Abstract
\(z\)-Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated. The scaling for negative particle production in \({\text{Au}} + {\text{Au}}\) collisions from BES-I program at RHIC is demonstrated. The scaling variable \(z\) depends on the momentum fractions of the colliding objects carried by the interacting constituents, and on the momentum fractions of the fragmenting objects in the scattered and recoil directions carried by the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final state are expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function \(\psi (z)\) reveals energy, angular, multiplicity, and flavor independence. It has a power behavior at high \(z\) (high \({{p}_{T}}\)). Based on the entropy principle and \(z\)-scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated. New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed.
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REFERENCES
E. Eichten, K. Lane and M. Peskin, Phys. Rev. Lett. 50, 811 (1983).
E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56, 4 (1984).
I. Antoniadis, Phys. Lett. B 246, 377 (1990).
N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B 429, 263 (1998).
I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B 436, 257 (1998).
L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).
L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).
S. Dimopoulos and G. L. Landsberg, Phys. Rev. Lett. 87, 161602 (2001).
S. B. Giddings and S. D. Thomas, Phys. Rev. D 65, 056010 (2002).
A. Barrau, J. Grain, and S. Alexeyev, Phys. Lett. B 584, 114 (2004).
B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
L. Nottale, Fractal Space-Time and Microphysics (World Scientific, Singapore, 1993).
J. Feder, Fractals (Plenum, New York, 1988).
L. M. Lederman and C. T. Hill, Symmetry and the Beautiful Universe (Prometheus Books, Amherst, NY, 2004)
H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1971).
H. E. Stanley, Rev. Mod. Phys. 71, S358 (1999).
C. Domb, The Critical Point: A Historical Introduction to the Modern Theory of Critical Phenomena (Taylor and Francis, London, 1996).
