Heavy Quark Fragmentation Research Articles

A fixed-order calculation of the heavy-quark fragmentation function in e+e− collisions

We use a recently completed O(α s 2) fixed-order calculation of the heavy-flavour production cross section in e + e − collisions to compute the heavy-quark fragmentation function. We fit the result of our calculation, convoluted with a Peterson fragmentation function, to available data for charm production, and thus obtain a value for the parameter ϵ in the Peterson function. We discuss the relevance of mass effects and of subleading terms in our calculation.

Second stage string fragmentation model

A string model, advocated by Bowler, provides a physical and intuitive picture of heavy quark fragmentation. When supplemented by an ad hoc factor of $(1\ensuremath{-}z),$ to suppress fragmentation near $z=1,$ it supplies an excellent fit to the data. We extend Bowler's model by accounting for the further decay of the massive mesonic states produced by the initial string breaking. We find that each subsequent string break and cascade decay beyond the first, introduces a factor of $(1\ensuremath{-}z).$ Furthermore we find that including a finite mass for the quarks, which pop out of the vacuum and split the string, forces the first string breaking to produce massive states requiring further decay. This sequence terminates at the second stage of fragmentation where only relatively ``light'' heavy meson systems are formed. Thus we naturally account for the phenomenologically required factor of $(1\ensuremath{-}z).$ We also predict that the ratio of (primary) fragments vector/(vector plus scalar) should be 0.61. Our second stage string fragmentation model provides an appealing picture of heavy quark fragmentation.

THE HEAVY QUARK FRAGMENTATION FUNCTION AND THE MULTIPLICITY DIFFERENCE BETWEEN HEAVY AND LIGHT QUARK HADRONIC EVENTS IN e+e- ANNIHILATION IN THE LONGITUDINAL PHASE SPACE MODEL

The heavy quark fragmentation function and the multiplicity difference between heavy and light quark hadronic events are explained in a unified framework, namely the longitudinal phase space model. Good agreement of the predictions with data has been achieved.

Relativistic and binding energy corrections to heavy quark fragmentation to polarised quarkonium

Abstract We calculate the fragmentation function for a charm quark to decay inclusively into transversely and longitudinally polarised J / ψ , including relativistic and binding energy corrections in powers of the quark relative velocity v . We use these fragmentation functions to calculate the asymmetry in the angular distribution of leptons produced in the subsequent decay of J / ψ . We point out that the inclusion of the said corrections reduces this asymmetry from 5% to about 2%.

Resolved Photoproduction of J/ψ at HERA**The project supported by National Natural Science Foundation of China

The J/ψ photoproduction via resolved photon process at HERA is studied. It turns out that the J/ψ production is dominated by the leading order production process in low pt range (pt < 4 GeV), while in the high pt range (pt > 4 GeV), it is dominated by the fragmentation processes. The difference of J/ψ cross section caused by using GRV and DO photon structure functions is large, especially in the large negative rapidity range. Hence it is possible to use the J/ψ photoproduction process to probe the parton distribution of photon and proton, as well as to test the gluon and heavy quark fragmentation of J/ψ from the perturbative QCD.

Fragmentation functions for baryons in a quark-diquark model

A perturbative QCD calculation of heavy flavor quark fragmentation into heavy flavor baryons is developed along the lines of corresponding heavy meson models. The non-perturbative formation of the baryon is accomplished by implementing the quark-diquark model of the baryons. Diquark color form factors are used to enable the integration over the virtual heavy quark momentum. The resulting spin independent functions for charmed and bottom quarks to fragment into charmed and bottom baryons with spin 1/2 and 3/2 are compared with recent data. Predictions are made for the spin dependent fragmentation functions as well, particularly for the functions $\hat{g}_1$ and $\hat{h}_1$ in the case of spin 1/2 baryons.

