Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions
Abstract
:1. Introduction
2. Frameworks
2.1. Generating Datasets with LICM
2.2. Deep Neural Networks
3. Results and Analyses
4. Summary
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Radovic, A.; Williams, M.; Rousseau, D.; Kagan, M.; Bonacorsi, D.; Himmel, A.; Aurisano, A.; Terao, K.; Wongjirad, T. Machine learning at the energy and intensity frontiers of particle physics. Nature 2018, 560, 41–48. [Google Scholar] [CrossRef] [PubMed]
- Carleo, G.; Cirac, I.; Cranmer, K.; Daudet, L.; Schuld, M.; Tishby, N.; Vogt-Maranto, L.; Zdeborová, L. Machine learning and the physical sciences. Rev. Mod. Phys. 2019, 91, 045002. [Google Scholar] [CrossRef]
- Mehta, P.; Bukov, M.; Wang, C.H.; Day, A.G.R.; Richardson, C.; Fisher, C.K.; Schwab, D.J. A high-bias, low-variance introduction to Machine Learning for physicists. Phys. Rept. 2019, 810, 1–124. [Google Scholar] [CrossRef]
- Pang, L.G.; Zhou, K.; Su, N.; Petersen, H.; Stöcker, H.; Wang, X.N. An equation-of-state-meter of quantum chromodynamics transition from deep learning. Nat.Commun. 2018, 9, 210. [Google Scholar] [CrossRef] [PubMed]
- Huang, H.; Xiao, B.; Liu, Z.; Wu, Z.; Mu, Y.; Song, H. Applications of deep learning to relativistic hydrodynamics. Phys. Rev. Res. 2021, 3, 023256. [Google Scholar] [CrossRef]
- Steinheimer, J.; Pang, L.; Zhou, K.; Koch, V.; Randrup, J.; Stoecker, H. A machine learning study to identify spinodal clumping in high energy nuclear collisions. J. High Energy Phys. 2019, 12, 122. [Google Scholar] [CrossRef]
- Aoki, Y.; Endrodi, G.; Fodor, Z.; Katz, S.D.; Szabo, K.K. The Order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature 2006, 443, 675–678. [Google Scholar] [CrossRef]
- Bazavov, A.; Bhattacharya, T.; Cheng, M.; DeTar, C.; Ding, H.T.; Gottlieb, S.; Gupta, R.; Hegde, P.; Heller, U.M.; Karsch, F.; et al. The chiral and deconfinement aspects of the QCD transition. Phys. Rev. D 2012, 85, 054503. [Google Scholar] [CrossRef]
- Shuryak, E.V. Quantum Chromodynamics and the Theory of Superdense Matter. Phys. Rept. 1980, 61, 71–158. [Google Scholar] [CrossRef]
- Afanasiev, S.V.; Anticic, T.; Barna, D.; Bartke, J.; Barton, R.A.; Behler, M.; Betev, L.; Bialkowska, H.; Billmeier, A.; Blume, C.; et al. Energy dependence of pion and kaon production in central Pb + Pb collisions. Phys. Rev. C 2002, 66, 054902. [Google Scholar] [CrossRef]
- Song, H.; Heinz, U.W. Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions. Phys. Rev. C 2008, 77, 064901. [Google Scholar] [CrossRef]
- Song, H.; Bass, S.A.; Heinz, U.; Hirano, T.; Shen, C. 200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid. Phys. Rev. Lett. 2011, 106, 192301, Erratum: Phys. Rev. Lett. 2012, 109, 139904. [Google Scholar] [CrossRef] [PubMed]
- Shen, C.; Heinz, U.; Huovinen, P.; Song, H. Radial and elliptic flow in Pb+Pb collisions at the Large Hadron Collider from viscous hydrodynamic. Phys. Rev. C 2011, 84, 044903. [Google Scholar] [CrossRef]
- Matsui, T.; Satz, H. J/ψ Suppression by Quark-Gluon Plasma Formation. Phys. Lett. B 1986, 178, 416–422. [Google Scholar] [CrossRef]
- Andronic, A.; Braun-Munzinger, P.; Redlich, K.; Stachel, J. Statistical hadronization of charm in heavy ion collisions at SPS, RHIC and LHC. Phys. Lett. B 2003, 571, 36–44. [Google Scholar] [CrossRef]
- Rapp, R.; Blaschke, D.; Crochet, P. Charmonium and bottomonium production in heavy-ion collisions. Prog. Part. Nucl. Phys. 2010, 65, 209–266. [Google Scholar] [CrossRef]
- Qin, G.Y.; Wang, X.N. Jet quenching in high-energy heavy-ion collisions. Int. J. Mod. Phys. E 2015, 24, 1530014. [Google Scholar] [CrossRef]
