Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions

Abstract

We calculate the single transverse spin asymmetry (STSA) in polarized proton-proton ($p^{\uparrow }+p$) and polarized proton-nucleus ($p^{\uparrow }+A$) collisions ($A_N$) generated by a partonic lensing mechanism. The polarized proton is considered in the quark-diquark model while its interaction with the unpolarized target is calculated using the small-$x$/saturation approach, which includes multiple rescatterings and small-$x$ evolution. The phase required for the asymmetry is caused by a final-state gluon exchange between the quark and diquark, as is standard in the lensing mechanism of Brodsky, Hwang and Schmidt. Our calculation combines the lensing mechanism with small-$x$ physics in the saturation framework. The expression we obtain for the asymmetry $A_N$ of the produced quarks has the following properties: (i) The asymmetry is generated by the dominant elastic scattering contribution and $1/N_c^2$ suppressed inelastic contribution (with $N_c$ the number of quark colors); (ii) The asymmetry grows or oscillates with the produced quark's transverse momentum $p_T$ until the momentum reaches the saturation scale $Q_s$, and then only falls off as $1/p_T$ for larger momenta; (iii) The asymmetry decreases with increasing atomic number $A$ of the target for $p_T$ below or near $Q_s$, but is independent of $A$ for $p_T$ significantly above $Q_s$. We discuss how these properties may be qualitatively consistent with the data on $A_N$ published by the PHENIX collaboration and with the preliminary data on $A_N$ reported by the STAR collaboration.

