We establish a comprehensive theoretical framework for the electron-positron single-inclusive annihilation (SIA) process that incorporates higher-twist contributions up to twist-4 and investigate the possible relevance of these effects in low-energy reactions. Through a systematic collinear expansion of the hadronic tensor, we derive the complete set of structure functions in terms of collinear fragmentation functions (FFs), explicitly including multiparton correlators up to the four-parton level. To evaluate the possible impact of these power corrections, we estimate the twist-4 unpolarized FF $D_3$ using a spectator model and compute the normalized differential cross section for $π^0$ production. Our illustrative numerical estimation indicates that the interplay between kinematic hadron mass corrections and the higher-twist $D_3$ contribution can partially improve the description of recent BESIII data in the relatively low-$z$ region. The $Q$-dependence of this contribution is consistent with the expected power suppression of twist-4 terms. These findings suggest that higher-twist contributions are relevant for studies of hadronization dynamics at low energies and motivate more complete future analyses including all twist-4 FFs.
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…
We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive e^+ e^- annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are s…
The recent measurements of azimuthal single spin asymmetries by the HERMES collaboration at DESY may shed some light on presently unknown fragmentation and distribution functions. We present a study of such functions and give some estimates of weighted integrals directly related to those measurements.
The positivity constraints to the structure functions for the inclusive spin-half baryon production by a time-like photon fragmentation are investigated. One conclusion is that $\hat F$, which arises from the hadronic final-state interactions, is subjected to an inequality between its absolute value and the two spin-independent structure functions. On the basis of this finding, we derive a formula through which the upper limits can be given for the transverse polarization of the inclusively detected spin-half baryons in unpolarized electron-positron annihilation. The derived upper bound suppli…
The Collins fragmentation function is extracted from HERMES data on azimuthal single spin asymmetries in semi-inclusive deeply inelastic scattering, and BELLE data on azimuthal asymmetries in electron positron annihilations. A Gaussian model is assumed for the distribution of transverse parton momenta and predictions are used from the chiral quark-soliton model for the transversity distribution function. We find that the HERMES and BELLE data yield a consistent picture of the Collins fragmentation function which is compatible with COMPASS data and the information previously obtained from an an…
The final-state interaction effects on the inclusive two-particle production in electron-positron annihilation are investigated within the context of the one-photon annihilation approximation. Such effects are characterized by one structure function in the decomposition of the hadronic tensor. On the basis of the positivity, we derived an inequality to bound this structure function. The price to access it experimentally is to polarize longitudinally one of the initial-state beam, to say, the electron beam, and measure the corresponding single spin asymmetry. By combining the Callan-Gross relat…
We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. Th…
Transverse momentum asymmetry in the semi-inclusive electron positron annihilation process
College of Nuclear Equipment and Nuclear Engineering, Yantai University（烟台大学核装备与核工程学院）；School of Physics and Optoelectronic Engineering, Shandong University of Technology（山东理工大学物理与光电工程学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院现代物理研究所南方核科学理论中心）；Key Laboratory of Particle Physics and Particle Irradiation (MOE), Institute of Frontier and Interdisciplinary Science, Shandong University（山东大学前沿交叉科学高等研究中心粒子物理与粒子辐照教育部重点实验室）
To have an analytic understanding of the higher-twist structure functions, we calculate twist four longitudinal structure function for a positronium-like bound state in weak coupling light-front QED. We find that in the weakly coupled system, the fermionic part of $F_L$ is related to the kinetic energy of the fermions and not to the interaction. We verify a previously proposed sum rule in this limit, which in this case reduces to a relation connecting the kinetic and the potential energies to the binding energy of positronium. Using the analytic form of the wave function of positronium in this…
We study semi-inclusive DIS with a transversely polarized target in the approach of collinear factorization. The effects related with the transverse polarization are at twist-3. We derive the complete result of twist-3 contributions to the relevant hadronic tensor at leading order of $α_s$, and construct correspondingly experimental observables. Measuring these observables will help to extract the twist-2 transversity distribution, twist-3 distributions and twist-3 fragmentation functions of the produced unpolarized hadron. A detailed comparison with the approach of transverse-momentum-depende…
We consider the momentum distribution and the polarization of an inclusive heavy fermion in a process assumed to arise from standard-model (SM) $s$-channel exchange of a virtual $γ$ or $Z$ with a further contribution from physics beyond the standard model involving $s$-channel exchanges. The interference of the new physics amplitude with the SM $γ$ or $Z$ exchange amplitude is expressed entirely in terms of the space-time signature of such new physics. Transverse as well as longitudinal polarizations of the electron and positron beams are taken into account. Similarly, we consider the cases of…
Two twist-3 processes are discussed. We first present a simple estimate of the longitudinal-transverse spin asymmetry in the polarized Drell-Yan process. We next derive a cross section for the semi-inclusive production of a polarized spin-1/2 baryon in the DIS of an unpolarized electron off the polarized nucleon.
