Accessing quark helicity in e+e−e^+e^- and SIDIS via dihadron correlations

The correlation between the longitudinal polarization of a fragmenting quark and the transverse momenta of the produced hadrons was predicted over two decades ago. Nevertheless, experimental searches in the electron-positron annihilation process, both through the so-called jet handedness measurements by the {\tt SLD} Collaboration and more recently via the measurements of the azimuthal asymmetry containing the helicity-dependent dihadron fragmentation function (DiFF) by the $\textrm{BELLE}$ Collaboration, did not yield a signal. We will first discuss our recent explanation of the zero result at $\textrm{BELLE}$, and the two new methods for accessing the helicity-dependent DiFFs both in the electron-positron annihilation experiments, and in the semi-inclusive deep inelastic scattering (SIDIS) experiments with a longitudinally polarized target. We will also for the first time describe yet another, new method for accessing the helicity-dependent DiFFs in SIDIS using polarized beam asymmetry. Finally, we will present a new Monte Carlo calculation of the specific Fourier moments of the helicity-dependent DiFF entering in to the new asymmetries, performed within the extended quark-jet model, and compare the results to those for the interference DiFF.Comment: 5 pages, 1 figure. To appear in PoS DIS201

Studies of Azimuthal Modulations in Two Hadron Fragmentation of a Transversely Polarised Quark

We study the azimuthal modulations of dihadron fragmentation functions (DiFFs) of a transversely polarised quark using an NJL-jet based model that incorporates the Collins effect for single hadron emission. The DiFFs are extracted as Monte Carlo (MC) averages of corresponding multiplicities using their probabilistic interpretation. To simplify the model and highlight the possible mechanisms that create this modulation, we choose the elementary Collins function to be proportional to the elementary unpolarised fragmentation and a constant probability ($P_{SF}$) for the quark to flip its spin after a single hadron emission. Moreover, as a leading order calculation, only one of the produced hadrons in the decay chain of the quark is produced with elementary Collins modulation. We calculate the dependence of the polarised DiFFs on various angles such as the azimuthal angle of the single hadron and the angle of the two hadron production plane $\varphi_R$ for several values of $P_{SF}$. We observe that the polarised DiFFs for oppositely charged pion pairs exhibit a $\sin(\varphi_R)$ modulation. This effect is induced purely via the elementary Collins effect and persists even when the quark completely depolarises after a single hadron emission ($P_{SF}=0.5$). Moreover, similar sine modulations are present in the distribution of pion pairs with respect to the azimuthal angle of their total transverse momentum, $\varphi_T$.Comment: 10 pages, 12 figures - small updates and added references, to comply with the version to be published in PL

1/Nc Expansion in QCD: Double-Line Counting Rules and the Undeservingly Discarded U(1) Ghost

The 1/Nc expansion is one of the very few methods we have for generating a systematic expansion of QCD at the energy scale relevant to hadron structure. The present formulation of this theory relies on the double-line notation for calculating the leading order of a diagram in the 1/Nc expansion, where the local SU(Nc) gauge symmetry is substituted by a U(Nc) symmetry and the associated U(1) ghost field is ignored. In the current work we demonstrate the insufficiency of this formulation for describing certain non-planar diagrams. We derive a more complete set of Feynman rules that include the U(1) ghost field and provide a useful tool for calculating both color factors and 1/Nc orders of all color-singlet diagrams