- Liu, Y.; Chen, B.; Xu, N.; Zhuang, P. Υ Production as a Probe for Early State Dynamics in High Energy Nuclear Collisions at RHIC. Phys. Lett. B 2011, 697, 32–36. [Google Scholar] [CrossRef]
- Yan, L.; Zhuang, P.; Xu, N. Competition between J/ψ suppression and regeneration in quark-gluon plasma. Phys. Rev. Lett. 2006, 97, 232301. [Google Scholar] [CrossRef]
- Altenkort, L.; Kaczmarek, O.; Larsen, R.; Mukherjee, S.; Petreczky, P.; Shu, H.-T.; Stendebach, S. Heavy Quark Diffusion from 2+1 Flavor Lattice QCD with 320 MeV Pion Mass. Phys. Rev. Lett. 2023, 130, 231902. [Google Scholar] [CrossRef]
- Qin, G.Y.; Ruppert, J.; Gale, C.; Jeon, S.; Moore, G.D.; Mustafa, M.G. Radiative and collisional jet energy loss in the quark-gluon plasma at RHIC. Phys. Rev. Lett. 2008, 100, 072301. [Google Scholar] [CrossRef] [PubMed]
- Guo, X.F.; Wang, X.N. Multiple scattering, parton energy loss and modified fragmentation functions in deeply inelastic e A scattering. Phys. Rev. Lett. 2000, 85, 3591–3594. [Google Scholar] [CrossRef] [PubMed]
- Zhang, B.W.; Wang, E.; Wang, X.N. Heavy quark energy loss in nuclear medium. Phys. Rev. Lett. 2004, 93, 072301. [Google Scholar] [CrossRef] [PubMed]
- He, M.; Fries, R.J.; Rapp, R. Heavy Flavor at the Large Hadron Collider in a Strong Coupling Approach. Phys. Lett. B 2014, 735, 445–450. [Google Scholar] [CrossRef]
- Cao, S.; Luo, T.; Qin, G.Y.; Wang, X.N. Linearized Boltzmann transport model for jet propagation in the quark-gluon plasma: Heavy quark evolution. Phys. Rev. C 2016, 94, 014909. [Google Scholar] [CrossRef]
- Ke, W.; Xu, Y.; Bass, S.A. Modified Boltzmann approach for modeling the splitting vertices induced by the hot QCD medium in the deep Landau-Pomeranchuk-Migdal region. Phys. Rev. C 2019, 100, 064911. [Google Scholar] [CrossRef]
- Chen, B.; Jiang, L.; Liu, X.H.; Liu, Y.; Zhao, J. X(3872) production in relativistic heavy-ion collisions. Phys. Rev. C 2022, 105, 054901. [Google Scholar] [CrossRef]
- Chen, B.; Zhao, J. Bottomonium Continuous Production from Unequilibrium Bottom Quarks in Ultrarelativistic Heavy Ion Collisions. Phys. Lett. B 2017, 772, 819–824. [Google Scholar] [CrossRef]
- Akamatsu, Y.; Asakawa, M.; Kajimoto, S.; Rothkopf, A. Quantum dissipation of a heavy quark from a nonlinear stochastic Schrödinger equation. J. High Energy Phys. 2018, 7, 29. [Google Scholar] [CrossRef]
- Adamczyk, L.; Adkins, J.K.; Agakishiev, G.; Aggarwal, M.M.; Ahammed, Z.; Ajitanand, N.N.; Alekseev, I.; Anderson, D.M.; Aoyama, R.; Aparin, A.; et al. Measurement of D0 Azimuthal Anisotropy at Midrapidity in Au+Au Collisions at = 200 GeV. Phys. Rev. Lett. 2017, 118, 212301. [Google Scholar] [CrossRef]
- Abelev, B.; Adam, J.; Adamová, D.; Adare, A.M.; Aggarwal, M.M.; Rinella, G.A.; Agnello, M.; Agocs, A.G.; Agostinelli, A.; Ahammed, Z.; et al. D meson elliptic flow in non-central Pb-Pb collisions at = 2.76 TeV. Phys. Rev. Lett. 2013, 111, 102301. [Google Scholar] [CrossRef] [PubMed]
- Abelev, B.B.; Ajaz, M.; Khan, K.H.; Sleymanov, M.K.; Zaman, A. Azimuthal anisotropy of D meson production in Pb-Pb collisions at = 2.76 TeV. Phys. Rev. C 2014, 90, 034904. [Google Scholar] [CrossRef]
- Adam, J.; Adamová, D.; Aggarwal, M.M.; Rinella, G.A.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahn, S.U.; Aimo, I.; Aiola, S.; et al. Centrality dependence of high-pT D meson suppression in Pb-Pb collisions at = 2.76 TeV. J. High Energy Phys. 2015, 11, 205. [Google Scholar] [CrossRef]
