Quark Fragmentation Functions Research Articles

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 $$\alpha _{s}^{{(5)}}({{M}_{Z}}) = 0.1205\begin{array}{*{20}{c}} { + 0.0016} \\ {0.0020} \end{array}.$$

Fragmentation production of ground state spin-1/2 heavy baryons including the Fermi motion of constituents

We analytically compute the process-independent fragmentation functions of heavy quarks to fragment into ground state triply heavy baryons considering the Fermi motion effect of their constituent quarks. The effect of Fermi motion is basically included in the baryon wave functions so in all previous studies, a delta function form was approximated for the baryon wave functions which corresponds to ignoring this effect. Here, we study for the first time the effect of nonperturbative dynamics of baryon bound state considering a typical wave function which is different from the delta function and is the nonrelativistic limit of the solution of Bethe-Salpeter equation with the QCD kernel. Our analytical results will be presented for the fragmentation processes $b\rightarrow\Omega_{bbc}$ and $c\rightarrow\Omega_{ccb}$ through a scalar bc diquark intermediated.

Novel mechanism for suppression of heavy flavored mesons in heavy ion collisions

Production of heavy flavored hadrons from fragmentation of heavy quarks represents an alternative probe for a medium created after heavy ion collisions. We demonstrate that observed strong suppression of heavy flavored D and B mesons, produced with high transverse momenta pT, is caused by final state interactions with such a medium. The space-time pattern of hadronization of a highly virtual heavy quark is controlled predominantly by intensive gluon radiation, which is ceased at a short time scale in accordance with perturbative QCD calculations and LEP measurements of the fragmentation functions. However, production of heavy flavored hadrons lasts a long time due to prompt multiple breakups of produced colorless (pre)hadrons in the medium. This fact together with the specific shape of heavy quark fragmentation function, peaked at large z, allows to explain the observed strong suppression of D and B mesons in a good accord with data.

Transverse momentum spectra at threshold for groomed heavy quark jets

We present the transverse momentum spectrum for a heavy hadron at threshold in a groomed jet initiated by a heavy quark. The cross section is doubly differential in the energy fraction of an identified heavy hadron in the jet and its transverse momentum measured with respect to the groomed (recoil free) jet axis. The grooming is implemented using a soft-drop grooming algorithm and helps us in mitigating the effects of Non-Global logarithms and pile up. For the particular case of a B meson, we identify two distinct regimes of the transverse momentum spectrum and develop an EFT within the formalisms of Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) for each of these regions. We show how each region can be matched smoothly into the other to provide a prediction for the perturbative transverse momentum spectrum. The EFT also predicts the scaling behavior of the leading non-perturbative power corrections and implements a simple shape function to account for hadronization. We work in the threshold region where the heavy hadron carries most of the energy of the jet since in this regime, we have a very good discriminating power between heavy quark and gluon initiated jets. We observe that the shape of the spectrum is independent of the energy of the jet over a large range of transverse momentum. We propose that this spectrum can be used as a probe of evolution for heavy quark TMD fragmentation function. At the same time, it can be treated as a jet substructure observable for probing Quark-Gluon Plasma (QGP).

Revisiting heavy quark radiative energy loss in nuclei within the high-twist approach

We revisit the calculation of multiple parton scattering of a heavy quark in nuclei within the framework of recently improved high-twist factorization formalism, in which gauge invariance is ensured by a delicate setup of the initial partons' transverse momenta. We derive a new result for medium modified heavy quark fragmentation functions in deeply inelastic scattering. It is consistent with the previous calculation of light quark energy loss in the massless limit, but leads to a new correction term in the heavy quark case, which vanishes in the soft gluon radiation limit. We show numerically the significance of the new correction term in the calculation of heavy quark energy loss as compared to previous studies and with soft gluon radiation approximation.

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.

Measurement of multiplicities of charged hadrons, pions and kaons in DIS at COMPASS

Precise measurements of multiplicities of charged hadrons, pions and kaons in deep inelastic scattering were performed. The data were obtained by the COMPASS Collaboration by scattering 160 GeV muons off an isoscalar 6LiD target. The results were obtained in three-dimensional bins of the Bjorken scaling variable x, the relative virtual-photon energy y, and the fraction z of the virtual-photon energy carried by the produced hadron. A leading-order pQCD analysis was performed using the pion multiplicity results to extract quark fragmentation functions into pions. The results for the sum of the z-integrated multiplicities for pions and for kaons, differ from earlier results from the HERMES experiment. The results from the sum of the z-integrated K+ and K- multiplicities at high x point to a value of the non-strange quark fragmentation function larger than obtained by the earlier DSS fit.

