New study of the Boer-Mulders function: Implications for the quark and hadron transverse momenta
E. Christova, D. Kotlorz, E. Leader
备注：
15 pages, 9 figures (22 eps plots). This is a more complete study of the subject than in our previous paper arXiv:1909.08218. In this version, Sec. II and V are modified, Fig.5 is replaced, with corresponding slight modifications in the Conclusions; matches published version in Phys.Rev.D
In series of papers the Boer-Mulders function for a given quark flavour has been extracted: (i) from data on semi-inclusive deep inelastic scattering, using the simplifying, but theoretically inconsistent, assumption that it is proportional to the Sivers function for each quark flavour and (ii) from data on Drell-Yan reactions. In earlier papers, using the semi-inclusive deep inelastic COMPASS deuteron data on the $\langle\cosϕ_h\rangle$ and $\langle\cos 2 ϕ_h\rangle$ asymmetries, we extracted the collinear $x_{_{\!B}}$ dependence of the Boer-Mulders function for the sum of the valence quarks $Q_V=u_V + d_V$ using a small number of model dependent assumptions and found a significant disagreement with the analysis in (i). In the present paper, we provide a more complete analysis of the semi-inclusive deep inelastic scattering reaction, including a discussion of higher twist and interaction-dependent terms, and also a comparison with the Boer-Mulders function extracted from data on the Drell-Yan reaction. We confirm that the proportionality relation of the BM function to the Sivers function, for each quark flavour, fails badly, but find that it holds rather well if applied to the nonsinglet valence-quark combination, $Q_V$. We also find good agreement with the results of the Drell-Yan analysis. Furthermore, we obtain interesting information on the quark transverse momentum densities in the nucleon and on the hadron transverse momentum dependence in quark fragmentation.
We extract the Boer-Mulders functions for the proton by combining the unpolarized pd and pp Drell-Yan data measured by the E866/NuSea Collaboration by the assumption that the $\cos 2ϕ$ asymmetry is from the Boer-Mulders function. Using the extracted Boer-Mulders functions, we present the predictions for the $\cos 2 ϕ$ asymmetries in future pp experiments at J-PARC and $p \bar{p}$ experiments at PANDA and PAX.
We find the light-cone wavefunction representations of the Sivers and Boer-Mulders distribution functions. A necessary condition for the existence of these representations is that the light-cone wavefunctions have complex phases. We induce the complex phases by incorporating the final-state interactions into the light-cone wavefunctions. For the scalar and axial-vector diquark models for nucleon, we calculate explicitly the Sivers and Boer-Mulders distribution functions from the light-cone wavefunction representations. We obtain the results that the Sivers distribution function has the opposit…
We extract the Boer-Mulders functions of valence and sea quarks in the proton from unpolarized $p+D$ Drell-Yan data measured by the FNAL E866 Collaboration. Using these Boer-Mulders functions, we calculate the $\cos 2 ϕ$ asymmetries in unpolarized $pp$ Drell-Yan processes, both for the FNAL E866/NuSea and the BNL Relativistic Heavy Ion Collider (RHIC) experiments. We also estimate the $\cos 2 ϕ$ asymmetries in the unpolarized $p\bar{p}$ Drell-Yan processes at GSI.
The sign of the Boer-Mulders function $h_1^\perp$ is related to the sign of the GPD $\bar{E}_T$ through the mechanism of chromodynamic lensing. Model calculations of the sign of $\bar{E}_T$ indicate that the sign of $h_1^\perp$ may be the same in all ground state hadrons.
