Gluon Fragmentation Functions Research Articles

Bc meson production at the Tevatron revisited

CDF recently measured the quantity σ(B c +) σ(B +) BR(B c +→J/ψℓ +ν) BR(B +→J/ψK +) , from which we determine the ratio σ(B c +) σ( b ̄ ) to be (2.08 +1.06 −0.95)×10 −3. In this note, we show that the ratio σ(B c +) σ( b ̄ ) obtained by dividing the σ( B c +) by the leading order σ( b ̄ ) is consistent with this derived CDF measurement. We calculate the cross section σ( B c +) using the perturbative QCD fragmentation functions of Braaten, Cheung, and Yuan and the corresponding induced gluon fragmentation functions, with the charm-quark mass m c as a parameter. We also estimate the parameter m c from the CDF data and then predict the production rate at RunII.

Measurement of the quark and gluon fragmentation functions in Z $^0$ hadronic decays

The transverse, longitudinal and asymmetric components of the fragmentation function are measured from the inclusive charged particles produced in $e^+e^-$ collisions at LEP. As in deep inelastic scattering, these data are important for tests of QCD. The transverse $\sigma_T$ and longitudinal $\sigma_L$ components of the total hadronic cross section $\sigma_{tot}$ are evaluated from the measured fragmentation functions. They are found to be $\sigma_T/\sigma_{tot}=0.949\pm 0.001(stat.)\pm 0.007(syst.)$ and $\sigma_L/\sigma_{tot}=0.051\pm 0.001(stat.)\pm 0.007(syst.)$ respectively. The strong coupling constant is calculated from $\sigma_L/\sigma_{tot}$ in next-to-leading order of perturbative QCD, giving \[ \alpha_s(M_Z)=0.120\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale) . \] Including non-perturbative power corrections leads to \[ \alpha_s(M_Z)=0.101\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale) . \] The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity, \[ \langle n^{ch}\rangle = 21.21 \pm 0.01(stat.)\pm 0.20(syst.) \] The fragmentation functions and multiplicities in $b\overline{b}$ and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated.

Measurement of the quark and gluon fragmentation functions in Z

Measurement of the quark and gluon fragmentation functions in Z

Investigation of the splitting of quark and gluon jets

The splitting processes in identied quark and gluon jets are investigated using longitudinal and transverse observables. The jets are selected from symmetric three-jet events measured in Z decays with the Delphi detector in 1991-1994. Gluon jets are identied using heavy quark anti-tagging. Scaling violations in identied gluon jets are observed for the rst time. The scale energy dependence of the gluon fragmentation function is found to be about two times larger than for the corresponding quark jets, consistent with the QCD expectation CA=CF . The primary splitting of gluons and quarks into subjets agrees with fragmentation models and, for specic regions of the jet resolution y, with NLLA calculations. The maximum of the ratio of the primary subjet splittings in quark and gluon jets is 2:77 0:11 0:10. Due to non-perturbative eects, the data are below the expectation at small y. The transition from the perturbative to the non-perturbative domain appears at smaller y for quark jets than for gluon jets. Combined with the observed behaviour of the higher rank splittings, this explains the relatively small multiplicity ratio between gluon and quark jets.

Quark and gluon fragmentation functions into photons

The fragmentation functions of quarks and gluons into photons are studied beyond the Leading Logarithm approximation. We address the nature of the initial conditions of the evolution equation solutions and study problems related to factorization scheme invariance. The possibility of measuring these distributions in LEP experiments is discussed, and a comparison with existing data is made.

Quark and gluon fragmentation functions into photons

The fragmentation functions of quarks and gluons into photons are studied beyond the Leading Logarithm approximation. We address the nature of the initial conditions of the evolution equation solutions and study problems related to factorization scheme invariance. The possibility of measuring these distributions in LEP experiments is discussed, and a comparison with existing data is made.

Order αs( Q2) QCD corrections to the polarised e+e− → ΛX

The importance of polarised gluons fragmenting into Λ in polarised e + e − annihilation is discussed using the Altarelli-Parisi evolution equations satisfied by the quark and gluon fragmentation functions. In this context, the polarised fragmentation function g l Λ(x, Q 2) appearing in the cross section is discussed within the parton model. We relate this fragmentation function to the quark, anti-quark and gluon fragmentation functions and also find the QCD corrections to order α s .

