Improved opacity expansion for medium-induced parton splitting

Abstract

We present a new expansion scheme to compute the rate for parton splittings in dense and finite QCD media. In contrast to the standard opacity expansion, our expansion is performed around the harmonic oscillator whose characteristic frequency depends on the typical transverse momentum scale generated in the splitting. The first two orders account for the high frequency regime that is dominated by single hard scatterings together with the regime of multiple soft scatterings at low frequency. This provides the tools to go beyond the leading logarithmic approximation and compare to the full numerical solution to the corresponding Schrödinger equation across a wide range of gluon frequencies. We investigate the sensitivity of our results to varying the separation scale that defines the leading order. Finally, the application to Monte Carlo event generators is discussed.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    S. Peigne and A.V. Smilga, Energy losses in a hot plasma revisited, Phys. Usp.52 (2009) 659 [arXiv:0810.5702].

  2. [2]

    Y. Mehtar-Tani, J.G. Milhano and K. Tywoniuk, Jet physics in heavy-ion collisions, Int. J. Mod. Phys. A28 (2013) 1340013 [arXiv:1302.2579] [INSPIRE].

  3. [3]

    J.-P. Blaizot and Y. Mehtar-Tani, Jet Structure in Heavy Ion Collisions, Int. J. Mod. Phys. E24 (2015) 1530012 [arXiv:1503.05958] [INSPIRE].

  4. [4]

    R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B483 (1997) 291 [hep-ph/9607355] [INSPIRE].

  5. [5]

    R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss and pT broadening of high-energy partons in nuclei, Nucl. Phys. B484 (1997) 265 [hep-ph/9608322] [INSPIRE].

  6. [6]

    B.G. Zakharov, Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD, JETP Lett.63 (1996) 952 [hep-ph/9607440] [INSPIRE].

  7. [7]

    B.G. Zakharov, Radiative energy loss of high-energy quarks in finite size nuclear matter and quark-gluon plasma, JETP Lett.65 (1997) 615 [hep-ph/9704255] [INSPIRE].

  8. [8]

    P.B. Arnold, G.D. Moore and L.G. Yaffe, Photon and gluon emission in relativistic plasmas, JHEP06 (2002) 030 [hep-ph/0204343] [INSPIRE].

  9. [9]

    U.A. Wiedemann, Gluon radiation off hard quarks in a nuclear environment: Opacity expansion, Nucl. Phys. B588 (2000) 303 [hep-ph/0005129] [INSPIRE].

  10. [10]

    M. Gyulassy, P. Levai and I. Vitev, Reaction operator approach to nonAbelian energy loss, Nucl. Phys. B594 (2001) 371 [nucl-th/0006010] [INSPIRE].

  11. [11]

    G. Ovanesyan and I. Vitev, Medium-induced parton splitting kernels from Soft Collinear Effective Theory with Glauber gluons, Phys. Lett. B706 (2012) 371 [arXiv:1109.5619] [INSPIRE].

  12. [12]

    M.D. Sievert and I. Vitev, Quark branching in QCD matter to any order in opacity beyond the soft gluon emission limit, Phys. Rev. D98 (2018) 094010 [arXiv:1807.03799] [INSPIRE].

  13. [13]

    M.D. Sievert, I. Vitev and B. Yoon, A complete set of in-medium splitting functions to any order in opacity, Phys. Lett. B795 (2019) 502 [arXiv:1903.06170] [INSPIRE].

  14. [14]

    X.-N. Wang and X.-f. Guo, Multiple parton scattering in nuclei: Parton energy loss, Nucl. Phys. A696 (2001) 788 [hep-ph/0102230] [INSPIRE].

  15. [15]

    A. Majumder, Hard collinear gluon radiation and multiple scattering in a medium, Phys. Rev. D85 (2012) 014023 [arXiv:0912.2987] [INSPIRE].

  16. [16]

    P.B. Arnold and C. Dogan, QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime, Phys. Rev. D78 (2008) 065008 [arXiv:0804.3359] [INSPIRE].