We calculate the contribution of the higher-twist Feynman diagrams to the large-$p_T$ inclusive gluon production cross-section in $πp$ collisions in case of the running coupling and frozen coupling approaches within perturbative and holographic QCD. The structure of infrared renormalon singularities of the higher-twist subprocess cross-section is obtained and the resummed higher-twist cross- sections (Borel sum) with the ones obtained in the framework of the frozen coupling approach and leading-twist cross-section are compared and analyzed.
We derive the twist-3 gluon fragmentation function (FF) contribution to the transversely polarized hyperon production in semi-inclusive deep inelastic scattering, $ep\to eΛ^\uparrow X$, 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-$…
This article gives results on several jet algorithms in electron-positron annihilation: Considered are the exclusive sequential recombination algorithms Durham, Geneva, Jade-E0 and Cambridge, which are typically used in electron-positron annihilation. In addition also inclusive jet algorithms are studied. Results are provided for the inclusive sequential recombination algorithms Durham, Aachen and anti-kt, as well as the infrared-safe cone algorithm SISCone. The results are obtained in perturbative QCD and are NNNLO for the two-jet rates, NNLO for the three-jet rates, NLO for the four-jet rate…
We study the contribution of the twist-3 fragmentation function to the single-transverse spin asymmetry in semi-inclusive deep inelastic scattering within the framework of the collinear factorization. Making use of the Ward-Takahashi identity in QCD, we establish the formalism in the Feynman gauge to calculate the non-pole contribution of the twist-3 fragmentation function to the asymmetry and derive the complete cross-section formula in the leading order QCD perturbation theory. The obtained twist-3 hadronic tensor is shown to satisfy the electromagnetic gauge-invariance. The behavior in the …
The inclusive $Υ(1S,2S,3S)$ photoproduction at the future Circular-Electron-Positron-Collider (CEPC) is studied based on the non-relativistic QCD (NRQCD). Including the contributions from both direct and resolved photons, we present different distributions for $Υ(1S,2S,3S)$ production and the results show there will be considerable events, which means that a well measurements on the $Υ$ photoprodution could be performed to further study on the heavy quarkonium physics at electron-positron collider in addition to hadron colliders. This supplement study is very important to clarify the current s…
We show that a new beam-spin asymmetry appears in deep inelastic inclusive lepto-production at low transverse momenta when a hadron in the target fragmentation region is observed in association with another hadron in the current fragmentation region. The beam leptons are longitudinally polarized while the target nucleons are unpolarized. This asymmetry is a leading-twist effect generated by the correlation between the transverse momentum of quarks and the transverse momentum of the hadron emitted by the target. Experimental signatures of this effect are discussed.
By applying the collinear expansion to the semi-inclusive hadron production process $e^++e^-\to h+\bar q(jet)+X$ at high energies, we construct a theoretical framework where the leading and higher twist contributions at the leading perturbative QCD can be calculated systematically. With this framework, we calculate the contributions up to twist-3 for spin-0, spin-1/2 and spin-1 hadrons respectively. We present the results for the hadronic tensors, the differential cross sections, the azimuthal asymmetries, and the polarizations of the hadrons.
