In this paper we present an analysis of the multiple hadron production induced by primary heavy quarks in e+e- annihilation with the account of most complete and corrected experimental data. In the framework of perturbative QCD, new theoretical bounds on the asymptotically constant differences of the multiplicities in processes with light and heavy quarks are given.
The multiple hadron production in the events induced by the heavy primary quarks in $e^+e^-$ annihilation is reconsidered with account of corrected experimental data. New value for the multiplicity in $b\bar{b}$ events is presented on the basis of pQCD estimates.
The explicit expression for the R-ratio of electron-positron annihilation into hadrons, which properly accounts for all the effects due to continuation of the spacelike perturbative results into the timelike domain, is obtained at an arbitrary loop level. Several equivalent ways to derive a commonly employed approximation of the R-ratio are recapped and the impact of discarded in the latter higher-order pi2-terms on the evaluation of the strong running coupling is elucidated. The obtained results substantially facilitate the theoretical study of electron-positron annihilation into hadrons and …
In this paper, we present an extraction of the contribution from the "{\it residual}" light charged hadrons to the inclusive unidentified light charged hadron fragmentation functions (FFs) at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) accuracy in perturbative QCD. Considering the contributions from charged pion, kaon and (anti)proton FFs from recent {\tt NNFF1.0} analysis of charged hadron FFs, we determine the small but efficient {\it residual} charged hadron FFs from QCD analysis of all available single inclusive unidentified charged hadron data se…
The BaBar collaboration has an extensive program of studying hadronic cross sections in low-energy e+e- collisions, accessible via initial-state radiation. Our measurements allow significant improvements in the precision of the predicted value of the muon anomalous magnetic moment. These improvements are necessary for illuminating the current ~3.6 sigma difference between the predicted and the experimental values. We have published results on a number of processes with two to six hadrons in the final state. We report here the results of recent studies with final states that constitute the main…
We provide a brief summary of recent developments in QCD calculations in and beyond fixed-order perturbation theory, for observables in $e^{+}e^{-}$ annihilation as well as hadron collisions.
We present evidence for small oscillations we observe in electron-positron and proton-antiproton annihilation data, with a periodicity of 76+-2 MeV, independent of the beam energy. We discuss some possible scenarios to explain the phenomenon.
We study factorization of processes involving two fragmentation functions in the case of very small transverse momenta. We consider two-hadron production in inclusive $e^+ e^-$ annihilation and demonstrate a new simple and illustrative method of factorization for such processes including leading order $α_S$ corrections.
It is shown that simple extension of the modified negative binomial distribution describes negatively charged particle multiplicity distributions in e+e- annihilation, measured in the whole phase space, as well as the modified negative binomial.
The experimental charged particles multiplicity distributions in $e^+e^-$ annihilation to hadrons are compared with the distributions obtained by PYTHIA. The ratio $χ^2$/degrees of freedom is calculated for 6 energies at $\sqrt{s}$ 14 -- 206.2 GeV. The necessity of more subtle tuning of PYTHIA at the energy of $Z^0$ peak is discussed.
It is shown that charged hadron multiplicity distributions in restricted (pseudo)rapidity intervals in e+e- annihilation and in e+p scattering at HERA are quite well described by the modified negative binomial distribution and its simple extension.
We study the scaling regime of hadron-(anti)-hadron annihilation into a deeply virtual photon and a real photon, H anti-H -> gamma^* gamma, and deep backward virtual Compton scattering, gamma^* H -> H gamma. We advocate that there is a kinematical region where the scattering amplitude factorizes into a short-distance matrix element and a long-distance dominated object: a transition distribution amplitude which describes the hadron to photon transition.