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.

Power corrections and renormalons in Transverse Momentum Distributions

We study the power corrections to Transverse Momentum Distributions (TMDs) by analyzing renormalon divergences of the perturbative series. The renormalon divergences arise independently in two constituents of TMDs: the rapidity evolution kernel and the small-b matching coefficient. The renormalon contributions (and consequently power corrections and non-perturbative corrections to the related cross sections) have a non-trivial dependence on the Bjorken variable and the transverse distance. We discuss the consistency requirements for power corrections for TMDs and suggest inputs for the TMD phenomenology in accordance with this study. Both unpolarized quark TMD parton distribution function and fragmentation function are considered.

COMPASS results on proton longitudinal spin structure function g1and quark fragmentation functions

We present a few recent highlights from the COMPASS experiment at CERN, related to the nucleon spin and structure: the proton spin structure function g1 p (x) measured using 200 GeV polarized muons, together with a QCD fit of g1 world data; pion and kaon multiplicities in DIS in view of constraining quark fragmentation functions.The statistical precision on g1 p is improved by a factor of ~2 at low x. A reevaluation of the Bjorken sum rule based on COMPASS data alone confirms its validation within 9% accuracy. An NLO QCD fit to g1 world data leads to a value of the quark spin contribution to the nucleon spin ΔΣ, between 0.26 and 0.36 at Q2 = 3 (GeV/c)2 , the size of the uncertainty being driven by the unknown shape of the polarized parton distributions.The results on pion and kaon multiplicities produced in DIS of muons off an isoscalar target constitute an impressive data set of more than 400 points in π and 400 in K, covering a large kinematical domain in (x, z, Q2 ), which will be used in future NLO QCD fits to extract quark fragmentation functions into π and K. A LO fit is performed to extract the favoured and unfavoured quark fragmentation functions into pions.

Novel scenario for production of heavy flavored mesons in heavy ion collisions

The observed strong suppression of heavy flavored hadrons produced with high $p_T$, is caused by final state interactions with the created dense medium. Vacuum radiation of high-pT heavy quarks ceases at a short time scale, as is confirmed by pQCD calculations and by LEP measurements of the fragmentation functions of heavy quarks. Production of a heavy flavored hadrons in a dense medium is considerably delayed due to prompt breakup of the hadrons by the medium. This causes a strong suppression of the heavy quark yield because of the specific shape of the fragmentation function. The parameter-free description is in a good accord with available data.

Effective Field Theory approach to heavy quark fragmentation

Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy Quark Effective Theory (HQET) we determine the $b$-quark fragmentation function from electron-positron annihilation data at the $Z$-boson peak at next-to-next-to leading order, with next-to-next-to leading log resummation of DGLAP logarithms, and next-to-next-to-next-to leading log resummation of endpoint logarithms. This analysis improves, by one order, the previous extraction of the $b$-quark fragmentation function. We find that while the addition of the next order in the calculation does not much shift the extracted form of the fragmentation function, it does reduce theoretical errors indicating that the expansion is converging. Using an approach based on effective field theory allows us to systematically control theoretical errors. While the fits of theory to data are generally good, the fits seem to be hinting that higher order correction from HQET may be needed to explain the $b$-quark fragmentation function at smaller values of momentum fraction.

Impacts of B-factory measurements on determination of fragmentation functions from electron–positron annihilation data

Fragmentation functions are determined for the pion and kaon by global analyses of charged-hadron production data in electron-positron annihilation. Accurate measurements were reported by the Belle and BaBar collaborations for the fragmentation functions at the center-of-mass energies of 10.52 GeV and 10.54 GeV, respectively, at the KEK and SLAC B factories, whereas other available $e^+e^-$ measurements were mostly done at higher energies, mainly at the $Z$ mass of 91.2 GeV. There is a possibility that gluon fragmentation functions, as well as quark fragmentation functions, are accurately determined by scaling violation. We report our global analysis of the fragmentation functions especially to show impacts of the B-factory measurements on the fragmentation function determination. Our results indicate that the fragmentation functions are determined more accurately not only by the scaling violation but also by high-statistical nature of the Belle and BaBar data. However, there are some tensions between the Belle and BaBar data in comparison with previous measurements. We also explain how the flavor dependence of quark fragmentation functions and the gluon function are separated by using measurements at different $Q^2$ values. In particular, the electric and weak changes are different depending on the quark type, so that a light-quark flavor separation also became possible in principle due to the precise data at both $\sqrt{s}\simeq 10.5$ GeV and 91.2 GeV.