The polarised Λ production in QCD

The Q 2 evolution of polarised parton fragmentation functions is discussed using the Altarelli-Parisi evolution equations. The first moments of both the polarised quark and gluon fragmentation functions are shown to behave in a similar fashion at very high energies. This analysis is applicable to any hard processes involving the production of polarised hadrons. The polarised Λ hyperon production in e + e − annihilation where this can be realised is considered. We present complete α s ( Q 2) corrections to the asymmetries discussed in the paper of Burkardt and Jaffe which demonstrates the extraction of various polarised fragmentation functions. To this order, these corrections are found to be scheme dependent similar to that of structure functions.

Dimensional regularization in quarkonium calculations

Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed that allows dimensional regularization to be used consistently to regularize the infrared and ultraviolet divergences that arise in these perturbative calculations. We illustrate the method by calculating the leading color-octet terms and the leading color-singlet terms in the gluon fragmentation functions for arbitrary quarkonium states. We resolve a discrepancy between two previous calculations of the gluon fragmentation functions for the spin-triplet P-wave quarkonium states.

Inclusive hadron production in photon-photon collisions at next-to-leading order.

We study inclusive charged-hadron production in collisions of quasireal photons at NLO in perturbative QCD, using fragmentation functions recently extracted from PEP and LEP1 data. We superimpose the direct (DD), single-resolved (DR), and double-resolved (RR) gamma-gamma channels. First, we confront existing data taken by TASSO at PETRA and by MARK II at PEP with our NLO calculations. We also make comparisons with the neutral-kaon to charged-hadron ratio measured by MARK II. Then, we present NLO predictions for LEP2, a next-generation e+e- linear collider (NLC) in the TESLA design, and a Compton collider obtained by converting a NLC. We analyze transverse-momentum and rapidity spectra with regard to the scale dependence, the interplay of the DD, DR, and RR components, the sensitivity to the gluon density in the resolved photon, and the influence of gluon fragmentation. It turns out that the inclusive measurement of small-p_T hadrons at a Compton collider would greatly constrain the gluon density of the photon and the gluon fragmentation function.

Pion and kaon production in e+e- and ep collisions at next-to-leading order.

We present new sets of fragmentation functions for charged pions and kaons, both at leading and next-to-leading order. They are fitted to data on inclusive charged-hadron production in $e^+e^-$ annihilation taken by TPC at PEP ($\sqrt s=29$~GeV) and to similar data by ALEPH at LEP, who discriminated between events with charm, bottom, and light- flavour fragmentation in their charged-hadron sample. We treat all partons independently and to properly incorporate the charm and bottom thresholds. Due to the sizeable energy gap between PEP and LEP, we are sensitive to the scaling violation in the fragmentation process, which allows us to extract a value for the asymptotic scale parameter of QCD, $\Lambda$. Recent data on inclusive charged-hadron production in tagged three-jet events by OPAL and similar data for longitudinal electron polarization by ALEPH allow us to pin down the gluon fragmentation functions. Our new fragmentation functions lead to an excellent description of a multitude of other $e^+e^-$ data on inclusive charged-hadron production, ranging from $\sqrt s=5.2$~GeV to LEP energy. In addition, they agree nicely with the transverse-momentum spectra of single charged hadrons measured by H1 and ZEUS in photoproduction at the $ep$ collider HERA, which represents a nontrivial check of the factorization theorem of the QCD-improved parton model.

Measurement of the longitudinal, transverse and asymmetry fragmentation functions at LEP

The fragmentation function for the process e+e−→h+X, whereh represents a hadron, may be decomposed into transverse, longitudinal and asymmetric contributions by analysis of the distribution of polar production angles. A number of new tests of QCD have been proposed using these fragmentation functions, but so far no data have been published on the separate components. We have performed such a separation using data on charged particles from hadronic Z0 decays atOpal, and have compared the results with the predictions of QCD. By integrating the fragmentation functions, we determine the average charged particle multiplicity to be\(\overline {n_{ch} } = 21.05 \pm 0.20\). The longitudinal to total cross-section ratio is determined to be σL/σtot=0.057±0.005. From the longitudinal fragmentation function we are able to extract the gluon fragmentation function. The connection between the asymmetry fragmentation function and electroweak asymmetrics is discussed.