The description of the polarized quark hadronization process is one of the most challenging problems in the physics of strong interactions. The various single hadron and dihadron fragmentation functions, that quantify this process, are determined by analyzing the inclusive production of hadrons in electron-positron semi-inclusive annihilation process (SIA). These, in turn, are used to extract the transverse momentum dependent parton distribution functions from the experiments on semi-inclusive deep inelastic scattering process (SIDIS), elucidating the spin-orbit correlations in nucleon. Here w…
Inclusive hadron production in $e^+e^-$ annihilation has long been used to study both single hadron fragmentation functions (FF) and dihadron fragmentation functions (DiFF). In particular, the polarized DiFFs can be accessed in electron-positron annihilation by measuring azimuthal correlations between two back-to-back pairs of hadrons in the center of mass system, where the relevant structure functions can be expressed as convolutions of two (polarized) DiFFs. Here we explore the advantages of measuring the inclusive back-to-back production of a single hadron on one side against a hadron pair …
In the framework of quark-hadron duality, the cross section values of charmonium and doubly charmed baryon production in $e^+e^-$-annihilations have been estimated at interaction energy $\sqrt{s}=10.6$ GeV. It has been shown that the approach under discussion allows to resolve some contradictions between the experimental data and pQCD predictions.
A new treatment of Bose-Einstein correlations is incorporated in a space-time parton-shower model for e+ e- annihilation into hadrons. Two alternative afterburners are discussed, and we use a simple calculable model to demonstrate that they reproduce successfully the size of the hadron emission region. One of the afterburners is used to calculate two-pion correlations in e+ e- -> Z^0 -> hadrons and e+ e- -> W+ W- -> hadrons. Results are shown with and without resonance decays, for correlations along and transverse to the thrust jet axis in these two classes of events.
We study the structures in cross sections and R ratios concerning electron-positron annihilation reactions, for open-strangeness, open-charm and open-beauty hadron-pair production, from the perspective of a recently developed production formalism. Special attention is paid to non-resonant contributions. Known, tentative, and yet unknown resonances are spotted, with estimates for their masses and widths.
We discuss the production of two hadrons in e+e- annihilation within the framework of perturbative QCD. The cross section for this process is calculated to next-to-leading order accuracy with a selection of variables that allows the consideration of events where the two hadrons are detected in the same jet. In this configuration we contemplate the possibility that the hadrons come from a double fragmentation of a single parton. The double-fragmentation functions required to describe the transition of a parton to two hadrons are also necessary to completely factorize all collinear singularities…
We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha_s^4 n_f^2 to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full O(alpha_s^4) correction to $e^+ e^- annihilation into hadrons and the Higgs decay rate into hadrons respectively. They discriminate between different widely used estimates of the full result.
We discuss the production of hadrons in $e^+e^-$ collisions at $\sqrt s=91$ GeV. We address the question wether the particle yields measured in the final states are consistent with the statistical model predictions. In the model formulation we account for exact conservation of all relevant quantum numbers using the canonical description of the partition function. Within our model the validity of the thermodynamical approach to quantify particle production in $e^+e^-$ annihilations is not obvious.
We study the production of two almost back-to-back hadrons from the annihilation of an electron and a positron, allowing for the polarization of all particles involved. In particular, we conduct a general (model-independent) structure function decomposition of the cross section for the case $e^+e^- \to γ^* \to h_ah_bX$. Moreover, using the parton model we calculate the relevant structure functions in terms of twist-2 transverse momentum dependent (TMD) fragmentation functions (FFs). We also give results for the situation $e^+e^- \to Z^* \to h_ah_bX$ (including $γ$-$Z$ interference) within this…
We compute the inclusive spectrum of produced particles in e+e- annihilation in confining gauge theories that have a gravity dual and show that the momentum distribution exhibits the thermal behavior.
The charged particles multiplicity distribution in the KNO form is discussed in processes of $e^+e^-$ annihilation at energies $\sqrt{s}$ 14 -- 206.2 GeV. The experimental data are compared to data, obtained with Monte Carlo simulation in PYTHIA in the Lund quark string model. It is shown, that both experimental and simulated data are described by the same distribution function in the KNO form. It is shown, that the KNO scaling is consequence of quark string hadronization dynamics in the Lund string model.
