8550415  />and respectively) in p + p collisions at = 7 TeV at LHC would be,

for (8)

and

for (9)

For the calculation of the rapidity distribution from the Equation (4) we can make use of a standard relation as given below:

(10)

For p + p collisions, the calculated rapidity distribution equation at RHIC-energy = 200 GeV is

, (11)

In a similar fashion, the SCM-based rapidity distribution equation at LHC-energy = 7 TeV in p + p collisions has been given hereunder

. (12)

4.2. Invariant Yields in d + Au, Cu + Cu and Au + Au Collisions at RHIC-Energy

= 200 GeV

From the expression (4), we arrive at the invariant yields for the J/Ψ production in reactions for mid and forward-rapidities.

for (13)

and

for (14)

For the case of Cu + Cu most central collisions (0% - 20%) at RHIC, the SCM-based calculated theoretical invariant yields for the rapidities and are given by the following equations respectively;

for, (15)

and

for. (16)

Similarly, for Au + Au collisions at = 200 GeV at RHIC, the equations of transverse momenta spectra for 0% - 20% centrality regions are given by the undernoted relations.

for,(17)

and

for. (18)

For calculating the values of NR, in general, we have used the values of from Refs. [11] and [15].

4.3. The Nuclear Modification Factor RAB

There is yet another very important observable called nuclear modification factor (NMF), denoted here by which for the production of J/Ψ is defined by [16]

(19)

The SCM-based results on NMFs for Cu + Cu and Au + Au collisions for forward rapidities are deduced on the basis of Equation (6), Equation (15), Equation (17) and Equation (19) and they are given by the undernoted relations

, (20)

and

. (21)

herein the value of to be used is [17] for Cu + Cu collisions and for Au + Au collisions it is taken as [18].

4.4. Analysis of the Figures

In Figures 1(a) and (b), we have drawn the total inclusive cross-sections for the production of J/Ψ-mesons in p + p collisions in different rapidities at RHIC and LHC energies = 200 GeV and 7 TeV respectively. The solid lines in the figures are depicting the SCM modelbased results with the help of the Equations (6)-(9) while the experimental measurements are taken from Ref. [19, 20] respectively.

In Figure 2 we have plotted the rapidity distributions for J/Ψ-production in p + p collisions at = 200 GeV. Data in the figure are taken from Ref. [21] and the line shows the SCM-based output.

Similarly, in Figure 3, we have drawn the rapidity distribution for J/Ψ production in p + p collisions at = 7 TeV as function of y. The solid lines depict the SCM-based results [Equation (12)] and the points indicate the experimental measurements [22].

(a)(b)

Figure 1. Plot of the invariant cross-section for J/Ψ production in proton-proton collisions at (a) = 200 GeV and (b) = 7 TeV as function of. The data points are from [19] for (a) and from [20] for (b). The solid curves show the SCM-based results.

Figure 2. Plot of the rapidity distribution for J/Ψ production in proton-proton collisions at = 200 GeV as function of y. The data points are from [15,21]. The solid curves show the SCM-based results (Equation (11)).

Figure 3. Plot of the rapidity distribution for J/Ψ production in p + p collisions at = 7 TeV as function of y. The data points are from [22]. The solid curves show the SCM-based results (Equations (15) and (16)).

In Figure 4, we have drawn the solid lines depicting the SCM-based results for invariant yields for J/Ψ production in d + Au collisions at = 200 GeV with the help of two Equations (13) and (14) against the experimental measurements [15].

The experimental results for the invariant yields of J/Ψ production as a function of transverse momenta for Cu + Cu collisions at = 200 GeV are taken from Ref. [16] at centrality 0% - 20% and are plotted in Figure 5. The solid lines in the figure show the SCM-induced results.

Figure 4. Plot of the invariant yields for J/Ψ production in d + Au collisions at = 200 GeV as function of. The data points are from [15]. The solid curves show the SCMbased results.

In the Figure 6, the solid lines are the plots of SCMbased invariant yields vs. as described by Equations (17) and (18) at forward and mid-rapidities for Au + Au collisions at = 200 GeV, while the dotted curve in the Fig. shows results of coalescence model [12]. The experimental data points in the Figure 6 for the invariant yields of J/Ψ production as a function of transverse momenta at centrality values 0% - 20% and at the rapidities and respectively are taken from the PHENIX Collaboration [15].

Figure 5. Transverse momenta spectra at and for J/Ψ production in Cu + Cu central collisions at = 200 GeV. The data are taken from [16]. The solid curves depict the SCM-based results.