Surprises from quarkonium decay into photons

The perturbative QCD approach to quarkonium decay into a photon and hadrons is reconsidered. It is shown that a consistent treatment within perturbative QCD calls for the introduction of a fragmentation contribution which has been neglected so far. The ensuing phenomenological implications are discussed, and, in particular, the possibility of measuring the gluon fragmentation function of the photon is addressed. *To appear in the proceedings of the workshop QCD94, Montpellier, July '94.

Scaling violation in e +e − fragmentation functions: QCD evolution, hadronization and heavy quark mass effects

Test of QCD in the process e +e − → hX, where h is any hadron species, or any charged hadron, are proposed, concentrating on the following topics: decomposition of the total inclusive cross section into transverse, longitudinal and asymmetric parts; extraction of the gluon fragmentation function from the longitudinal part; flavour sum rules for the asymmetric part; power corrections due to quark masses and hadronization; measurement of α s from a next-to-leading order analysis of scaling violation. We conclude that a number of novel tests can be performed using the very high statistics available at LEP, and that a comparison between LEP and lower-energy data, together with information on heavy quark fragmentation and some model-dependent assumptions about hadronization, could provide a useful measurement of α s.

Bc meson productions via induced gluon fragmentation

Glouns cannot directly fragment into B c mesons until at order α s 3. However, the Altarelli-Parisi evolution of the b- quark fragmentation functions D b→B c (Z) and D b→B c ∗ (Z) from the heavy quark mass scales up to the collider energy scale Q can induce the gluon fragmentation functions D g→B c (Z) and D g→B c ∗ (Z) , respectively, at the order α s 3 log ( Q/ m b, c ) through the gluon splitting g→ b . We will determine these induced gluon fragmentation functions. The B c meson productions due to the induced gluon fragmentation will be evaluated and compared to the productios by the direct b- quark fragmentation. The contribution from the induced gluon fragmentation is found to be a fairly large portion of the total B c and B c ∗ meson productions, and therefore cannot be ignored.

EXTRACTING GLUON FRAGMENTATION FUNCTIONS IN HADRON-HADRON COLLISIONS

Two methods for extracting gluon fragmentation functions in π±p, [Formula: see text] and pp collisions are proposed. The only inputs are valence-quark distribution functions which we know much better than other structure functions and fragmentation functions. So better extraction of gluon fragmentation functions can be obtained.

Scheme invariant higher order QCD predictions for large pT photoproduction reactions

Higher order QCD corrections for large p T photoproduction are calculated. The ambiguity in the choice of the QCD large scales is dealt with using various algorithms, in particular the principle of minimal sensitivity. The optimized predictions are then compared with experiment. It is shown that photoproduction provides good tests of QCD and allows us to determine the value of Λ QCD as well as the gluon fragmentation function.

Photoproduction of charged hadrons at large transverse momenta

A quantitative test of QCD from high energy photoproduction of large transverse momentum charged hadrons, using incident γ energies between 50 and 150 GeV, is presented. The inclusive hadron P 1 and P t distributions show a clear excess over the VDM contribution. This excess is found to be in good agreement with second-order QCD calculations. This agreement does not depend critically on the choice of the gluon fragmentation function, and is observed over the large kinematical domain covered by this experiment.

A method for extracting gluon-fragmentation functions from jet-events

A simple algorithm to extract gluon fragmentation functions from two- and three-jet events ine+e−-annihilation is discussed.

Large- Et processes as a main source of hadrons at very high energies

The production of large- q t gluon jets in very-high-energy hadron collisions near the center of the rapidity plateau is studied in perturbative QCD. It is shown that at s → ∞ the processes with q t ∼ Λ exp[1.26( ln s) 1 2 ] become the main source of secondary hadrons. The inclusive cross sections dσ jet dy dq t 2 , the multiplicity distribution dn jet dy and the transverse energy distribution dE t dy are calculated at SPS collider energy. The hadron spectrum dσ h dp t 2 is obtained using a reasonable gluon fragmentation function. It appears to be in good agreement with the recent collider data.