We apply collinear expansion to inclusive hadron production in $e^+e^-$ annihilation and derive a formalism suitable for systematic study of leading as well as higher twist contributions to fragmentation functions at the tree level. We make the calculations for hadrons with spin-0, spin-1/2 as well as spin-1 and obtain the results in terms of different components of fragmentation functions for the hadronic tensors, the differential cross section as well as hadron polarizations in different cases. The results show a number of interesting features such as the existence of transverse polarization…
We present the results of the tree-level calculation of inclusive two-hadron production in electron-positron annihilation via one photon up to subleading order in 1/Q. We consider the situation where the two hadrons belong to different, back-to-back jets. We include polarization of the produced hadrons and discuss azimuthal dependences of asymmetries. New asymmetries are found, in particular there is a leading cos(2 phi) asymmetry, which is even present when hadron polarization is absent, since it arises solely due to the intrinsic transverse momenta of the quarks.
We study, at leading order in the large number of colours expansion and within the Resonance Chiral Theory framework, the odd-intrinsic-parity $e^+ e^- \rightarrow π^+ π^- (π^0, η)$ cross-sections in the energy regime populated by hadron resonances, namely $3 \, m_π \lsim E \lsim 2 \, \mbox{GeV}$. In addition we implement our results in the Monte Carlo generator PHOKHARA 7.0 and we simulate hadron production through the radiative return method.
The nearly energy independent hadron emitter dimension $r$, measured in $e^+e^-$ annihilation in the energy range 10 to 91 GeV via the Bose-Einstein correlation of two identical charged pions, is shown to be well accounted for by choosing the hadron jets as independent pion sources. To this end the known normalised factorial cumulant moments dependence on particle sources is adapted to the Bose-Einstein correlation formalism to yield a relation between $r$ and these sources. This approach is also able to account for the measured $r$ values obtained for the $Z^0$ decays into two and three hadro…
The production of four hadronic jets in e+e- collisions above the Z pole is dominated by the QCD e+e- --> qqqq,qqgg processes and, for sufficiently high energy, the electroweak e+e- --> W+W- --> qqqq process. However there is another mechanism for producing four jets, e+e- --> Z gg --> qqgg, which can be regarded as a `hadronic return' to the Z pole. We investigate this new process in detail
We provide complete analytic expressions for the isolated prompt photon production cross section in $e^+e^-$ annihilation reactions through one-loop order in quantum chromodynamics (QCD) perturbation theory. Functional dependences on the isolation cone size $δ$ and isolation energy parameter $ε$ are derived. The energy dependence as well as the full angular dependence of the cross section on $θ_γ$ are displayed, where $θ_γ$ specifies the direction of the photon with respect to the $e^+e^-$ collision axis. We point out that conventional perturbative QCD factorization breaks down for isolated ph…
We point out that the fragmentation of a strange quark into nucleons versus antinucleons is not necessarily identical $D_{p/s}(z,Q^2) \neq D_{\bar p/s}(z,Q^2)$, even though the perturbative contributions from gluon splitting and evolution are $p \leftrightarrow \bar p$ symmetric. The observation of such asymmetries in the hadronization of strange and other heavy quarks can provide insight into the nonperturbative mechanisms underlying jet fragmentation in QCD.
We apply the positive-weight Monte Carlo method of Nason for simulating QCD processes accurate to Next-To-Leading Order to the case of e+e- annihilation to hadrons. The method entails the generation of the hardest gluon emission first and then subsequently adding a `truncated' shower before the emission. We have interfaced our result to the Herwig++ shower Monte Carlo program and obtained better results than those obtained with Herwig++ at leading order with a matrix element correction.
The two-body mesonic $B$ decays induced only via a single $W$-exchange or annihilation quark diagram, such as $B^-_u\rightarrow D^{(*)-}_sK^{(*)0}$ and $\bar{B}^0_d\rightarrow D^{(*)+}_sK^{(*)-}$, are analyzed in the factorization approximation. We estimate the branching ratios for those transitions into two pseudoscalar mesons, and find them to be negligibly small. The significant effect of final-state rescattering is illustrated by taking $B^-_u\rightarrow D^-\bar{K}^0$ for example.
