Abstract
We study the evolution of an energetic jet which propagates in an anisotropic quark-gluon plasma, as created in the intermediate stages of ultrarelativistic heavy-ion collisions. We argue that the partons of the jet should acquire a non-zero average polarisation proportional to the medium anisotropy. We first observe that the medium anisotropy introduces a difference between the rates for transverse momentum broadening along the two directions perpendicular to the jet axis. In turn, this difference leads to a polarisation-dependent bias in the BDMPS-Z rates for medium-induced gluon branching. Accordingly, the daughter gluons in a branching process can carry net polarisation even if their parent gluon was unpolarised. Using these splitting rates, we construct kinetic equations which describe the production and transmission of polarisation via multiple branching in an anisotropic medium. The solutions to these equations show that polarisation is efficiently produced via quasi-democratic branchings, but then it is rapidly washed out by the subsequent branchings, due to the inability of soft gluons to keep trace of the polarisation of their parents. Based on that, we conclude that a net polarisation for the jet should survive in the final state if and only if the medium anisotropy is sizeable as the jet escapes the medium.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Casalderrey-Solana and C.A. Salgado, Introductory lectures on jet quenching in heavy ion collisions, Acta Phys. Polon. B 38 (2007) 3731 [arXiv:0712.3443] [INSPIRE].
G.-Y. Qin and X.-N. Wang, Jet quenching in high-energy heavy-ion collisions, Int. J. Mod. Phys. E 24 (2015) 1530014 [arXiv:1511.00790] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, Jet Structure in Heavy Ion Collisions, Int. J. Mod. Phys. E 24 (2015) 1530012 [arXiv:1503.05958] [INSPIRE].
J.D. Bjorken, Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region, Phys. Rev. D 27 (1983) 140 [INSPIRE].
R. Baier, A.H. Mueller, D. Schiff and D.T. Son, ‘Bottom up’ thermalization in heavy ion collisions, Phys. Lett. B 502 (2001) 51 [hep-ph/0009237] [INSPIRE].
A. Dumitru, Y. Guo, A. Mocsy and M. Strickland, Quarkonium states in an anisotropic QCD plasma, Phys. Rev. D 79 (2009) 054019 [arXiv:0901.1998] [INSPIRE].
Y. Burnier, M. Laine and M. Vepsalainen, Quarkonium dissociation in the presence of a small momentum space anisotropy, Phys. Lett. B 678 (2009) 86 [arXiv:0903.3467] [INSPIRE].
L. Thakur, N. Haque, U. Kakade and B.K. Patra, Dissociation of quarkonium in an anisotropic hot QCD medium, Phys. Rev. D 88 (2013) 054022 [arXiv:1212.2803] [INSPIRE].
L. Dong et al., The complex heavy-quark potential in an anisotropic quark-gluon plasma — Statics and dynamics, JHEP 09 (2022) 200 [arXiv:2205.10349] [INSPIRE].
J. Prakash, M. Kurian, S.K. Das and V. Chandra, Heavy quark transport in an anisotropic hot QCD medium: Collisional and Radiative processes, Phys. Rev. D 103 (2021) 094009 [arXiv:2102.07082] [INSPIRE].
T. Song, P. Moreau, J. Aichelin and E. Bratkovskaya, Exploring non-equilibrium quark-gluon plasma effects on charm transport coefficients, Phys. Rev. C 101 (2020) 044901 [arXiv:1910.09889] [INSPIRE].
P. Romatschke and M. Strickland, Collisional energy loss of a heavy quark in an anisotropic quark-gluon plasma, Phys. Rev. D 71 (2005) 125008 [hep-ph/0408275] [INSPIRE].
R. Ryblewski and M. Strickland, Dilepton production from the quark-gluon plasma using (3 + 1)-dimensional anisotropic dissipative hydrodynamics, Phys. Rev. D 92 (2015) 025026 [arXiv:1501.03418] [INSPIRE].
