Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

Valeriy Kizka

doi:doi:10.11648/j.ns.20240902.13

Review Article |

| Peer-Reviewed

Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

Valeriy Kizka^*

Published in Nuclear Science (Volume 9, Issue 2)

Received: 21 May 2024 Accepted: 14 June 2024 Published: 29 June 2024

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √s_NN = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √s_NN = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1^st order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √s_NN = 3.5 GeV. The critical endpoint of 2^nd order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √s_NN =12 GeV to 15 GeV, the critical endpoint of 1^st order – at around √s_NN = 20 GeV. The boundary of smooth (2^nd order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √s_NN = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √s_NN = 15 GeV to 20 GeV, the boundary of sharp (1^st order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √s_NN = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √s_NN = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.

Published in	Nuclear Science (Volume 9, Issue 2)
DOI	10.11648/j.ns.20240902.13
Page(s)	40-50
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Quark-Gluon Plasma, Quarkyonic Matter, Heavy Ion Collisions, QCD Phase Diagram, Kolmogorov Criteria

References

[1]	Laplace P-S. Théorie Analytique des Probabilités. Oeuvres Complètes 7 (3^rd edition). Paris: Courcier 1820: lxxvii.
[2]	Airy G. B. On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations. London: Macmillan and Company, 1861.
[3]	V. A. Kizka, V. S. Trubnikov, K. A. Bugaev, D. R. Oliinychenko. A possible evidence of the hadron-quark-gluon mixed phase formation in nuclear collisions. arXiv: 1504.06483 [hep-ph]. https://doi.org/10.48550/arXiv.1504.06483
[4]	V. Kizka. Comparison of the 3-Fluid Dynamic Model with Experimental Data. Nuclear Science. 2023, 7(3), 39-44. https://doi.org/10.11648/j.ns.20220703.11
[5]	V. A. Kizka. On the Quantum Nature of a Fireball Created in Ultrarelativistic Nuclear Collisions. New Frontiers in Physical Science Research. 2022, 1, 52–62. https://doi.org/10.9734/bpi/nfpsr/v1/3541A
[6]	The STAR Collaboration. Production of Protons and Light Nuclei in Au+Au Collisions at √s_NN = 3 GeV with the STAR Detector. arXiv: 2311.11020 [nucl-ex]. https://doi.org/10.48550/arXiv.2311.11020
[7]	W. Feller. On the Kolmogorov-Smirnov limit theorems for empirical distributions. Annals of Math. Stat. 1948, 19, 177–189. https://doi.org/10.1214/aoms/1177730243
[8]	W. Cassing et al. Parton/hadron dynamics in heavy-ion collisions at FAIR energies. EPJ Web of Conferences. 2015, 95, 01004. https://doi.org/10.1051/epjconf/20159501004
[9]	W. Cassing, E. L. Bratkovskaya. Parton-Hadron-String Dynamics: an off-shell transport approach for relativistic energies. Nucl. Phys. A. 2009, 831, 215-242. https://doi.org/10.1016/j.nuclphysa.2009.09.007
[10]	J. Geiss, W. Cassing, C. Greiner. Strangeness Production in the HSD Transport Approach from SIS to SPS energies. Nucl. Phys. A. 1998, 644, 107–138. https://doi.org/10.1016/S0375-9474(98)80011-0
[11]	W. Cassing, E. L. Bratkovskaya. Hadronic and electromagnetic probes of hot and dense nuclear matter. Physics Reports. 1999, 308, 65–233. https://doi.org/10.1016/S0370-1573(98)00028-3
[12]	E. L. Bratkovskaya et al. The QGP phase in relativistic heavy-ion collisions. Proceedings of the International Symposium on Exciting Physics. Makutsi-Range, South Africa, 2011, 13–20 November. https://doi.org/10.1007/978-3-319-00047-3_19
[13]	E. L. Bratkovskaya et al. Properties of the partonic phase at RHIC within PHSD. 27th Winter Workshop on Nuclear Dynamics (WWND) in Colorado. 2011, USA on February 6–13. https://doi.org/10.1088/1742-6596/316/1/012027
[14]	T. Anticic et al. (NA49 Collaboration). System-size and centrality dependence of charged kaon and pion production in nucleus-nucleus collisions at 40 AGeV and 158 AGeV beam energy. Phys. Rev. C. 2012, 86, 054903. https://doi.org/10.1103/PhysRevC.86.054903
[15]	T. Anticic et al. (NA49 Collaboration). System-size dependence of Lambda and Xi production in nucleus-nucleus collisions at 40A and 158 AGeV measured at the CERN Super Proton Synchrotron. Phys. Rev. C. 2009, 80, 034906. https://doi.org/10.1103/PhysRevC.80.034906
