Measurement of the ^0

The production rate of b and ar{b} hadrons in pp collisions are not expected to be strictly identical, due to imbalance between quarks and anti-quarks in the initial state. This phenomenon can be naively related to the fact that the ar{b} quark produced in the hard scattering might combine with a u or d valence quark from the colliding protons, whereas the same cannot happen for a b quark. This thesis presents the analysis performed to determine the production asymmetries of B^0 and B^0_s. The analysis relies on data samples collected by the LHCb detector at the Large Hadron Collider (LHC) during the 2011 and 2012 data takings at two different values of the centre of mass energy sqrt{s}=7 TeV and at sqrt{s}=8 TeV, corresponding respectively to an integrated luminosity of 1 fb^{-1} and of 2 fb^{-1}. The production asymmetry is one of the key ingredients to perform measurements of CP violation in b-hadron decays at the LHC, since CP asymmetries must be disentangled from other sources. The measurements of the production asymmetries are performed in bins of p_mathrm{T} and eta of the B-meson. The values of the production asymmetries, integrated in the ranges 4 < p_mathrm{T} < 30 GeV/c and 2.5<eta<4.5, are determined to be: egin{equation} A_mathrm{P}(B^0)= (-1.00pm0.48pm0.29)\%, onumber end{equation} egin{equation} A_mathrm{P}(B^0_s)= (phantom{-}1.09pm2.61pm0.61)\%, onumber end{equation} where the first uncertainty is statistical and the second is systematic. The measurement of A_mathrm{P}(B^0) is performed using the full statistics collected by LHCb so far, corresponding to an integrated luminosity of 3 fb^{-1}, while the measurement of A_mathrm{P}(B^0_s) is realized with the first 1 fb^{-1}, leaving room for improvement. No clear evidence of dependences on the values of p_mathrm{T} and eta is observed. The results presented in this thesis are the most precise measurements available up to date.