The collimation $C$ of a hadronic event in the e^+e^- annihilation is defined as the average of $\cosθ$, $C=<\cosθ>$, where $θ$ is the angle of each hadron measured from the thrust axis, and the average is over all the hadrons produced in an event. It is an infrared-stable event-shape parameter. $1-\bar C$, the difference between the unity and the average collimation at a given energy, is proportional to the anomalous dimension of the hadron multiplicity at the leading order in MLLA. Its next-to-leading order corrections are calculated.
In reference to the recently observed high Q^2, large x events in deep-inelastic positron-proton scattering at HERA, various leptoquark and supersymmetric scenarios are discussed. We study the impact of virtual leptoquark or R-parity breaking squark exchange as well as generic contact interaction on the production of quark-antiquark pairs in $e^+e^-$ annihilation, in particular at LEP2.
Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to next-to-leading order in $α_s$ and leading order in $v^2$ using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The notorious infrared divergences due to soft gluons, i.e., the Logarithms associated with the binding energy, encountered in previous perturbative calculations of $1^{+-}$ quarkonium decays are found to be explicitly cancelle…
We present the leading unpolarized and single spin asymmetries in inclusive two-hadron production in electron-positron annihilation at the Z pole. The azimuthal dependence in the unpolarized differential cross section of almost back-to-back hadrons is a leading cos(2 phi) asymmetry, which arises solely due to the intrinsic transverse momenta of the quarks. An extensive discussion on how to measure this asymmetry and the accompanying time-reversal odd fragmentation functions is given. A simple estimate indicates that the asymmetry could be of the order of a percent.
A novel method of studying e+e- annihilation into hadrons using initial state radiation at e+e- colliders is described. After brief history of the method, its theoretical foundations are considered. Numerous experiments in which exclusive cross sections of e+e- annihilation into hadrons below the center-of-mass energy of 5 GeV have been measured are presented. Some applications of the results obtained to fundamental tests of the Standard Model are listed.
Fragmentation functions of pion, kaon, and nucleon are determined by global analyses of hadron-production data in $e^+e^-$ annihilation. It is particularly important that uncertainties of the fragmentation functions are estimated for the first time. We found that light-quark and gluon fragmentation functions have large uncertainties, so that one should be careful in using these functions for hadron-production processes in heavy-ion collisions and lepton scattering. The analysis is extended to possible exotic hadron search by fragmentation functions. We found that internal structure of $f_0 (98…
Electron-positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for e^+ e^- annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process e^+ e^- \to γ+γ^* and the emission of two real hard photons: e^+ e^- \to γ+ γ+ γ^*. A Monte Carlo gener…
The processes of D^{(*)}-mesons and Λ_c-baryons production in e^+e^--annihilation at 10.58 GeV and 91.18 GeV energies are concerned. At the 10.58 GeV energy the production of charmed particles via the B-mesons decays is also concerned. Scaling violation of the fragmentation functions is calculated at the NLL-accuracy. Nonperturbative fragmentation functions are retrieved from the experimental data of B-factories and are approximated by simple analytic expressions. It is proved, that the difference between nonperturbative fragmentation functions of mesons and baryons can be easily explained by …
The cross section for back-to-back hadron pair production in $e^+e^-$ annihilation provides access to the dihadron fragmentation functions (DiFF) needed to extract nucleon parton distribution functions from the semi-inclusive deep inelastic scattering (SIDIS) experiments with two detected final state hadrons. Particular attention is given to the so-called interference DiFF (IFF), which makes it possible to extract the transversity parton distribution of the nucleon in the collinear framework. However, previously unnoticed discrepancies were recently highlighted between the definitions of the I…
We report on the analytic calculation of the second-order QCD corrections to semi-inclusive hadron production in electron-positron annihilation. The calculation of the single-particle inclusive cross-section in time-like kinematics is performed in Mellin N-space and uses an algorithmic evaluation of inclusive phase-space integrals, based on the unitarity cutting rules and integration-by-parts. We obtain splitting functions and coefficient functions up to second order in the strong coupling alpha_s. Our results are in agreement with earlier calculations in the literature by Rijken and van Neerv…
Recursive solution for a general homogeneous in time pure birth branching process with simultaneous production of any number of particles and with continuous evolution parameter is given. Calculational algorithm based on the use of Koenigs function and functional Schroder equation is described. It is shown that multiplicity distributions in e+e- annihilation into hadrons for c.m. energies up to 189 GeV are well described by the modified negative binomial distribution, explained by simple pure birth branching process without multiple simultaneous particle production. The energy dependence of th…
We show that, based on the idea of string fragmentation, the production rates of light flavored mesons and baryons originating from fragmentation can be described by the spin, the binding energy of the particle, and a strangeness suppression factor. Apart from a normalization factor, $e^+ e^-$ data at different center-of-mass energies can be described simultaneously. Applying to the heavy flavor production, we find that our predictions are in good agreement with data.