  17. [17]

    B.G. Zakharov, On the energy loss of high-energy quarks in a finite size quark-gluon plasma, JETP Lett.73 (2001) 49 [hep-ph/0012360] [INSPIRE].

  18. [18]

    P.B. Arnold, High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation, Phys. Rev. D80 (2009) 025004 [arXiv:0903.1081] [INSPIRE].

  19. [19]

    S. Caron-Huot and C. Gale, Finite-size effects on the radiative energy loss of a fast parton in hot and dense strongly interacting matter, Phys. Rev. C82 (2010) 064902 [arXiv:1006.2379] [INSPIRE].

  20. [20]

    X. Feal and R. Vazquez, Intensity of gluon bremsstrahlung in a finite plasma, Phys. Rev. D98 (2018) 074029 [arXiv:1811.01591] [INSPIRE].

  21. [21]

    W. Ke, Y. Xu and S.A. Bass, Modified Boltzmann approach for modeling the splitting vertices induced by the hot QCD medium in the deep Landau-Pomeranchuk-Migdal region, Phys. Rev. C100 (2019) 064911 [arXiv:1810.08177] [INSPIRE].

  22. [22]

    C. Andres, L. Apolin´ario and F. Dominguez, Medium-induced gluon radiation with full resummation of multiple scatterings for realistic parton-medium interactions, arXiv:2002.01517 [INSPIRE].

  23. [23]

    Y. Mehtar-Tani, Gluon bremsstrahlung in finite media beyond multiple soft scattering approximation, JHEP07 (2019) 057 [arXiv:1903.00506] [INSPIRE].

  24. [24]

    G. Moliere, Theory of the scattering of fast charged particles. 2. Repeated and multiple scattering, Z. Naturforsch. A3 (1948) 78.

  25. [25]

    E. Iancu, K. Itakura and D.N. Triantafyllopoulos, Cronin effect and high p-perpendicular suppression in the nuclear gluon distribution at small x, Nucl. Phys. A742 (2004) 182 [hep-ph/0403103] [INSPIRE].

  26. [26]

    J. Barata and Y. Mehtar-Tani, Improved opacity expansion at NNLO for medium induced gluon radiation, arXiv:2004.02323 [INSPIRE].

  27. [27]

    P. Aurenche, F. Gelis and H. Zaraket, A simple sum rule for the thermal gluon spectral function and applications, JHEP05 (2002) 043 [hep-ph/0204146] [INSPIRE].

  28. [28]

    P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 2. Beyond leading log, JHEP05 (2003) 051 [hep-ph/0302165] [INSPIRE].

  29. [29]

    S. Caron-Huot, O(g) plasma effects in jet quenching, Phys. Rev. D79 (2009) 065039 [arXiv:0811.1603] [INSPIRE].

  30. [30]

    X.-N. Wang and M. Gyulassy, Gluon shadowing and jet quenching in A + A collisions at \( \sqrt{s} \) = 200 GeV, Phys. Rev. Lett.68 (1992) 1480 [INSPIRE].

  31. [31]

    M. Abramowitz and I. Stegun eds., Handbook of Mathematical Functions, Dover Publications, New York U.S.A. (1965).

  32. [32]

    P.B. Arnold, Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium, Phys. Rev. D79 (2009) 065025 [arXiv:0808.2767] [INSPIRE].

  33. [33]

    B. Schenke, C. Gale and S. Jeon, MARTINI: An Event generator for relativistic heavy-ion collisions, Phys. Rev. C80 (2009) 054913 [arXiv:0909.2037] [INSPIRE].

  34. [34]

    C. Park, S. Jeon and C. Gale, Jet modification with medium recoil in quark-gluon plasma, Nucl. Phys. A982 (2019) 643 [arXiv:1807.06550] [INSPIRE].

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Author information

Affiliations

Authors

Corresponding author

Correspondence to Konrad Tywoniuk.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 1910.02032

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mehtar-Tani, Y., Tywoniuk, K. Improved opacity expansion for medium-induced parton splitting. J. High Energ. Phys. 2020, 187 (2020). https://doi.org/10.1007/JHEP06(2020)187

Download citation

Keywords

  • Heavy Ion Phenomenology
  • Jets