Gluon Fragmentation Functions Research Articles

T-odd transverse momentum dependent gluon fragmentation functions in a spectator model

We present a model calculation of the T-odd transverse momentum dependent (TMD) gluon fragmentation functions for a spin-1/2 hadron. Our model is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle, which is considered to be on-shell. We consider the effect of the gluon exchange to calculate all necessary one-loop diagrams for the gluon-gluon correlation functions. Two out of four one-loop diagrams give sizeable contributions to the fragmentation functions. We obtain analytical expressions for the four T-odd TMD fragmentation functions of the gluon. We also provide numerical results on the z-dependence and kT-dependence of the fragmentation functions.

Automated calculation of jet fragmentation at NLO in QCD

We present FMNLO, a framework to combine general-purpose Monte Carlo generators and fragmentation functions (FFs). It is based on a hybrid scheme of phase-space slicing method and local subtraction method, and accurate to next-to-leading order (NLO) in QCD. The new framework has been interfaced to MG5_aMC@NLO and made publicly available in this work. We demonstrate its unique ability by giving theoretical predictions of various fragmentation measurements at the LHC, followed by comparison with the data. With the help of interpolation techniques, FMNLO allows for fast calculation of fragmentation processes for a large number of different FFs, which makes it a promising tool for future fits of FFs. As an example, we perform a NLO fit of parton fragmentation functions to unidentified charged hadrons using measurements at the LHC. We find the ATLAS data from inclusive dijet production show a strong constraining power. Notable disparities are found between our gluon FF and that of BKK, DSS and NNFF, indicating the necessities of additional constraints and data for gluon fragmentation function.

T-even transverse momentum dependent gluon fragmentation functions in a spectator model

We present a model calculation of transverse momentum dependent (TMD) gluon fragmentation functions in both spin-1/2 and spin-0 hadrons. Our approach is based on the postulation that a time-like off-shell gluon can fragment into a hadron and a single spectator particle. So far, such spectator models have been restricted to TMD distribution functions of quarks and gluon as well TMD fragmentation function of quarks. The effective coupling between the gluon-hadron-spectator system is described by a vertex composed of two form factors. We obtain analytical expressions for the four T-even TMD fragmentation functions of the gluon. We also provide numerical results on the z-dependence and kT-dependence of the fragmentation functions. Our analysis reveals the non-negligible impact of these fragmentation functions, which could potentially be explored in forthcoming experimental measurements.

New derivation of the twist-3 gluon fragmentation contribution to polarized hyperon production

A novel method of formulating the twist-3 gluon fragmentation function contribution to hyperon polarization in the proton-proton collision is presented. The method employs a covariant gauge and takes full advantage of the Ward-Takahashi identities before performing the collinear expansion. It provides a robust way of constructing the general cross section formula and also a clear understanding for the absence of the ghostlike terms in the twist-3 cross section in the leading order with respect to the QCD coupling constant.

Resummation effects in the bottom-quark fragmentation function

We compute the perturbative component of the fragmentation function of the b quark to the best of the present theoretical knowledge. The fixed-order calculation to order {alpha}_s^2 of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order- {alpha}_s^2 corrections are accounted for exactly, and logarithmically enhanced contributions from loops of b quarks are included. This requires the calculation of the Mellin transform of the order- {alpha}_s^2 result in the whole complex plane for the Mellin variable, which we provide for the first time for all the fragmenting partons. Evolution is performed to next-to-next-to-leading log accuracy, and mixing with the gluon fragmentation function is taken into account. The perturbative fragmentation functions are made available via LHAPDF grids.

Gluon fragmentation into Bc(*) in NRQCD factorization

The universal fragmentation functions of gluon into the flavored quarkonia $B_c$ and (polarized) $B_c^*$ are computed within NRQCD factorization framework, at the lowest order in velocity expansion and strong coupling constant. It is mandatory to invoke the DGLAP renormalization program to render the NRQCD short-distance coefficients UV finite in a point-wise manner. The calculation is facilitated with the sector decomposition method, with the final results presented with high numerical accuracy. This knowledge is useful to enrich our understanding toward the large-$p_T$ behavior of $B_c^{(*)}$ production at LHC experiment.

Twist-3 gluon fragmentation contribution to hyperon polarization in semi-inclusive deep inelastic scattering

We derive the twist-3 gluon fragmentation function (FF) contribution to the transversely polarized hyperon production in semi-inclusive deep inelastic scattering, $ep\ensuremath{\rightarrow}e{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}X$, in the leading order (LO) with respect to the QCD coupling in the framework of the collinear twist-3 factorization. Together with the known result for the contribution from the twist-3 distribution in the proton and the twist-3 quark FFs for the hyperon, this completes the LO cross section for this process. The constraint relations among the twist-3 FFs are taken into account. The formula is relevant to large-${P}_{T}$ hyperon production in the future electron-ion-collider experiment.