Chirally odd generalized parton distributions (GPDs) and the Boer-Mulders function provide valuable information about spin-orbit correlations for quarks in nucleons and other hadrons. We compare results for the relevant GPD $\bar{E}^q_T$ from a variety of phenomenological models as well as recent lattice results. We find that $\bar{E}^q_T>0$ for nucleons as well as the pion and for both $u$ and $d$ quark. As a result, the corresponding Boer Mulders functions are all expected to be negative. The sign of $\bar{E}^q_T$ arises from the relative sign between the upper and lower Dirac components for…
We present a phenomenological analysis of the $\cos 2 ϕ$ asymmetry recently measured by the COMPASS and HERMES collaborations in unpolarized semi-inclusive deep inelastic scattering. In the kinematical regimes explored by these experiments the asymmetry arises from transverse-spin and intrinsic transverse-momentum effects. We consider the leading-twist contribution, related to the so-called Boer-Mulders transverse-polarization distribution $h_1^{\perp}(x, k_T^2)$, and the twist-4 Cahn contribution, involving unpolarized transverse-momentum distribution functions. We show that a reasonably good…
The fractured Boer-Mulders functions describe an inriguing class of polarization effects for the production of baryons in the target fragmentation region of deep-inelastic processes. These functions characterize transverse momentum asymmetries related to the spin orientation for different flavors of axial vector diquarks in an unpolarized ensemble of protons just as the familiar Boer-Mulders functions characterize transverse momentum asymmetries connected to the spin orientation of quarks in unpolarized targets. The asymmetries of the fractured Boer-Mulders effect originating in the proton dis…
At present, the Boer-Mulders function for a given quark flavour has been extracted from data on semi-inclusive deep inelastic scattering using the simplifying, but theoretically inconsistent, assumption that it is proportional to the Sivers function for each quark flavour. In this paper, using the latest semi-inclusive deep inelastic COMPASS deuteron data on the $\langle\cosϕ_h\rangle$ and $\langle\cos 2 ϕ_h\rangle$ asymmetries we extract the collinear $x_B$-dependence of the Boer-Mulders function for the sum of the valence quarks $Q_V=u_V + d_V$ in an essentially model independent way, and fi…
We present a phenomenological analysis of the $q_{\mathrm{T}}$-weighted transverse spin dependent azimuthal asymmetry recently measured by the COMPASS Collaboration in polarized pion-proton Drell-Yan process. In the kinematical regimes explored by experiments, we consider the leading-twist contributions from the Boer-Mulders distribution functions $h_{1}^{\perp}(x,k_{\mathrm{T}}^{2})$ of both the pion and the proton, the transversity distribution $h_{1}(x,k_{\mathrm{T}}^{2})$ and the pretzelosity distribution $h_{1\mathrm{T}}^{\perp}(x,k_{\mathrm{T}}^{2})$ of the proton, with the unpolarized t…
We obtain the leading twist T-odd quark transverse momentum dependent parton distribution functions (TMDs) of the proton, namely the Sivers function, $f_{1T}^{\perp q}(x,p_\perp^2)$, and the Boer-Mulders function, $h_1^{\perp q}(x,p_\perp^2)$, in a light-front quark-diquark model constructed with the wave functions predicted by the soft-wall AdS/QCD. The gluon rescattering is crucial to predict a nonzero T-odd TMDs. We study the utility of a nonperturbative $SU(3)$ gluon rescattering kernel going beyond the usual approximation of perturbative $U(1)$ gluons. The spin asymmetries in semi-inclusi…
We show that measuring the $\cos 2ϕ$ angular dependence in unpolarized Drell-Yan processes with $π^-$ beams colliding on proton and deuteron targets can determine the ratio of the Boer-Mulders functions for $d$ and $u$ quarks inside the proton $h_1^{\perp,d}/h_1^{\perp,u}$, which is still lack of theoretical constraint. The comparison of the $\cos 2 ϕ$ asymmetries measured in unpolarized $π^- p$ and $π^- D$ Drell-Yan processes, which are accessible at CERN by the COMPASS collaboration, can help to discriminate whether $h_1^\perp$ effects or QCD vacuum effects are preferred by data.
Using a previous extraction of the quark Boer-Mulders distributions from semiinclusive deep inelastic scattering data, we fit the unpolarized Drell-Yan data on the $\cos 2 ϕ$ asymmetry, determining the antiquark Boer-Mulders distributions. A good agreement with the data is found in the region of low $q_T$, where the transverse-momentum factorization approach applies.