Collins Fragmentation Function within NJL-jet Model

The NJL-jet model is extended to accommodate hadronization of a transversely polarized quark in order to explore the Collins effect within a multihadron emission framework. This is accomplished by calculating the polarized quark spin flip probabilities after a pseudoscalar hadron emission and the elementary Collins functions. The model is used to calculate the number densities of the hadrons produced in the polarized quark's decay chain. The full Collins fragmentation function is extracted from the sine modulation of the polarized number densities with respect to the polar angle between the initial quark's spin and hadron's transverse momentum. Two cases are studied here. First, a toy model for elementary Collins function is used to study the features of the transversely polarized quark-jet model. Second, a full model calculation of transverse momentum dependent pion and kaon Collins functions is presented. The remarkable feature of our model is that the 1/2 moments of the favored Collins fragmentation functions are positive and peak at large values of z but decrease and oscillate at small values of z. The 1/2 moments of the unfavored Collins functions have comparable magnitude and opposite sign to the favored functions, vanish at large z and peak at small values of z. This feature is observed for both the toy and full models and can be attributed to the quark-jet picture of hadronization. Moreover, the transverse momentum dependencies of the model Collins functions differ significantly from the Gaussian form widely used in the empirical parametrizations. Finally, a naive interpretation of the Schafer-Teryaev sum rule is proven not to hold in our model, where the transverse momentum conservation is explicitly enforced. This is attributed to the sizable average transverse momentum of the remnant quark that needs to be accounted for to satisfy the transverse momentum sum-rule.Comment: 15 pages, 22 figures. v2 - minor changes/additions to conform to the journal published versio

Monte-Carlo Approach to Calculating the Fragmentation Functions in NJL-Jet Model

Recent studies of the fragmentation functions using the Nambu--Jona-Lasinio (NJL) - Jet model have been successful in describing the quark fragmentation functions to pions and kaons. The NJL-Jet model employs the integral equation approach to solve for the fragmentation functions in quark-cascade description of the hadron emission process, where one assumes that the initial quark has infinite momentum and emits an infinite number of hadrons. Here we introduce a Monte Carlo (MC) simulation method to solve for the fragmentation functions,, that allows us to relax the above mentioned approximations. We demonstrate that the results of MC simulations closely reproduce the solutions of the integral equations in the limit where a large number of hadrons are emitted in the quark cascade. The MC approach provides a strong foundation for the further development of the NJL-Jet model that might include many more hadronic emission channels with decays of the possible produced resonances, as well as inclusion of the transverse momentum dependence (TMD), all of which are of considerable importance to the experimental studies of the transverse structure of hadrons.Comment: 5 pages, 3 figures, Proceedings of "TROPICAL QCD II Workshop

Kaon fragmentation function from NJL-jet model

The NJL-jet model provides a sound framework for calculating the fragmentation func- tions in an effective chiral quark theory, where the momentum and isospin sum rules are satisfied without the introduction of ad hoc parameters [1]. Earlier studies of the pion fragmentation func- tions using the Nambu-Jona-Lasinio (NJL) model within this framework showed good qualitative agreement with the empirical parameterizations. Here we extend the NJL-jet model by including the strange quark. The corrections to the pion fragmentation function and corresponding kaon fragmen- tation functions are calculated using the elementary quark to quark-meson fragmentation functions from NJL. The results for the kaon fragmentation function exhibit a qualitative agreement with the empirical parameterizations, while the unfavored strange quark fragmentation to pions is shown to be of the same order of magnitude as the unfavored light quark's. The results of these studies are expected to provide important guidance for the analysis of a large variety of semi-inclusive data.Comment: 6 pages, 9 figures, Proceedings of "Achievements and New Directions in Subatomic Physics: Workshop in Honour of Tony Thomas's 60th Birthday

Dihadron Fragmentation Functions within the NJL-jet Model

Dihadron Fragmentation Functions (DFF) provide a vast amount of information on the intricate details of the parton hadronization process. Moreover, they provide a unique access to the "clean" extraction of nucleon transversity parton distribution functions in semi inclusive deep inelastic two hadron production process with a transversely polarised target. The NJL-jet model has been extended for calculations of light and strange quark unpolarised DFFs to pions, kaons and several vector mesons. This is accomplished by using the probabilistic interpretation of the DFFs, and employing the NJL-jet hadronization model in the Monte Carlo simulations that includes the transverse momentum of the produced hadrons. The strong decays of the vector mesons and the subsequent modification of the pseudoscalar meson DFFs are also considered. The resulting pseudoscalar meson DFFs are strongly influenced by the decays of the relevant vector mesons. This is because of the large combinatorial factors involved in counting the number of the hadron pairs that include the decay products. The evolution of the DFFs from the model scale to a typical experimental scale has also been performed.Comment: 11 pages, 11 figure