Lensing mechanism meets small- x physics: Single transverse spin asymmetry in p ↑ + p and p ↑ + A collisions

Kovchegov, Yuri V.; Santiago, M. Gabriel

doi:10.1103/PhysRevD.102.014022

Title: Lensing mechanism meets small- $x$ physics: Single transverse spin asymmetry in $p^{↑} + p$ and $p^{↑} + A$ collisions

Abstract

We calculate the single transverse spin asymmetry (STSA) in polarized proton-proton (p^↑+p) and polarized proton-nucleus (p^↑+A) collisions (AN) 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/$$N^{2}_{c}$$ 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 AN published by the PHENIX collaboration and with the preliminary data on AN reported by the STAR collaboration.

Authors:

; Santiago, M. Gabriel

Publication Date:: 2020-07-14

Research Org.:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1638419

Alternate Identifier(s):: OSTI ID: 1770386

Grant/Contract Number:: SC0004286

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 1; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Kovchegov, Yuri V., and Santiago, M. Gabriel. Lensing mechanism meets small- x physics: Single transverse spin asymmetry in p ↑ + p and p ↑ + A collisions.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.102.014022.

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                    Kovchegov, Yuri V., & Santiago, M. Gabriel. Lensing mechanism meets small- x physics: Single transverse spin asymmetry in p ↑ + p and p ↑ + A collisions.  United States.  https://doi.org/10.1103/PhysRevD.102.014022

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                    Kovchegov, Yuri V., and Santiago, M. Gabriel. Tue .  
"Lensing mechanism meets small- x physics: Single transverse spin asymmetry in p ↑ + p and p ↑ + A collisions".  United States.  https://doi.org/10.1103/PhysRevD.102.014022.

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@article{osti_1638419,

  title        = {Lensing mechanism meets small- x physics: Single transverse spin asymmetry in p ↑ + p and p ↑ + A collisions},

  author       = {Kovchegov, Yuri V. and Santiago, M. Gabriel},

  abstractNote = {We calculate the single transverse spin asymmetry (STSA) in polarized proton-proton (p↑+p) and polarized proton-nucleus (p↑+A) collisions (AN) 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 AN of the produced quarks has the following properties: (i) The asymmetry is generated by the dominant elastic scattering contribution and 1/$N^{2}_{c}$ suppressed inelastic contribution (with Nc the number of quark colors); (ii) The asymmetry grows or oscillates with the produced quark's transverse momentum pT until the momentum reaches the saturation scale Qs, and then only falls off as 1/pT for larger momenta; (iii) The asymmetry decreases with increasing atomic number A of the target for pT below or near Qs, but is independent of A for pT significantly above Qs. We discuss how these properties may be qualitatively consistent with the data on AN published by the PHENIX collaboration and with the preliminary data on AN reported by the STAR collaboration.},

  doi          = {10.1103/PhysRevD.102.014022},

  journal      = {Physical Review D},

  number       = 1,

  volume       = 102,

  place        = {United States},

  year         = {2020},

  month        = {7}

}

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Two-gluon correlations in heavy–light ion collisions: Energy and geometry dependence, IR divergences, and <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msub></mml:math>-factorization
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Title: Lensing mechanism meets small- x physics: Single transverse spin asymmetry in p ↑ + p and p ↑ + A collisions

Abstract

Citation Formats

Fragmentation of transversely polarized quarks probed in transverse momentum distributions journal, May 1993

Transverse single spin asymmetries at small x and the anomalous magnetic moment journal, April 2014

Small- x Asymptotics of the Quark Helicity Distribution journal, January 2017

The spin dependent odderon in the diquark model journal, September 2016

Nonlinear QCD meets data: A global analysis of lepton-proton scattering with running coupling Balitsky-Kovchegov evolution journal, August 2009

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The Color Glass Condensate journal, November 2010

Production of q q ¯ pairs in proton-nucleus collisions at high energies journal, September 2006

Evolution at small : The color glass condensate journal, October 2005

Subleading- corrections in non-linear small-x evolution journal, May 2009

Cronin effect and high- p T suppression in pA collisions journal, November 2003

Non-Abelian Weizsäcker-Williams field and a two-dimensional effective color charge density for a very large nucleus journal, November 1996

Relations between generalized and transverse momentum dependent parton distributions journal, August 2007

Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy journal, December 2015

New mechanism for generating a single transverse spin asymmetry journal, August 2012

Quark jets scattering from a gluon field: From saturation to high p t journal, January 2019

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Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus journal, May 1997

Sub-eikonal corrections to scattering amplitudes at high energy journal, January 2019

Hard-scattering scaling laws for single-spin production asymmetries journal, January 1991

Single-spin production asymmetries from the hard scattering of pointlike constituents journal, January 1990

Gluon TMD in particle production from low to moderate x journal, June 2016

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Orbital angular momentum at small x journal, March 2019

Single spin asymmetry scaling in the forward rapidity region at RHIC journal, August 2011

