy ν, the fraction z of this energy transferred to the hadron, and the hadron transverse momentum squared pt2. The multiplicity ratio is strongly reduced in the nuclear medium at low ν and high z, with significant differences among the various hadrons. The distribution of the hadron transverse momentum is broadened towards high pt2 in the nuclear medium, in a manner resembling the Cronin effect previously observed in collisions of heavy ions and protons with nuclei.

Multiplicities and particle production at LEP

Recent results on hadron multiplicities in heavy and light quark fragmentation above the Z peak (OPAL), and multiplicity distribution analysis (L3) and inclusive f_1 production (DELPHI) in hadronic Z decays are presented.

Inclusive analysis of the b quark fragmentation function in Z decays at LEP

A study of b quark hadronisation is presented using inclusively reconstructed B hadrons in about four million hadronic Z decays recorded in 1992-2000 with the OPAL detector at LEP. The data are compared to different theoretical models, and fragmentation function parameters of these models are fitted. The average scaled energy of weakly decaying B hadrons is determined to be <xe>=0.7193+-0.0016(stat)+0.0036-0.0031(syst)

Factorization approach for inclusive production of doubly heavy baryon

We study inclusive production of doubly heavy baryon at a e+e− collider and at hadron colliders through fragmentation. We study the production by factorizing nonpertubative and perturbative effects. In our approach the production can be thought as a two-step process: a pair of heavy quarks can be produced perturbatively and then the pair is transformed into the baryon. The transformation is nonperturbative. Since a heavy quark moves with a small velocity in the baryon in its rest frame, we can use NRQCD to describe the transformation and perform a systematic expansion in the small velocity. At the leading order we find that the baryon can be formed from two states of the heavy-quark pair, one state is with the pair in 3S1 state and in color 3̄, another is with the pair in 1S0 state and in color 6. Two matrix elements are defined for the transformation from the two states, their perturbative coefficients in the contribution to the cross section at a e+e− collider and to the function of heavy quark fragmentation are calculated. Our approach is different than previous approaches where only the pair in 3S1 state and in color 3̄ is taken into account. Numerical results for e+e− colliders at the two B-factories and for hadronic colliders LHC and Tevatron are given.

Fragmentation of quarks and gluuons

Experimental results on the hadronisation process under special consideration of the differences between quark and gluon fragmentation are presented.

Multiplicities, fluctuations and correlations

The recent results on hadron multiplicities in heavy and light quark fragmentation, multiplicity local fluctuations and multiparticle correlations submitted to the Conference are reviewed.

SPIN ALIGNMENT OF VECTOR MESON IN HIGH ENERGY REACTIONS

The recent data on the polarization of vector meson at LEP show that the vector mesons favor the helicity zero state. We calculate the helicity density matrix of vector meson which contains a polarized fragmenting quark by adding the spin of the fragmenting quark and that of the antiquark created in the fragmentation. The data at LEP imply a significant polarization for the antiquark in the opposite direction as that of the fragmenting quark. We extend the calculations to other reactions and make predictions for vector mesons in deeply inelastic lepton-nucleon scatterings and polarized pp collisions.

Multiple parton scattering in nuclei: beyond helicity amplitude approximation

Multiple parton scattering and induced parton energy loss in deeply inelastic scattering (DIS) off heavy nuclei is studied within the framework of generalized factorization in perturbative QCD with a complete calculation beyond the helicity amplitude (or soft bremsstrahlung) approximation. Such a calculation gives rise to new corrections to the modified quark fragmentation functions. The effective parton energy loss is found to be reduced by a factor of 5/6 from the result of helicity amplitude approximation.