The sensitivity to the $\rm sin2\beta$ parameter descrbing 
the CP violation in the $\rm B^0_d/\bar{B^0}_d$ system has already 
been estimated at D\O~ in the $\rm J/\Psi+K^0_s$ channel where 
J/\Psi--> \mu^-\mu^+ to be:
 \delta sin2\beta = 0.15 ~for~{\cal{L}}=2~fb^{-1}

We investigate here the improvement that could be made on this 
number by the use of the \jpsi channel. This implies the neccessity 
of a low \PT di-electron triggering. Such triggers have been 
defined in D0-note 3506 for the central pseudo-rapidity region 
and in D0-note 3566 in the forward region. Both algorithms are based  
on the combination of preshower and calorimeter information at 
level 1 and at level 2. With the efficiencies given in the cited 
references, 5,000 B^0/B^0bar mesons are expected to be 
triggered during the run II. 
The effects of the full reconstruction of the events, detailed in 
D0-note 3228, and of the use of the different tagging methods 
described in CDF-ref. are then evaluated. We conclude 
that a sensitivity of 
      \delta sin2\beta = 0.24 for L=2 fb^{-1} 
is achievable in this channel alone, leading to a combined 
sensitivity of (ee+mumu):
      \delta sin2\beta = 0.125 for L=2 fb^{-1} 
This number corresponds to a 4-5 sigma significance in the 
direct measurement of the CP violation in B system.