We calculate the time reversal odd (T-odd) generalized transverse momentum dependent parton distributions (GTMDs) $F^o_{1,2}$ and $H^o_{1,1}$ in a light-front quark-diquark model based on ADS/QCD. In the limit of zero momentum transfer, these reduce to the Sivers and Boer-Mulders TMDs respectively. We have incorporated both scalar and axial vector diquarks in the model and obtained an overlap representation of the GTMDs using the light-front wave functions (LFWFs). Contribution from the final state interaction is incorporated at the level of one gluon exchange as a phase factor in the LFWF. We…
A major experimental program is presently underway to determine the Sivers, Boer-Mulders and transversity distributions, vital for understanding the internal structure of the nucleon. To this end we consider the Sivers, Boer-Mulders and transversity azimuthal asymmetries of the difference cross sections of hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized target l+N\to l'+h+X, h=π^\pm, K^\pm, h^\pm. We show that on deuteron target these asymmetries are particularly simple and determine the sum of the valence-quark Q_V=u_V+d_V transverse momentum depen…
The naive time reversal odd (``T-odd'') parton distribution $h_{1}^{\perp}$, the so-called Boer-Mulders function, for both up ($u$) and down ($d$) quarks is considered in the diquark spectator model. While the results of different articles in the literature suggest that the signs of the Boer-Mulders function in semi-inclusive DIS for both flavors $u$ and $d$ are the same and negative, a previous calculation in the diquark-spectator model found that $h_{1}^{\perp(u)}$ and $h_{1}^{\perp(d)}$ have different signs. The flavor dependence is of significance for the analysis of the azimuthal $\cos(2ϕ…
At present, the Boer-Mulders (BM) functions are extracted from asymmetry data using the simplifying assumption of their proportionality to the Sivers functions for each quark flavour. Here we present two independent tests for this assumption. We subject COMPASS data on semi-inclusive deep inelastic scattering on the $\langle\cosϕ_h\rangle$, $\langle\cos 2ϕ_h\rangle$ and Sivers asymmetries to these tests. Our analysis shows that the tests are satisfied with the available data if the proportionality constant is the same for all quark flavours, which does not correspond to the flavour dependence …
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 $f_1$ and Boer-Mulders function $h_1^\perp$ 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 extracti…
The Boer-Mulders transverse momentum-dependent parton distribution (TMD) characterizes polarized quark transverse momentum in an unpolarized hadron. Techniques previously developed for lattice calculations of nucleon TMDs are applied to the pion. These techniques are based on the evaluation of matrix elements of quark bilocal operators containing a staple-shaped Wilson connection. Results for the Boer-Mulders transverse momentum shift in the pion, obtained at a pion mass of $m_π = 518\, \mbox{MeV} $, are presented and compared to corresponding results in the nucleon.
We apply the MIT bag model to study the Boer-Mulders function of the pion, a $T$-odd function that describes the transverse polarization distribution of the quark inside the pion. We simulate the effect of the gauge link through the "one-gluon-exchange" approximation. We consider both the quark helicity nonflip and double-flip contributions. The result in the MIT bag model is compared with those in the spectator models.