Nonlinear gluon evolution in the color glass condensate: II journal, May 2002

Helicity-dependent generalization of the JIMWLK evolution journal, December 2019

The renormalization group equation for the color glass condensate journal, June 2001

Proton spin structure at small-x journal, October 2019

Nonlinear gluon evolution in the color glass condensate: I journal, September 2001

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The saturation scale and its x-dependence from Λ polarization studies journal, January 2009

Saturation effects in deep inelastic scattering at low Q 2 and its implications on diffraction journal, November 1998

Wilson renormalization group for low x physics: Gluon evolution at finite parton density journal, November 1998

Transverse single spin asymmetry in Drell-Yan production in polarized pA collisions journal, July 2015

Chromodynamic lensing and transverse single spin asymmetries journal, April 2004

AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks journal, July 2011

Single transverse-spin asymmetries in forward pion production at high energy: Incorporating small- x effects in the target journal, October 2006

Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation journal, September 1998

Odderon in the color glass condensate journal, October 2005

Forward Neutral-Pion Transverse Single-Spin Asymmetries in p + p Collisions at s = 200 GeV journal, November 2008

QCD asymmetry and polarized hadron structure function measurement journal, January 1985

Energy Dependence of the Cronin Effect from Nonlinear QCD Evolution journal, February 2004

Gluon distribution functions for very large nuclei at small transverse momentum journal, April 1994

Inclusive two-gluon and valence-quark-gluon production in DIS and p A collisions journal, December 2004

Saturation physics and deuteron–gold collisions at RHIC journal, January 2006

Single transverse-spin asymmetries in hadronic pion production journal, November 1998

On the small-x evolution of the color quadrupole and the Weizsäcker–Williams gluon distribution journal, November 2011

Next-to-next-to-eikonal corrections in the CGC journal, January 2016

Nuclear Dependence of the Transverse-Single-Spin Asymmetry for Forward Neutron Production in Polarized p + A Collisions at s N N = 200 GeV journal, January 2018

Intrinsic glue distribution at very small x journal, May 1997

Gluon saturation and initial conditions for relativistic heavy ion collisions journal, May 2014

Transverse single spin asymmetry in direct photon production in polarized p A collisions journal, August 2014

Small-x behavior and parton saturation: A QCD model journal, April 1990

Saturation in diffractive deep inelastic scattering journal, November 1999

Initial-state interactions and single-spin asymmetries in Drell–Yan processes journal, October 2002

Operator expansion for high-energy scattering journal, March 1996

Single spin asymmetry in forward p A collisions. II. Fragmentation contribution journal, January 2017

Wilson renormalization group for low x physics: Towards the high density regime journal, November 1998

Transverse Quark Polarization in Large- p T Reactions, e + e − Jets, and Leptoproduction: A Test of Quantum Chromodynamics journal, December 1978

Green’s function in the color field of a large nucleus journal, August 1994

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Parton saturation and Npart scaling of semi-hard processes in QCD journal, May 2003

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Single Spin Asymmetries from a Single Wilson Loop journal, March 2016

Inclusive jet production off the nucleus in the perturbative QCD with Nc→∞ journal, June 2000

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Title: Lensing mechanism meets small- $x$ physics: Single transverse spin asymmetry in $p^{↑} + p$ and $p^{↑} + A$ collisions

Fragmentation of transversely polarized quarks probed in transverse momentum distributions
journal, May 1993

Transverse single spin asymmetries at small $x$ and the anomalous magnetic moment
journal, April 2014

Small- $x$ Asymptotics of the Quark Helicity Distribution
journal, January 2017

The spin dependent odderon in the diquark model
journal, September 2016

Nonlinear QCD meets data: A global analysis of lepton-proton scattering with running coupling Balitsky-Kovchegov evolution
journal, August 2009

Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering
journal, May 2002

Small-x asymptotics of the gluon helicity distribution
journal, October 2017

Single-spin asymmetries in semi-inclusive deep inelastic scattering and Drell-Yan processes
journal, July 2013

The Color Glass Condensate
journal, November 2010

Production of $q \bar{q}$ pairs in proton-nucleus collisions at high energies
journal, September 2006

Evolution at small : The color glass condensate
journal, October 2005

Subleading- corrections in non-linear small-x evolution
journal, May 2009

Cronin effect and high- $p_{T}$ suppression in pA collisions
journal, November 2003

Non-Abelian Weizsäcker-Williams field and a two-dimensional effective color charge density for a very large nucleus
journal, November 1996

Relations between generalized and transverse momentum dependent parton distributions
journal, August 2007

Distribution of Linearly Polarized Gluons and Elliptic Azimuthal Anisotropy in Deep Inelastic Scattering Dijet Production at High Energy
journal, December 2015

New mechanism for generating a single transverse spin asymmetry
journal, August 2012

Quark jets scattering from a gluon field: From saturation to high $p_{t}$
journal, January 2019

Sivers function in the quasiclassical approximation
journal, March 2014

Helicity evolution at small $x$ : Flavor singlet and nonsinglet observables
journal, January 2017