Perturbative prediction for parton fragmentation into heavy hadron

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 non-perturbative parts. In our approach the non-perturbative parts can be defined as matrix elements in heavy quark effective theory, the shape of the functions being predicted by perturbative QCD. In this work we neglect the 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 the leading log approximation with experimental results from e + e − colliders and find a deviation below or at the 10% level. Adding the effect of higher orders in α s it can be expected to reduce this deviation. The size of the matrix elements appearing at the order we consider for several types of heavy hadrons is determined.

Measurement of theBhadron energy distribution inZ0decays

We have measured the B hadron energy distribution in Z0 decays using a sample of semi-leptonic B decays recorded in the SLD experiment at SLAC. The energy of each tagged B hadron was reconstructed using information from the lepton and a partially reconstructed charm-decay vertex. We compared the scaled energy distribution with several models of heavy quark fragmentation. The average scaled energy of primary B hadrons was found to be <x_E_B> = 0.716 +- 0.011 (stat.) +0.022 -0.021 (syst.).

Relativistic and binding energy corrections to heavy quark fragmentation functions

We calculate the fragmentation function for a charm quark to decay inclusively into $S$-wave charmonium states, including relativistic and binding energy corrections in powers of the quark relative velocity $v$. We also use these fragmentation functions to estimate their contribution to the production rate of ${\ensuremath{\eta}}_{c}$ and $J/\ensuremath{\psi}$ in ${Z}^{0}$ decay. These corrections contribute about $38$% to the integrated $c\ensuremath{\rightarrow}J/\ensuremath{\psi}+X$ fragmentation. For ${\ensuremath{\eta}}_{c},$ these corrections are found to be small.

Form Factors for Exclusive Semileptonic B Decays

We investigate the form factors for exclusive semileptonic decays of B meson to D, D*, based on the parton picture and helped by the results of the HQET. We obtain the numerical results for the slope of the Isgur–Wise function, which is consistent with the experimental results, and we extract the dependence of hadronic form factors on q2 by varying the input heavy quark fragmentation function without the nearest pole dominance ansätze.

Non-perturbative corrections to heavy quark fragmentation in e+e− annihilation

We estimate the non-perturbative power-suppressed corrections to heavy flavour fragmentation and correlation functions in e + e − annihilation, using a model based on the analysis of one-loop Feynman graphs containing a massive gluon. This approach corresponds to the study of infrared renormalons in the large- n f limit of QCD, or to the assumption of an infrared-finite effective coupling at low scales. We find that the leading corrections to the heavy quark fragmentation function are of order λ M , where λ is a typical hadronic scale (λ ∼ 0.4 GeV) and M is the heavy quark mass. The inclusion of higher corrections corresponds to convolution with a universal function of M(1 − x) concentrated at values of its argument of order λ, in agreement with intuitive expectations. On the other hand, corrections to heavy quark correlations are very small, of the order of (λ Q) p , where Q is the centre-of-mass energy and p ≥ 2.

Color-singlet psi Q production at e+e- colliders.

We calculate in closed form the complete ${\mathcal O}(\alpha_s^2)$ color-singlet differential cross section for $e^+e^- \to \gamma^* \to \psi_Q+X$ scattering. The cross section reduces at high energies to a heavy quark fragmentation form. We find that the energy scale at which the approximate fragmentation result becomes reliable exceeds the $\psi_Q$ mass by more than an order of magnitude. We also discuss the color-singlet model's predictions for direct $J/\psi$ angular and energy distributions at CLEO.

A derivation of the heavy quark fragmentation function in annihilation

We extend the kinematic analysis on heavy quark fragmentation initiated by Bjorken and Suzuki to derive the fragmentation function of the heavy quarks. Considering the thrust axis is not necessarily along the relative momentum direction of the initial quark pair, indeed the contribution of the heavy hadrons which locate at non-leading rapidity positions may be as important to the results as those at the leading position. A quite good agreement between data and our prediction is achieved.

Fragmentation of heavy quarks in polarized quarkonium in the effective heavy quark theory

Fragmentation of abantiquark into polarized Bc* mesons has been studied within the framework of the effective theory of heavy quarks. The functions ofb fragmentation into longitudinally polarized and transversely polarizedb S-wave states have been calculated with precise account for corrections of the first order in 1/mb. The results are shown to agree with the corresponding calculations in quantum chromodynamics.