In the framework of a newly developed factorization formalism which is based on NRQCD, explicit cancellations are shown for the infrared divergences that appeared in the previously calculated hadronic annihilation decay rates of P-wave and D-wave heavy quarkonia. We extend them to a more general case that to leading order in $v^2$ and next-to-leading order in $α_s$, the infrared divergences in the annihilation amplitudes of color-singlet $Q\bar{Q}(^{2S+1}L_J)$ pair can be removed by including the contributions of color-octet operators $Q\bar{Q}(^{2S+1}(L-1)_{J'})$, $Q\bar{Q}(^{2S+1}(L-3)_{J''}…
High-energy behavior of R-ratio of electron-positron annihilation into hadrons is studied. In particular, it is argued that at any given order of perturbation theory the re-expansion of the R-ratio in the ultraviolet asymptotic can be reduced to the form of power series in the naive continuation of the strong running coupling into the timelike domain. The convergence range of the re-expanded R-ratio and the corresponding higher-order pi2-terms are discussed.
We present nonperturbative fragmentation functions (FFs) for bottom-flavored ($B$) hadrons both at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the $\overline{\mathrm{MS}}$ factorization scheme with five massless quark flavors. They are determined by fitting all available experimental data of inclusive single $B$-hadron production in $e^+e^-$ annihilation, from the ALEPH, DELPHI, and OPAL Collaborations at CERN LEP1 and the SLD Collaboration at SLAC SLC. The uncertainties in these FFs as well as in the corresponding observables are estimated using t…
The forward-backward asymmetry is an important measurable quantity which can enable independent determination of the neutral-current couplings of fermions. In this paper, we extend the definition of the asymmetry from the partonic level to the hadronic level by calculating this asymmetry of the hadron pair in the semi-inclusive electron position annihilation process. Semi-inclusive implies that a back-to-back jet is also measured in addition to the hadron pair. Due to the limitation of the factorization theorem, we calculate this process up to leading order twist-4 level by applying the collin…
We calculate the transverse momentum dependence in the production of two back-to-back hadrons in electron-positron annihilations at the medium/large energy scales of BES-III and BELLE experiments. We use the parameters of the transverse-momentum-dependent (TMD) fragmentation functions that were recently extracted from the semi-inclusive deep-inelastic-scattering multiplicities at low energy from HERMES. TMD evolution is applied according to different approaches and using different parameters for the nonperturbative part of the evolution kernel, thus exploring the sensitivity of our results to …
Semi-inclusive deep inelastic Scattering (SIDIS) has been a very successful tool to investigate the partonic structure of the nucleon over the last decade. Compared to inclusive DIS, information about the quantum numbers of the struck quark can be inferred from the identity, distribution and polarization of the final state hadrons. Up to now, virtually all knowledge about the quark-gluon structure of the nucleon from SIDIS has been gained from distributions of independently observed scalar hadrons. However, given the amount of data current and future experiments at JLab, RHIC, KEK and the EIC …
The strong corrections to the R-ratio of electron-positron annihilation into hadrons are studied at the higher-loop levels. Specifically, the essentials of continuation of the spacelike perturbative results into the timelike domain are elucidated. The derivation of a general form of the commonly employed approximate expression for the R-ratio (which constitutes its truncated re-expansion at high energies) is delineated, the appearance of the pertinent $π^2$-terms is expounded, and their basic features are examined. It is demonstrated that the validity range of such approximation is strictly li…