J. Churchill, L. Yan, S. Jeon and C. Gale, Emission of electromagnetic radiation from the early stages of relativistic heavy-ion collisions, Phys. Rev. C 103 (2021) 024904 [arXiv:2008.02902] [INSPIRE].
M. Coquet et al., Intermediate mass dileptons as pre-equilibrium probes in heavy ion collisions, Phys. Lett. B 821 (2021) 136626 [arXiv:2104.07622] [INSPIRE].
T. Lappi and L. McLerran, Some features of the glasma, Nucl. Phys. A 772 (2006) 200 [hep-ph/0602189] [INSPIRE].
E. Iancu and R. Venugopalan, The Color glass condensate and high-energy scattering in QCD, in Quark-gluon plasma 3, R.C. Hwa and X.-N. Wang eds., World Scientific (2003), p. 249–3363 [https://doi.org/10.1142/9789812795533_0005] [hep-ph/0303204] [INSPIRE].
F. Gelis, E. Iancu, J. Jalilian-Marian and R. Venugopalan, The Color Glass Condensate, Ann. Rev. Nucl. Part. Sci. 60 (2010) 463 [arXiv:1002.0333] [INSPIRE].
F. Gelis, Color Glass Condensate and Glasma, Int. J. Mod. Phys. A 28 (2013) 1330001 [arXiv:1211.3327] [INSPIRE].
F. Gelis, Initial state and thermalization in the Color Glass Condensate framework, Int. J. Mod. Phys. E 24 (2015) 1530008 [arXiv:1508.07974] [INSPIRE].
A. Kumar, B. Müller and D.-L. Yang, Spin polarization and correlation of quarks from the glasma, Phys. Rev. D 107 (2023) 076025 [arXiv:2212.13354] [INSPIRE].
J. Berges, K. Boguslavski, S. Schlichting and R. Venugopalan, Turbulent thermalization process in heavy-ion collisions at ultrarelativistic energies, Phys. Rev. D 89 (2014) 074011 [arXiv:1303.5650] [INSPIRE].
J. Berges, K. Boguslavski, S. Schlichting and R. Venugopalan, Universal attractor in a highly occupied non-Abelian plasma, Phys. Rev. D 89 (2014) 114007 [arXiv:1311.3005] [INSPIRE].
A. Ipp, D.I. Müller and D. Schuh, Anisotropic momentum broadening in the 2 + 1D Glasma: analytic weak field approximation and lattice simulations, Phys. Rev. D 102 (2020) 074001 [arXiv:2001.10001] [INSPIRE].
A. Ipp, D.I. Müller and D. Schuh, Jet momentum broadening in the pre-equilibrium Glasma, Phys. Lett. B 810 (2020) 135810 [arXiv:2009.14206] [INSPIRE].
A. Kurkela and Y. Zhu, Isotropization and hydrodynamization in weakly coupled heavy-ion collisions, Phys. Rev. Lett. 115 (2015) 182301 [arXiv:1506.06647] [INSPIRE].
A. Kurkela et al., Effective kinetic description of event-by-event pre-equilibrium dynamics in high-energy heavy-ion collisions, Phys. Rev. C 99 (2019) 034910 [arXiv:1805.00961] [INSPIRE].
X. Du and S. Schlichting, Equilibration of weakly coupled QCD plasmas, Phys. Rev. D 104 (2021) 054011 [arXiv:2012.09079] [INSPIRE].
M.E. Carrington, A. Czajka and S. Mrowczynski, Jet quenching in glasma, Phys. Lett. B 834 (2022) 137464 [arXiv:2112.06812] [INSPIRE].
M.E. Carrington, A. Czajka and S. Mrowczynski, Transport of hard probes through glasma, Phys. Rev. C 105 (2022) 064910 [arXiv:2202.00357] [INSPIRE].
S. Mrowczynski, Plasma instability at the initial stage of ultrarelativistic heavy ion collisions, Phys. Lett. B 314 (1993) 118 [INSPIRE].
