We study the single spin asymmetry (SSA) induced by purely gluonic correlation inside a nucleon, in particular, by the three-gluon correlation functions in the transversely polarized nucleon, $p^\uparrow$. This contribution is embodied as a twist-3 mechanism in the collinear factorization framework and controls the SSA to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $ep^\uparrow \rightarrow eDX$. We define the relevant three-gluon correlation functions in the nucleon, and determine their complete set at the twsit-3 level taking into account symmetry constraints in QCD. We derive the single-spin-dependent cross section for the $D$-meson production in SIDIS, taking into account all the relevant contributions at the twist-3 level. The result is obtained in a manifestly gauge-invariant form as the factorization formula in terms of the three-gluon correlation functions and reveals the five independent structures with respect to the dependence on the azimuthal angle for the produced $D$ meson. We also demonstrate the remarkable relation between the twist-3 single-spin-dependent cross section and twist-2 cross sections for the $D$-meson production, as a manifestation of universal structure behind the SSA in a variety of hard processes.
In this paper we study the double longitudinal spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering (SIDIS). We calculate a unknown twist-3 dihadron fragmentation function $\widetilde{D}^\sphericalangle$ within a spectator model which has been used successfully in describing the dihadron production in both the unpolarized and the single polarized processes. The collinear picture, in which the transverse momentum of the final state hadron pair is integrated out, has been considered. The $\cosϕ_R$ azimuthal asymmetry arises from the coupling $e_L H_1^\sphericalangle$…
We investigate the transverse target spin asymmetry $A^{\sinϕ_{S}}_{UT}$ for the unpolarized $Λ$ production in semi-inclusive deep inelastic scattering with the transverse momentum of the final-state lambda hyperon being integrated out. The asymmetry is contributed by the product of the transversity distribution function $h_1(x)$ of the nucleon and the collinear twist-3 fragmentation function $\tilde{H}(z)$ of the $Λ$ hyperon. The later one originates from the quark-gluon-quark correlation and is a naive time-reversal-odd function. We calculate $\tilde{H}$ of the $Λ$ hyperon by adopt a diquark…
We investigate the transverse momentum weighted azimuthal asymmetry with a $\sin\left(3ϕ_h -ϕ_S\right)$ modulation in electroproduction of charged pion production off the transversely polarized proton. The asymmetry is contributed by the product of the second transverse-moment of the pretzelosity distribution function and the first transverse-moment of the Collins function. Using the extracted result for the proton pretzelosity and the available parametrization for the pion Collins function, we numerically predict the $P_{hT}^3$-weighted $\sin\left(3ϕ_h -ϕ_S\right)$ asymmetry for charged pion …
Single Transverse-Spin Asymmetry in Open Charm Production in SIDIS
讨论了在半包容DIS（SIDIS），$e p^\uparrow \rightarrow e D X$中大横动量$D$介子产生中观察到的单横自旋不对称性。这种贡献体现为共线因子分解中的twist-3机制，它是由横极化核子内部的纯胶子关联，特别是三胶子关联效应引起的。我们导出了首阶QCD中相应SSA的第一个完整公式，揭示了产生的$D$介子的五种独立结构对方位角的依赖关系.我们的结果服从普遍的结构背后的SSA在各种硬过程。本文给出了与未来电子离子对撞机相关的运动学条件下$D$ -介子产生的SSA公式的数值计算。
We consider the azimuthal distribution of the final observed hadron in semi-inclusive deep-inelastic scattering and the lepton pair in the Drell-Yan process. In particular, we focus on the $\cos ϕ$ modulation of the unpolarized cross section and on its dependence upon transverse momentum. At low transverse momentum, for these observables we propose a factorized expression based on tree-level approach and conjecture that the same formula is valid in transverse-momentum dependent (TMD) factorization when written in terms of subtracted TMD parton distributions. Our formula correctly matches with …
We investigate the single transverse-spin asymmetry with a $\sin (ϕ_h-ϕ_S)$ modulation in the charged Kaon produced and in $Λ$ hyperon produced SIDIS process within the theoretical framework of transverse momentum dependent (TMD) factorization at the next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of Sivers function and the unpolarized fragmentation function $D_1$ for the produced hadron. The parametrization for the proton Qiu-Sterman function, which is closely related to the Sivers function, is adopted to numerically estimate the Sivers asymmetry at the kine…
We investigate the transverse momentum weighted Sivers asymmetries in the processes with transversely polarized proton target, including the $\frac{P_{hT}}{zM_p}\sin (ϕ_h-ϕ_S)$ weighted asymmetry in charged hadron production in semi-inclusive deeply inelastic scattering (SIDIS) and the $\frac{q_T}{M_p}\sin (ϕ_S)$ weighted asymmetry in $π^- p$ Drell-Yan process. Due to the integration over the transverse momentum, the weighted asymmetries can be expressed as the product of the transverse-moments of the transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation fu…
We analyze the Sivers asymmetry in both Drell-Yan (DY) production and semi-inclusive deep inelastic scattering (SIDIS), while considering properly defined transverse momentum dependent parton distribution and fragmentation functions and their QCD evolution. After finding a universal non-perturbative spin-independent Sudakov factor that can describe reasonably well the world's data of SIDIS, DY lepton pair and $W/Z$ production in unpolarized scatterings, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. Then we make…