Quantum structure of the non-Abelian Weizsäcker-Williams field for a very large nucleus
journal, May 1997

Sub-eikonal corrections to scattering amplitudes at high energy
journal, January 2019

Hard-scattering scaling laws for single-spin production asymmetries
journal, January 1991

Single-spin production asymmetries from the hard scattering of pointlike constituents
journal, January 1990

Gluon TMD in particle production from low to moderate x
journal, June 2016

Single transverse spin asymmetries
journal, October 1991

Orbital angular momentum at small x
journal, March 2019

Single spin asymmetry scaling in the forward rapidity region at RHIC
journal, August 2011

Nonlinear gluon evolution in the color glass condensate: II
journal, May 2002

Helicity-dependent generalization of the JIMWLK evolution
journal, December 2019

The renormalization group equation for the color glass condensate
journal, June 2001

Proton spin structure at small-x
journal, October 2019

Nonlinear gluon evolution in the color glass condensate: I
journal, September 2001

Comparison of spin asymmetries and cross sections in π0 production by 200 GeV polarized antiprotons and protons
journal, May 1991

The saturation scale and its x-dependence from Λ polarization studies
journal, January 2009

Saturation effects in deep inelastic scattering at low $Q^{2}$ and its implications on diffraction
journal, November 1998

Wilson renormalization group for low x physics: Gluon evolution at finite parton density
journal, November 1998

Transverse single spin asymmetry in Drell-Yan production in polarized pA collisions
journal, July 2015

Chromodynamic lensing and transverse single spin asymmetries
journal, April 2004

AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
journal, July 2011

Single transverse-spin asymmetries in forward pion production at high energy: Incorporating small- $x$ effects in the target
journal, October 2006

Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
journal, September 1998

Odderon in the color glass condensate
journal, October 2005

Forward Neutral-Pion Transverse Single-Spin Asymmetries in $p + p$ Collisions at $\sqrt{s} = 200 GeV$
journal, November 2008

QCD asymmetry and polarized hadron structure function measurement
journal, January 1985

Energy Dependence of the Cronin Effect from Nonlinear QCD Evolution
journal, February 2004

Gluon distribution functions for very large nuclei at small transverse momentum
journal, April 1994

Inclusive two-gluon and valence-quark-gluon production in DIS and $p A$ collisions
journal, December 2004

Saturation physics and deuteron–gold collisions at RHIC
journal, January 2006

Single transverse-spin asymmetries in hadronic pion production
journal, November 1998

On the small-x evolution of the color quadrupole and the Weizsäcker–Williams gluon distribution
journal, November 2011

Next-to-next-to-eikonal corrections in the CGC
journal, January 2016

Nuclear Dependence of the Transverse-Single-Spin Asymmetry for Forward Neutron Production in Polarized $p + A$ Collisions at $\sqrt{s_{N N}} = 200 GeV$
journal, January 2018

Intrinsic glue distribution at very small $x$
journal, May 1997

Gluon saturation and initial conditions for relativistic heavy ion collisions
journal, May 2014

Transverse single spin asymmetry in direct photon production in polarized $p A$ collisions
journal, August 2014

Small-x behavior and parton saturation: A QCD model
journal, April 1990

Saturation in diffractive deep inelastic scattering
journal, November 1999

Initial-state interactions and single-spin asymmetries in Drell–Yan processes
journal, October 2002

Operator expansion for high-energy scattering
journal, March 1996

Single spin asymmetry in forward $p A$ collisions. II. Fragmentation contribution
journal, January 2017

Wilson renormalization group for low x physics: Towards the high density regime
journal, November 1998

Transverse Quark Polarization in Large- $p_{T}$ Reactions, $e^{+} e^{-}$ Jets, and Leptoproduction: A Test of Quantum Chromodynamics
journal, December 1978

Green’s function in the color field of a large nucleus
journal, August 1994

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 $\sqrt{s_{N N}} = 200 GeV$
journal, September 2019

Rapidity loss, spin, and angular asymmetries in the scattering of a quark from the color field of a proton or nucleus
journal, July 2020

Fragmentation contribution to the transverse single-spin asymmetry in proton–proton collisions
journal, June 2013

Universality of unintegrated gluon distributions at small $x$
journal, May 2011

Diffractive structure function in a quasiclassical approximation
journal, August 1999

Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions
journal, July 2014

Parton saturation and Npart scaling of semi-hard processes in QCD
journal, May 2003

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering
journal, March 2002

Single Spin Asymmetries from a Single Wilson Loop
journal, March 2016

Inclusive jet production off the nucleus in the perturbative QCD with Nc→∞
journal, June 2000

Analyzing power in inclusive π+ and π− production at high xF with a 200 GeV polarized proton beam
journal, August 1991

Towards an explanation of transverse single-spin asymmetries in proton-proton collisions: The role of fragmentation in collinear factorization
journal, June 2014

Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution
journal, February 2016

Baryon stopping and valence quark distribution at small x
journal, January 2004

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980