Factorizing the cross section for single hadron production in $e^+e^-$ annihilations, differential in $z_h$, $P_T$ and thrust, is a highly non trivial task. We have devised a factorization scheme that allows us to recast the $e^+e^- \to hX$ cross section in the convolution of a perturbatively calculable coefficient and a universal Transverse Momentum Dependent (TMD) Fragmentation Function (FF). The predictions obtained from our NLO-NLL perturbative computation, together with a simple ansatz to model the non-perturbative part of the TMD, are applied to the experimental measurements of the BELLE…
The precise determination of the cross section for electron-positron annihilation into hadrons is one of the central tasks of ongoing experiments at low energy colliders. These measurements have to be complemented by Monte Carlo generators which simulate a large number of final states and include higher order radiative corrections. With this motivation in mind the generator PHOKHARA is extended to allow for the simulation of final states with zero, one or two real photons. At the same time corrections from the emission of one or two virtual photons are included, such that a full next-to-next-t…
The annihilation of the $B_c$ meson to leptons and inclusive light hadrons is analyzed in the framework of nonrelativistic QCD (NRQCD) factorization. We find that the decay mode, which escapes from the helicity suppression, contributes a sizable fraction width. According to the analysis, the branching ratio due to the contribution from the color-singlet component of the meson $B_c$ can be of order (10^{-2}). We also estimate the contributions from the color-octet components. With the velocity scaling rule of NRQCD, we find that the color-octet contributions are sizable too, especially, in cert…
We present the complete leading-order results for the azimuthal dependences and polarization observables in $e^+e^-\to h_1 h_2 + X$ processes, where the two hadrons are produced almost back-to-back, within a transverse momentum dependent (TMD) factorization scheme. We consider spinless (or unpolarized) and spin-1/2 hadron production and give the full set of the corresponding quark and gluon TMD fragmentation functions (TMD-FFs). By adopting the helicity formalism, which allows for a more direct probabilistic interpretation, single- and double-polarization cases are discussed in detail. Simplif…
We provide complete analytic expressions for the inclusive prompt photon production cross section in hadronic final states of $e^+e^-$ annihilation reactions through one-loop order in quantum chromodynamics perturbation theory. Computed explicitly are direct photon production through first order in the electromagnetic strength $α_{em}$ and the quark-to-photon and gluon-to-photon fragmentation contributions through first order in the strong coupling $α_s$. The full angular dependence of the cross sections is displayed, separated into transverse $(1 +\cos ^2θ_γ)$ and longitudinal $(\sin ^2θ_γ)$ …
The reactions of electron-positron to nucleon-antinucleon pairs are studied in a non-perturbative quark model. The work suggests that the two-step process, in which the primary quark-antiquark pair forms first a vector meson which in turn decays into a hadron pair, is dominant over the one-step process in which the primary quark-antiquark pair is directly dressed by additional quark-antiquark pairs to form a hadron pair. To reproduce the experimental data of the reactions of electron-positron to proton-antiproton and electron-positron to neutron-antineutron a D-wave omega-like vector meson wit…
We study the transverse momentum distributions of single inclusive hadron production in ${e^ + }{e^ - }$ annihilation processes. Although the only available experimental data are scarce and quite old, we find that the fundamental features of transverse momentum dependent (TMD) evolution, historically addressed in Drell-Yan processes and, more recently, in Semi-inclusive deep inelastic scattering processes, are visible in ${e^ + }{e^ - }$ annihilations as well. Interesting effects related to its non-perturbative regime can be observed. We test two different parameterizations for the $p_\perp$ d…