- Sirunyan, A.M.; Tumasyan, A.; Adam, W.; Ambrogi, F.; Asilar, E.; Bergauer, T.; Brandstetter, J.; Brondolin, E.; Dragicevic, M.; Erö, J.; et al. Measurement of prompt and nonprompt charmonium suppression in PbPb collisions at 5.02 TeV. Eur. Phys. J. C 2018, 78, 509. [Google Scholar] [CrossRef] [PubMed]
- Tumasyan, A.; Adam, W.; Andrejkovic, J.W.; Bergauer, T.; Chatterjee, S.; Damanakis, K.; Dragicevic, M.; Del Valle, A.E.; Hussain, P.S.; Jeitler, M. Measurements of the azimuthal anisotropy of charmonia in PbPb collisions at = 5.02 TeV. J. High Energy Phys. 2023, 2023, 115. [Google Scholar]
- Bernhard, J.E.; Moreland, J.S.; Bass, S.A.; Liu, J.; Heinz, U. Applying Bayesian parameter estimation to relativistic heavy-ion collisions: Simultaneous characterization of the initial state and quark-gluon plasma medium. Phys. Rev. C 2016, 94, 024907. [Google Scholar] [CrossRef]
- Auvinen, J.; Bernhard, J.E.; Bass, S.A.; Karpenko, I. Investigating the collision energy dependence of η/s in the beam energy scan at the BNL Relativistic Heavy Ion Collider using Bayesian statistics. Phys. Rev. C 2018, 97, 044905. [Google Scholar] [CrossRef]
- Novak, J.; Novak, K.; Pratt, S.; Vredevoogd, J.; Coleman-Smith, C.; Wolpert, R. Determining Fundamental Properties of Matter Created in Ultrarelativistic Heavy-Ion Collisions. Phys. Rev. C 2014, 89, 034917. [Google Scholar] [CrossRef]
- Pratt, S.; Sangaline, E.; Sorensen, P.; Wang, H. Constraining the Eq. of State of Super-Hadronic Matter from Heavy-Ion Collisions. Phys. Rev. Lett. 2015, 114, 202301. [Google Scholar] [CrossRef]
- Xu, Y.; Bernhard, J.E.; Bass, S.A.; Nahrgang, M.; Cao, S. Data-driven analysis for the temperature and momentum dependence of the heavy-quark diffusion coefficient in relativistic heavy-ion collisions. Phys. Rev. C 2018, 97, 014907. [Google Scholar] [CrossRef]
- Cacciari, M.; Greco, M.; Nason, P. The p(T) spectrum in heavy-flavour hadroproduction. J. High Energy Phys. 1998, 9805, 007, arXiv:hep-ph/9803400. [Google Scholar] [CrossRef]
- Cacciari, M.; Frixione, S.; Nason, P. The p(T) spectrum in heavy-flavor photoproduction. J. High Energy Phys. 2001, 103, 006, arXiv:hep-ph/0102134. [Google Scholar] [CrossRef]
- Ball, R.D.; Bertone, V.; Carrazza, S.; Deans, C.S.; Del Debbio, L.; Forte, S.; Guffanti, A.; Hartland, N.P.; Latorre, J.I.; Rojo, J.; et al. Parton distributions for the LHC Run II. J. High Energy Phys. 2015, 4, 40. [Google Scholar] [CrossRef]
- Eskola, K.J.; Paukkunen, H.; Salgado, C.A. EPS09: A New Generation of NLO and LO Nuclear Parton Distribution Functions. J. High Energy Phys. 2009, 4, 65. [Google Scholar] [CrossRef]
- Yang, M.; Zheng, S.; Tong, B.; Zhao, J.; Ouyang, W.; Zhou, K.; Chen, B. Bottom energy loss and nonprompt J/ψ production in relativistic heavy ion collisions. Phys. Rev. C 2023, 107, 054917. [Google Scholar] [CrossRef]
- Cao, S.; Qin, G.Y.; Bass, S.A. Heavy-quark dynamics and hadronization in ultrarelativistic heavy-ion collisions: Collisional versus radiative energy loss. Phys. Rev. C 2013, 88, 044907. [Google Scholar] [CrossRef]
- Greco, V.; Ko, C.M.; Rapp, R. Quark coalescence for charmed mesons in ultrarelativistic heavy ion collisions. Phys. Lett. B 2004, 595, 202–208. [Google Scholar] [CrossRef]
- Schenke, B.; Jeon, S.; Gale, C. Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics. Phys. Rev. Lett. 2011, 106, 042301. [Google Scholar] [CrossRef]
- Schenke, B.; Jeon, S.; Gale, C. (3+1)D hydrodynamic simulation of relativistic heavy-ion collisions. Phys. Rev. C 2010, 82, 014903. [Google Scholar] [CrossRef]
- Altenkort, L.; Eller, A.M.; Kaczmarek, O.; Mazur, L.; Moore, G.D.; Shu, H.T. Heavy quark momentum diffusion from the lattice using gradient flow. Phys. Rev. D 2021, 103, 014511. [Google Scholar] [CrossRef]
