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*Fits of C+C m_t plots at mid-rapidity with hydrodynamic "blast" function* <BR>

see       arXiv:nucl-ex/0307010v1 (eq.16)  or <BR>
                arXiv:hep-ph/9612336v1<BR>
(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) <BR>
rho = 1/tanh(beta), beta = beta_max*r;  <BR>
<BR>
3 parameters: A, beta_max (blast or b) and T (slope)<BR>


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 :<BR>
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: <br />
    <img src="%ATTACHURLPATH%/c1c_pluto_mtfit_blast.gif" alt="PLUTO up: T=58MeV, b=0 down: T=58, b=0.3 left: fitted distribution right: chi2contour plot b vs T (1, 2, 3 sigma)"  width="1650" height="1191"  />

Now exp data:


   * C+C 1 !AGeV: <br />
    <img src="%ATTACHURLPATH%/c1c_mtfit_blast_exp.gif" alt="C+C 1 !AGeV"  width="1646" height="1193"  />

   * C+C 2 !AGeV: <br />
    <img src="%ATTACHURLPATH%/c2c_mtfit_blast_exp.gif" alt="C+C 2 !AGeV"  width="1646" height="1193"  />

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+: <br />
    <img src="%ATTACHURLPATH%/c2c_mtfit_pip_exp_contour1.gif" alt="pi+"  width="696" height="474"  />

   * pi-: <br />
    <img src="%ATTACHURLPATH%/c2c_mtfit_pim_exp_contour1.gif" alt="pi-"  width="696" height="474"  />

-- Main.PavelTlusty - 28 May 2008

Topic attachments
I	Attachment	Action	Size	Date	Who	Comment
gif	c1c_mtfit_blast_exp.gif	manage	68.7 K	28 May 2008 - 12:59	PavelTlusty	C+C 1 AGeV
gif	c1c_pluto_mtfit_blast.gif	manage	54.6 K	28 May 2008 - 12:38	PavelTlusty	PLUTO up: T=58MeV, b=0 down: T=58, b=0.3 left: fit right: chi2contour plot b vs T
gif	c2c_mtfit_blast_exp.gif	manage	61.5 K	28 May 2008 - 13:01	PavelTlusty	C+C 2 AGeV
gif	c2c_mtfit_pim_exp_contour1.gif	manage	5.6 K	28 May 2008 - 13:10	PavelTlusty	pi-
gif	c2c_mtfit_pip_exp_contour1.gif	manage	5.6 K	28 May 2008 - 13:08	PavelTlusty	pi+

Topic revision: r1 - 28 May 2008, PavelTlusty

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