Proton fragmentation functions considering finite-mass corrections

We present new sets of proton fragmentation functions describing the production of protons from the gluon and each of the quarks, obtained by a global fit to all relevant data sets extracted from the single-inclusive electron-positron annihilation. Our analysis is in good agreement with $e^+e^-$ annihilation data. We also impose the finite-mass effects of proton in our calculations, a topic with a very little attention paid to in the literatures. Proton mass effects turn out to be appreciable for the gluon and light quark fragmentation functions, so the inclusion of finite-mass effects tends to improve the overall description of the data by reducing the minimized $\chi^2$ values, significantly. As an application, we also apply the extracted fragmentation functions to make our predictions for the scaled-energy distribution of protons inclusively produced in top quark decays at next-to-leading order, relying on the universality and scaling violations of fragmentation functions.

Gluon fragmentation functions in the Nambu–Jona-Lasinio model

We derive gluon fragmentation functions in the Nambu-Jona-Lasinio (NJL) model by treating a gluon as a pair of color lines formed by fictitious quark and anti-quark ($q\bar q$). Gluon elementary fragmentation functions are obtained from the quark and anti-quark elementary fragmentation functions for emitting specific mesons in the NJL model under the requirement that the $q\bar q$ pair maintains in the flavor-singlet state after meson emissions. An integral equation, which iterates the gluon elementary fragmentation functions to all orders, is then solved to yield the gluon fragmentation functions at a model scale. It is observed that these solutions are stable with respect to variation of relevant model parameters, especially after QCD evolution to a higher scale is implemented. We show that the inclusion of the gluon fragmentation functions into the theoretical predictions from only the quark fragmentation functions greatly improves the agreement with the SLD data for the pion and kaon productions in $e^+e^-$ annihilation. Our proposal provides a plausible construct for the gluon fragmentation functions, which are supposed to be null in the NJL model.

Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target

Precise measurements of charged-kaon multiplicities in deep inelastic scattering were performed. The results are presented in three-dimensional bins of the Bjorken scaling variable x, the relative virtual-photon energy y, and the fraction z of the virtual-photon energy carried by the produced hadron. The data were obtained by the COMPASS Collaboration by scattering 160 GeV muons off an isoscalar 6 LiD target. They cover the kinematic domain 1 (GeV/c)2 < Q2 < 60 (GeV/c)^2 in the photon virtuality, 0.004 < x < 0.4, 0.1 < y < 0.7, 0.20 < z < 0.85, and W > 5 GeV/c^2 in the invariant mass of the hadronic system. The results from the sum of the z-integrated K+ and K- multiplicities at high x point to a value of the non-strange quark fragmentation function larger than obtained by the earlier DSS fit.

Multiplicities of charged pions and charged hadrons from deep-inelastic scattering of muons off an isoscalar target

Multiplicities of charged pions and unidentified hadrons produced in deep-inelastic scattering were measured in bins of the Bjorken scaling variable $x$, the relative virtual-photon energy $y$ and the relative hadron energy $z$. Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam and an isoscalar target ($^6$LiD). They cover the kinematic domain in the photon virtuality $Q^2$ > 1(GeV/c$)^2$, $0.004 < x < 0.4$, $0.2 < z < 0.85$ and $0.1 < y < 0.7$. In addition, a leading-order pQCD analysis was performed using the pion multiplicity results to extract quark fragmentation functions.

Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution

We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for $u$ and $d$ quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in $e^+e^-$ annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.

COMPASS Measurement of Pion and Kaon Multiplicities and Extraction of Quark Fragmentation Functions into Pions

We present preliminary COMPASS results on pion and kaon multiplicities produced in semi inclusive deep inelastic scattering of 160[Formula: see text]GeV muons off an isoscalar ([Formula: see text]LiD) target. The results constitute an impressive data set of more than 400 points in p and 400 in K, covering a large x,Q[Formula: see text] and z domain in a fine binning, which will be used in future QCD fits at next to leading order to extract quark fragmentation functions. We show results of a first leading order fit performed to extract the favored and unfavored quark fragmentation functions into pions D[Formula: see text] and D[Formula: see text].