A major experimental program is presently underway worldwide to determine the fundamental non-perturbative functions, the Sivers, Boer-Mulders and transversity distributions, which are vital for an understanding of the internal structure of the nucleon. However, at present, many simplifying assumptions are used in extracting these functions from the data. We demonstrate that if the binning of the data in Q^2 is small enough so that Q^2-evolution can be neglected inside a bin, then one can obtain stringent tests of these assumptions. Failure to satisfy these tests implies that the presently ext…
We calculate the two leading-twist transverse momentum dependent distribution functions of the pion meson, the unpolarized distribution $f_{1π}(x,\bm{k}^2_T)$ and the Boer-Mulders function $h_{1π}^\perp (x,\bm{k}^2_T)$, using the pion wave functions derived from a light-cone approach. The evolution effect of the first $\bm k_T$-moment of the pion Boer-Mulders function is studied by employing an approximate evolution kernel. Using the model resulting distributions, we predict the transverse momentum weighted $\cos2ϕ$ azimuthal asymmetry in the unpolarized $π^- p$ Drell-Yan process which can be …
At present, the Boer-Mulders (BM) function for a given quark flavour is extracted from data on semi-inclusive deep inelastic scattering (SIDIS) using the simplifying assumption that it is proportional to the Sivers function for that flavour. In a recent paper we suggested that the consistency of this assumption could be tested using information on so-called difference asymmetries, i.e. the difference between the asymmetries in the production of particles and their anti-particles. In this paper, using the SIDIS COMPASS deuteron data on the $\langle\cosϕ_h\rangle$, $\langle\cos 2 ϕ_h\rangle$ and…
Sign Reversal of Boer-Mulders Functions from Semi-inclusive Deep-Inelastic Scattering to the Drell-Yan Process
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Central University（中央大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；South Texas College（南德克萨斯学院）
We compute the leading-twist T-odd quasi-distributions of the proton in a spectator model with scalar and axial-vector diquarks: the quasi Sivers function $\tilde{f}_{1T}^\perp(x, k_T^2; P_z)$ and the quasi Boer-Mulders function $\tilde{h}_1^\perp(x, k_T^2; P_z)$. We obtain the quark-quark correlators in the four-dimensional Euclidian space by replacing $γ^+$ and $σ^{i+}$ in the light-cone frame with $γ_z$ and $σ_{iz}$. We show by analytical calculation that the results of $\tilde{f}_{1T}^\perp$ and $\tilde{h}_1^\perp$ derived from the correlators can reduce to the expressions of the correspon…
A general formalism for the evaluation of time reversal odd parton distributions is applied here to calculate the Boer-Mulders function. The same formalism when applied to evaluate the Sivers function led to results which fulfill the Burkardt sum rule quite well. The calculation here has been performed for two different models of proton structure: a constituent quark model and the MIT bag model. In the latter case, important differences are found with respect to a previous evaluation in the same framework, a feature already encountered in the calculation of the Sivers function. The results obt…
We predict the twist-2 Transverse Momentum Dependent parton distribution functions (TMDs) of the pion, namely the unpolarized quark TMD, $f_{1}(x, k_\perp)$, and the transversely polarized quark TMD, also known as the Boer-Mulders function, $h^\perp_{1}(x, k_\perp)$, using a holographic light-front pion wavefunction with dynamical spin effects. These spin effects, in conjunction with gluon rescattering, are crucial to predict a non-zero holographic Boer-Mulders function. We investigate the use of a non-perturbative SU(3) gluon rescattering kernel, thus going beyond the usual approximation of p…
The three-dimensional momenta of quarks inside a hadron are encoded in transverse momentum-dependent parton distribution functions (TMDs). This work presents an exploratory lattice QCD study of a TMD observable in the pion describing the Boer-Mulders effect, which is related to polarized quark transverse momentum in an unpolarized hadron. Particular emphasis is placed on the behavior as a function of a Collins-Soper evolution parameter quantifying the relative rapidity of the struck quark and the initial hadron, e.g., in a semi-inclusive deep inelastic scattering (SIDIS) process. The lattice c…
Results for the naive-time-reversal-odd quark distributions in a light-cone quark model are presented. The final-state interaction effects are generated via single-gluon exchange mechanism. The formalism of light-cone wave functions is used to derive general expressions in terms of overlap of wave-function amplitudes describing the different orbital angular momentum components of the nucleon. In particular, the model predictions show a dominant contribution from S- and P-wave interference in the Sivers function and a significant contribution also from the interference of P and D waves in the B…
