central_xsec_howto.txt

March 9, 2004

I have implemented some new flags to help calculate the "central" cross
section in simc_semi.

The basic idea is that, starting with a model cross section that describes
the data well, we can extract the experimental cross section using:

sigma_exp = Ndata/Nsimc * sigma_model

In simc_semi, we want the cross section at some fixed Q2 and xbj and binning
in either z or pt2.  The modifications to simc_semi will allow you to dump
the "central" cross section event-by-event to the ntuple. The central cross
section is given in terms of

	sigcent = dSigma/( dOmega_e dE_e dOmega_had dE_had) 

in units of microbarns/MeV**2/sr**2.  The fixed Q2 and xbj are taken from the
beam energy and central spectrometer settings.

If you are binning in z, pt2 is fixed at some constant value that you control 
in the input file.  The z-binning is also determined in the input file where 
you control z_min, z_max, and the number of bins.  Using the same input 
parameters, you can likewise bin in pt2 and pick some constant z.  

The new flags of interest are:

sigc_flag = 0  ;  Set this to 0 to bin in z, or 1 to bin in pt2
sigc_nbin = 10 ; number of bins in z or pt2 for "central" cross section calc
sigc_kin_min = 0.31  ; minumum z (or pt2) for central cross section calc 
sigc_kin_max = 0.43  ; maximum z (or pt2) for central cross section calc
sigc_kin_ind = 0.005 ; value for 'independent' variable (pt2 in GeV2 if 
	             ; binning in z)

The above example is for binning in z.  One might use the settings below to bin
in pt2.


sigc_flag = 1         ; bin in pt2
sigc_nbin = 10        ; number of bins for "central" cross section calc
sigc_kin_min = 0.0    ; minumum pt2  for central cross section calc 
sigc_kin_max = 0.02   ; maximum  pt2 for central cross section calc
sigc_kin_ind = 0.37  ; value for 'independent' variable, z in this case


Some new variables in the ntuple are:

sigcent - already defined above. the lab cross section
centjac - the "central" jacobian that converts dz dpt2 dphi -> dE_h dOmega_h
	you can get dSigma/(dOmega_e dE_e dz dPt2 dphi) by taking 
	-> sigcent/centjac
zi = E_hadron/nu at the vertex.  This is what's used in the model
pt2i + the transverse momentum at the vertex

If you plot, for example, sigcent vs. zi after running simc in the mode that
calculates the z-binned central cross section, you should see a step-like
pattern, i.e., a constant cross section for a range in z equal to the bin 
width.

Something like:

	   ---
	      ---
	         ---
		    ---
		       ---


Note that if you plot vs. the reconstructed z, the pattern will be smeared 
around because of multiple scattering, energy loss, etc.


To get the cross section as a function of z, one can then define the normalized
yields per z-bin of data and Monte Carlo multiplied by the central cross 
section in each zi bin or

sig_exp (z-vertex) = Ndata (z-reconstructed) * sig_model(z-vertex)
		     -----------------------
                     Nsimc (z-reconstructed)