Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution

Kovchegov, Yuri V.; Sievert, Matthew D.

doi:10.1016/j.nuclphysb.2015.12.008

Title: Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution

Abstract

We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) of a large nucleus using the tools of saturation physics. By generalizing the quasi-classical Glauber–Gribov–Mueller/McLerran–Venugopalan approximation to allow for the possibility of spin–orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large “nucleus.” To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer–Mulders distribution. Here, we observe that spin–orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.

Authors:: Kovchegov, Yuri V.; Sievert, Matthew D.

Publication Date:: Mon Feb 01 00:00:00 EST 2016

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States); The Ohio State Univ., Columbus, OH (United States)

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

OSTI Identifier:: 1234126

Alternate Identifier(s):: OSTI ID: 1253276; OSTI ID: 1604446

Report Number(s):: BNL-112020-2016-JA
Journal ID: ISSN 0550-3213; S0550321315004289; PII: S0550321315004289

Grant/Contract Number:: SC0004286; SC0012704; SC00112704

Resource Type:: Published Article

Journal Name:: Nuclear Physics. B

Additional Journal Information:: Journal Name: Nuclear Physics. B Journal Volume: 903 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Kovchegov, Yuri V., and Sievert, Matthew D. Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution.  Netherlands: N. p., 2016. 
Web.  doi:10.1016/j.nuclphysb.2015.12.008.

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                    Kovchegov, Yuri V., & Sievert, Matthew D. Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution.  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2015.12.008

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                    Kovchegov, Yuri V., and Sievert, Matthew D. Mon .  
"Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution".  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2015.12.008.

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@article{osti_1234126,

  title        = {Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution},

  author       = {Kovchegov, Yuri V. and Sievert, Matthew D.},

  abstractNote = {We set up a formalism for calculating transverse-momentum-dependent parton distribution functions (TMDs) of a large nucleus using the tools of saturation physics. By generalizing the quasi-classical Glauber–Gribov–Mueller/McLerran–Venugopalan approximation to allow for the possibility of spin–orbit coupling, we show how any TMD can be calculated in the saturation framework. This can also be applied to the TMDs of a proton by modeling it as a large “nucleus.” To illustrate our technique, we calculate the quark TMDs of an unpolarized nucleus at large-x: the unpolarized quark distribution and the quark Boer–Mulders distribution. Here, we observe that spin–orbit coupling leads to mixing between different TMDs of the nucleus and of the nucleons. We then consider the evolution of TMDs: at large-x, in the double-logarithmic approximation, we obtain the Sudakov form factor. At small-x the evolution of unpolarized-target quark TMDs is governed by BK/JIMWLK evolution, while the small-x evolution of polarized-target quark TMDs appears to be dominated by the QCD Reggeon.},

  doi          = {10.1016/j.nuclphysb.2015.12.008},

  journal      = {Nuclear Physics. B},

  number       = C,

  volume       = 903,

  place        = {Netherlands},

  year         = {Mon Feb 01 00:00:00 EST 2016},

  month        = {Mon Feb 01 00:00:00 EST 2016}

}

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Title: Calculating TMDs of a large nucleus: Quasi-classical approximation and quantum evolution

Abstract

Citation Formats

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Evolution of Gluon TMD at Low and Moderate x journal, January 2015

Unitarity and the BFKL pomeron journal, March 1995

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

Universal features of JIMWLK and BK evolution at small x journal, July 2004

Diffractive structure function in a quasiclassical approximation journal, August 1999

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

Sudakov double logarithms resummation in hard processes in the small- x saturation formalism journal, December 2013

Initial-state interactions in the unpolarized Drell-Yan process journal, March 2003

Spin in Relativistic Quantum Theory journal, December 2012

Explicitly covariant light-front dynamics and relativistic few-body systems journal, July 1998

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

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

Exclusive processes in perturbative quantum chromodynamics journal, November 1980

Back-to-back jets in QCD journal, December 1981

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

Quantum chromodynamics and other field theories on the light cone journal, August 1998

Hard nuclear processes and microscopic nuclear structure journal, April 1988

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

Parton model and deep inelastic scattering on nuclei journal, March 1975

Transverse-momentum-dependent parton distribution function and jet transport in a nuclear medium journal, June 2008

k t Factorization for Hard Processes in Nuclei journal, January 2011

Reggeon interactions in perturbative QCD journal, September 1995

Transversity and Collins functions from SIDIS and e + e − data journal, March 2007

Regge asymptotics of scattering with flavour exchange in QCD journal, September 1995