System of evolution equations for quark and gluon jet quenching with broadening

We propose a system of evolution equations that describe in-medium time-evolution of transverse-momentum-dependent quark and gluon fragmentation functions. Furthermore, we solve this system of equations using Monte Carlo methods. We then quantify the obtained solutions in terms of a few characteristic features, namely the average transverse momentum langle |k|rangle and energy contained in a cone, which allow us to see different behaviour of quark and gluon initiated final-state radiation. In particular, the later allows us to conclude that in the gluon-initiated processes there is less energy in a cone, so that the quark jet is more collimated.

Twist-3 gluon fragmentation contribution to polarized hyperon production in unpolarized proton-proton collision

Understanding the origin and mechanism of the transverse polarization of hyperons produced in unpolarized proton-proton collision, $pp\to \Lambda^\uparrow X$, has been one of the long-standing issues in high-energy spin physics. In the framework of the collinear factorization applicable to large-$p_T$ hadron productions, this phenomenon is a twist-3 observable which is caused by multi-parton correlations either in the initial protons or in the process of fragmentation into the hyperon. We derive the twist-3 gluon fragmentation function (FF) contribution to this process in the leading order (LO) with respect to the QCD coupling constant. Combined with the known results for the contribution from the twist-3 distribution function and the twist-3 quark FF, this completes the LO twist-3 cross section. We also found that the model independent relations among the twist-3 gluon FFs based on the QCD equation of motion and the Lorentz invariance property of the correlation functions guarantee the color gauge invariance and the frame-independence of the cross section.

Fragmentation function of g \u2192 Qoverline{Q} (3 {S}_1^{left[8right]} ) in soft gluon factorization and threshold resummation

We study the fragmentation function of the gluon to color-octet 3S1 heavy quark-antiquark pair using the soft gluon factorization (SGF) approach, which expresses the fragmentation function in a form of perturbative short-distance hard part convoluted with one-dimensional color-octet 3S1 soft gluon distribution (SGD). The short distance hard part is calculated to the next-to-leading order in αs and all orders in velocity expansion. By deriving and solving the renormalization group equation of the SGD, threshold logarithms are resummed to all orders in perturbation theory. The comparison with gluon fragmentation function calculated in NRQCD factorization approach indicates that the SGF formula resums a series of velocity corrections in NRQCD which are important for phenomenological study.

NLO QCD corrections to gluon fragmentation function into ηb and ηc based on the Suzuki's model

In this work, we calculate the fragmentation function (FF) of gluon splitting into the quarkonium bound state at next-to-leading order perturbative QCD. To this end, we apply the well-established Suzuki's model which is convenient to consider the polarization states of produced quarkonium. To be specific, we restrict ourselves to the fragmentation of gluon into the S-wave pseudoscalar mesons ηc and ηb. We will compare our results with the one computed at the leading-order (LO) to show the effects of higher order radiative corrections. Our results show that the NLO radiative corrections may improve the LO FFs up to 70%, so this shows the importance of NLO corrections.

Exact relations for twist-3 gluon distribution and fragmentation functions from operator identities

We perform a systematic study on the twist-3 gluon distribution and fragmentation functions which appear in the collinear twist-3 factorization for hard inclusive processes. Three types of twist-3 distribution and fragmentation functions, i.e., intrinsic, kinematical, and dynamical ones, which are necessary to describe all kinds of twist-3 cross sections, are related to each other by the operator identities based on the QCD equation of motion and the Lorentz invariance properties of the correlation functions. We derive the exact relations for all twist-3 gluonic distribution and fragmentation functions for a spin-$1/2$ hadron. Those relations allow one to express intrinsic and kinematical twist-3 gluon functions in terms of the twist-2 and dynamical twist-3 functions, which provides a basis for the renormalization of intrinsic and kinematical twist-3 functions. In addition, those model independent relations are crucial to guarantee gauge invariance and frame independence properties of the twist-3 cross sections.

Transverse parton distribution and fragmentation functions at NNLO: the gluon case

We calculate in this paper the perturbative gluon transverse momentum dependent parton distribution functions (TMDPDFs) and fragmentation functions (TMDFFs) using the exponential regulator for rapidity divergences. We obtain results for both unpolarized and linearly polarized distributions through next-to-next-to leading order in strong coupling constant, and through mathcal{O} (ϵ2) in dimensional regulator. We find a nontrivial momentum conservation sum rule for the linearly polarized component for both TMDPDFs and TMDFFs in the mathcal{N} = 1 super-Yang-Mills theory. The TMDFFs are used to calculate the two-loop gluon jet function for the energy-energy correlator in Higgs gluonic decay in the back-to-back limit.