- Brambilla, N.; Leino, V.; Petreczky, P.; Vairo, A. Lattice QCD constraints on the heavy quark diffusion coefficient. Phys. Rev. D 2020, 102, 074503. [Google Scholar] [CrossRef]
- Liu, S.Y.F.; Rapp, R. Spectral and transport properties of quark–gluon plasma in a nonperturbative approach. Eur. Phys. J. A 2020, 56, 44. [Google Scholar] [CrossRef]
- Scardina, F.; Das, S.K.; Minissale, V.; Plumari, S.; Greco, V. Estimating the charm quark diffusion coefficient and thermalization time from D meson spectra at energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider. Phys. Rev. C 2017, 96, 044905. [Google Scholar] [CrossRef]
- ALICE collaboration. Prompt D0, D+, and D*+ production in Pb–Pb collisions at = 5.02 TeV. J. High Energy Phys. 2022, 1, 174. [Google Scholar] [CrossRef]
- Altenkort, L.; de la Cruz, D.; Kaczmarek, O.; Larsen, R.; Moore, G.D.; Mukherjee, S.; Petreczky, P.; Shu, H.T.; Stendebach, S. Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD. arXiv 2023, arXiv:2311.01525. [Google Scholar]
- Casalderrey-Solana, J.; Teaney, D. Heavy quark diffusion in strongly coupled N=4 Yang-Mills. Phys. Rev. D 2006, 74, 085012. [Google Scholar] [CrossRef]
- Andreev, O. Drag Force on Heavy Quarks and Spatial String Tension. Mod. Phys. Lett. A 2018, 33, 1850041. [Google Scholar] [CrossRef]
- Combridge, B.L. Associated Production of Heavy Flavor States in p p and anti-p p Interactions: Some QCD Estimates. Nucl. Phys. B 1979, 151, 429–456. [Google Scholar] [CrossRef]
- Caron-Huot, S.; Moore, G.D. Heavy quark diffusion in perturbative QCD at next-to-leading order. Phys. Rev. Lett. 2008, 100, 052301. [Google Scholar] [CrossRef] [PubMed]
- Caron-Huot, S.; Moore, G.D. Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order. J. High Energy Phys. 2008, 2, 081. [Google Scholar] [CrossRef]
- Das, S.K.; Scardina, F.; Plumari, S.; Greco, V. Toward a solution to the RAA and v2 puzzle for heavy quarks. Phys. Lett. B 2015, 747, 260–264. [Google Scholar] [CrossRef]
- Baier, R.; Dokshitzer, Y.L.; Mueller, A.H.; Peigne, S.; Schiff, D. Radiative energy loss and p(T) broadening of high-energy partons in nuclei. Nucl. Phys. B 1997, 484, 265–282. [Google Scholar] [CrossRef]
- He, M.; Fries, R.J.; Rapp, R. Ds-Meson as Quantitative Probe of Diffusion and Hadronization in Nuclear Collisions. Phys. Rev. Lett. 2013, 110, 112301. [Google Scholar] [CrossRef]
- Barnard, J.; Dawe, E.N.; Dolan, M.J.; Rajcic, N. Parton Shower Uncertainties in Jet Substructure Analyses with Deep Neural Networks. Phys. Rev. D 2017, 95, 014018. [Google Scholar] [CrossRef]
Parameters | Region |
---|---|
Shadow factor | |
with | |
T-dependence | |
-dependence |
Parameters | Mean Values | Standard Deviation |
---|---|---|
Shadow factor | 0.050 | |
0.90 | ||
with | ||
T-dependence | 2.32 | |
-dependence | 0.12 |
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Guo, R.; Li, Y.; Chen, B. Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions. Entropy 2023, 25, 1563. https://doi.org/10.3390/e25111563
Guo R, Li Y, Chen B. Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions. Entropy. 2023; 25(11):1563. https://doi.org/10.3390/e25111563
Chicago/Turabian StyleGuo, Rui, Yonghui Li, and Baoyi Chen. 2023. "Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions" Entropy 25, no. 11: 1563. https://doi.org/10.3390/e25111563
APA StyleGuo, R., Li, Y., & Chen, B. (2023). Machine Learning Approach to Analyze the Heavy Quark Diffusion Coefficient in Relativistic Heavy Ion Collisions. Entropy, 25(11), 1563. https://doi.org/10.3390/e25111563