We investigate the $\sin (ϕ_Λ-ϕ_S)$ single-spin asymmetry in the transversely polarized $Λ$ production in semi-inclusive deeply inelastic scattering process within the framework of the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function $D_{1T}^\perp$ of the $Λ$ hyperon and the unpolarized TMD distribution function $f_1$ of the target nucleon. We apply two sets of $D_{1T}^{\perp,Λ^\uparrow/q}$, the spectator diquark model result and available parametrization, to numerically estimate the $\sin (ϕ_Λ-ϕ_S)$…
We present a study on the double longitudinal-spin asymmetry of dihadron production in semi-inclusive deep inelastic scattering, in which the total transverse momentum of the final-state hadron pairs is integrated out. In particular, we investigate the origin of the $\cosϕ_R$ azimuthal asymmetry for which we take into account the coupling of the helicity distribution $g_1$ and the twist-3 dihadron fragmentation function $\widetilde{D}^{\sphericalangle}$. We calculate the $s$-wave and $p$-wave interference term $\widetilde{D}^{\sphericalangle}_{ot}$ in a spectator model. We estimate the $\cosϕ_…
We study the $\sin2ϕ_h$ azimuthal asymmetry of charged and neutral pion productions off the longitudinally polarized nucleon targets in semi-inclusive deeply inelastic scattering (SIDIS) process within the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the TMD distribution $h_{1L}^{\perp}$ and the Collins fragmentation function $H_{1}^\perp$. We adopt the Wandzura-Wilczek-type~(WW-type) approximation for $h_{1L}^{\perp}$ and two different parametrizations on the nonperturbative part of TMD evolution for $h_{1L}^{\perp}$ and $H_{1}^\perp$. …
In this paper we study the single spin asymmetry $A_{UT}^{\sin(ϕ_h-ϕ_S)}$ of a single hadron production in semi-inclusive deep inelastic scattering (SIDIS) within the framework of transverse momentum dependent (TMD) factorization up to next-to-leading logarithmic (NLL) order of QCD. The asymmetry is contributed by the convolution of the Sivers function and the unpolarized fragmentation function. Specifically, the Sivers function in the coordinate space and perturbative region can be represented as the convolution of the $C$-coefficients and the corresponding collinear correlation functions, am…
In the fragmentation of a transversely polarized quark a left-right asymmetry, the Collins asymmetry, is expected for each hadron produced in the process $μN \rightarrow μ' h^{+} h^{-} X$. Similarly, an asymmetry is also expected for the hadron pair, the dihadron asymmetry. Both asymmetries have been measured to be different from zero on transversely polarised proton targets and have allowed for first extractions of the transversity distributions. From the high statistics COMPASS data we have further investigated these asymmetries getting strong indications that the two mechanisms are driven b…
We study the $\cos{ϕ_h}$ azimuthal asymmetry in double polarized semi-inclusive pion production by considering dynamical twist-3 effects. In particular, we evaluate the role of the transverse momentum dependent distributions $e_L(x, k_T^2)$ and $g_L^\perp(x, k_T^2)$ on the asymmetry. Using two different sets of spectator model results for these distributions, we predict the $\cos{ϕ_h}$ asymmetry of $π^+$, $π^-$, and $π^0$ at the kinematic configuration available at CLAS, HERMES and COMPASS. Our estimates show that the asymmetries are positive for all the pions and could be accessed by CLAS and…
We study the Sivers asymmetry in semi-inclusive deep inelastic scattering: the three-gluon correlation function contribution. At the cross section level, we establish the matching between the twist-3 collinear factorization approach and the transverse momentum dependent factorization formalism at the moderate transverse momentum region. The so-called coefficient functions when one expands the quark Sivers function in terms of three-gluon correlation functions are derived, which are essential components in the usual transverse momentum dependent evolution formalism. Finally we calculate the tra…
The transverse-spin asymmetry $A^{\sinϕ_{S_Λ}}_{UUT}$ in $Λ$ production in SIDIS within the collinear framework
Centre for Theoretical and Computational Physics, College of Physics, Qingdao University（青岛大学物理学院理论计算物理中心）；School of Physics, Southeast University（东南大学物理学院）
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 $h_L\, H_{1}^{\sphericalangle}$ as well as the coupling $g_1 \,\widetilde{G}^{\sphericalangle}$. We calculate the unknown twist-3 dihadron fragmentation function $\widetilde{G}^{\sphericalangle}$ using a spectator model which is successful in describing the dihadron production in the unpo…
New data on the Sivers azimuthal asymmetry measured in semi-inclusive deep-inelastic scattering processes have recently been released by the COMPASS Collaboration at CERN. Their increased precision and their particular binning, in terms of $Q^2$ as well as $x$, motivates a new extraction of the Sivers function, within the framework of a simple and transparent parametrization. Signals of TMD effects visible in the Sivers asymmetries are critically assessed. A thorough study of the uncertainties affecting the extracted Sivers function is presented, including the low-$x$ and large-$x$ regions.
