Abstract
Based on statistical thermal approaches, the transverse momentum distribution of the well-identified produced particles, π+, π–, K+, K–, p, and \(\bar {p}\), is studied. We aim at introducing a novel almost entirely empirical estimation for the inclusive chemical potential μ. From the partition function of a grand-canonical ensemble, we propose a generic expression for the dependence of μ on the rapidity y. Then, by fitting this expression with the experimental results of the most central p⊥ and d2N/2πp⊥dp⊥dy, at 7.7, 11.5, 19.6, 27, 39, 130, 200 GeV, we introduce a generic expression for the rapidity dependence of for all particle yields, at different energies, μ = a + by2. The resulting energy dependence reads \(\sqrt {{{s}_{{{\text{NN}}}}}} \) = c[(μ – a)/b]d/2. As a validation test, we show that the proposed approach reproduces excellently the rapidity spectra of various particle yields measured, at different energies.
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REFERENCES
B. B. Back et al. (PHOBOS Collab.), Phys. Rev. C 65, 061901 (2002).
S. Ahmad, A. Ahmad, A. Chandra, M. Zafar, and M. Irfan, Adv. High Energy Phys. 2013, 836071 (2013).
A. Tawfik, M. Y. El-Bakry, D. M. Habashy, M. T. Mohamed, and E. Abbas, Int. J. Mod. Phys. E 25, 1650018 (2016).
A. Tawfik, Phys. Rev. C 88, 035203 (2013).
A. Tawfik, Nucl. Phys. A 922, 225 (2014).
A. Tawfik, Adv. High Energy Phys. 2013, 574871 (2013).
A. Tawfik, Nucl. Phys. A 764, 387 (2006).
A. Tawfik, Europhys. Lett. 75, 420 (2006).
A. Tawfik, J. Phys. G 31, S1105 (2005).
J. P. Bondorf, S. Garpman, and J. Zimanyi, Nucl. Phys. A 296, 320 (1978).
A. N. Tawfik, Int. J. Mod. Phys. A 29, 1430021 (2014).
J. Letessier, J. Rafelski, and A. Tounsi, Phys. Rev. C 50, 406 (1994).
J. Adam et al. (ALICE Collab.), Nat. Phys. 13, 535 (2017).
J. Cleymans and K. Redlich, Phys. Rev. Lett. 81, 5284 (1998).
V. Magas and H. Satz, Eur. Phys. J. C 32, 115 (2003).
S. Uddin, J. S. Ahmad, W. Bashir, and R. A. Bhat, J. Phys. G 39, 015012 (2012).
F. Becattini, J. Cleymans, and J. Strumpfer, PoS(CPOD07), 012 (2007).
F. Becattini and J. Cleymans, J. Phys. G 34, S959 (2007).
J. Cleymans, J. Phys. G 35, 044017 (2008).
J. Cleymans, J. Strumpfer, and L. Turko, Phys. Rev. C 78, 017901 (2008).
S. Uddin, J. S. Ahmad, M. A. Bashir, and R. A. Bhat, Acta Phys. Polon. B 41, 2433 (2010).
S. Uddin, M. Ali, J. Shabir, and M. F. Mir, (2009).
S. Uddin, M. Ali, J. Shabir, and M. Farooq Mir, (2009).
J. Letessier and J. Rafelski, Hadrons and Quark-Gluon Plasma (Cambridge Univ. Press, Cambridge, 2004).
A. Tawfik, Phys. Rev. D 71, 054502 (2005).
A. Tawfik, E. Gamal, and A. G. Shalaby, Int. J. Mod. Phys. A 30, 1550131 (2015).
A. N. Tawfik and E. Abbas, Phys. Part. Nucl. Lett. 12, 521 (2015).
A. Andronic, P. Braun-Munzinger, and J. Stachel, Nucl. Phys. A 772, 167 (2006).
L. Adamczyk et al. (STAR Collab.), Phys. Rev. C 96, 044904 (2017).
B. I. Abelev et al. (STAR Collab.), Phys. Rev. C 79, 034909 (2009).
A. Andronic, P. Braun-Munzinger, and J. Stachel, Acta Phys. Polon. B 40, 1005 (2009).
I. G. Bearden et al. (BRAHMS Collab.), Phys. Rev. Lett. 90, 102301 (2003).
I. G. Bearden et al. (BRAHMS Collab.), Phys. Rev. Lett. 94, 162301 (2005).
J. Baechler et al. (NA35 Collab.), Phys. Rev. Lett. 72, 1419 (1994).
J. Bartke et al. (NA35 Collab.), Z. Phys. C 48, 191 (1990).
B. B. Back et al. (PHOBOS Collab.), Phys. Rev. Lett. 85, 3100 (2000).
I. C. Arsene, et al., Phys. Lett. B 687, 36 (2010).
Z.-W. Lin, S. Pal, C. M. Ko, B.-A. Li, and B. Zhang, Phys. Rev. C 64, 011902 (2001).
F. Siklr et al. (NA49 Collab.), Nucl. Phys. A 661, 45c (1999).
B. Biedron and W. Broniowski, Phys. Rev. C 75, 054905 (2007).
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Tawfik, A.N., Abdel Wahab, M., Yassin, H. et al. Almost Entirely Empirical Estimation for Chemical Potential. J. Exp. Theor. Phys. 130, 506–516 (2020). https://doi.org/10.1134/S1063776120030176
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DOI: https://doi.org/10.1134/S1063776120030176