1 | \subsection{The longitudinal and kinky strings are produced |
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2 | in hadronic collisions.} |
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3 | |
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4 | \subsection{The number of the cut Pomerons.} |
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5 | |
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6 | \hspace{1.0em}In the case of a nondiffractive interaction we can |
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7 | determine $n$ of cut Pomerons or $2n$ produced strings according to |
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8 | probability \cite{AGK74} |
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9 | \begin{equation} |
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10 | \label{SLKS1} |
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11 | p^{(n)}_{ij}(\vec{ b}_i-\vec{ b}_j,s) |
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12 | =c^{-1}\exp{\{-2u(b_{ij}^2,s)\}} |
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13 | \frac{[2u(b_{ij}^2,s)]^{n}}{n!}. |
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14 | \end{equation} |
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15 | |
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16 | \subsubsection{Separation of the longitudinal soft strings from |
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17 | the kinky hard strings.} |
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18 | |
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19 | \hspace{1.0em}We assume \cite{ASGABP95}, \cite{WDFHO97} that each cut |
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20 | Pomeron can be substituted either by the two longitudinal soft strings |
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21 | or by the two kinky hard strings. |
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22 | |
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23 | At the moment it is not completely clear how to choose which cut |
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24 | pomeron should be |
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25 | substituted by longitudinal and which one should be |
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26 | substituted by kinky strings. |
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27 | |
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28 | One recipe is based on the eikonal model \cite{RCT94}, \cite{WDFHO97} |
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29 | \begin{equation} |
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30 | \label{SLKS2}u(b_{ij}^2,s)=u_{soft}(b_{ij}^2,s) + u_{hard}(b_{ij}^2,s). |
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31 | \end{equation} |
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32 | The soft eikonal part is defined as |
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33 | \begin{equation} |
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34 | \label{SLKS3}u_{soft}(b_{ij}^2,s) = |
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35 | \frac{\gamma _{soft}}{\lambda_{soft} (s)}(s/s_0)^{\Delta_{soft}} |
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36 | \exp (-b_{ij}^2/4\lambda_{soft} (s)). |
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37 | \end{equation} |
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38 | The hard part is calculated according to |
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39 | \begin{equation} |
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40 | \label{SLKS4}u_{hard}(b_{ij}^2,s)= |
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41 | \frac{\sigma_{jet}}{8\pi\lambda_{hard}(s)} |
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42 | (s/s_0)^{\Delta_{hard}} |
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43 | \exp (-b_{ij}^2/4\lambda_{hard} (s)). |
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44 | \end{equation} |
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45 | The $\sigma_{jet}=0.027$ mbarn and $\Delta_{hard}=0.47$ were found from the fit of the two--jet |
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46 | experimental cross section \cite{UA1}. Then from the global fit of |
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47 | the total and |
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48 | elastic cross sections for $pp$ collisions the values of $\gamma_{soft} = 35.5$ mbarn, $\Delta_{soft}= |
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49 | 0.07$ and $R^2_{hard} = R^2_{soft} = 3.56$ GeV$^{-2}$ were |
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50 | found. |
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51 | |
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52 | Thus we can examine each cut Pomeron and substitute it by two kinky |
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53 | strings with probability |
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54 | \begin{equation} |
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55 | \label{SLKS5} |
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56 | P_{hard}(b^2_{ij},s) = \frac{u_{hard}(b_{ij}^2,s)}{u_{soft}(b_{ij}^2,s)+ |
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57 | u_{hard}(b_{ij}^2,s)}. |
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58 | \end{equation} |
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59 | |
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