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Pseudorapidity dependence of the $p_T$ spectra of charged hadrons in $pp$ collisions at $\sqrt{s}$ = 0.9 and 2.36 TeV

We report the predictions of different Monte Carlo event generators including HIJING, Pythia, and QGSJETII in comparison with the experimental data measured by the CMS Collaboration at CERN in proton-proton ($pp$) collisions at center-of-mass energy $\sqrt{s}$ = 0.9 and 2.36 TeV. The CMS experimental transverse momentum ($p_T$ or $p_{\perp}$) spectra of charged hadrons were measured for pseudorapidity range 0 $\le$ $η$ $\le$ 2.4 with bin width of $η$ = 0.2 (for $p_T$ from 0.1 to 2 GeV/$c$) and a single bin of $η$ for $\lvert$$η$$\rvert$ $<$ 2.4 (for $p_T$ from 0.1 to 4 GeV/$c$). Pythia reproduced the $p_T$ spectra with reasonable agreement for most of the $p_T$ range. It depicts better results in the case of the $|η|<$ 2.4 than HIJING and QGSJETII which could reproduce the spectra in a limited $p_T$ range. Furthermore, to analyze the $p_T$ spectra of charged hadrons measured by the CMS Collaboration, we used a three component function (structured from the Boltzmann distribution) and the $q$-dual function (from the $q$-dual statistics) to extract parameter values relevant for the study of bulk properties of hadronic matter at high energy. We have also applied the two analytic functions over the model predictions. The values extracted by the functions from the HIJING and Pythia models are closer to the experimental data than the QGSJETII model. Although the models could reproduce the $p_T$ spectra of all charged particles in some of the $p_T$ range but none of them could reproduce the distributions over the entire $p_T$ range and in all the pseudorapidity regions.