# Quark Matter 2012

12-18 August 2012
US/Eastern timezone

## Why the formula $\mean{dN_{ch}^{AA}/d\eta}=\mean{dN_{ch}^{pp}/d\eta} [x N_{part}/2 +(1-x) N_{coll}]$ should be deprecated

16 Aug 2012, 16:00
2h

Poster Global and collective dynamics

### Speaker

Michael Tannenbaum (Brookhaven National Laboratory (US))

### Description

\bc {\large \bf{ Why the formula\\ $\mean{dN_{\rm ch}^{AA}/d\eta}=\mean{dN_{\rm ch}^{pp}/d\eta} [x N_{\rm part}/2 +(1-x) N_{\rm coll}]$\\ should be deprecated}} \bs Abstract for Quark Matter 2012 poster \bs \underline{Michael J. Tannenbaum}~$^{a)}$ $^{a)}$ Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000, USA The fact that the multiplicity density in A+A collisions increases faster than the number of participants has led to the popular formula $\mean{dN_{\rm ch}^{AA}/d\eta}=\mean{dN_{\rm ch}^{pp}/d\eta} [x N_{\rm part}/2 +(1-x) N_{\rm coll}]$ with the implication that point-like hard-scattering contributes to the total charge multiplicity or $\sum E_T$ distributions. For $\sqrt{s}=630$ GeV $\bar{p}-p$ collisions, the UA2 collaboration~\cite{UA2PLB165} measured that the hard-scattering component of $\sum E_T$ distributions only becomes apparent at the level of $\sim 1/500$ the total cross-section, clearly indicating that the contribution of hard-process to the multiplicity and $\sum E_T$ distributions is negligible. The universal behavior of $\mean{dN_{\rm ch}^{AA}/(0.5N_{\rm part}d\eta)}$ as a function of $N_{\rm part}$ at RHIC and LHC over the range $7\leq \sqrt{s_{NN}}\leq 2760$ GeV, in spite of the dramatic increase in the ratio of $N_{\rm coll}/N_{\rm part}$ due to the increasing N-N interaction cross section, is another indication. Finally, an $E_T$ distribution which satisfies the popular formula for $\mean{dN_{\rm ch}^{AA}/d\eta}$ will be demonstrated and shown to look nothing like any measured $\sum E_T$ distribution. A more reasonable nuclear geometrical description has been given previously~\cite{Voloshin,De,Nouicer} and will be tested with recent data. \begin{thebibliography}{9} \bibitem{UA2PLB165} UA2 Collab., \Journal{\PLB}{165}{441-448}{1985}. \bibitem{Voloshin} S.~Eremin and S.~Voloshin, \Journal{\PRC}{67}{064905}{2003}. \bibitem{De} B.~De and S.~Bhattacharyya, \Journal{\PRC}{71}{024903}{2005}. \bibitem{Nouicer} R. Nouicer, \Journal{\EPJC}{49}{281}{2007}. \end{thebibliography} \end{document}

### Primary author

Michael Tannenbaum (Brookhaven National Laboratory (US))

 Slides