A more reliable treatment of transverse momentum dependent physics and in particular transverse single spin asymmetries is urgently required, e.g. for polarized pA physics including novel effects like color entanglement. We argue that the measurement of azimuthal angular correlations of photons and jets produced in pA collisions provides a direct access to the novel gluon distribution $G_4$ that enters into many such processes.
Quantum entanglement in electron-nucleus collisions: Role of the linearly polarized gluon distribution
National Centre for Nuclear Research（国家核研究中心）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；RIKEN BNL Research Center, Brookhaven National Laboratory（理研布鲁克海文研究中心，布鲁克海文国家实验室）；School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We explore polarized heavy quarkonium production using the color evaporation model at leading order. We present the polarized to total yield ratio as a function of center of mass energy and rapidity in $p+p$ collisions. At energies far above the $Q \overline Q$ production threshold, we find charmonium and bottomonium production to be longitudinally polarized ($J_z=0$). The quarkonium states are also longitudinally polarized at central rapidity, becoming transversely polarized ($J_z=\pm1$) at the most forward rapidities.
We study the possibility to probe the unpolarized and linearly polarized transverse momentum- dependent gluon distributions in unpolarized pp collision in charmonium and bottomonium produc- tion, employing non-relativistic QCD (NRQCD) based color octet model within transverse momentum dependent (TMD) factorization framework. The transverse momentum (p T ) and rapidity distributions of J/ψ and Υ(1S) at LHCb, RHIC and AFTER energies are estimated. Significant modulations in transverse momentum spectrum of quarkonium in the low p T region is obtained when contributions of linearly polarized gluon…
Spin Correlation and Quantum Entanglement of Fermion Pairs in Transversely Polarized $e^-e^+$ Collisions
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；University of Pittsburgh（匹兹堡大学）；Beijing Normal University（北京师范大学）；Peking University（北京大学）
Manipulating Bell nonlocality and entanglement in polarized electron-positron annihilation
College of Physics Science and Technology, Hebei University（河北大学物理科学与技术学院）；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）；Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS（兰州大学重离子物理与加速器大科学装置研究中心与中国科学院近代物理研究所）
We study color entanglement effect for T-odd cases in collinear twist-3 factorization. As an example, we compute the transverse single spin asymmetry for direct photon production in pp collisions in pure collinear twist-3 approach. By analyzing the gauge link structure of the collinear gluon distribution on unpolarized target side, we demonstrate how color entanglement effect arises in the presence of the additional gluon attachment from polarized projectile. The result is consistent with that obtained from a hybrid approach calculation.
At present the color-octet mechanism is still an important and debatable part in the non-relativistic QCD(NRQCD). We find in this work that the polarized double charmonium production at the LHC may pose a stringent test on the charmonium production mechanism. Result shows that the transverse momentum($p_T$) scaling behaviors of double $J/ψ$ differential cross sections in color-singlet and -octet production mechanisms deviate distinctively from each other while $p_T$ is larger than 7 GeV. In color-octet mechanism, the two $J/ψ$s in one pair are mostly transversely polarized when $p_T\gg 2 m_c$,…
We study the transverse single spin asymmetry in direct photon production in pA collisions with incoming protons being transversely polarized. To facilitate the calculation, we formulate a hybrid approach in which the nucleus is treated in the Color Glass Condensate (CGC) framework while the collinear twist-3 formalism is applied on the proton side. It has been found that an additional term which arises from color entanglement shows up in the spin dependent differential cross section. The fact that this additional term is perturbatively calculable allows us to quantitatively study color entang…
We calculate the single transverse spin asymmetries(SSA) for forward inclusive particle production in pp and pA collisions using a hybrid approach. It is shown that the Sivers type contribution to the SSA drops out due to color entanglement effect, whereas the fragmentation contribution to the spin asymmetry is not affected by color entanglement effect. This finding offers a natural solution for the sign mismatch problem.
We present the study of accessing unpolarized and linearly polarized gluon TMDs in J/ψ and Υ(1S) production in unpolarized proton-proton collision at LHC, RHIC and AFTER energies. Non- relativistic QCD based color octet model (COM) is used for estimating quarkonium production rates within transverse momentum dependent factorization formalism. A comparison is drawn between the experimental data and the transverse momentum distribution of quarkonium obtained in COM and color evaporation model.