Parton saturation at small x and in large nuclei journal, October 1999

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

Inclusive gluon production in deep inelastic scattering at high parton density journal, March 2002

Polarized hyperons from pA scattering in the gluon saturation regime journal, March 2003

Unitarization of the BFKL Pomeron on a nucleus journal, March 2000

Asymptotic freedom in parton language journal, August 1977

The angular momentum controversy: What’s it all about and does it matter? journal, August 2014

Time-reversal odd distribution functions in leptoproduction journal, May 1998

Soft gluons in the infinite-momentum wave function and the BFKL pomeron journal, March 1994

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

Spin densities in the transverse plane and generalized transversity distributions journal, September 2005

Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes journal, August 1994

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

Sudakov Resummation in the Small- x Saturation Formalism journal, February 2013

Factorization and high-energy effective action journal, June 1999

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

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

Sivers asymmetry of Drell-Yan production in the small- $x$ regime
journal, February 2013

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

Process dependent nuclear $k_{⊥}$ broadening effect
journal, October 2013

The complete tree-level result up to order 1/Q for polarized deep-inelastic leptoproduction
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Quark contribution to the small- $x$ evolution of color dipole
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Running coupling and power corrections in non-linear evolution at the high-energy limit
journal, March 2007

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

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

Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange
journal, March 1983

Flavor singlet contribution to the structure functiong 1 at small-x
journal, December 1996

Origin of model relations among transverse-momentum dependent parton distributions
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Studying the perturbative Reggeon
journal, January 2000

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

Semihard processes in QCD
journal, November 1983

The Color Glass Condensate
journal, November 2010

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

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

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

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

Triumvirate of running couplings in small-x evolution
journal, March 2007

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

Operator expansion for high-energy scattering
journal, March 1996

Linearly polarized gluon distributions in the color dipole model
journal, February 2012

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

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

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

Discrete symmetries on the light front and a general relation connecting the nucleon electric dipole and anomalous magnetic moments
journal, February 2006

Sivers function in the quasiclassical approximation
journal, March 2014

Renormalization group evolution of multi-gluon correlators in high energy QCD
journal, December 2011

Distribution of linearly polarized gluons inside a large nucleus
journal, September 2011

-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order
journal, November 2012

Evolution of Gluon TMD at Low and Moderate x
journal, January 2015

Unitarity and the BFKL pomeron
journal, March 1995

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

Universal features of JIMWLK and BK evolution at small x
journal, July 2004

Diffractive structure function in a quasiclassical approximation
journal, August 1999

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

Sudakov double logarithms resummation in hard processes in the small- $x$ saturation formalism
journal, December 2013

Initial-state interactions in the unpolarized Drell-Yan process
journal, March 2003

Spin in Relativistic Quantum Theory
journal, December 2012

Explicitly covariant light-front dynamics and relativistic few-body systems
journal, July 1998

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

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

Exclusive processes in perturbative quantum chromodynamics
journal, November 1980

Back-to-back jets in QCD
journal, December 1981

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

Quantum chromodynamics and other field theories on the light cone
journal, August 1998

Hard nuclear processes and microscopic nuclear structure
journal, April 1988

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

Parton model and deep inelastic scattering on nuclei
journal, March 1975

Transverse-momentum-dependent parton distribution function and jet transport in a nuclear medium
journal, June 2008

$k_{t}$ Factorization for Hard Processes in Nuclei
journal, January 2011

Reggeon interactions in perturbative QCD
journal, September 1995

Transversity and Collins functions from SIDIS and $e^{+} e^{-}$ data
journal, March 2007

Regge asymptotics of scattering with flavour exchange in QCD
journal, September 1995

Parton saturation at small x and in large nuclei
journal, October 1999

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

Inclusive gluon production in deep inelastic scattering at high parton density
journal, March 2002

Polarized hyperons from pA scattering in the gluon saturation regime
journal, March 2003

Unitarization of the BFKL Pomeron on a nucleus
journal, March 2000

Asymptotic freedom in parton language
journal, August 1977

The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014

Time-reversal odd distribution functions in leptoproduction
journal, May 1998

Soft gluons in the infinite-momentum wave function and the BFKL pomeron
journal, March 1994

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

Spin densities in the transverse plane and generalized transversity distributions
journal, September 2005

Single and double BFKL pomeron exchange and a dipole picture of high energy hard processes
journal, August 1994

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

Sudakov Resummation in the Small- $x$ Saturation Formalism
journal, February 2013

Factorization and high-energy effective action
journal, June 1999

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