Fits of C+C m_t plots at mid-rapidity with hydrodynamic "blast" function

see arXiv:nucl-ex/0307010v1 (eq.16) or
arXiv:hep-ph/9612336v1
(1/mt**2)*dN/dmt = A * integral{ r* K_1(mt*cosh(rho)/T) * I_0(pt*sinh(rho)/T) dr }, integral over r=(0,1)
rho = 1/tanh(beta), beta = beta_max*r;

3 parameters: A, beta_max (blast or b) and T (slope)

First again check of the formula on the "ideal" PLUTO distribution for 1 GeV with T=58 MeV and b=0 (and A_2=0) - upper plots and the same with T=58 MeV and b=0.3 - lower plots :
The fits do not reproduce the input parameter to PLUTO - inverse slope and blast. Only in the 1st case b=0 is reproduced correctly, but also in this case the inverse slope differs from the original value (fitted 64 vs input 58 MeV). The PLUTO m_t spectrum shape (upper left) is pure exponential, when fitted by expo, it gives correct result T=58. Moreover the fitting function used here does not give exponential function for case b=0. Do I have a bug in the function?

• PLUTO up: T=58MeV, b=0 down: T=58, b=0.3 left: fit right: chi2contour plot b vs T:
  

Now exp data:

• C+C 1 AGeV:
  

• C+C 2 AGeV:
  

In case of 2 AGeV there are several minima, therefore parameters errors (mainly) for pi+ are wrong. See 1 sigma contours in detail here:

• pi+:
  

• pi-:
  

-- PavelTlusty - 28 May 2008