Narrow Results

In this paper, we have studied the spectra of strange particles in pp collision at $\sqrt{s}$ = 0.9 TeV by using different simulation models, EPOS-1.99, SIBYLL-2.3c, QGSJETII-04 and EPOS-LHC. The transverse momentum and rapidity distribution in the $p_T$ range of $0<p_T<10$ GeV/c and $0<p_T<2$ GeV/c, respectively, are investigated for the strange particles, $K_s^o$, $\mathrm{\Lambda }$, ${\mathrm{\Xi }}^{-}$. Similarly, a comparative study is done for the ratio of $\mathrm{\Lambda }/K_s^o$ and ${\mathrm{\Xi }}^{-}/\mathrm{\Lambda }$ as a function of transverse momentum and rapidity. The validity of simulation models is tested by comparing simulation results to the CMS experimental data at $\sqrt{s}$ = 0.9 TeV. For $p_T$ distributions, the EPOS-LHC model in the $p_T$ range $p_T<0.3$ GeV/c, $p_T>8$ GeV/c and in $3.6<p_T<3.8$ GeV/c while EPOS-1.99 model in the $p_T$ range $2.5<p_T<2.8$ GeV/c and QGSJETII-04 model in the $p_T$ range $2.5<p_T<2.8$ GeV/c as well as, $3.6<p_T<3.8$ GeV/c explain the experimental data well. For the, $\mathrm{\Lambda }/K_s^o$ and ${\mathrm{\Xi }}^{-}/\mathrm{\Lambda }$ versus transverse momentum distributions, EPOS-LHC model in the $p_T$ range of, $2.4<p_T<2.6$ GeV/c and $1.6<p_T<1.8$ GeV/c, EPOS-1.99 model in the $p_T$ range, $1.7<p_T<2.2$ GeV/c, SIBYLL-2.3c model in the $p_T$ range, $1.4<p_T<1.6$ GeV/c and QGSJETII-04 model in the $p_T$ range $0.4<p_T<0.6$ GeV/c explain the experimental data very well. Similarly, for $\mathrm{\Lambda }/K_s^o$ and ${\mathrm{\Xi }}^{-}/\mathrm{\Lambda }$ versus rapidity distribution QGSJETII-04 predictions in the rapidity region, $0.4<\left|y\right|<0.6$, $1.4<\left|y\right|<1.6$, and $\left|y\right|>1.8$, while EPOS-LHC model in the region, $\left|y\right|>1.8$, very well explained the experimental data. Although good comparison of the models predictions with the experimental data is observed, none of them completely describe the experimental data the spectra of strange particles over the entire $p_T$ and $y$ range.

The Lorentz-group of transformations usually consists of linear transformations of the coordinates, keeping as invariant the norm of the four-vector in (Minkowski) space-time. Besides those linear transformations, one may construct different forms of nonlinear transformations of the coordinates keeping unchanged that respective invariant. In this paper we explore nonlinear transformations of second-order which have a natural interpretation within the framework of Yamaleev's concept of the counterpart of rapidity (co-rapidity). The purpose of developed concept is to show that the formulae for energy and momentum of the relativistic particle become regular near the zero-mass and speed of light states. Furthermore, in a covariant formulation, the co-rapidity is presented as a four-vector which admits an extension of the Lorentz-group of transformations. In this paper we additionally show, that in the same way as the rapidity is related to the electromagnetic field, the co-rapidity is related to the field of strengths, which are given by a four-vector. The corresponding equations of such a field are also constructed.