[16]	E. L. Bratkovskaya et al. Strangeness dynamics and transverse pressure in relativistic nucleus-nucleus collisions. Phys. Rev. C. 2004, 69, 054907. https://doi.org/10.1103/PhysRevC.69.054907
[17]	H. Weber, E. L. Bratkovskaya, W. Cassing, H. Stoecker. Hadronic observables from SIS to SPS energies - anything strange with strangeness? Phys. Rev. C. 2003, 67, 014904. https://doi.org/10.1103/PhysRevC.67.014904
[18]	W. Cassing, A. Palmese, P. Moreau, E. L. Bratkovskaya. Chiral symmetry restoration versus deconfinement in heavy-ion collisions at high baryon density. Phys. Rev. C. 2016, 93, 014902. https://doi.org/10.1103/PhysRevC.93.014902
[19]	V. P. Konchakovski, W. Cassing, V. D. Toneev. Impact of the initial size of spatial fluctuations on the collective flow in Pb-Pb collisions at √s_NN = 2.76 TeV. J. Phys. G: Nucl. Part. Phys. 2015, 42, 055106. https://doi.org/10.1088/0954-3899/42/5/055106
[20]	O. Linnyk et al. Hadronic and partonic sources of direct photons in relativistic heavy-ion collisions. Phys. Rev. C. 2015, 92, 054914. https://doi.org/10.1103/PhysRevC.92.054914
[21]	Pierre Moreau et al. (Anti-)strangeness production in heavy-ion collisions. Proceedings of the 15th International Conference on Strangeness in Quark Matter (SQM2015). 2015, 6-11 July, JINR, Dubna, Russia. https://doi.org/10.1088/1742-6596/668/1/012072
[22]	E. L. Bratkovskaya et al. Dilepton production from SIS to LHC energies. Proceedings of the 28th Winter Workshop on Nuclear Dynamics. 2012, Dorado del Mar, Puerto Rico, April 7-14. https://doi.org/10.1088/1742-6596/389/1/012016
[23]	O. Linnyk, E. L. Bratkovskaya, W. Cassing. Strangeness production within Parton-Hadron-String Dynamics (PHSD). J. Phys. G: Nucl. Part. Phys. 2010, 37, 094039. https://doi.org/10.1088/0954-3899/37/9/094039
[24]	A. Andronic et al. Hadron Production in Ultra-relativistic Nuclear Collisions: Quarkyonic Matter and a Triple Point in the Phase Diagram of QCD. Nucl. Phys. A. 2010, 837, 65–86. https://doi.org/10.1016/j.nuclphysa.2010.02.005
[25]	Ivanov Yu. B. Alternative Scenarios of Relativistic Heavy-Ion Collisions: I. Baryon Stopping. Phys. Rev. C. 2013, 87, 064904. https://doi.org/10.1103/PhysRevC.87.064904
[26]	D. A. Fogaca, S. M. Sanches Jr., R. Fariello, F. S. Navarra. Bubble dynamics and the quark-hadron phase transition in nuclear collisions. Phys. Rev. C. 2016, 93, 055204. arXiv: 1601.04596v1 [hep-ph]. https://doi.org/10.1103/PhysRevC.93.055204
[27]	V. I. Yukalov, E. P. Yukalova. Models of mixed hadron-quark-gluon matter. Proc. Sci. (ISHEPP). 2012, 046. https://doi.org/10.48550/arXiv.1301.6910
[28]	C. A. Dominguez, M. Loewe, Y. Zhang. Chiral symmetry restoration and deconfinement in QCD at finite temperature. Phys. Rev. D. 2012, 86, 034030. https://doi.org/10.1103/PhysRevD.86.034030
[29]	Y. Aoki et al. The order of the quantum chromodynamics transition predicted by the standard model of particle physics. Nature. 2006, 443, 675–67. https://doi.org/10.1038/nature05120
[30]	The NA61/SHINE Collaboration. Search for a critical point of strongly-interacting matter in central ⁴⁰Ar +⁴⁵Sc collisions at 13A-75A GeV/c beam momentum. arXiv: 2401.03445 [nucl-ex]. https://doi.org/10.48550/arXiv.2401.03445
[31]	Barnabas Porfy. Femtoscopy at NA61/SHINE using symmetric Lévy sources in central ⁴⁰Ar+⁴⁵Sc from 40A GeV/c to 150A GeV/c. arXiv: 2406.02242 [nucl-ex]. https://doi.org/10.48550/arXiv.2406.02242
[32]	Dylan Neff. Probing the nature of the QCD phase transition with higher-order net-proton number fluctuation and local parton density fluctuation measurements at RHIC-STAR. arXiv: 2405.20929 [nucl-ex]. https://doi.org/10.48550/arXiv.2405.20929
[33]	Dylan Neff. Recent Highlights from STAR BES Phase II. arXiv: 2405.20928 [nucl-ex]. https://doi.org/10.48550/arXiv.2405.20928
[34]	M. Kozhevnikova, Yu. B. Ivanov. Light Nuclei Production in Au+Au Collisions at √s_NN = 3 GeV within Thermodynamical Approach: Bulk Properties and Collective Flow. arXiv: 2311.08092 [nucl-th]. https://doi.org/10.48850/arXiv.2311.08092
[35]	Yu. B. Ivanov, M. Kozhevnikova. What Can We Learn from Directed Flow at STAR-FXT Energies? arXiv: 2403.02787 [nucl-th]. https://doi.org/10.48850/arXiv.2403.02787

