The small x gluon and b(b)over-bar production at the LHC

We study open b (b) over bar production at large rapidity at the LHC in an attempt to pin down the gluon distribution at very low x. For the LHC energy of 7 TeV, at next-to-leading order (NLO), there is a large factorization scale uncertainty. We show that the uncertainty can be greatly reduced if events are selected in which the transverse momenta of the two B-mesons balance each other to some accuracy, that is vertical bar p(1T) + p(2T)vertical bar < k(0). This will fix the scale mu F similar or equal to k(0), and will allow the LHCb experiment, in particular, to study the x-behaviour of gluon distribution down to x similar to 10(-5), at rather low scales, mu similar to 2 GeV. We evaluate the expected cross sections using, for illustrative purposes, various recent sets of Parton Distribution Functions.