I. Zborovský and M. V. Tokarev, Phys. Rev. D 75, 094008 (2007).
I. Zborovský and M. V. Tokarev, Int. J. Mod. Phys. A 24, 1417 (2009).
M. V. Tokarev and I. Zborovský, Int. J. Mod. Phys. A 32, 1750029 (2017).
M. Tokarev, A. Kechechyan, and I. Zborovský, Nucl. Phys. A 993, 121646 (2020).
M. V. Tokarev, I. Zborovský, A. O. Kechechyan, and T. G. Dedovich, Phys. Part. Nucl. 51, 141 (2020).
M. G. Albrow et al. (CHLM Collab.), Nucl. Phys. B 56, 333 (1973).
B. Alper et al. (BS Collab.), Nucl. Phys. B 100, 237 (1975).
F. W. Büsser et al. (CCRS Collab.), Nucl. Phys. B 106, 1 (1976).
K. Guettler et al. (BSM Collab.), Phys. Lett. B 64, 111 (1976).
K. Guettler et al. (BSM Collab.), Nucl. Phys. B 116, 77 (1976).
D. Antreasyan et al., Phys. Rev. D 19, 764 (1979).
D. Drijard et al. (CDHW Collab.), Nucl. Phys. B 208, 1 (1982).
D. E. Jaffe et al., Phys. Rev. D 40, 2777 (1989).
J. Adams et al. (STAR Collab.), Phys. Lett. B 616, 8 (2005).
J. Adams et al. (STAR Collab.), Phys. Lett. B 637, 161 (2006).
B. I. Abelev et al. (STAR Collab.), Phys. Rev. C 75, 064901 (2007).
J. Adams et al. (STAR Collab.), Phys. Rev. C 71, 064902 (2005).
B. I. Abelev et al. (STAR Collab.), Phys. Rev. Lett. 97, 132301 (2006).
R. Witt (for STAR Collab.), J. Phys. G: Nucl. Part. Phys. 31, S863 (2005).
A. Adare et al. (PHENIX Collab.), Phys. Rev. D 83, 052004 (2011).
G. Agakishiev et al. (STAR Collab.), Phys. Rev. Lett. 108, 072302 (2012).
A. Adare et al. (PHENIX Collab.), Phys. Rev. C 90, 054905 (2014).
J. Adams et al. (STAR Collab.), Phys. Rev. Lett. 92, 112301 (2004).
F. W. Busser et al. (CCRS Collab.), Phys. Lett. B 61, 309 (1976).
H. Kichimi et al., Phys. Rev. D 20, 37 (1979).
D. Drijard et al. (CDHW Collab.), Z. Phys. C 12, 217 (1982).
T. Akesson et al. (AFS Collab.), Nucl. Phys. B 203, 27 (1982), Nucl. Phys. B 229, 541(E) (1983).
J. Adams et al. (STAR Collab.), Phys. Lett. B 612, 181 (2005).
A. Aduszkiewicz et al. (NA61/SHINE Collab.), Eur. Phys. J. C 76, 198 (2016).
S. V. Afanasiev et al. (NA49 Collab.), Phys. Lett. B 491, 59 (2000).
T. Anticic et al. (NA49 Collab.), Phys. Rev. C 84, 064909 (2011).
F. Abe et al. (CDF Collab.), Phys. Rev. Lett. 74, 2626 (1995).
S. Abachi et al. (DØ Collab.), Phys. Rev. Lett. 74, 2632 (1995).
V. M. Abazov et al. (DØ Collab.), Phys. Lett. B 693, 515 (2010).
S. Chatrchyan et al. (CMS Collab.), Eur. Phys. J. C 73, 2339 (2013).
V. Khachatryan et al. (CMS Collab.), Eur. Phys. J. C 75, 542 (2015).
V. Khachatryan et al. (CMS Collab.), Phys. Rev. D 94, 072002 (2016).
CMS Collab., CMS PAS TOP-16-011.
G. Aad et al. (ATLAS Collab.), Phys. Rev. D 90, 072004 (2014).
G. Aad et al. (ATLAS Collab.), J. High Energy Phys., No. 06, 100 (2015).
G. Aad et al. (ATLAS Collab.), Phys. Rev. D 93, 032009 (2016).
G. Aad et al. (ATLAS Collab.), Eur. Phys. J. C 76, 538 (2016).
V. M. Abazov et al. (DØ Collab.), Phys. Rev. D 90, 092006 (2014).
G. Aad et al. (ATLAS Collab.), Eur. Phys. J. C 73, 2509 (2013).
G. Aad et al. (ATLAS Collab.), Phys. Rev. D 86, 014022 (2012).
M. Aaboud et al. (ATLAS Collab.), J. High Energy Phys., No. 09, 020 (2017).
CMS Collab., PAS-SMP-12-012.
S. Chatrchyan et al. (CMS Collab.), Phys. Rev. D 87, 112002 (2013).
B. Abelev et al. (ALICE Collab.), Phys. Lett. B 722, 262 (2013).
B. Abbott et al. (DØ Collab.), Phys. Rev. D 64, 032003 (2001).
V. D. Elvira, “Measurement of the inclusive jet cross sections at TeV with the DØ Detector,” PhD Thesis (Univ., Buenos Aires, Argentina, 1995).
V. M. Abazov et al. (DØ Collab.), Phys. Lett. B 525, 211 (2002).
V. M. Abazov et al. (DØ Collab.), Phys. Rev. Lett. 101, 062001 (2008).
M. Begel (for the DØ Collab.), hep-ex/0305072.
V. M. Abazov et al. (DØ Collab.), Phys. Rev. D 85, 052006 (2012).
F. Abe et al. (CDF Collab.), Phys. Rev. Lett. 77, 438 (1996).
T. Affolder et al. (CDF Collab.), Phys. Rev. D 64, 032001 (2001), Phys. Rev. D 65, 039903(E) (2002).
A. Abulencia et al. (CDF Collab.), Phys. Rev. Lett. 96, 122001 (2006).
A. Abulencia et al. (CDF Collab.), Phys. Rev. D 74, 071103(R) (2006).
A. Abulencia et al. (CDF Collab.), Phys. Rev. D 75, 092006 (2007).
T. Aaltonen et al. (CDF Collab.), “Fermilab Tevatron collider using a cone-based jet algorithm,” Phys. Rev. D 78, 052006 (2008), Phys. Rev. D 79, 119902(E) (2009).
M. V. Tokarev, I. Zborovský, and T. G. Dedovich, Int. J. Mod. Phys. A 27, 1250115 (2012).
M. M. Aggarwal et al. (STAR Collab.), “An experimental exploration of the QCD phase diagram: The search for the critical point and the onset of deconfinement,” arXiv: 1007.2613.
B. I. Abelev et al. (STAR Collab.), Phys. Rev. C 96, 044904 (2017).
M. Tokarev (for the STAR Collab.), Int. J. Mod. Phys. Conf. Ser. 39, 1560103 (2015).
I. Zborovský, Int. J. Mod. Phys. A 33, 1850057 (2018).
ACKNOWLEDGMENTS
The investigation of (I.Z.) was supported by the RVO61389005 institutional support and by the MEYS of the Czech Republic under the contracts LTT18021 and LTT17018.
Presented at 40th International Conference on High Energy Physics, 28 July–6 August, 2020, Prague, Czech Republic.
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Zborovský, I., Tokarev, M. Self-Similarity, Fractality and Entropy Principle in Collisions of Hadrons and Nuclei at Tevatron, RHIC and LHC. Phys. Part. Nuclei Lett. 18, 302–314 (2021). https://doi.org/10.1134/S1547477121030110
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DOI: https://doi.org/10.1134/S1547477121030110