Figure 6. Plot of the invariant yields for J/Ψ production in Au + Au collisions at = 200 GeV as function of. The data points are from [21]. The solid curve shows the SCM-based results while the dotted curve depicts the Coalescence Model [12].

In Figure 7(a), we plot vs. for 0% - 20% central region in Cu + Cu and Au + Au collisions at = 200 GeV. The solid lines in the figure show the SCM-based results (Equations (20) and (21)) against the experimentally measured results [15,16]. The dotted lines in the figure. represent the double Color Filtering approach [13].

And in Figure 7(b), we plot vs. for 0% - 20% central region in Au + Au collisions at =

200 GeV and for Pb + Pb collisions at = 2.76 TeV. The solid lines in the figure show the SCM-based calculations for different part>’s. The Values of part>’s are taken from Ref. [17]. The the experimentally measured results from Refs. [11,23] respectively. The dashed lines in the figure. represent the Gluon Saturation approach [11].

5. Summary and Outlook

Let us first concentrate on what we have achieved here: 1) The features related to pT—spectra for J/Ψ production in some particle-particle and nuclear collisions at various high energies have been reproduced quite successfully; 2) The characteristics of rapidity spectra in p + p collisions at TeV energies have been brought out somewhat modestly satisfactorily; 3) The features of nuclear modification factors in Cu + Cu, Au + Au and Pb + Pb reactions at RHIC and LHC energies have also been brought out with the help of the applied model. Besides, some of our model-based results have also been compared with the performances on the same observables by some competing models of “standard” variety. And these comparisons with data and the results obtained by some other models reveal that SCM-based results describe the features of the data, at least, not inferior to the performance by the other approaches grounded on the “Standard” model ilk. In the past such were the recurrent observations made by us valid for many other obsevables measured in the various high statistics high energy particle and nuclear experiments.

Thus, summing up our past experiences and consider-

(a)(b)

Figure 7. (a) Plot of the for J/Ψ production in Cu + Cu and Au + Au collisions at = 200 GeV as function of. The data points are from [15,16]. The solid and dotted curves show respectively the SCM and the Double Color Filter-oriented [13] results. (b) Plot of the vs. for J/Ψ production in Au + Au collisions at = 200 GeV and Pb + Pb collisions at = 2.76 TeV. The red circles depict Au + Au collisions [11] while the black squares represent Pb + Pb collisions [23]. The solid curves show the SCM-based results while the dotted curve depicts the Gluon Saturation Approach [11].

ing the weightage of the results reported here, we are forced to comment finally that this work essentially represents a case of paradigm shift in the domain of particle theory, as we have eschewed the conventional views of approach to J/Ψ production in the “standard” framework. And this is just the reflection of our radical views about the particle structure and the nature of particle collisions. Obviously we obtain the fair agreement with data on some observables without inductions of 1) any QGP concept; 2) any prognosis of suppression or enhancement of J/Ψ-production. The production of J/Ψ- particles resembles all other hadrons.

6. Acknowledgements

The authors would like to express their thankful gratitude to the learned Referee for his/her valuable remarks and constructive suggestions in improving the earlier draft of the manuscript.

