Summer04 Ab,Ac final result parameter scaling
=============================================

All measurements already conformed to the final LEPEWWG input parameters 
for the external inputs, but the dependence on the measured EW parametres
(Rb,Rc,b->l,chi...) still need to be corrected for the final EW fit results. 

Ab,Ac lepton: Input parameters correction to final LEP EWWG values were done 
           in summer 2001 for the combination tables, thus numbers differ
           from the publication already. 
           => Correct central value for summer 04 EW fit result.
Ab jet Q:  No parameter dependence specified other than Ac.
Ab K-tag:  very old result with no significance. No correction made.
Ab,Ac vtx Q/K:    
           => Correct central value for Rb,Rc dependence to summer 04 
              fit results.
Ac D*,D :  No parameter dependence specified other than Ac. 
     
For Ab<->Ac dependence, we standardized to SM values for Ac (Ab) when 
measuring Ab (Ac)    Ab=0.935+-0.035  (except D*,D analysis) 
                     Ac=0.667+-0.035 
We still want to keep it this way, instead of using the final fitted
central values of Ab,Ac, but we will use the final fitted errors. 
The final combination errors   dAb=+-0.0206
                               dAc=+-0.0274
So we don't scale the central alues for this, but just scale down the
Ab,Ac dependency error  0.035->0.0206; 0.035->0.0274: 
dAb due to dAc:  old err factor     new err 
     Ab lepton   0.0028  *274/350   0.0022       
     Ab jet Q    0.0011     "       0.0009
     Ab Vtx Q    0.0005     "       0.0004
dAc due to dAb:  old err   new err (*206/350) 
     Ac lepton   0.0080  *206/350   0.0047       
     Ac D*,D    -0.0018  *206/250  -0.0015
     Ac Vtx/K   -0.0007  *206/350  -0.0004      

Now Central value rescaling: 

Ab lepton   
---------                         
                  Summer04 LEPEWWG fit             
urb  & 0.2164     0.2163+-0.00066  
drb  & 0.0007     
urc  & 0.1674     0.1723+-0.00305
drc  & 0.0038
uchi & 0.1186     0.1250+-0.00394
dchi & 0.0043
ubl  & 10.62      10.712+-0.215
dbl  & 0.17     
ubcl & 8.07        8.006+-0.179
dbcl & 0.25
ucl  & 9.85        9.687+-0.313
dcl  & 0.32

                                 correction    error
  Rb  &  -0.0004   *(2163-2164)/7         0    *66/70    -0.0004
  Rc  &  +0.0007   *(1723-1674)/38  +0.0009    *31/38     0.0006
  chi &   0.0107   *(1250-1186)/43  +0.0159    *39/43     0.0097
  bl  &  -0.0032   *(1071-1062)/17  -0.0017    *21.5/17  -0.0040
  bcl &   0.0030   *(801-807)/25    -0.0007    *17.9/25   0.0021 
  cl  &   0.0012   *(969-985)/32    -0.0006    *1         0.0002
                                    -------
                                    +0.0138
 Ab = 0.9242 + 0.0138 = 0.9380

Ac lepton
--------- 
                                 correction     error
  Rb  &   0.0006                    -0.0001    *66/7=     0.0006
  Rc  &  -0.0092                    -0.0119    *31/38    -0.0075
  chi &   0.0026                     0.0039    *39/43     0.0024
  bl  &   0.0046                     0.0024    *21.5/17   0.0058
  bcl &  -0.0054                     0.0013    *17.9/25  -0.0039
  cl  &  -0.0129                     0.0065    *1        -0.0129
                                     ------ 
                                    +0.0021
  
 Ac = 0.5887 + 0.0021 = 0.5908   
 
Ab Vtx Q 
--------

results & 0.9190

                  summer04    corr    error 

uRb   &  0.2158   0.2163 
dRb   &  0.0008   0.00066
Rb    & -0.0027             -0.0017   0.0022         
    
uRc   &  0.1722   0.1723
dRc   &  0.0048   0.0031
Rc    &  0.0010                  0    0.0006

 Ab = 0.9190 - 0.0017 = 0.9173

Ac Vtx K
--------
 
results & 0.673 
                              corr    error                       
Rb    &  0.0020             +0.0013   0.0017
Rc    & -0.0019                  0   -0.0012 
               
 Ac = 0.6734 + 0.0013 = 0.6747