Tzu Chiang Yuan

Gluon fragmentation into heavy Quarkonium

The dominant production mechanism for heavy-quark--antiquark bound states with large transverse momentum is fragmentation, the splitting of a high energy parton into a quarkonium state and other partons. We show that the fragmentation functions [ital D]([ital z],[mu]) describing these processes can be calculated using perturbative QCD. We calculate the fragmentation functions for a gluon to split into [ital S]-wave quarkonium states to leading order in the QCD coupling constant.

Perturbative QCD fragmentation functions as a model for heavy-quark fragmentation

The perturbative QCD fragmentation functions for a heavy quark to fragment into heavy-light mesons are studied in the heavy-quark limit. The fragmentation functions for {ital S}-wave pseudoscalar and vector mesons are calculated to next-to-leading order in the heavy-quark mass expansion using the methods of heavy-quark effective theory. The results agree with the {ital m}{sub {ital b}}{r_arrow}{infinity} limit of the perturbative QCD fragmentation functions for {ital {bar b}} into {ital B}{sub {ital c}} and {ital B}{sub {ital c}}{sup *}. We discuss the application of the perturbative QCD fragmentation functions as a model for the fragmentation of heavy quarks into heavy-light mesons. Using this model we predict the fraction {ital P}{sub {ital V}} of heavy-light mesons that are produced in the vector meson state as functions of the longitudinal momentum fraction {ital z} and the transverse momentum relative to the jet axis. The fraction {ital P}{sub {ital V}} is predicted to vary from about 1/2 at small {ital z} to almost 3/4 near {ital z}=1.

PRODUCTION OF HEAVY QUARKONIUM IN HIGH-ENERGY COLLIDERS

▪ Abstract Recent data from the Tevatron collider have revealed that the production rate of prompt charmonium at large transverse momentum is orders of magnitude larger than the best theories of a few years ago had predicted. These surprising results can be understood by taking into account two recent developments that have dramatically revised the theoretical description of heavy-quarkonium production. The first is the realization that fragmentation must dominate at large transverse momentum, which implies that most charmonium in this kinematic region is produced by the hadronization of individual high-pT partons. The second is the development of a factorization formalism for quarkonium production based on nonrelativistic QCD that allows the formation of charmonium from color-octet pairs to be treated systematically. This review summarizes these theoretical developments and their implications for quarkonium production in high-energy colliders.

Gluon fragmentation into P wave heavy quarkonium

The fragmentation functions for gluons to split into P-wave heavy quarkonium states are calculated to leading order in the QCD coupling constant. Long-distance effects are factored into two nonperturbative parameters: the derivative of the radial wavefunction at the origin and a second parameter related to the probability for a heavy-quark-antiquark pair that is produced in a color-octet S-wave state to form a color-singlet P-wave bound state. The fragmentation probabilities for a high transverse momentum gluon to split into the P-wave charmonium states \chi_{c0}, \chi_{c1}, and \chi_{c2} are estimated to be 0.4 \times 10^{-4}, 1.8 \times 10^{-4}, and 2.4 \times 10^{-4}, respectively. This fragmentation process may account for a significant fraction of the rate for the inclusive production of \chi_{cJ} at large transverse momentum in p \bar p colliders.

Color-octet quarkonium production at the Z pole.

The direct production rate of {ital J}/{psi} via the color-octet mechanism is calculated at the {ital Z} resonance. The color-octet production process {ital Z}{r_arrow}{ital J}/{psi}{bar {ital qq}} is shown to have a substantial branching ratio as well as a distinctive energy spectrum, which can be used as a powerful tool to distinguish from the color-singlet direct production of the {ital J}/{psi}. {copyright} {ital 1996 The American Physical Society.}

Gluon fragmentation into spin-triplet S-wave quarkonium.

The leading color-singlet contribution to the fragmentation function for a gluon to split into spin-triplet {ital S}-wave quarkonium is presented. In the case of charmonium, we find that this color-singlet term is always negligible compared to the leading color-octet contribution.

Bc meson productions via induced gluon fragmentation

Abstract Glouns cannot directly fragment into Bc mesons until at orderαs3. 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 αs3 log (Q/mb,c) through the gluon splitting g→ b . We will determine these induced gluon fragmentation functions. The Bc 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.

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

At hadron colliders the dominant production mechanism of ({bar b}c) mesons with large transverse momentum is due to parton fragmentation. The authors compute in a model-independent way the production rates and transverse momentum spectra for 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{sub c} through electromagnetic and/or hadronic transitions, they all contribute to the inclusive production of B{sub c}. The contributions of the excited S-wave and P-wave states to the inclusive production of B{sub c} are 58 and 23%, respectively, and hence significant.

Hadronic production of {ital S}-wave and {ital P}-wave charmed {ital b} mesons via heavy quark fragmentation

At hadron colliders the dominant production mechanism of ({bar {ital b}}{ital c}) mesons with large transverse momentum is due to parton fragmentation. We compute the rates and transverse momentum spectra for production of {ital S}-wave and {ital P}-wave ({bar {ital b}}{ital c}) mesons at the Fermilab 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 {ital b}}{ital c}) mesons below the {ital BD} flavor threshold will cascade into the pseudoscalar ground state {ital B}{sub {ital c}} through electromagnetic and/or hadronic transitions, they all contribute to the inclusive production of {ital B}{sub {ital c}}. The contributions of the excited {ital S}-wave and {ital P}-wave states to the inclusive production of {ital B}{sub {ital c}} are 58 and 23 {percent}, respectively, and, hence, significant. {copyright} {ital 1996 The American Physical Society.}

Helicity probabilities for heavy quark fragmentation into excited mesons.

In the fragmentation of a heavy quark into a heavy meson whose light degrees of freedom have angular momentum 3/2, all the helicity probabilities are completely determined in the heavy quark limit up to a single probability {ital w}{sub 3/2}. We point out that this probability depends on the longitudinal momentum fraction {ital z} of the meson and on its transverse momentum {ital p}{sub {perpendicular}} relative to the jet axis. We calculate {ital w}{sub 3/2} as a function of scaling variables corresponding to {ital z} and {ital p}{sub {perpendicular}} by taking the heavy quark limit of the perturbative QCD fragmentation functions for a {ital b} quark to fragment into {ital P}-wave ({ital b{bar c}}) mesons. In this model, the light degrees of freedom prefer to have their angular momentum aligned transverse to, rather than along, the jet axis. The implications for the production of excited heavy mesons, such as {ital D}{sup **} and {ital B}{sup **}, are discussed.