S. Mrowczynski, B. Schenke and M. Strickland, Color instabilities in the quark-gluon plasma, Phys. Rept. 682 (2017) 1 [arXiv:1603.08946] [INSPIRE].
S. Hauksson, S. Jeon and C. Gale, Probes of the quark-gluon plasma and plasma instabilities, Phys. Rev. C 103 (2021) 064904 [arXiv:2012.03640] [INSPIRE].
P.B. Arnold, G.D. Moore and L.G. Yaffe, Effective kinetic theory for high temperature gauge theories, JHEP 01 (2003) 030 [hep-ph/0209353] [INSPIRE].
R. Baier and Y. Mehtar-Tani, Jet quenching and broadening: The Transport coefficient q-hat in an anisotropic plasma, Phys. Rev. C 78 (2008) 064906 [arXiv:0806.0954] [INSPIRE].
P. Romatschke, Momentum broadening in an anisotropic plasma, Phys. Rev. C 75 (2007) 014901 [hep-ph/0607327] [INSPIRE].
S. Hauksson, S. Jeon and C. Gale, Momentum broadening of energetic partons in an anisotropic plasma, Phys. Rev. C 105 (2022) 014914 [arXiv:2109.04575] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller and D. Schiff, Radiative energy loss of high-energy partons traversing an expanding QCD plasma, Phys. Rev. C 58 (1998) 1706 [hep-ph/9803473] [INSPIRE].
B.G. Zakharov, Quark energy loss in an expanding quark gluon plasma, in the proceedings of the 33rd Rencontres de Moriond: QCD and High-Energy Hadronic Interactions, Les Arcs France, March 21–28 (1998), p. 533–538 [hep-ph/9807396] [INSPIRE].
P.B. Arnold, Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium, Phys. Rev. D 79 (2009) 065025 [arXiv:0808.2767] [INSPIRE].
E. Iancu, P. Taels and B. Wu, Jet quenching parameter in an expanding QCD plasma, Phys. Lett. B 786 (2018) 288 [arXiv:1806.07177] [INSPIRE].
S.P. Adhya, C.A. Salgado, M. Spousta and K. Tywoniuk, Medium-induced cascade in expanding media, JHEP 07 (2020) 150 [arXiv:1911.12193] [INSPIRE].
P. Caucal, E. Iancu and G. Soyez, Jet radiation in a longitudinally expanding medium, JHEP 04 (2021) 209 [arXiv:2012.01457] [INSPIRE].
J. Barata, A.V. Sadofyev and C.A. Salgado, Jet broadening in dense inhomogeneous matter, Phys. Rev. D 105 (2022) 114010 [arXiv:2202.08847] [INSPIRE].
A.V. Sadofyev, M.D. Sievert and I. Vitev, Ab initio coupling of jets to collective flow in the opacity expansion approach, Phys. Rev. D 104 (2021) 094044 [arXiv:2104.09513] [INSPIRE].
C. Andres, F. Dominguez, A.V. Sadofyev and C.A. Salgado, Jet broadening in flowing matter: Resummation, Phys. Rev. D 106 (2022) 074023 [arXiv:2207.07141] [INSPIRE].
P. Romatschke and U. Romatschke, Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, Phys. Rev. Lett. 99 (2007) 172301 [arXiv:0706.1522] [INSPIRE].
R. Baier et al., Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B 483 (1997) 291 [hep-ph/9607355] [INSPIRE].
R. Baier et al., Radiative energy loss and p⊥-broadening of high-energy partons in nuclei, Nucl. Phys. B 484 (1997) 265 [hep-ph/9608322] [INSPIRE].
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].
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].
R. Baier, Y.L. Dokshitzer, A.H. Mueller and D. Schiff, Medium induced radiative energy loss: Equivalence between the BDMPS and Zakharov formalisms, Nucl. Phys. B 531 (1998) 403 [hep-ph/9804212] [INSPIRE].
