Papers
Topics
Authors
Recent
Search
2000 character limit reached

Progress in implementing the kinematical constraint into the small-x JIMWLK evolution equation

Published 23 May 2024 in hep-ph | (2405.14415v1)

Abstract: The most complete high-energy evolution of Wilson line operators is described by the set of equations called Balitsky-JIMWLK evolution equations. It is known from the studies of the linear - the BFKL - evolution equation that the leading corrections come from the kinematically enhanced double collinear logarithms. A method for resumming such logarithmic corrections to all orders for the Balitsky-Kovchegov equation is known under the name of kinematical constraint. In this work, we discuss the progress in implementing these corrections into the Langevin formulation of the JIMWLK equation. In particular, we introduce a set of correlation functions which are nonlocal in the rapidity variable. They appear in the construction of the kinematical constraint, however, their behavior with rapidity has not been investigated numerically so far. We derive their large-$N$ evolution equations, solve them numerically, and comment on their implications for the implementation of the full kinematical constraint.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (42)
  1. E. Iancu, A. Leonidov, and L. McLerran, “The colour glass condensate: An introduction,” 2002.
  2. J. Jalilian-Marian and Y. Kovchegov, “Saturation physics and deuteron–gold collisions at rhic,” Progress in Particle and Nuclear Physics, vol. 56, no. 1, p. 104–231, Jan. 2006. [Online]. Available: http://dx.doi.org/10.1016/j.ppnp.2005.07.002
  3. H. Weigert, “Evolution at small-x: The color glass condensate,” Progress in Particle and Nuclear Physics, vol. 55, no. 2, p. 461–565, Oct. 2005. [Online]. Available: http://dx.doi.org/10.1016/j.ppnp.2005.01.029
  4. F. Gelis and R. Venugopalan, “Lectures on multi-particle production in the glasma,” 2006.
  5. F. Gelis, T. Lappi, and R. Venugopalan, “High energy scattering in quantum chromodynamics,” International Journal of Modern Physics E, vol. 16, no. 09, p. 2595–2637, Oct. 2007. [Online]. Available: http://dx.doi.org/10.1142/S0218301307008331
  6. F. Gelis, E. Iancu, J. Jalilian-Marian, and R. Venugopalan, “The Color Glass Condensate,” Ann. Rev. Nucl. Part. Sci., vol. 60, pp. 463–489, 2010.
  7. P. Caucal, F. Salazar, B. Schenke, T. Stebel, and R. Venugopalan, “Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO,” JHEP, vol. 08, p. 062, 2023.
  8. ——, “Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small x: Complete NLO Results and Predictions,” Phys. Rev. Lett., vol. 132, no. 8, p. 081902, 2024.
  9. I. Balitsky, “Operator expansion for high-energy scattering,” Nuclear Physics B, vol. 463, no. 1, p. 99–157, Mar. 1996. [Online]. Available: http://dx.doi.org/10.1016/0550-3213(95)00638-9
  10. J. Jalilian-Marian, A. Kovner, A. Leonidov, and H. Weigert, “The bfkl equation from the wilson renormalization group,” Nuclear Physics B, vol. 504, no. 1–2, p. 415–431, Oct. 1997. [Online]. Available: http://dx.doi.org/10.1016/S0550-3213(97)00440-9
  11. ——, “Wilson renormalization group for lowxphysics: Towards the high density regime,” Physical Review D, vol. 59, no. 1, Nov. 1998. [Online]. Available: http://dx.doi.org/10.1103/PhysRevD.59.014014
  12. A. Kovner, J. G. Milhano, and H. Weigert, “Relating different approaches to nonlinear qcd evolution at finite gluon density,” Physical Review D, vol. 62, no. 11, Oct. 2000. [Online]. Available: http://dx.doi.org/10.1103/PhysRevD.62.114005
  13. E. Iancu, A. Leonidov, and L. McLerran, “Nonlinear gluon evolution in the color glass condensate: I,” Nuclear Physics A, vol. 692, no. 3–4, p. 583–645, Sep. 2001. [Online]. Available: http://dx.doi.org/10.1016/S0375-9474(01)00642-X
  14. ——, “The renormalization group equation for the color glass condensate,” Physics Letters B, vol. 510, no. 1–4, p. 133–144, Jun. 2001. [Online]. Available: http://dx.doi.org/10.1016/S0370-2693(01)00524-X
  15. E. Ferreiro, E. Iancu, A. Leonidov, and L. McLerran, “Nonlinear gluon evolution in the color glass condensate: Ii,” Nuclear Physics A, vol. 703, no. 1–2, p. 489–538, May 2002. [Online]. Available: http://dx.doi.org/10.1016/S0375-9474(01)01329-X
  16. Y. V. Kovchegov, “Small-x f2subscript𝑓2f_{2}italic_f start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT structure function of a nucleus including multiple pomeron exchanges,” Physical Review D, vol. 60, no. 3, Jun. 1999. [Online]. Available: http://dx.doi.org/10.1103/PhysRevD.60.034008
  17. H. Weigert, “Unitarity at small bjorken x,” Nuclear Physics A, vol. 703, no. 3–4, p. 823–860, Jun. 2002. [Online]. Available: http://dx.doi.org/10.1016/S0375-9474(01)01668-2