arXiv comment23 pages, 10 figures

References in corpus (90)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Nonlinear Gluon Evolution in the Color Glass Condensate: I
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• The Color Glass Condensate
• Fragmentation of Transversely Polarized Quarks Probed in Transverse Momentum Distributions
• The Wilson renormalization group for low x physics: towards the high density regime
• Green's Functions in the Color Field of a Large Nucleus
• Nonlinear Gluon Evolution in the Color Glass Condensate: II
• Leading-twist Single-transverse-spin asymmetries: Drell-Yan and Deep-Inelastic Scattering
• Unitarization of the BFKL Pomeron on a Nucleus
• The Renormalization Group Equation for the Color Glass Condensate
• Saturation in Diffractive Deep Inelastic Scattering
• Final-State Interactions and Single-Spin Asymmetries in Semi-Inclusive Deep Inelastic Scattering
• The Intrinsic Glue Distribution at Very Small x
• The Wilson renormalization group for low x physics: Gluon evolution at finite parton density
• Unitarity at small Bjorken x
• Universality of Unintegrated Gluon Distributions at small x
• Non-Abelian Weizsacker-Williams field and a two-dimensional effective color charge density for a very large nucleus
• Factorization and high-energy effective action
• Saturation Physics and Deuteron--Gold Collisions at RHIC
• Evolution at small x_bj: The Color Glass Condensate
• Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
• Single Transverse-Spin Asymmetries in Hadronic Pion Production
• Cronin Effect and High-p_T Suppression in pA Collisions
• Initial-State Interactions and Single-Spin Asymmetries in Drell-Yan Processes
• Relations between generalized and transverse momentum dependent parton distributions
• AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
• Inclusive Gluon Production in DIS at High Parton Density
• Parton saturation and N_part scaling of semi--hard processes in QCD
• Gluon saturation and initial conditions for relativistic heavy ion collisions
• Non-linear QCD meets data: A global analysis of lepton-proton scattering with running coupling BK evolution
• Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus
• Energy Dependence of the Cronin Effect from Non-Linear QCD Evolution
• Azimuthal and Single Spin Asymmetries in Hard Scattering Processes
• Forward Neutral Pion Transverse Single Spin Asymmetries in p+p Collisions at \sqrt{s}=200 GeV
• Measurement of Transverse Single-Spin Asymmetries for Mid-rapidity Production of Neutral Pions and Charged Hadrons in Polarized p+p Collisions at sqrt(s) = 200 GeV
• Inclusive Two-Gluon and Valence Quark-Gluon Production in DIS and pA
• Odderon in the Color Glass Condensate
• Towards an explanation of transverse single-spin asymmetries in proton-proton collisions: the role of fragmentation in collinear factorization
• Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
• The distribution of linearly polarized gluons and elliptic azimuthal anisotropy in DIS dijet production at high energy
• Chromodynamic Lensing and Transverse Single Spin Asymmetries
• Subleading-N_c corrections in non-linear small-x evolution
• Fragmentation contribution to the transverse single-spin asymmetry in proton-proton collisions
• Diffractive Structure Function in a Quasi-Classical Approximation
• Gluon orbital angular momentum at small-$x$
• Gluon TMD in particle production from low to moderate x
• Helicity Evolution at Small $x$: Flavor Singlet and Non-Singlet Observables
• Sub-eikonal corrections to scattering amplitudes at high energy
• Small-$x$ Helicity Evolution: an Operator Treatment
• On the small-x evolution of the color quadrupole and the Weizsäcker-Williams gluon distribution
• Helicity Evolution at Small-x
• Small-$x$ asymptotics of the quark helicity distribution
• A New Mechanism for Generating a Single Transverse Spin Asymmetry
• Small-$x$ Asymptotics of the Gluon Helicity Distribution
• Baryon Stopping and the Valence Quark Distribution at Small x
• Inclusive jet production on the nucleus in the perturbative QCD with $N_c\to \infty$
• Helicity-dependent generalization of the JIMWLK evolution
• Next-to-next-to-eikonal corrections in the CGC
• Single spin asymmetries from a single Wilson loop
• Transverse single spin asymmetries at small x and the anomalous magnetic moment
• Small-$x$ Asymptotics of the Quark Helicity Distribution: Analytic Results
• Proton Spin Structure at Small-$x$
• Single Spin Asymmetry Scaling in the Forward Rapidity Region at RHIC
• Production of q bar-q Pairs in Proton-Nucleus Collisions at High Energies
• Two-Gluon Correlations in Heavy-Light Ion Collisions: Energy and Geometry Dependence, IR Divergences, and $k_T$-Factorization
• Calculating TMDs of a Large Nucleus: Quasi-Classical Approximation and Quantum Evolution
• Quark jets scattering from a gluon field: from saturation to high $p_t$
• Rapidity loss, spin and angular asymmetries in scattering of a quark from color field of a proton (nucleus)
• Orbital Angular Momentum at Small $x$
• Single-Spin Asymmetries in Semi-inclusive Deep Inelastic Scattering and Drell-Yan Processes
• Gluon TMDs in quarkonium production
• Single transverse-spin asymmetries in forward pion production at high energy: incorporating small-x effects in the target
• Sivers Function in the Quasi-Classical Approximation
• Valence Quark Transversity at Small $x$
• The spin dependent odderon in the diquark model
• Polarized Hyperons from pA Scattering in the Gluon Saturation Regime
• Transverse single spin asymmetry in direct photon production in polarized pA collisions
• Single spin asymmetry in forward $pA$ collisions II: Fragmentation contribution
• Single Spin Asymmetry in Forward $pA$ Collisions
• Nuclear dependence of the transverse single-spin asymmetry in the production of charged hadrons at forward rapidity in polarized $p+p$, $p+$Al, and $p+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV
• Single spin asymmetry in forward $pA$ collisions: Phenomenology at RHIC
• Baryon Stopping in Proton-Nucleus Collisions
• The saturation scale and its x-dependence from Lambda polarization studies
• Transverse single spin asymmetry in Drell-Yan production in polarized pA collisions
• Nuclear dependence of the transverse-single-spin asymmetry for forward neutron production in polarized $p$$+$$A$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV

Cited by in corpus (6)

• Quark Sivers Function at Small $x$: Spin-Dependent Odderon and the Sub-Eikonal Evolution
• Comparison of transverse single-spin asymmetries for forward ${\pi }^0$ production in polarized $pp$, $p\mathrm{Al}$ and $p\mathrm{Au}$ collisions at nucleon pair c.m. energy $\sqrt{s_{\mathrm{NN}}}=200$ GeV
• On the odderon mechanism for transverse single spin asymmetry in the Wandzura-Wilczek approximation
• Transverse single-spin asymmetry of charged hadrons at forward and backward rapidity in polarized $p$+$p$, $p$+Al, and $p$+Au collisions at $\sqrt{s_{NN}}=200$ GeV}
• Single spin asymmetry in forward $pA$ collisions from Pomeron-Odderon interference
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$