SUSY-Like Relation of the Splitting Functions in Evolution of Gluon and Quark Multiplicities

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order (NNNLO), in the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations for the first Mellin moments $${{D}_{{q,g}}}({{\mu }^{2}})$$ of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. This relationship strongly improves previous treatments by allowing for an exact solution of the evolution equations. The fit of the world data of $${{D}_{{q,g}}}({{\mu }^{2}})$$ for charged hadrons measured in $${{e}^{ + }}{{e}^{ - }}$$ annihilation leads to $$\alpha _{s}^{{(5)}}({{M}_{Z}}) = 0.1205\begin{array}{*{20}{c}} { + 0.0016} \\ {0.0020} \end{array}.$$

Impact of unidentified light charged hadron data on the determination of pion fragmentation functions

In this paper a new comprehensive analysis of parton-to-pion fragmentation functions (FFs) is performed for the first time by including all experimental data sets on single inclusive pion as well as unidentified light charged hadron production in electron-positron ($e^+e^-$) annihilation. We determine the pion FFs along with their uncertainties using the standard "Hessian" technique at next-to-leading order (NLO) and next-to-next-to leading order (NNLO) in perturabative QCD. It is shown that the determination of pion FFs using simultaneously the data sets from pion and unidentified light charged hadron productions leads to the reduction of all pion FFs uncertainties especially for the case of strange quark and gluon FFs by significant factors. In this study, we have quantified the constraints that these data sets could impose on the extracted pion FFs. Our results also illustrate the significant improvement in the precision of FFs fits achievable by inclusion of higher order corrections. The improvements on both FFs uncertainties as well as fit quality have been clearly discussed.

SUSY-Like Relation in Evolution of Gluon and Quark Jet Multiplicities

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments D{q,g}(\mu2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. This relationship, which is independent of the number of quark flavors, strongly improves previous treatments by allowing for an exact solution of the evolution equations. So far, such relationships have only been known from supersymmetric QCD.

Charged hadron fragmentation functions from collider data

We present NNFF1.1h, a new determination of unidentified charged-hadron fragmentation functions (FFs) and their uncertainties. Experimental measurements of transverse-momentum distributions for charged-hadron production in proton-(anti)proton collisions at the Tevatron and at the LHC are used to constrain a set of FFs originally determined from electron–positron annihilation data. Our analysis is performed at next-to-leading order in perturbative quantum chromodynamics. We find that the hadron-collider data is consistent with the electron–positron data and that it significantly constrains the gluon FF. We verify the reliability of our results upon our choice of the kinematic cut in the hadron transverse momentum applied to the hadron-collider data and their consistency with NNFF1.0, our previous determination of the FFs of charged pions, kaons, and protons/antiprotons.

SUSY-like relation of the splitting functions in evolution of gluon and quark jet multiplicities

We show the new relationship [1] between the anomalous dimensions, resummed through next-to-next-to-leading-logarithmic order, in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for the first Mellin moments Dq,g(μ2) of the quark and gluon fragmentation functions, which correspond to the average hadron multiplicities in jets initiated by quarks and gluons, respectively. So far, such relationships have only been known from supersymmetric (SUSY) QCD. Exploiting available next-to-nextto- next-to-leading-order (NNNLO) information on the ratio D+g (μ2)=D+q (μ2) of the dominant plus components, the fit of the world data of Dq,g(μ2) for charged hadrons measured in e+e- annihilation leads to α(5)s (MZ) = 0:1205 +0:0016 -0:0020.

Fragmentation of ω and ϕ mesons in e+e− and pp collisions at NLO

A combined analysis of both [Formula: see text] (LEP, SLD) and [Formula: see text] (RHIC-PHENIX and LHC-ALICE) hadroproduction processes are done for the first time for the vector meson nonet at the next-to-leading order (NLO) using a model with broken SU(3) symmetry. The transverse momentum ([Formula: see text]) and rapidity ([Formula: see text]) dependence of the differential cross-section for [Formula: see text] and [Formula: see text] mesons of the [Formula: see text] data are also discussed. The input universal quark (valence and singlet) fragmentation functions at a starting scale of [Formula: see text], after evolution, have values that are consistent with the earlier analysis for [Formula: see text] at NLO. However, the universal gluon fragmentation function is now well determined from this study with significantly smaller error bars, as the [Formula: see text] hadroproduction cross-section is particularly sensitive to the gluon fragmentation since it occurs at the same order as the quark fragmentation, in contrast to the [Formula: see text] hadroproduction process. Additional parameters involved in describing the strangeness and sea suppression and octet–singlet mixing are found to be close to the earlier analysis; in addition, a new relation between the gluon and sea suppression in [Formula: see text] and [Formula: see text] hadroproduction has been observed.

Analytical calculation for the gluon fragmentation into spin-tripletS-wave quarkonium

Fragmentation is the dominant mechanism for hadron production with high transverse momentum. For spin-triplet S-wave heavy quarkonium production, contribution of gluon fragmenting to color-singlet channel has been numerically calculated since 1993. However, there is still no analytic expression available up to now because of its complexity. In this paper, we calculate both polarization-summed and polarized fragmentation functions of gluon fragmenting to a heavy quark-antiquark pair with quantum number $^3S_1^{[1]}$. Our calculations are performed in two different frameworks. One is the widely used nonrelativistic QCD factorization, and the other is the newly proposed soft gluon factorization. In either case, we calculate at both leading order and next-to-leading order in velocity expansion. All of our final results are presented in terms of compact analytic expressions.