In this paper we study the single longitudinal spin asymmetry $A_{UL}^{\sin(ϕ_h-ϕ_R)}$ of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) via helicity-dependent dihadron fragmentation function (DiFF), which describes the correlation of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair. Recently experimental searching for this azimuthal asymmetry in dihadron SIDIS by the COMPASS Collaboration yielded a very small signal. Here we calculate this unknown T-odd DiFF $G_1^\perp$ using a spectator model to access the a…
Nuclear dependence of azimuthal asymmetry in semi-inclusive deep inelastic scattering
在广义因式分解的框架下，半包容深度非弹性散射（SIDIS）截面可以表示为共线硬部分和横动量相关（TMD）部分子分布和关联的乘积.研究了方位角不对称性<cos θ> $ 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 the azimuthal asymmetry $ < \cos θ>$。结果表明，方位角不对称性被多部分子散射抑制，抑制的横向动量依赖于核子中扭曲2和3夸克分布的相对形状。本文利用核子中TMD扭曲2和3夸克分布的高斯近似，证明了方位角不对称性的核依赖性，并估计了碎裂引起的拖尾效应。
Information on the Sivers distribution and the Collins fragmentation functions and their transverse momentum dependence is mainly based on fitting single spin asymmetry data from semi-inclusive deep inelastic scattering (SIDIS). Independent information, respectively on the Sivers distribution and the Collins fragmentation, can be obtained from Drell-Yan and $e^+e^-$ annihilation processes. In the SIDIS case, the transverse momentum of the final observed hadron, which is the quantity measured, is generated both by the average transverse momentum in the distribution and in the fragmentation func…
The single longitudinal spin asymmetry $A_{UL}^{\sin(2ϕ_h-2ϕ_R)}$ of dihadron production in semi-inclusive deep inelastic scattering (SIDIS) is examined through helicity-dependent dihadron fragmentation function (DiFF) $G_1^\perp$. The correlation of the longitudinal polarization of a fragmenting quark with the transverse momenta of the produced hadron pair is illustrated by this DiFF. The experimental investigation for this azimuthal asymmetry in dihadron SIDIS by the COMPASS Collaboration has lately yielded a very small signal. Here, the unknown T-odd dihadron fragmentation function $G_1^\pe…
In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of $Λ_{QCD}$, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than $Λ_{QCD}$ but much smaller than $Q$ which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be fac…
Motivated by a novel origin of transverse single spin asymmetry (SSA) in semi-inclusive Deep Inelastic Scattering (SIDIS) uncovered by some of us, we quantitatively investigate its impact on the theoretical understanding of the mechanism responsible for SSA. This new contribution from the quark-initiated channel first appears in two-loop perturbation theory and involves the $g_T(x)$ distribution. We point out another entirely analogous piece from the gluon-initiated channel proportional to the gluon helicity distribution $ΔG(x)$. Both contributions are solely expressed in terms of twist-two po…
We present model predictions of Collins asymmetries for proton in the SIDIS process for $π^+$ and $π^-$ channels. We use a recently proposed light-front quark-diquark model for proton with the light-front wave functions predicted in soft-wall AdS/QCD. The model predictions are compared with the HERMES and COMPASS data.
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 a…
Preliminary results obtained by the COMPASS experiment for longitudinal-spin-dependent azimuthal asymmetries in single-hadron muoproduction off protons are presented for the first time. The analysis was carried out on the full data sample collected by COMPASS with longitudinally polarized proton ($NH_3$) target in 2007 and 2011 using 160~\gvc and 200~\gvc muon beams, correspondingly. Within QCD parton model approach extracted asymmetries are giving access to the specific convolutions of certain transverse-momentum-dependent \textit{twist-2} and \textit{higher twist} parton distribution functio…