U.A. Wiedemann and M. Gyulassy, Transverse momentum dependence of the Landau-Pomeranchuk-Migdal effect, Nucl. Phys. B 560 (1999) 345 [hep-ph/9906257] [INSPIRE].
U.A. Wiedemann, Gluon radiation off hard quarks in a nuclear environment: Opacity expansion, Nucl. Phys. B 588 (2000) 303 [hep-ph/0005129] [INSPIRE].
J.-P. Blaizot, E. Iancu and Y. Mehtar-Tani, Medium-induced QCD cascade: democratic branching and wave turbulence, Phys. Rev. Lett. 111 (2013) 052001 [arXiv:1301.6102] [INSPIRE].
J.-P. Blaizot, F. Dominguez, E. Iancu and Y. Mehtar-Tani, Probabilistic picture for medium-induced jet evolution, JHEP 06 (2014) 075 [arXiv:1311.5823] [INSPIRE].
J.-P. Blaizot and E. Iancu, The Quark gluon plasma: Collective dynamics and hard thermal loops, Phys. Rept. 359 (2002) 355 [hep-ph/0101103] [INSPIRE].
J.I. Kapusta and C. Gale, Finite-temperature field theory: Principles and applications, Cambridge University Press (2011) [https://doi.org/10.1017/CBO9780511535130] [INSPIRE].
E. Braaten and R.D. Pisarski, Soft Amplitudes in Hot Gauge Theories: A General Analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].
J. Frenkel and J.C. Taylor, High Temperature Limit of Thermal QCD, Nucl. Phys. B 334 (1990) 199 [INSPIRE].
J.P. Blaizot and E. Iancu, Kinetic equations for long wavelength excitations of the quark-gluon plasma, Phys. Rev. Lett. 70 (1993) 3376 [hep-ph/9301236] [INSPIRE].
S. Mrowczynski and M.H. Thoma, Hard loop approach to anisotropic systems, Phys. Rev. D 62 (2000) 036011 [hep-ph/0001164] [INSPIRE].
P. Romatschke and M. Strickland, Collective modes of an anisotropic quark gluon plasma, Phys. Rev. D 68 (2003) 036004 [hep-ph/0304092] [INSPIRE].
S. Mrowczynski, A. Rebhan and M. Strickland, Hard loop effective action for anisotropic plasmas, Phys. Rev. D 70 (2004) 025004 [hep-ph/0403256] [INSPIRE].
S. Caron-Huot, O(g) plasma effects in jet quenching, Phys. Rev. D 79 (2009) 065039 [arXiv:0811.1603] [INSPIRE].
P. Aurenche, F. Gelis and H. Zaraket, A Simple sum rule for the thermal gluon spectral function and applications, JHEP 05 (2002) 043 [hep-ph/0204146] [INSPIRE].
C.A. Salgado and U.A. Wiedemann, A Dynamical scaling law for jet tomography, Phys. Rev. Lett. 89 (2002) 092303 [hep-ph/0204221] [INSPIRE].
C.A. Salgado and U.A. Wiedemann, Calculating quenching weights, Phys. Rev. D 68 (2003) 014008 [hep-ph/0302184] [INSPIRE].
J.-P. Blaizot, F. Dominguez, E. Iancu and Y. Mehtar-Tani, Medium-induced gluon branching, JHEP 01 (2013) 143 [arXiv:1209.4585] [INSPIRE].
R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and collider physics, Cambridge University Press (2011) [https://doi.org/10.1017/CBO9780511628788] [INSPIRE].
Y.V. Kovchegov, D. Pitonyak and M.D. Sievert, Small-x Asymptotics of the Gluon Helicity Distribution, JHEP 10 (2017) 198 [arXiv:1706.04236] [INSPIRE].
T. Altinoluk, G. Beuf, A. Czajka and A. Tymowska, Quarks at next-to-eikonal accuracy in the CGC: Forward quark-nucleus scattering, Phys. Rev. D 104 (2021) 014019 [arXiv:2012.03886] [INSPIRE].