We present a first calculation of transverse momentum dependent nucleon observables in dynamical lattice QCD employing non-local operators with staple-shaped, "process-dependent" Wilson lines. The use of staple-shaped Wilson lines allows us to link lattice simulations to TMD effects determined from experiment, and in particular to access non-universal, naively time-reversal odd TMD observables. We present and discuss results for the generalized Sivers and Boer-Mulders transverse momentum shifts for the SIDIS and DY cases. The effect of staple-shaped Wilson lines on T-even observables is studie…
At leading twist the transverse-momentum dependent parton distributions of the pion consist of two functions, the unpolarized $f_{1,π}(x,\boldsymbol k^{\, 2}_\perp)$ and the Boer-Mulders function $h_{1,π}^{\perp}(x,\boldsymbol k^{\, 2}_\perp)$. We study both functions within a light-front constituent model of the pion, comparing the results with different pion models and the corresponding nucleon distributions from a light-front constituent model. After evolution from the model scale to the relevant experimental scales, the results for the collinear pion valence parton distribution function $f…
The spin asymmetries in SIDIS associated with $T$-odd TMDs are presented in a light-front quark-diquark model of a proton. To incorporate the effects of the final state interaction, the light front wave functions are modified to have a phase factor which is essential to have Sivers or Boer-Mulders functions. The Sivers and Boer-Mulder asymmetries are compared with HERMES and COMPASS data.
We present Monte Carlo simulations of both the Sivers and the Boer-Mulders effects in the polarized Drell-Yan $π^\pm p^\uparrow \to μ^+ μ^- X$ process at the center-of-mass energy $\sqrt{s} \sim 14$ GeV reachable at COMPASS with pion beams of energy 100 GeV. For the Sivers effect, we adopt two different parametrizations for the Sivers function to explore the statistical accuracy required to extract unambiguous information on this parton density. In particular, we verify the possibility of checking its predicted sign change between Semi-Inclusive Deep-Inelastic Scattering (SIDIS) and Drell-Yan …
We calculate the non-zero Boer-Mulders functions of sea quarks inside the proton in a meson-baryon fluctuation model. The results show that the transverse spin effects of sea quarks in an unpolarized nucleon are sizable. Using the obtained antiquark Boer-Mulders functions, we estimate the $\cos 2 ϕ$ asymmetries in the unpolarized $pp$ and $p D$ Drell-Yan processes at FNAL E866/NuSea experiments. The prediction for the $\cos 2 ϕ$ asymmetries in the unpolarized $pp$ Drell-Yan process at the BNL Relativistic Heavy Ion Collider (RHIC) is also given.
We study the $\cos 2 ϕ$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the non perturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from $<\cos 2 ϕ>$ some information about the Boer--Mulders function $h_1^{\perp}$, which represents a transverse--polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where $<\cos 2 ϕ>$ is dominate…
We calculate the Boer-Mulders effect contribution to the $\cos2ϕ$ azimuthal asymmetry of unpolarized dilepton production near the $Z$-pole. Based on the tree-level expression in the transverse momentum dependent factorization framework, we show that the corresponding asymmetry near the $Z$-pole is negative, which is opposite to the asymmetry in the low $Q^2$ region, dominated by the production via a virtual photon. We calculate the asymmetry generated by the Boer-Mulders effect near the $Z$-pole at RHIC, with $\sqrt{s}=500$ GeV. We find that the magnitude of the asymmetry is several percent, a…
Fixed-target unpolarized Drell-Yan experiments often feature an acceptance depending on the polar angle of the lepton tracks in the laboratory frame. Typically leptons are detected in a defined angular range, with a dead zone in the forward region. If the cutoffs imposed by the angular acceptance are independent of the azimuth, at first sight they do not appear dangerous for a measurement of the cos(2ϕ)-asymmetry, relevant because of its association with the violation of the Lam-Tung rule and with the Boer-Mulders function. On the contrary, direct simulations show that up to 10 percent asymmet…