  18. J.-P. Blaizot, E. Iancu, and H. Weigert, “Non linear gluon evolution in path-integral form,” Nuclear Physics A, vol. 713, no. 3–4, p. 441–469, Jan. 2003. [Online]. Available: http://dx.doi.org/10.1016/S0375-9474(02)01299-X
  19. K. Rummukainen and H. Weigert, “Universal features of jimwlk and bk evolution at small x,” Nuclear Physics A, vol. 739, no. 1–2, p. 183–226, Jul. 2004. [Online]. Available: http://dx.doi.org/10.1016/j.nuclphysa.2004.03.219
  20. T. Lappi and H. Mäntysaari, “On the running coupling in the JIMWLK equation,” Eur. Phys. J. C, vol. 73, no. 2, p. 2307, 2013.
  21. T. Lappi, “Gluon spectrum in the glasma from jimwlk evolution,” Physics Letters B, vol. 703, no. 3, p. 325–330, Sep. 2011. [Online]. Available: http://dx.doi.org/10.1016/j.physletb.2011.08.011
  22. A. Dumitru, J. Jalilian-Marian, T. Lappi, B. Schenke, and R. Venugopalan, “Renormalization group evolution of multi-gluon correlators in high energy qcd,” Physics Letters B, vol. 706, no. 2–3, p. 219–224, Dec. 2011. [Online]. Available: http://dx.doi.org/10.1016/j.physletb.2011.11.002
  23. T. Lappi and H. Mäntysaari, “On the running coupling in the jimwlk equation,” The European Physical Journal C, vol. 73, no. 2, Feb. 2013. [Online]. Available: http://dx.doi.org/10.1140/epjc/s10052-013-2307-z
  24. S. Schlichting and B. Schenke, “The shape of the proton at high energies,” Physics Letters B, vol. 739, p. 313–319, Dec. 2014. [Online]. Available: http://dx.doi.org/10.1016/j.physletb.2014.10.068
  25. B. Schenke and S. Schlichting, “3d glasma initial state for relativistic heavy ion collisions,” Physical Review C, vol. 94, no. 4, Oct. 2016. [Online]. Available: http://dx.doi.org/10.1103/PhysRevC.94.044907
  26. P. Korcyl, “Numerical package for solving the JIMWLK evolution equation in C++,” SoftwareX, vol. 16, p. 100887, 9 2020.
  27. S. Cali, K. Cichy, P. Korcyl, P. Kotko, K. Kutak, and C. Marquet, “On systematic effects in the numerical solutions of the JIMWLK equation,” Eur. Phys. J. C, vol. 81, no. 7, p. 663, 2021.
  28. P. Korcyl, “Finite volume effects in the McLerran–Venugopalan initial condition for the JIMWLK equation,” Eur. Phys. J. C, vol. 82, no. 4, p. 369, 2022.
  29. B. Andersson, G. Gustafson, and J. Samuelsson, “The Linked dipole chain model for DIS,” Nucl. Phys. B, vol. 467, pp. 443–478, 1996.
  30. J. Kwiecinski, A. D. Martin, and P. J. Sutton, “Constraints on gluon evolution at small x,” Z. Phys. C, vol. 71, pp. 585–594, 1996.
  31. G. P. Salam, “A Resummation of large subleading corrections at small x,” JHEP, vol. 07, p. 019, 1998.
  32. K. J. Golec-Biernat, L. Motyka, and A. M. Stasto, “Diffusion into infrared and unitarization of the BFKL pomeron,” Phys. Rev. D, vol. 65, p. 074037, 2002.
  33. L. Motyka and A. M. Stasto, “Exact kinematics in the small x evolution of the color dipole and gluon cascade,” Phys. Rev. D, vol. 79, p. 085016, 2009.
  34. G. Beuf, “Improving the kinematics for low-x𝑥xitalic_x QCD evolution equations in coordinate space,” Phys. Rev. D, vol. 89, no. 7, p. 074039, 2014.
  35. E. Iancu, J. D. Madrigal, A. H. Mueller, G. Soyez, and D. N. Triantafyllopoulos, “Resumming double logarithms in the QCD evolution of color dipoles,” Phys. Lett. B, vol. 744, pp. 293–302, 2015.
  36. Y. Hatta and E. Iancu, “Collinearly improved JIMWLK evolution in Langevin form,” JHEP, vol. 08, p. 083, 2016.
  37. B. Ducloué, E. Iancu, A. H. Mueller, G. Soyez, and D. N. Triantafyllopoulos, “Non-linear evolution in QCD at high-energy beyond leading order,” JHEP, vol. 04, p. 081, 2019.
  38. B. Ducloué, E. Iancu, G. Soyez, and D. N. Triantafyllopoulos, “HERA data and collinearly-improved BK dynamics,” Phys. Lett. B, vol. 803, p. 135305, 2020.
  39. H. Mäntysaari, N. Mueller, F. Salazar, and B. Schenke, “Multigluon correlations and evidence of saturation from dijet measurements at an electron-ion collider,” Phys. Rev. Lett., vol. 124, p. 112301, Mar 2020. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.124.112301
  40. T. Lappi, B. Schenke, S. Schlichting, and R. Venugopalan, “Tracing the origin of azimuthal gluon correlations in the color glass condensate,” Journal of High Energy Physics, vol. 2016, no. 1, Jan. 2016. [Online]. Available: http://dx.doi.org/10.1007/JHEP01(2016)061
  41. F. Dominguez, C. Marquet, and B. Wu, “On multiple scatterings of mesons in hot and cold qcd matter,” Nuclear Physics A, vol. 823, no. 1–4, p. 99–119, May 2009. [Online]. Available: http://dx.doi.org/10.1016/j.nuclphysa.2009.03.008
  42. J.-P. Blaizot, F. Gelis, and R. Venugopalan, “High energy pa collisions in the color glass condensate approach ii: quark pair production,” Nuclear Physics A, vol. 743, no. 1–3, p. 57–91, Oct. 2004. [Online]. Available: http://dx.doi.org/10.1016/j.nuclphysa.2004.07.006
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Authors (3)

  1. P. Korcyl 
  2. L. Motyka 
  3. T. Stebel 

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free