We investigate the theoretical framework of the cos 2φ azimuthal asymmetry contributed by the coupling of two Boer-Mulders functions in the dilepton production unpolarized πp Drell-Yan process by applying the transverse momentum dependent factorization at leading order. We adopt the model calculation results of the unpolarized distribution function f1 and Boer-Mulders function h ⊥ 1 of pion meson from the light-cone wave functions. We take into account the transverse momentum evolution effects for both the distribution functions of pion and proton by adopting the existed extraction of the nonperturbative Sudakov form factor for the pion and proton distribution functions. An approximate kernel is included to deal with the energy dependence of the Boer-Mulders function related twist-3 correlation function T (σ) q,F (x, x) needed in the calculation. We numerically estimate the Boer-Mulders asymmetry νBM as the functions of xp, xπ, xF and qT considering the kinematics at COMPASS Collaboration. 13.85.Qk, 13.88.+e I. INTRODUCTIONThe Boer-Mulders function is a transverse momentum dependent (TMD) parton distribution function (PDF) that describes the transverse-polarization asymmetry of quarks inside an unpolarized hadron [1,2]. Arising from the correlation between the quark transverse spin and the quark transverse momentum, the Boer-Mulders function manifests novel spin structure of hadrons [3]. For a while the very existence of the Boer-Mulders function was not as obvious. This is because, similar to its counterpart, the Sivers function, the Boer-Mulders function was thought to be forbidden by the time-reversal invariance of QCD [4]. For this reason, they are classified as T-odd distributions. However, model calculations incorporating gluon exchange between the struck quark and the spectator [5,6], together with a re-examination [7] on the time-reversal argument, show that T-odd distributions actually do not vanish. It was found that the gauge-links [7][8][9][10] in the operator definition of TMD distributions play an essential role for a nonzero Boer-Mulders function.As a chiral-odd distribution, the Boer-Mulders function has to be coupled with another chiral-odd distribution/fragmentation function to survive in a high energy scattering process. Two promising processes for accessing the Boer-Mulders function are the Drell-Yan and the semi-inclusive deep inelastic scattering (SIDIS) processes. In the former case, the corresponding observables are the cos 2φ azimuthal angular dependence of the final-state dilepton, which is originated by the convolution of two Boer-Mulders functions from each hadron. This effect was originally proposed by Boer [1] to explain the violation of the Lam-Tung relation observed in πN Drell-Yan process[11], a phenomenon which cannot be understood from purely perturbative QCD effects [12][13][14]. Similar asymmetry was also observed in the pd and pp Drell-Yan processes, and the corresponding data were applied to extract the proton Boer-Mulders function [15][16][17][18]. Besides the parmater...

No abstract

We study the single longitudinal-spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering process. We consider the collinear picture in which the transverse momentum of the final-state hadron pair is integrated out, such that the sin ϕ R azimuthal asymmetry arises from the coupling h L H ∢ 1 as well as the coupling g 1G ∢. We calculate the unknown twist-3 dihadron fragmentation functionG ∢ using a spectator model which is successful in describing the dihadron production in the unpolarized process. Using the spectator model results for the quark distributions and dihadron fragmentation functions, we estimate the sin ϕ R asymmetry of dihadron production in semi-inclusive deep inelastic scattering at the kinematics of COMPASS and compare it with the COMPASS preliminary data. In addition, the prediction on the sin ϕ R asymmetry at the typical kinematics of the future Electron Ion Collider is also presented. In order to test the reliability of the spectator model estimate, we compare the model result for the distribution h L with the Wandzura-Wilczek approximation for that distribution, and compare H ∢ 1 with the existing parametrization. Although the asymmetry is dominated by the h L H ∢ 1 term, we find that the contribution from the g 1G ∢ term should also be taken into account in certain kinematical region.

No abstract

We investigate the transverse polarization of the $$\Lambda $$ Λ hyperon in the processes $$e^+e^-\rightarrow \Lambda ^\uparrow \pi ^\pm X$$ e + e - → Λ ↑ π ± X and $$e^+e^-\rightarrow \Lambda ^\uparrow K^\pm X$$ e + e - → Λ ↑ K ± X within the framework of the transverse momentum dependent (TMD) factorization. The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function (PFF) $$D_{1T}^\perp $$ D 1 T ⊥ of the lambda hyperon and the unpolarized fragmentation function $$D_1$$ D 1 of pion/kaon. We adopt the spectator diquark model result for $$D_{1T}^{\perp }$$ D 1 T ⊥ to numerically estimate the transverse polarization in $$e^+e^-\rightarrow \Lambda ^\uparrow h X$$ e + e - → Λ ↑ h X process at the kinematical region of Belle Collaboration. To implement the TMD evolution formalism of the fragmentation functions, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the fragmentation functions of the $$\Lambda $$ Λ , pion and kaon. It is found that our prediction on the polarization in the $$\Lambda \pi ^+$$ Λ π + production and $${\bar{\Lambda }} \pi ^-$$ Λ ¯ π - is consistent with the recent Belle measurement in size and sign, while the model predictions on the polarizations in $$\Lambda \pi ^-$$ Λ π - and $$\Lambda K^\pm $$ Λ K ± productions show strong disagreement with the Belle data. The reason for the discrepancies is discussed and possible approaches to improve the calculation in the future are also discussed.