We present the complete twist-4 results for the semi-inclusive annihilation process $e^+ +e^- \to h+ \bar q+X$ at the tree level of perturbative quantum chromodynamics. The calculations are carried out by using the formalism obtained by applying the collinear expansion to this process where the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. We present the results for structure functions in terms of gauge invariant fragmentation functions up to twist-4 and the corresponding results for the azimuthal asymmetries and polarizations of…
We extend the analysis of two-hadron fragmentation functions to the subleading twist, discussing also the issue of color gauge invariance. Our results can be used anywhere two unpolarized hadrons are semi-inclusively produced in the same fragmentation region, also at moderate values of the hard scale Q. Here, we consider the example of polarized deep-inelastic production of two hadrons and we give a complete list of cross sections and spin asymmetries up to subleading twist. Among the results, we highlight the possibility of extracting the transversity distribution with longitudinally polarize…
We present for the first time the complete twist-4 result for the semi-inclusive deeply inelastic scattering $e^- N \to e^-qX$ with polarized electron and proton beams at the tree level of pQCD. The calculations have been carried out using the formulism obtained after collinear expansion where the multiple gluon scattering are taken into account and gauge links are obtained automatically in a systematical way. The results show in particular that there are twist-4 contributions to all the eight twist-2 structure functions for $e^- N \to e^-hX$ that correspond to the eight twist-2 transverse mom…
As a possible source of the single transverse spin asymmetry, we study the contribution from purely gluonic correlation represented by the twist-3 ``three-gluon correlation" functions in the transversely polarized nucleon. We first define a complete set of the relevant three-gluon correlation functions, and then derive its contribution to the twist-3 single-spin-dependent cross section for the $D$-meson production in semi-inclusive deep inelastic scattering, which is relevant to determine the three-gluon correlations. Our cross-section formula differs from the corresponding result in the liter…
We study the production of polarized $Λ$-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized $Λ$-hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find …
We analyze higher twist effect in photoproduction of quarkonium, where the quarkonium is a spin-triplet, S-wave state. We find that the nonperturbative effect of next-to-leading twist is contained in three correlation functions related to the initial hadron and some of the effect of next-to-leading twist is only suppressed by the inverse of the mass square of the quarkonium. A naive estimation indicates that the effect can be significant for charmonium. In the analysis we only take the leading order in the small velocity expansion for the nonperturbative parts related to the quarkonium. Possib…
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 discuss the single-spin asymmetry in semi-inclusive DIS, $e p^\uparrow \to e πX$, based on the twist-3 mechanism in the collinear factorization relevant for the pion production with the large transverse-momentum. This updates our previous study by including, in particular, the contributions induced by the novel partonic subprocesses, and allows us to derive the entire formula for the corresponding single-spin asymmetry associated with a complete set of the twist-3 quark-gluon correlation functions in the transversely polarized nucleon. We discuss the correspondence with the results obtained…
We discuss the dependence on the flavor of the intrinsic transverse momentum in unpolarized transverse-momentum-dependent distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) analyzing data of semi-inclusive deep-inelastic scattering (SIDIS) released by the HERMES collaboration. Adopting a flavor-dependent Gaussian model in the transverse momentum and neglecting QCD evolution, we find interesting evidences concerning the flavor dependence in TMD FFs, whereas the indications are weaker in TMD PDFs and deserve further investigations. Inclusions of new data sets of SIDIS, elect…
We discuss the evidence for the presence of QCD saturation effects in the data collected in d+Au collisions at RHIC. In particular we focus our analysis on forward hadron yields and azimuthal correlations. Approaches alternative to the CGC description of these two observables are discussed in parallel.