Y.V. Kovchegov and M.G. Santiago, Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution, JHEP 11 (2021) 200 [Erratum ibid. 09 (2022) 186] [arXiv:2108.03667] [INSPIRE].
J. Casalderrey-Solana and E. Iancu, Interference effects in medium-induced gluon radiation, JHEP 08 (2011) 015 [arXiv:1105.1760] [INSPIRE].
A. Kurkela and U.A. Wiedemann, Picturing perturbative parton cascades in QCD matter, Phys. Lett. B 740 (2015) 172 [arXiv:1407.0293] [INSPIRE].
L. Fister and E. Iancu, Medium-induced jet evolution: wave turbulence and energy loss, JHEP 03 (2015) 082 [arXiv:1409.2010] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, Energy flow along the medium-induced parton cascade, Annals Phys. 368 (2016) 148 [arXiv:1501.03443] [INSPIRE].
U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci. 63 (2013) 123 [arXiv:1301.2826] [INSPIRE].
C. Gale, S. Jeon and B. Schenke, Hydrodynamic Modeling of Heavy-Ion Collisions, Int. J. Mod. Phys. A 28 (2013) 1340011 [arXiv:1301.5893] [INSPIRE].
M. Luzum and H. Petersen, Initial State Fluctuations and Final State Correlations in Relativistic Heavy-Ion Collisions, J. Phys. G 41 (2014) 063102 [arXiv:1312.5503] [INSPIRE].
M. Alqahtani, M. Nopoush and M. Strickland, Relativistic anisotropic hydrodynamics, Prog. Part. Nucl. Phys. 101 (2018) 204 [arXiv:1712.03282] [INSPIRE].
P. Caucal, E. Iancu, A.H. Mueller and G. Soyez, Vacuum-like jet fragmentation in a dense QCD medium, Phys. Rev. Lett. 120 (2018) 232001 [arXiv:1801.09703] [INSPIRE].
P. Caucal, E. Iancu and G. Soyez, Deciphering the zg distribution in ultrarelativistic heavy ion collisions, JHEP 10 (2019) 273 [arXiv:1907.04866] [INSPIRE].
P. Caucal, E. Iancu, A.H. Mueller and G. Soyez, Nuclear modification factors for jet fragmentation, JHEP 10 (2020) 204 [arXiv:2005.05852] [INSPIRE].
Y. Mehtar-Tani, S. Schlichting and I. Soudi, Jet thermalization in QCD kinetic theory, arXiv:2209.10569 [https://doi.org/10.1007/JHEP05(2023)091] [INSPIRE].
J.C. Collins, Fragmentation of transversely polarized quarks probed in transverse momentum distributions, Nucl. Phys. B 396 (1993) 161 [hep-ph/9208213] [INSPIRE].
D. Amrath, A. Bacchetta and A. Metz, Reviewing model calculations of the Collins fragmentation function, Phys. Rev. D 71 (2005) 114018 [hep-ph/0504124] [INSPIRE].
BaBar collaboration, Measurement of Collins asymmetries in inclusive production of charged pion pairs in e+e− annihilation at BABAR, Phys. Rev. D 90 (2014) 052003 [arXiv:1309.5278] [INSPIRE].
M. Anselmino et al., Transversity and Collins functions from SIDIS and e+e− data, Phys. Rev. D 75 (2007) 054032 [hep-ph/0701006] [INSPIRE].
Acknowledgments
S.H. would like to thank Charles Gale for inspiring discussions during the early stages of this project. E.I. would like to thank Yuri Kovchegov for useful exchanges concerning the sub-eikonal corrections to the high energy scattering off a potential.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2303.03914
Rights and permissions
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.
About this article
Cite this article
Hauksson, S., Iancu, E. Jet polarisation in an anisotropic medium. J. High Energ. Phys. 2023, 27 (2023). https://doi.org/10.1007/JHEP08(2023)027
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)027