Single top vs STT
==================

(from Ann Heinson, 18 Dec. 1998)

input: 
   * Lum = 2000 pb^-1  +- 5%
   * sigma(tb) = 0.894 pb +- 6%, sigma(tbq) = 2.44 pb +- 11%
   * BR(W -> l nu, tau -> l nu) = 0.2222, BR(W -> QQ) = 0.6667 
   * Sig : Bgd = 1 : 2 for LC (lepton channel)    [from TeV2000]
               = 1 : 4 for HC (hadron channel)    [guess]
	           [note t tbar -> alljets is 18 : 6.9 = 2.6 : 1)
   * signal acceptance:
      LC: 5%  [slightly less than TeV2000, same as run1,
                  i.e. better tagging efficiency, but tighter cuts]
	   Delta epsilon = 7%  [run1 scaled to run2]
      HC: 2.5% [guess]
            [half of lepton channel 
	      -- cf. t tbar - > alljets run  = 5%
	            (80% hit in trigger wrt LC, rest is tighter cuts)]
	   Delta epsilon = 7%  [run1 scaled to run2]
	   
  number of signal events: S = lum. * sigma *  BR * epsilon
  
  
             S   DeltaS_stat  DeltaS_tot  B   DeltaB  Delta sigma_m  Delta V_tb
			 
tb W* LC    19.9    4.5           5.3    39.7   2.8       38             19
tb W* HC    29.8    5.5          10.0   119.2   8.3       47             24
tqb Wg LC   54.2    7.4          10.6   108.4   7.6       25             14
tqb Wg HC   81.3    9.0          24.5   325.3  22.8 	  37             19 
	   	       	  	    
				    
				 
  notes: 
     -  S, B = number of events (signal, background)
     -  Delta sigma_m = relative total uncertainty on measured cross section;
     -  Delta sigma_t = relative uncertainty on theoretical cross section;	                    
     -  Delta V_tb = (1/2) sqrt{(Delta sigma_m)^2 + Delta sigma_t)^2},
     -  Delta sigma_m, Delta sigma_t and Delta V_tb in %			    	
		   			    
 conclusion:				    
   no STT -- only lepton channel  line 1 + line 3  =>      11.3%
   with STT -- also hadron channel line 2 + line 4    =>   14.9%
                                   combined LC + HC   =>    9.0%   
   
   (cf. Ann Heinson et al PRD: combined single top -> lepton + jets for run2:
        Delta sigma_m = 19%
	Delta sigma_t = 16%
	Delta V_tb    = 12%   )
	
	
---------------------------------------
additional explanation from Ann:

    Hi Horst,

In the PRD we did the calculation for measuring tb and tqb combined
because the statistics are low and the search difficult, and so there was
only one contribution from things like the error on the integrated
luminosity automatically. Here this is also true, even though two
otherwise independent measurements are made. Other 100% correlated
contributions to the two measurements would include things like the pdf
and the modeling of ISR and FSR. However these are not separated out in
this error estimate so you can't easily account for this double counting
into the overall error. Other sources of uncertainty in the estimate are
larger than this.

The two processes qQ->tB and qg->tq'B are independent. (I have used the
CompHEP notation here were a capital letter particle is an antiparticle.)
The first is an s-channel process and the second a t-channel one and there
is no interference between the two. The B in the first process is made
with the t at a Wtb coupling. In the second process the B comes from g->bB
and the t is made alone, from a Wb fusion (virtual b). The q' comes from
the radiation of the virtual W from the q. Because there is no common
final state with the processes, and hence no interference between them,
you can search for and study the two processes completely separately. Of
course because they look rather similar to each other some of the events
from each process will pass the cuts searching for the other process and
will contribute in a small way to the background but this is not a
problem and does not invalidate the results.

On Tue, 22 Dec 1998, Horst D. Wahl wrote:

> Hello Ann,
> 
>  Sorry to bother you again. About the uncertainty on V_tb:
> In estimating the total uncertainty, I assumed that every channel gives an
> independent measurement of V_tb; under this
> assumption,
>    (1/sigma)^2 = (1/sigma_tb)^2 + (1/sigma_tbq)^2 ;
> this gives the numbers I quoted. 
> This is presumably a wrong assumption, since the tb and tbq data are not
> independent; (or are they?)
> In your PRD you seem to have assumed that they are.
> 
> Regards,
> Horst
> 
>