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…
A quantity of particular experimental interest is the forward-backward asymmetry in the angular distribution of positively and negatively charged fermions produced in $Z^0$ decays. Measurements of this asymmetry can enable independent determinations of the neutral-current couplings of these fermions, i.e. the $Z^0$ boson couplings for left- and right-handed fermions, respectively. Due to the quark confinement, however, it is difficult to determine the electroweak interactions of quarks, especially for light quarks. In the hadron production electron positron annihilation process, the parton mod…
The contribution of the higher-twist mechanism to the large-$p_T$ inclusive gluon production cross section in $πp$ collisions is calculated in case of the principle of maximum conformality and Brodsky-Lepage-Mackenzie approaches in the dependence of the pion distribution amplitudes. The higher-twist cross sections obtained in the framework of the principle of maximum conformality and Brodsky-Lepage-Mackenzie approaches, and compared and analyzed in relation to the leading-twist cross sections and each other.
We investigate the resummation of large logarithmic perturbative corrections to hadron production in electron-positron annihilation and semi-inclusive deep-inelastic scattering. We find modest, but significant, enhancements of hadron multiplicities in the kinematic regimes accessible in present high-precision experiments. Our results are therefore relevant for the determination of hadron fragmentation functions from data for these processes.
We present new functional form of pion and kaon fragmentation functions up to next-to-leading order obtained through a global fit to single-inclusive electron-positron annihilation data and also employ, the semi-inclusive deep inelastic scattering asymmetry data from HERMES and COMPASS to determine fragmentation functions. Also we apply very recently electron-positron annihilation data from BaBar and Belle at $\sqrt{s}=10.54$ GeV and $\sqrt{s}=10.52$ GeV, respectively. In this analysis we consider the impression of semi-inclusive deep inelastic scattering asymmetry data on the fragmentation fu…
We study the single spin asymmetry (SSA) for the pion production with large transverse momentum p_T in semi-inclusive deep inelastic scattering $ep^\uparrow\to eπX$. We derive the twist-3 cross section formula for SSA, focussing on the soft-gluon-pole contributions associated with the twist-3 distribution for the nucleon and with the twist-3 fragmentation function for the pion. We present a simple estimate of the asymmetries due to each twist-3 effect from nucleon and pion, respectively, by fixing the overall strength of the relevant nonperturbative quantities by the data on the SSA A_N in $p^…
We investigate the $sin ϕ$ azimuthal asymmetry in the semi-inclusive deep-inelastic lepton scattering off longitudinally polarized nucleon target arising from the time reversal odd structures. The order 1/Q contributions of the leading twist and twist-three distribution and fragmentation functions to that asymmetry for the certain kinematical conditions are numerically estimated.
We study the single spin asymmetry in the transversely polarized proton production and the lambda hyperon production in semi-inclusive deep inelastic scattering with a $\sin ϕ_{S_h}$ modulation, in which $S_h$ is the azimuthal angle of the transverse spin of the final hadron. The theoretical interpretation for the asymmetry is presented as the convolution of the twist-3 quark transverse momentum dependent distributions and twist-2 fragmentation functions. We investigate the role of the twist-3 distribution functions $h(x, p_T^2)$, $f^\perp(x, p_T^2)$ and $g^\perp(x, p_T^2)$ and the twist-2 fra…
We study the single spin asymmetry (SSA) for the pion production in semi-inclusive deep inelastic scattering, $ep^\uparrow\to eπX$, in the framework of the collinear factorization. We derive the complete cross section formula associated with the twist-3 quark-gluon correlation functions for the transversely polarized nucleon, including all types of pole (hard-pole, soft-fermion-pole and soft-gluon-pole) contributions which produce the strong interaction phase necessary for SSA. We prove that the partonic hard part from each pole contribution satisfies certain constraints from Ward identities f…
Establishing the twist-3 formalsim for the single transverse spin asymmetry, we present a complete single-spin-dependent cross section for SIDIS, $ep^\uparrow\to eπX$, associated with the twist-3 distribution for the transversely polarized nucleon. We emphasize that the consistency condition from the Ward identities for color gauge invariance is crucial to prove factorization property of the cross section.
Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse-momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry <cosϕ>$ of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of…
We have compared the existing experimental data on the leading power corrections to the structure functions $F_2(x,Q^2), F_3(x,Q^2)$, and $F_L(x,Q^2)$ with the IR-renormalon model predictions for higher-twist contributions. Our analysis shows that the model properly describes the x-dependence, but typically falls short by a factor 2 or 3 as far as the magnitude of higher twist corrections is concerned.
