Hard/soft scaling Equation is wrong

From: Michael Murray (murray@CyclotronMail.tamu.edu)
Date: Wed Nov 21 2001 - 10:41:17 EST

  • Next message: Stephen J. Sanders: "latest version uploaded to kansas account"

        Dear Jens Jorgen,
                     the Hard/soft scaling equation we use is
    incorrect and clearly in contradiction to Fig 5.
                   
    
    "... we fit the observed dependencies to a functional
    $dN/d\eta/(N_{part}/2)=\alpha\cdot
         N_{part}+\beta \cdot N_{coll}$. 
    For rapidities $\eta=$ 0 and 3.0 we   obtain:
         $\alpha=0.98 \pm 0.10$ and , $1.05 \pm 0.08$ and
         $\beta=0.25  \pm 0.04,        0.09 \pm 0.03$ respectively.
    
    So at eta=3, beta is almost zero and this equation says that
    dN/dEta * 2/Npart should grow linearly with Npart with a slope
    of 1.05. However in Fig 5 we see that for eta=3.
    dN/dEta * 2/Npart =~ 1.05 independent of Npart 
    
    In Kharzee and Leven (which is now PLB {\bf B 523} 79 (2001))
    the following equation is used.
    
    dN                 Npart
    --   = (1-X)*npp * -----  + X*npp *Ncoll
    dEta                 2
    
    Thus I think that we should write
    dN             Npart
    --   = alpha * -----  + Beta * Ncoll
    dEta             2
    
    I think this is what Trine fitted to. 
    It is also clear that the errors on alpha and beta are 
    anticorrelated since the total value of dN/dEta is fixed.
    
    Therefore I suggest that we use +- for the errors on alpha
    and -+ for the errors on beta.
    
    The corresponding latex is
     Using for   $N_{coll}$ the
         values estimated in ~\cite{Kharzeev_and_Nardi} we fit the observed
         dependencies to a functional $dN/d\eta=\alpha\cdot
         N_{part}/2+\beta \cdot N_{coll}$. For pseudorapidities $\eta=$ 0 and 3.0 we
       obtain:
         $\alpha=0.98 \pm 0.10$ and , $1.05 \pm 0.08$ and
         $\beta=0.25 \mp 0.04,  0.09 \mp 0.03$ respectively.
         For comparison we find $\alpha=0.99 \pm 0.09, 0.99 \pm 0.07, $
         and $\beta=0.18 \mp 0.04, 0.02 \mp 0.04 $ at
         $\sqrt{s_{NN}}$=130 GeV. 
    
    and the new ref [3] is
      \bibitem{Kharzeev_and_Levin} D. Kharzeev and E. Levin %nucl- th/0108006
       Phys. Lett. {\bf B 523} 79 (2001), and private communication. %
    
    
    Michael Murray, Cyclotron TAMU, 979 845 1411 x 273, Fax 1899
    



    This archive was generated by hypermail 2b30 : Wed Nov 21 2001 - 10:41:48 EST