We use the Boer-Mulders functions parameterized from unpolarized $p+D$ Drell-Yan data by the FNAL E866/NuSea Collaboration combined with recently extracted Collins functions to calculate the $\cos 2 ϕ$ asymmetries in unpolarized semi-inclusive deeply inelastic scattering (SIDIS) processes both for ZEUS at Hadron Electron Ring Accelerator (HERA) and Jefferson Lab experiments (JLab), and to compare our results with their data. We also give predictions for the $\cos 2 ϕ$ asymmetries of SIDIS in the kinematical regime of HERMES Collaboration, and the forthcoming JLab experiments. We predict that t…
In the factorized picture of semi-inclusive deep inelastic scattering the naive time reversal-odd parton distributions exist by virtue of the gauge link which is intrinsic to their definition. The link structure describes initial/final-state interactions of the active parton due to soft gluon exchanges with the target remnant. Though these interactions are non-perturbative, calculations of final-state interaction have been performed in a perturbative one-gluon approximation. We include higher-order contributions by applying non-perturbative eikonal methods to calculate the Boer-Mulders functio…
Previously we showed that, based only on C and SU(2) invariance, the difference cross sections of hadrons with opposite charge in SIDIS e+N\to l+h+X is expressed solely in terms of the valence-quark densities and certain non-singlet combinations of FFs. This allowed to determine these quantities in a model independent way. Now we extend this approach to processes when the transverse momentum of the final hadron is measured as well. We show that the difference cross sections of unpolarized SIDIS on proton and deuterium targets, d\s_N^{h^+-h^-}, d\s_N^{π^+-π^-} and d\s_N^{K^+-K^-}, are expressed…
Generalized parton distributions describe the distribution of partons in the transverse plane. For transversely polarized quarks and/or nucleons, these impact parameter dependent parton distributions are not axially symmetric. These transverse distortions can be related to spin-orbit correlations as well as to (intuitively) to transverse single-spin asymmetries, allowing novel insights into quark orbital angular momentum from measurements of the Sivers and Boer-Mulders functions.
We argue the existence of new $k_\perp$-dependent functions which can be manifested in the Drell-Yan (SIDIS)-like processes. The presented new functions resemble the well-known Boer-Mulders function associated with the quark spin asymmetry, but in contrast they are sensitive to the transverse motion of partons inside the hadron due to the collective alignment of quark spin vectors.
We investigate the origin of the cos 2 phi azimuthal asymmetry in unpolarized semiinclusive DIS. The contributions to this asymmetry arising from the intrinsic transverse motion of quarks are explicitly evaluated, and predictions for the HERMES and COMPASS kinematic regimes are presented. We show that the effect of the leading-twist Boer-Mulders function h_1^perp(x, k_T^2), which describes a correlation between the transverse momentum and the transverse spin of quarks, is quite significant and may also account for a part of the cos 2 phi asymmetry measured by ZEUS in the perturbative domain.
The measurement of azimuthal modulations in hadron leptoproduction on unpolarized nucleons allows to get information on the intrinsic transverse momentum $\langle k_T^2 \rangle$ of quarks in a nucleon through both the Cahn effect and the Boer-Mulders function. We have compared the azimuthal asymmetries in the cross section of $160\, \rm{GeV}/c$ muons scattered off an unpolarised deuteron target as measured by COMPASS with a Monte Carlo program, based on the ${}^3P_0$ model of quark anti-quark pair production at string breaking, which accounts for the Cahn effect. Large differences have been ob…
Using the light-front holographic model, we study the transverse momentum dependent parton distributions (TMDs) for the case of pion. At leading twist, the unpolarized parton distribution function $ f_{1π}(x,\bfk^{2}) $ and the Boer-Mulders function $ h_{1π}^{\bot}(x,\bfk^{2}) $ are obtained for pion. We calculate both the functions using the light-front holographic model with spin improved wave function and compare the predicted results with available results of other models. In order to provide inputs in predicting future experimental data, a LO evolution is performed from model scale to exp…
T-odd distributions like Sivers and Boer-Mulders functions are normally modeled using few-body models. In the present work I want to follow the completely opposite point of view, and study a high-energy proton-proton Drell-Yan where both the annihilating partons are wee, and one (at least) comes from a high-order Fok state of the parent proton, i.e. a state where a large number N of partons is present. I show that rescattering between active and spectator partons is modified, with suppression of those terms that are needed to build T-odd parton distributions.