We investigate the single transverse-spin asymmetry with a sin(2φ − φS) modulation in the pioninduced Drell-Yan process within the theoretical framework of the transverse momentum dependent factorization. The asymmetry is contributed by the convolution of the Boer-Mulders function and the transversity. We adopt the model results for the distributions of the pion meson from the light-cone wavefunction approach and the available parametrization for the distributions of the proton to numerically estimate the sin(2φ − φS) asymmetry in π − p Drell-Yan at the kinematics of the COMPASS at CERN. To implement the TMD evolution formalism of parton distribution functions, we apply the recently extracted nonperturbative Sudakov form factor associated with the distribution functions of the proton and the pion. It is found that our prediction on the single transverse-spin dependent asymmetry sin(2φ − φS) as functions of xp, xπ, xF and q ⊥ is qualitatively consistent with the recent COMPASS measurement in both sign and magnitude. I. INTRODUCTIONThe Boer-Mulders function, denoted by h ⊥ 1 , is one of the eight transverse momentum dependent (TMD) parton distribution functions (PDFs) describing the partonic structure of hadrons at leading-twist level. It represents the transversely polarization asymmetry of quarks inside an unpolarized hadron [1,2] arising from the correlation between the quark spin and the quark transverse momentum, thereby it manifests the novel structure of hadrons. However, the very existence of the Boer-Mulders function was not so obvious. Similar to its chiral-even partner-the Sivers function f ⊥ 1T [3], the Boer-Mulder function was initially thought to vanish under the constraint of (naive) time reversal invariance of QCD [4]. The situation was changed after explicit model calculations [5][6][7] incorporating gluon exchange between the struck quark and the spectator shows that the T-odd distributions can actually survive. The crucial ingredient in the argument is the Wilson lines (or the gauge links) appearing in the full gange-invariant definition of TMDs [8,9]. The presence of the Wilson lines also indicates that the T-odd distributions, such as Sivers function and the Boer-Mulders function are process dependent, i.e., they change sign [6][7][8] between the semi-inclusive deeply inelastic scattering and Drell-Yan process, a vital prediction which needs verification by future experimental measurement. In the last decades, the Boer-Mulders function of the proton as well as that of the pion has been studied intensively in literature [7, by models and phenomenological analysis.As the Boer-Mulders function is a chiral-odd distribution function, it has to be coupled with another chirlal-odd distribution/fragmentation function to survive in a high energy scattering process. A promising process for accessing the Boer-Mulders function is the unpolarized Drell-Yan process, which displays an azimuthal dependence of the finalstate dilepton with the cos 2φ modulation. As proposed by Boer [2], the coupling of two Boer-...

We investigate the single transverse-spin asymmetry with a sin(φ − φS) modulation in the transversely polarized Λ hyperon production process e + e − → Λ ↑ πX within the framework of the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the transversely polarized fragmentation function D ⊥ 1T and the unpolarized fragmentation function D1. We adopt the spectator diquark model result for D ⊥ 1T to numerically estimate the sin(φ − φS) asymmetry in e + e − → Λ ↑ πX process at the kinematical region of Belle and BaBar Collaboration. We also apply the recent parameterized result for D ⊥1T to perform the calculation as a comparison. To implement the TMD evolution formalism of the fragmentation functions, we use the nonperturbative Sudakov form factor associated with the fragmentation functions of the Λ and the pion. It is found that our prediction on the sin(φ − φS) asymmetry as functions of P hT , z1 and z2 is sizable and could be measured at Belle and BaBar.

A tumbler screen type residual film–impurity mixture wind separator as a key equipment for secondary utilization of farmland residual film. During the working process, the proportion of impurities in the separated waste mulch film intermittently increases, resulting in poor working stability of the device, which may hamper long-term operation. In this study, the material inside the separation unit was continuously monitored, and the main factor affecting separator per-formance was determined to be the challenges in the effective depolymerization of some residual film–impurity mixtures. The principles of agglomeration and depolymerization of the residual film–impurity mixtures were analyzed using computational fluid dynamics (CFD) and discrete element method (DEM) flow-solid coupling simulation methods. The key factor affecting the disaggregation of the mixture was the collision force between the residual film–impurity mixture and the trommel screen. The collision force was maximum when the residual film–impurity mixture first collided with the trommel screen when it was fed into the separation device. As determined by force analyses, the key factors affecting the collision force of the process were the material feeding amount and the structure of the inlet. Furthermore, simulations were carried out for different inlet structure forms; the evaluation index was the maximum collision force of the residual film–impurity mixture agglomerate on the trommel screen. The best disaggregation effect was obtained with a square feed inlet and at a feeding rate of 202 kg/h. A prototype was built using these specifications for verification. The average value of the ratio of impurities in the re-sidual film was 6.966%, the coefficient of variation was 7.38%, and the dispersion of statistical results was small. The ratio of impurities in the residual film was kept constant during the con-tinuous operation of the wind separator. Thus, this study analyzed the agglomerate disaggregation process and provided theoretical insights for deter-mining the optimal structures of the inlets of various cleaning devices and the feeding volumes.