The single spin asymmetries for a longitudinally polarized lepton beam or a longitudinally polarized nucleon target in semi-inclusive deep-inelastic scattering are twist-3 observables. We study these asymmetries in a simple diquark spectator model of the nucleon. Analogous to the case of transverse target polarization, non-vanishing asymmetries are generated by gluon exchange between the struck quark and the target system. It is pointed out that the coupling of the virtual photon to the diquark is needed in order to preserve electromagnetic gauge invariance at the twist-3 level. The calculatio…
We consider the inclusive production of hadrons in lepton-nucleon scattering. For a transversely polarized nucleon this reaction shows a left-right azimuthal asymmetry, which we compute this asymmetry in both TMD and in twist-3 collinear factorization formalisms. All non-perturbative parton correlators of the calculation are fixed through information from other hard processes. Our results for the left-right asymmetry agree in sign with recent data for charged pion production from the HERMES Collaboration and from Jefferson Lab. We discuss similarities and differences of two formalisms.
Multiple scattering leads to transverse momentum broadening of the struck quark in semi-inclusive deeply inelastic scatterings (SIDIS). Nuclear broadening of the transverse momentum squared at the leading twist is determined by the twist-four collinear quark-gluon correlation function of the target nucleus that is in turn related to the jet transport parameter inside the nuclear medium. The twist-six contributions to the transverse momentum broadening are calculated as power corrections $\sim 1/Q^2$. Such power corrections are found to have no extra nuclear enhancement beyond the twist-four ma…
We derive a general framework for describing semi-inclusive deep-inelastic lepton-nucleon scattering in terms of the unintegrated parton distributions and other higher twist parton correlations. Such a framework provides a consistent approach to the calculation of inclusive and semi-inclusive cross sections including higher twist effects. As an example, we calculate the azimuthal asymmetries to the order of 1/Q in semi-inclusive process with transversely polarized target. A non-vanishing single-spin asymmetry in the ``triggered inclusive process'' is predicted to be 1/Q suppressed with a part …
We investigate the single-spin asymmetries in inclusive and exclusive processes of electron-proton scattering and electron-positron annihilation. In the decomposition of hadronic tensor, a Lorentz symmetric spin-dependent term is generally present. The existence of such a term implies single-spin asymmetries in these processes and these single-spin asymmetries for baryons can be understood in a unified manner. We argue that it is important to measure the single-spin asymmetries in both inclusive and exclusive processes for the $Λ$ production at the present B-factories. This will lead to the fi…
We present a systematic calculation of the current jet production semi-inclusive deeply inelastic scattering process at the Electron-Ion Collider energy. Contributions from weak interactions are considered which give rise to parity violating effects. We consider the general form of the polarized electron beam scattering off the polarized target which has spin 1. The calculations are carried out up to twist-3 level in the quantum chromodynamics parton model by applying the collinear expansion where multiple gluon scattering is taken into account and gauge links are obtained automatically. We pr…
We derive the complete twist-3 single-spin-dependent cross section for semi-inclusive DIS, $ep^\uparrow\to eπX$, associated with the complete set of the twist-3 quark-gluon correlation functions in the transversely polarized nucleon, extending our previous study. The cross section consists of five independent structure functions with different azimuthal dependences, consistently with the transverse-momentum-dependent (TMD) factorization approach in the low $q_T$ region. Correspondence with the inclusive DIS limit and comparison with the TMD approach are briefly discussed.
In the two papers published recently, we apply collinear expansion to both inclusive ($e^+ e^- \to h+X$) and semi-inclusive ($e^+ e^- \to h + \bar q + X$) hadron production in $e^+ e^-$ annihilation to derive a formalism suitable for a systematic study of leading as well as higher twist contributions to fragmentation functions at the tree level. We carry out the calculations for hadrons with spin-0, spin-1/2 as well as spin-1. This proceeding is mainly a summary of these two papers.
