According to this Sequential Chain Model (SCM), high energy hadronic interactions boil down, essentially, to the pion-pion interactions; as the protons are conceived in this model as, where is a spectator particle needed for the dynamical generation of quantum numbers of the nucleons [5] - [11] .

The inclusive cross-section of the -meson produced in the collisions at high energies has been calculated by using field theoretical calculations and Feynman diagram techniques with the infinite momentum frame approximation method. The inclusive cross-section is given by the undernoted relation [5] - [11]

with

where is the normalisation factor which will increase as the inelastic cross-section increases and it is different for different energy and for various collisions. The terms, ,

in Equation (1) represent the transverse momentum, Feynman Scaling

variable respectively. The in Equation (2) is the square of the c.m. energy.

of the expression (1) is the “constituent rearrangement term”. It arises out of the partons inside the

proton. At high energy interaction processes the partons undergo some dissipation losses due to impact and impulses of the projectile on the target. This term essentially provides a damping term in terms of a power law. The exponent of, i.e., varies on both the collision process and the specific -range. We have to parametrize this term with the view of two physical points, viz., the amount of momentum transfer and the contributions from a phase factor arising out of the rearrangement of the constituent partons. The relation for is to be given by [12]

where denotes the average number of participating nucleons and values are to be obtained phenomenologically from the fits to the data-points.

Similarly, for kaons of any specific variety (, , or) we have

with

And for the antiproton production in collision at high energies, the derived expression for inclusive cross-section is

with

In order to transform the inclusive cross-section from to collisions (here, stands for, and, as the case may be), we use the undernoted relation [13] ;

Here, in the above equation [Equation (8)], the first factor gives a measure of the number of wounded nucle- ons i.e. of the probable number of participants, wherein gives the probability cross-section of collision with “B” nucleus (target), had all the nucleons of A suffered collisions with B-target. And has just the same physical meaning, with A and B replaced. Furthermore, is the nucleon (proton)-nucleus (A) inter- action cross-section, is the inelastic nucleon (proton)-nucleus (B) reaction cross-section and is the inelastic AB cross-section for the collision of nucleus A and nucleus B. The values of, , have been worked here out by the following formula [14]

with mb,.

The second term in expression (8) is a physical factor related with energy degradation of the secondaries due to multiple collision effects. The parameter occurring in this term is a measure of the fraction of the nucleons that suffer energy loss. The maximum value of is unity, while all the nucleons suffer energy loss. This parameter is usually to be chosen [13] , depending on the centrality of the collisions and the nature of the secondaries.

We can write from expression (8), the transformed SCM-based transverse-momentum distributions for -type reactions in the following generalized notation:

where, for example, the parameter can be written in the following form:

In a similar way, the values of of Equation (10) have been calculated with the help of Equation (1), Equation (2). The values of, , and have been calculated accordingly by using Equations (4)-(8). Moreover, for calculation for transverse momenta distribution of antiproton production, the the exponen-

tial part will be .

of the expression (10) have been calculated by using Equation (3).

The model-based and ratios as a function of at energies TeV have been obtain- ed from the expression (10) and Table 2. Data in Figure 3(a) and Figure 3(b), for different centralities, viz., for 0% - 5%, 20% - 30% and 70% - 80%, are taken from Ref [16] . Lines in the figure show the theoretical plots.

For the calculation of rapidity distribution, we can make use of the following standard relation [17] ,

By using Equation (1), Equation (8), Table 2 and Equation (12), we arrive at the SCM-based rapidity dis- tribution, which is given hereunder;

The of the above equation (Equation (13)) has come from of Equation (11) with.

In Figure 4, we have plotted theoretical versus with the help of above equation [Equation (13)] against experimental background [18] . The dotted line in this figure shows the Gaussian fit [18] .

The nuclear modification factor (NMF) is defined as ratio of charged particle yield in to that in, scaled by the number of binary nuclear collisions [19] and is given hereunder

where is related with the average nuclei thickness function by the following relation [19]

Here, is the total inelastic cross section of interactions.

The is related to by the following relation [13] :

In the region, ,.

The SCM-based results on NMF’s for, and in central collisions at energies

TeV are deduced on the basis of Equation (10), Table 1 and Table 2. The equations in connection with, and are give by the following relations and they are plotted in Figure 5 against. The solid lines in the figure show the theoretical results, while the points show the experimentally measured results [20] ;