Skip to main content
SpringerLink
Log in

Color Effects for Transverse Momentum Dependent Parton Distribution Functions in Hadronic Processes

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

In the Drell–Yan process (DY) a quark and an antiquark, coming from two different protons, produce a colorless virtual photon. In the proton description, we include transverse momentum dependent parton distribution functions (TMD PDFs), which go beyond the ordinary collinear PDFs. As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when one looks at azimuthal asymmetries. Matrix elements used in the description of hadronic processes, such as DY, require the inclusion of gauge links, coming from gluon contributions in the process, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state the color flow between different parts of the process causes entanglement. We show that in the process of color disentangling each gauge link remains sensitive to this color flow. After disentanglement, we find that particular combinations of TMDs require a different numerical color factor than one might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as the DY process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ralston J.P., Soper D.E.: Production of dimuons from high-energy polarized proton–proton collisions. Nucl. Phys. B 152, 109 (1979)

    Article  ADS  Google Scholar 

  2. Tangerman R.D., Mulders P.J.: Intrinsic transverse momentum and the polarized Drell–Yan process. Phys. Rev. D 51, 3357–3372 (1995)

    Article  ADS  Google Scholar 

  3. Boer D.: Investigating the origins of transverse spin asymmetries at RHIC. Phys. Rev. D 60, 014012 (1999)

    Article  ADS  Google Scholar 

  4. Sivers D.W.: Single-spin production asymmetries from the hard scattering of pointlike constituents. Phys. Rev. D 41, 83 (1990)

    Article  ADS  Google Scholar 

  5. Collins J.C.: Fragmentation of transversely polarized quarks probed in transverse momentum distributions. Nucl. Phys. B 396, 161–182 (1993)

    Article  ADS  Google Scholar 

  6. Collins J.C.: Leading-twist single-transverse-spin asymmetries: Drell–Yan and deep-inelastic scattering. Phys. Lett. B 536, 43–48 (2002)

    Article  ADS  Google Scholar 

  7. Brodsky S.J., Hwang D.S., Schmidt I.: Initial-state interactions and single-spin asymmetries in Drell–Yan processes. Nucl. Phys. B 642, 344–356 (2002)

    Article  ADS  Google Scholar 

  8. Bomhof C.J., Mulders P.J., Pijlman F.: The construction of gauge-links in arbitrary hard processes. Eur. Phys. J. C 47, 147–162 (2006)

    Article  ADS  Google Scholar 

  9. Buffing M.G.A., Mukherjee A., Mulders P.J.: Generalized universality of higher transverse moments of quark transverse momentum dependent correlators. Phys. Rev. D 86, 074030 (2012)

    Article  ADS  Google Scholar 

  10. Buffing M.G.A., Mulders P.J.: Gauge links for transverse momentum dependent correlators at tree-level. JHEP 1107, 065 (2011)

    Article  ADS  Google Scholar 

  11. Buffing M.G.A., Mulders P.J.: Color entanglement for azimuthal asymmetries in the Drell–Yan process. Phys. Rev. Lett. 112, 092002 (2014)

    Article  ADS  Google Scholar 

  12. Bacchetta A., Diehl M., Goeke K., Metz A., Mulders P.J., Schlegel M.: Semi-inclusive deep inelastic scattering at small transverse momentum. JHEP 0702, 093 (2007)

    Article  ADS  Google Scholar 

  13. Boer D., Mulders P.J., Pijlman F.: Universality of T-odd effects in single spin and azimuthal asymmetries. Nucl. Phys. B 667, 201–241 (2003)

    Article  ADS  Google Scholar 

  14. Efremov A.V., Teryaev O.V.: On spin effects in quantum chromodynamics. Sov. J. Nucl. Phys. 36, 140 (1982)

    Google Scholar 

  15. Efremov A.V., Teryaev O.V.: QCD asymmetry and polarized hadron structure function measurement. Phys. Lett. B 150, 383 (1985)

    Article  ADS  Google Scholar 

  16. Qiu J.-W., Sterman G.F.: Single transverse spin asymmetries. Phys. Rev. Lett. 67, 2264–2267 (1991)

    Article  ADS  Google Scholar 

  17. Qiu J.-W., Sterman G.F.: Single transverse spin asymmetries in direct photon production. Nucl. Phys. B 378, 52–78 (1992)

    Article  ADS  Google Scholar 

  18. Qiu J.-W., Sterman G.F.: Single transverse-spin asymmetries in hadronic pion production. Phys. Rev. D 59, 014004 (1998)

    Article  ADS  Google Scholar 

  19. Kanazawa Y., Koike Y.: Chiral-odd contribution to single-transverse spin asymmetry in hadronic pion production. Phys. Lett. B 478, 121–126 (2000)

    Article  ADS  Google Scholar 

  20. Metz A.: Gluon-exchange in spin-dependent fragmentation. Phys. Lett. B 549, 139–145 (2002)

    Article  ADS  Google Scholar 

  21. Collins J.C., Metz A.: Universality of soft and collinear factors in hard-scattering factorization. Phys. Rev. Lett. 93, 252001 (2004)

    Article  ADS  Google Scholar 

  22. Gamberg L.P., Mukherjee A., Mulders P.J.: Spectral analysis of gluonic pole matrix elements for fragmentation. Phys. Rev. D 77, 114026 (2008)

    Article  ADS  Google Scholar 

  23. Meissner S., Metz A.: Partonic pole matrix elements for fragmentation. Phys. Rev. Lett. 102, 172003 (2009)

    Article  ADS  Google Scholar 

  24. Gamberg L.P., Mukherjee A., Mulders P.J.: Model independent analysis of gluonic pole matrix elements and universality of transverse-momentum-dependent fragmentation functions. Phys. Rev. D 83, 071503 (2011)

    Article  ADS  Google Scholar 

  25. Rogers T.C., Mulders P.J.: No generalized transverse momentum dependent factorization in the hadroproduction of high transverse momentum hadrons. Phys. Rev. D 81, 094006 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theory Group, Nikhef and Department of Physics, Faculty of Science, VU University, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands

    M. G. A. Buffing & P. J. Mulders

Authors
  1. M. G. A. Buffing
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. J. Mulders
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. G. A. Buffing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Buffing, M.G.A., Mulders, P.J. Color Effects for Transverse Momentum Dependent Parton Distribution Functions in Hadronic Processes. Few-Body Syst 56, 337–342 (2015). https://doi.org/10.1007/s00601-014-0921-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-014-0921-4

Keywords

Search

Navigation