J/ψ and υ Photoproduction in Pb-Pb Collisions at Large Hadron Collider

Hard photoproduction of J/ψ and T at large hadron collider Pb-Pb collisions with center of mass energy 6300 AGeV is discussed in the process Pb + Pb → Pb + J/ψ(Γ) + X with three types of equivalent photon spectrum function. It turns out that in hard photoproduction the J/ψ cross section is dominated by the gluon and heavy quark fragmentation, especially the gluon fragmentation is very important at large pt, while the T cross section is dominated by the leading order process. It may be conclude from the result that the hard photoproduction processes can be used to test several important problems such as the gluon distribution in the nucleus, gluon and heavy quark fragmentation of J/ψ, and so on. In addition the process also provide a new way of testing the EMC effects.

Heavy quark fragmentation functions in the heavy quark effective theory.

We calculate fragmentation functions for a b-quark to fragment into color-singlet P-wave bound states $\bar c b$ in the Heavy Quark Effective Theory with the exact account of $O(1/m_b)$ corrections. We demonstrate an agreement of the obtained results with the corresponding calculations carried out in quantum chromodynamics.

Heavy quark fragmentation functions for D-wave quarkonium and charmed b-flavored mesons.

At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and $\bar bc$ mesons in high energy $e^+e^-$ and hadronic collisions is dominated by parton fragmentation. We calculate the heavy quark fragmentation functions into the D-wave quarkonium and $\bar bc$ mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the $\bar b c$ meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation probability for a $\bar b$ antiquark to split into the D-wave $\bar b c$ mesons is about $2 \times 10^{-5}$, which implies that only 2\% of the total pseudo-scalar ground state $B_c$ comes from the cascades of these orbitally excited states.

Hadronic production of S-wave and P-wave charmed b mesons via heavy quark fragmentation.

At hadron colliders the dominant production mechanism of $(\bar bc)$ mesons with large transverse momentum is due to parton fragmentation. We compute the rates and transverse momentum spectra for production of S-wave and P-wave $(\bar b c)$ mesons at the Tevatron via the direct fragmentation of the bottom antiquark as well as the Altarelli-Parisi induced gluon fragmentation. Since all the radially and orbitally excited $(\bar b c)$ mesons below the $BD$ flavor threshold will cascade into the pseudoscalar ground state $B_c$ through electromagnetic and/or hadronic transitions, they all contribute to the inclusive production of $B_c$. The contributions of the excited S-wave and P-wave states to the inclusive production of $B_c$ are 58 and 23\%, respectively, and hence significant.

Fragmentation production of doubly heavy baryons.

Baryons with a single heavy quark are being studied experimentally at present. Baryons with two units of heavy flavor will be abundantly produced not only at future colliders, but also at existing facilities. In this paper we study the production via heavy quark fragmentation of baryons containing two heavy quarks at the Fermilab Tevatron, the CERN LHC, DESY HERA, and the NLC. The production rate is woefully small at HERA and at the NLC, but significant at pp and pp\ifmmode\bar\else\textasciimacron\fi{} machines. We present distributions in various kinematical variables in addition to the integrated cross sections at hadron colliders. \textcopyright{} 1996 The American Physical Society.

Prompt psi and Upsilon production at LEP

Color-octet contributions to quarkonia production at LEP are studied herein. The short distance formation of heavy quark-antiquark pairs in color-octet configurations via gluon fragmentation processes is significantly enhanced relative to the creation of color-singlet pairs via heavy quark fragmentation. But the subsequent long distance hadronization of these colored pairs into physical quarkonium bound states is suppressed compared to the non-perturbative evolution of their colorless counterparts. We find that the overall LEP rates for gluon fragmentation into psi and Upsilon vector bosons exceed those from heavy quark fragmentation. Inclusion of the dominant color-octet quarkonium production channel reduces sizable discrepancies between previous predictions and recent measurements of prompt Z → J gy + X , Z → ψ′ + X and Z → Y + X branching fractions.