Fractional momentum correlations in multiple production of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>bosons and of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>pairs in high energy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mi>p</mml:mi></mml:math>collisions

Multiple parton collisions will represent a rather common feature in $pp$ collisions at the LHC, where regimes with very large momentum transfer may be studied and events rare in lower energy accelerators might occur with a significant rate. A reason of interest in large ${p}_{t}$ regimes is that, differently from low ${p}_{t}$, evolution will induce correlations in $x$ in the multiparton structure functions. We have estimated the cross section of multiple production of $W$ bosons with equal sign, where the correlations in $x$ induced by evolution are particularly relevant, and the cross section of $b\overline{b}b\overline{b}$ production, where the effects of evolution are much smaller. Our result is that, in the case of multiple production of $W$ bosons, the terms with correlations may represent a correction of the order of 40% of the cross sections, for $pp$ collisions at 1 TeV c.m. energy, and a correction of the order of 20% at 14 TeV. In the case of $b\overline{b}$ pairs the correction terms are of the order of 10--15% at 1 TeV and of the order of 5% at 14 TeV.