In the resummation of collinear gluons emitted together with active partons from the hadrons in the Drell-Yan process (DY) effects of color entanglement become important when the transverse directions are taken into account. It is then no longer possible to write the cross section as the convolution of two soft correlators and a hard part. We show that the color entanglement introduces additional color factors that must be taken into account in the extraction of transverse momentum dependent parton distribution functions (TMD PDFs) from azimuthal asymmetries. Examples where such effects matter…
We show that the linearly polarized gluon distributions appear in the color dipole model as we derive the full cross sections of the DIS dijet production and the Drell-Yan dijet ($γ^*$ jet correlation) process. Together with the normal Weizsäcker-Williams gluon distribution, the linearly polarized one will contribute to the DIS dijet production cross section as the coefficient of the $\cos(2 Δϕ) $ term in the correlation limit. We also derive the exact results for the cross section of the Drell-Yan dijet process, and find that the linearly polarized dipole gluon distribution which is identical…
We calculate the polarization of prompt $J/ψ$ and $Υ$(1S) production using the color evaporation model at leading order. We present the polarization parameter $λ_\vartheta$ as a function of center of mass energy and rapidity in $p+p$ collisions. We also compare the $x_F$ dependence to experimental results in $p$+Cu and $π$+W collisions, and predict the $x_F$ dependence in $p$+Pb collisions at fixed-target energies. At energies far above the $Q\overline{Q}$ production threshold, we find the prompt $J/ψ$ and $Υ$(1S) production to be longitudinally polarized with $λ_\vartheta^{J/ψ}=-0.51^{+0.05}_…
We compute the entanglement entropy of soft gluons in the wave function of a fast moving hadron and discuss its basic properties. We also derive the expression for entropy production in a high energy hadronic collision within the Color Glass formalism. We show that long range rapidity correlations give negative contribution to the production entropy. We calculate the (naturally defined) temperature of the produced system of particles, and show that it is proportional to the average transverse momentum of the produced particles.
We introduce the notion of the Color Glass Condensate (CGC) density matrix $\hatρ$. This generalizes the concept of probability density for the distribution of the color charges in the hadronic wave function and is consistent with understanding the CGC as an effective theory after integration of part of the hadronic degrees of freedom. We derive the evolution equations for the density matrix and show that the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of $\hatρ$ in the color charge density basis. We analyze the behavior of this density matrix under high …
In QCD with $N_c$ colors the anti-symmetric valence quark color space singlet state $\sim ε_{i_1\cdots i_{N_c}} |i_1,\cdots, i_{N_c}\rangle$ of the proton corresponds to the reduced density matrix $ρ_{ij}=(1/N_c) δ_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, $λ_i=1/N_c$, the purity $\mathrm{tr}~ρ^2 = 1/N_c$, and the von~Neumann entropy $S_\mathrm{vN}=\log(N_c)$ all indicate maximal entanglement of color. On the other hand, for $N_c\to\infty$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field (E…
The distribution of linearly polarized gluons inside a large nucleus is studied in the framework of the color glass condensate. We find that the Weizsäcker-Williams distribution saturates the positivity bound at large transverse momenta and is suppressed at small transverse momenta, whereas the dipole distribution saturates the bound for any value of the transverse momentum. We also discuss processes in which both distributions of linearly polarized gluons can be probed.
We study the transverse single spin asymmetry in Drell-Yan production in pA collisions with incoming protons being transversely polarized. We carry out the calculation using a newly developed hybrid approach. The polarized cross section computed in the hybrid approach is consistent with that obtained from the usual TMD factorization at low transverse momentum as expected, whereas at high transverse momentum, color entanglement effect is found to play a role in contributing to the spin asymmetry of Drell-Yan production, though it is a $1/N_c^2$ suppressed effect.
Spin-spin entanglement in diffractive heavy quark production
National Centre for Nuclear Research（国家核研究中心）；Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）；RIKEN BNL Research Center, Brookhaven National Laboratory（理化学研究所布鲁克海文研究中心）
We present the two-loop virtual amplitudes for heavy-quark pair production in light quark-antiquark annihilation and gluon fusion channels, including full spin and color dependence. We use expansions around kinematical limits and numerical integration to obtain results for the involved master integrals. From these, we determine the renormalised infrared finite remainders of the coefficients of amplitude decompositions in terms of color and spin structures. The remainders are given in form of numerical interpolation grids supported by expansions around the production threshold and the high ener…
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）
We calculate the Sivers and $\cos2ϕ$ azimuthal asymmetries in $J/ψ$ production in polarized and unpolarized semi-inclusive $ep$ collision respectively, using the formalism based on transverse momentum dependent parton distributions (TMDs). Non-relativistic QCD based color octet model is employed for calculating the $J/ψ$ production rate. The Sivers asymmetry in this process directly probes the gluon Sivers function. The estimated Sivers asymmetry at $z=1$ is negative which is in good agreement with COMPASS data. We also investigate the effect of TMD evolution on the Sivers asymmetry. The $\cos…
Studying Maximal Entanglement and Bell Nonlocality at an Electron-Ion Collider
The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；The Ohio State University（俄亥俄州立大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
We study inclusive $χ_{cJ}$ production with definite polarizations in polarized proton-proton collisions at $\sqrt{s}$ = 200 GeV and 500 GeV at RHIC by using non-relativistic QCD (NRQCD) color-octet mechanism. We present results of rapidity distribution of $χ_{c0}$, $χ_{c1}$ and $χ_{c2}$ production with specific polarizations in polarized p-p collisions at RHIC within the PHENIX detector acceptance range. We also present the corresponding results for the spin asymmetries.
