Using Eq. (5), we obtain Introducing a new notation, we obtain a more compact expression for Eq. (7) Eq. (9) enables us to calculate the single inclusive density as a function of the pseudo rapidity η . FIG. 2: Single inclusive density versus energy. The dotted data were taken from Ref.[27]. The square data points correspond to the experimental data from LHC by Alice Collaboration[2] at W = 900 GeV and the CMS collaboration[3] at W = 900 and 2360 GeV. 1 σ$_{in}$ dσ dy = 1 σ$_{in}$ ( Y ) { a$_{PP}$ (∫ d $^{2}$b ( α 2 g$_{1}$ ( b, Y/ 2 − y ) + β $^{2}$g$_{2}$ ( b, Y/ 2 − y )) × ∫ d $^{2}$b ( α 2 g$_{1}$ ( b, Y/ 2 + y ) + β $^{2}$g$_{2}$ ( b, Y/ 2 + y ) (7) − a$_{RP}$ ( α 2 g R 1 + β $^{2}$g R 2 ) ( α 2 ∫ d $^{2}$b ( α 2 g$_{1}$ ( b, Y/ 2 − y ) + β $^{2}$g$_{2}$ ( b, Y/ 2 − y )) e Δ R ( Y/ 2+ y ) + ∫ d $^{2}$b ( α 2 g$_{1}$ ( b, Y/ 2 + y ) + β $^{2}$g$_{2}$ ( b, Y/ 2 + y )) e Δ R ( Y/ 2 − y $^{)}$) } . V ( y ) = ∫ d $^{2}$b ˜ V ( b, y ) = ∫ d $^{2}$b ( α 2 g$_{1}$ ( b, Y/ 2 − y ) + β $^{2}$g$_{2}$ ( b, Y/ 2 − y )) , (8) 1 σ$_{in}$ dσ dy = 1 σ$_{in}$ ( Y ) { a$_{PP}$ V ( y/ 2 − y ) V ( Y/ 2 + y ) − a$_{RP}$ ( α 2 g R 1 + β $^{2}$g R 2 ) ( V ( Y/ 2 − y ) e (Δ R ( Y/ 2+ y ) + V ( Y/ 2 + y ) e (Δ R ( Y/ 2 − y $^{)}$) } . (9) (1/ $_{in}$)d /dy W 14000 GeV 10000 GeV 7000 GeV 1800 GeV 900 GeV 546 GeV 200 GeV 2360 GeV 0 1 2 3 4 5 6 7 1 2 3 4 5 6 4