Cite This Article

Plain Text BibTeX RIS

APA Style

Kizka, V. (2024). Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions. Nuclear Science, 9(2), 40-50. https://doi.org/10.11648/j.ns.20240902.13

Copy | Download

ACS Style

Kizka, V. Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions. Nucl. Sci. 2024, 9(2), 40-50. doi: 10.11648/j.ns.20240902.13

Copy | Download

AMA Style

Kizka V. Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions. Nucl Sci. 2024;9(2):40-50. doi: 10.11648/j.ns.20240902.13

Copy | Download

@article{10.11648/j.ns.20240902.13,
  author = {Valeriy Kizka},
  title = {Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions
},
  journal = {Nuclear Science},
  volume = {9},
  number = {2},
  pages = {40-50},
  doi = {10.11648/j.ns.20240902.13},
  url = {https://doi.org/10.11648/j.ns.20240902.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20240902.13},
  abstract = {Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √sNN = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √sNN = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1st order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √sNN = 3.5 GeV. The critical endpoint of 2nd order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √sNN =12 GeV to 15 GeV, the critical endpoint of 1st order – at around √sNN = 20 GeV. The boundary of smooth (2nd order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √sNN = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √sNN = 15 GeV to 20 GeV, the boundary of sharp (1st order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √sNN = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √sNN = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

AU  - Valeriy Kizka
Y1  - 2024/06/29
PY  - 2024
N1  - https://doi.org/10.11648/j.ns.20240902.13
DO  - 10.11648/j.ns.20240902.13
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 40
EP  - 50
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20240902.13
AB  - Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √sNN = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √sNN = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1st order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √sNN = 3.5 GeV. The critical endpoint of 2nd order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √sNN =12 GeV to 15 GeV, the critical endpoint of 1st order – at around √sNN = 20 GeV. The boundary of smooth (2nd order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √sNN = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √sNN = 15 GeV to 20 GeV, the boundary of sharp (1st order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √sNN = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √sNN = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.

VL  - 9
IS  - 2
ER  -

Copy | Download

Author Information

Valeriy Kizka

Department for Nuclear Power Plants Decommissioning, Institute for Safety Problems of Nuclear Power Plants, Chornobyl, Ukraine; Department of Experimental Nuclear Physics, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

Contact Email

http://orcid.org/0000-0003-1007-5295

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Kizka, V. (2024). Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions. Nuclear Science, 9(2), 40-50. https://doi.org/10.11648/j.ns.20240902.13

Copy | Download

ACS Style

Kizka, V. Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions. Nucl. Sci. 2024, 9(2), 40-50. doi: 10.11648/j.ns.20240902.13

Copy | Download

AMA Style

Kizka V. Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions. Nucl Sci. 2024;9(2):40-50. doi: 10.11648/j.ns.20240902.13

Copy | Download

@article{10.11648/j.ns.20240902.13,
  author = {Valeriy Kizka},
  title = {Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions
},
  journal = {Nuclear Science},
  volume = {9},
  number = {2},
  pages = {40-50},
  doi = {10.11648/j.ns.20240902.13},
  url = {https://doi.org/10.11648/j.ns.20240902.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ns.20240902.13},
  abstract = {Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √sNN = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √sNN = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1st order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √sNN = 3.5 GeV. The critical endpoint of 2nd order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √sNN =12 GeV to 15 GeV, the critical endpoint of 1st order – at around √sNN = 20 GeV. The boundary of smooth (2nd order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √sNN = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √sNN = 15 GeV to 20 GeV, the boundary of sharp (1st order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √sNN = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √sNN = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

AU  - Valeriy Kizka
Y1  - 2024/06/29
PY  - 2024
N1  - https://doi.org/10.11648/j.ns.20240902.13
DO  - 10.11648/j.ns.20240902.13
T2  - Nuclear Science
JF  - Nuclear Science
JO  - Nuclear Science
SP  - 40
EP  - 50
PB  - Science Publishing Group
SN  - 2640-4346
UR  - https://doi.org/10.11648/j.ns.20240902.13
AB  - Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √sNN = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √sNN = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1st order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √sNN = 3.5 GeV. The critical endpoint of 2nd order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √sNN =12 GeV to 15 GeV, the critical endpoint of 1st order – at around √sNN = 20 GeV. The boundary of smooth (2nd order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √sNN = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √sNN = 15 GeV to 20 GeV, the boundary of sharp (1st order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √sNN = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √sNN = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.

VL  - 9
IS  - 2
ER  -

Copy | Download