REFERENCES

  1. T. Matsui and H. Satz, “J/Ψ Suppression by Quark-Gluon Plasma Formation,” Physics Letters B, Vol. 178, No. 4, 1986, pp. 416-422. doi:10.1016/0370-2693(86)91404-8
  2. R. L. Thews and M. L. Mangano, “Momentum Spectra of Charmonium Produced in a Quarkgluon Plasma,” Physical Review C, Vol. 73, No. 1, 2006, Article ID: 014904. doi:10.1103/PhysRevC.73.014904
  3. P. Guptaroy, B. De, G. Sanyal and S. Bhattacharyya, “J/Ψ Production in High Energy Particle and Nuclear Collisions: Suppressed, Enhanced or Just Normal?” International Journal of Modern Physics A, Vol. 20, No. 20-21, 2005, pp. 5037-5058. doi:10.1142/S0217751X05020768
  4. P. Guptaroy, T. K. Garain and S. Bhattacharyya, “J/Ψ Production in Some RHIC Interactions at = 200 GeV and the Look into the System Size Effect,” Hadronic Journal, Vol. 31, No. 5, 2008, p. 451.
  5. P. Guptaroy, T. K. Garain, Goutam Sau, S. K. Biswas and S. Bhattacharyya, “Analysing J/Ψ Production in Various RHIC Interactions with a Version of Sequential Chain Model (SCM),” Hadronic Journal, Vol. 32, No. 1, 2009, p. 95.
  6. S. Bhattacharyya, “Collisions in Space Experiments at HighEnergies, Laboratory Experiments and Suggested Signatures of Quark Gluon-Plasma: An Alternative Approach to the Analysis of Actual Observations,” IL Nuovo Cimento C, Vol. 11, No. 1, 1988, pp. 51-65. doi:10.1007/BF02507895
  7. P. Guptaroy, G. Sau, S. K. Biswas and S. Bhattacharyya, “Understanding the Characteristics of Multiple Production of Light Hadrons in Cu + Cu Interactions at Various RHIC Energies—A Model-Based Analysis,” IL Nuovo Cimento B, Vol. 125, No. 9, 2010, p. 1071.
  8. P. Guptaroy, G. Sau, S. K. Biswas and S. Bhattacharyya, “On Production of Direct Photons and Neutral Pions in RHIC Experiments at = 200 GeV,” Modern Physics Letters A, Vol. 23, No. 14, 2008, pp. 1031-1046. doi:10.1142/S021773230802567X
  9. S. Bhattacharyya, “On Some Remarkable Differences between the pp Collider Results at CERN and pp Reaction at ISR Energies,” Journal of Physics G, Vol. 14, No. 1, 1988, pp. 9-17. doi:10.1088/0305-4616/14/1/005
  10. C. Y. Wong, “Introduction to High-Energy Heavy Ion Collisions,” World Scientific, Singapore, 1994. doi:10.1142/9789814277549
  11. A. Adare, et al., “J/Ψ Suppression at Forward Rapidity in Au + Au Collisions at =200 GeV,” Physical Review C, Vol. 84, No. 5, 2011, Article ID: 054912.
  12. D. E. Kahana and S. H. Kahana, “J/Ψ Production by Charm Quark Coalescence,” Journal of Physics G, Vol. 37, No. 11, 2010, Article ID: 115011. doi:10.1088/0954-3899/37/11/115011
  13. B. Z. Kopeliovich, “Puzzles of J/Ψ Production off Nuclei,” Nuclear Physics A, Vol. 854, No. 1, 2011, pp. 187-197.
  14. K. Nakamura, et al., “Review of Particle Physics,” Journal of Physics G, Vol. 37, No. 7A, 2010, Article ID: 075021. doi:10.1088/0954-3899/37/7A/075021
  15. A. Adare, et al., “Cold Nuclear Matter Effects on J/Ψ Production as Constrained by Deuteron-Gold Measurements at =200 GeV,” Physical Review C, Vol. 77, No. 2, 2008, Article ID: 024912. doi:10.1103/PhysRevC.77.024912
  16. A. Adare, et al., “J/Ψ Production in =200 GeV Cu + Cu Collisions,” Physical Review Letters, Vol. 101, No. 12, 2008, Article ID: 122301. doi:10.1103/PhysRevLett.101.122301
  17. B. Alver, et al., “System Size and Centrality Dependence of Charged Hadron Transverse Momentum Spectra in Au + Au and Cu + Cu Collisions at = 62.4 and 200 GeV,” Physical Review Letters, Vol. 96, No. 21, 2006, Article ID: 212301. doi:10.1103/PhysRevLett.96.212301
  18. S. S. Adler, et al., “Identified Charged Particle Spectra and Yields in Au + Au Collisions at = 200 GeV,” Physical Review C, Vol. 69, No. 3, 2004, Article ID: 034909. doi:10.1103/PhysRevC.69.034909
  19. A. Adare, et al., “J/Ψ Production versus Transverse Momentum and Rapidity in p + p Collisions at =200 GeV,” Physical Review Letters, Vol. 98, No. 23, 2007, Article ID: 232002. doi:10.1103/PhysRevLett.98.232002
  20. G. M. García, “Quarkonium Production Measurements with the ALICE Detector at the LHC,” Journal of Physics G, Vol. 37, No. 9, 2010, Article ID: 094051.
  21. A. Adare, et al., “Cold Nuclear Matter Effects on J/Ψ Yields as a Function of Rapidity and Nuclear Geometry in Deuteron-Gold Collisions at = 200 GeV,” 2010. arXiv:1010.1246v1 [nucl-ex]
  22. R. Arnaldi, “Measurement of J/Ψ Production in pp Collisions at = 2.76 and 7 TeV with ALICE,” Journal of Physics G, Vol. 38, No. 12, 2011, Article ID: 124106. doi:10.1088/0954-3899/38/12/124106
  23. P. Pillot, “J/Ψ Production at Forward Rapidity in Pb-Pb Collisions at = 2.76 TeV, Measured with the ALICE Detector,” Journal of Physics G, Vol. 38, No. 12, 2011, Article ID: 124111. doi:10.1088/0954-3899/38/12/124111

NOTES

*Corresponding author.

Journal Menu >>