We present a general formalism for the evaluation of time-reversal odd parton distributions. This formalism is applied to the evaluation of the two T-odd TMDs allowed at the twist-2 level, i.e., the Sivers and the Boer-Mulders functions. We have performed the calculation for two different models of proton structure: a non relativistic constituent quark model and the MIT bag model. The results obtained in both models are compared. So are the two T-odd functions. We comment on the fulfilment of the Burkardt sum rule as well as on the current status of T-odd TMDs in phenomenology.
The first moment of longitudinal and transverse spin densities of quarks in the nucleon are calculated in a light-front constituent quark model for the different cases of quark and nucleon polarization. Significant distortions are found for the transverse spin densities. In particular the Sivers function is predicted with opposite sign for up and down quarks and the Boer-Mulders function is predicted large and negative for both up and down quarks, in agreement with lattice calculations. Quite a different spin distribution is obtained for up and down quarks in the cases of quarks and proton tra…
In this talk, we examine the existing calculations of QCD evolution kernels for the scale dependence of two sets of twist-3 quark-gluon correlation functions, $T_{q,F}(x,x)$ and $T^{(σ)}_{q,F}(x,x)$, which are the first transverse-momentum-moment of the naive-time-reversal-odd Sivers and Boer-Mulders function, respectively. The evolution kernels at the leading order in strong coupling constant $α_s$ were derived by several groups with apparent differences. We identify the sources of discrepancies and are able to reconcile the results from various groups.
We review the current status and future prospect for probing the transverse momentum dependent (TMD) parton distributions using the Drell-Yan process. We focus on the Boer-Mulders and Sivers functions, which are expected to undergo a sign-change from semi-inclusive deep-inelastic scattering (SIDIS) to Drell-Yan process. The constraints of existing Drell-Yan and SIDIS experiments on the signs of these functions are discussed. Future Drell-Yan measurements for the TMDs are also presented.
We present a phenomenological analysis of the cos-phi and cos-2phi asymmetries in unpolarized semi-inclusive deep inelastic scattering, based on the recent multidimensional data released by the COMPASS and HERMES Collaborations. In the TMD framework, valid at relatively low transverse momenta, these asymmetries arise from intrinsic transverse momentum and transverse spin effects, and from their correlations. The role of the Cahn and Boer-Mulders effects in both azimuthal moments is explored up to order 1/Q. As the kinematics of the present experiments is dominated by the low-Q^2 region, higher…
Color Lorentz force on a transversely polarized quark in the nucleon
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Iowa State University（爱荷华州立大学）
Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally od…
Using a generalized parton model approach including spin and intrinsic parton motion effects, and assuming the validity of factorization for large p_T jet production in hadronic collisions, we study the azimuthal distribution around the jet axis of leading pions, produced in the jet fragmentation process. We identify the observable leading-twist azimuthal asymmetries for the unpolarized and single-polarized case related to both quark and gluon-originated jets. We account for all physically allowed combinations of the transverse momentum dependent (TMD) parton distribution and fragmentation fun…
The observed results for the azimuthal single spin asymmetries (SSAs) of the proton, measured in the semi-inclusive deep inelastic scattering (SIDIS), can be explained by the final-state interaction (FSI) from the gluon exchange between the outgoing quark and the target spectator system. SSAs require a phase difference between two amplitudes coupling the target with opposite spins to the same final state. We have used the model of light front wave functions (LFWFs) consisting of a spin-$\frac{1}{2}$ system as a composite of a spin-$\frac{1}{2}$ fermion and a spin-1 vector boson to estimate the…
