Fractional momentum correlations in multiple production of W bosons and of b-anti_b pairs in high energy pp collisions

TL;DR

This work investigates how QCD evolution induces correlations in the momentum fractions of partons participating in multiple parton interactions (MPI) in high-energy pp collisions. It develops a framework for evolving two-body parton distributions, separating factorized and correlated contributions, and applies it to high-resolution equal-sign W boson pair production and lower-resolution bbbar pair production across 1–14 TeV. The results show evolution-induced correlations can contribute up to ~40% of the W-pair MPI cross sections at 1 TeV (and ~20% at 14 TeV), while bbbar MPI receives smaller corrections (~5–10%), with the magnitude depending on the probing x and the chosen resolution scale. The study introduces a two-scale transverse density model to capture both low- and high-resolution correlations and highlights the importance of including x correlations in MPI analyses and in extracting sigma_eff at the LHC.

Abstract

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-bar_b b-bar_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-bar_b pairs the correction terms are of the order of 10-15% at 1 TeV and of the order of 5% at 14 TeV.

Figures (7)

• Figure 1: $gg$ correlation ratio for $x_1=x_2=x$, with factorization scale equal to the $W$ mass (solid- curve) and to the $b$ mass (dashed-curve).
• Figure 2: $qq$ correlation ratios for $x_1=x_2=x$, with factorization scale equal to the $W$ mass (solid- curves) and to the $b$ mass (dashed-curves).
• Figure 3: Left-panel: $b\bar{b}b\bar{b}$ inclusive cross-section as a function of center of mass energy; the dashed curve refers to the double-parton scattering factorized term $\sigma_{fact}^D$, while the upper and the lower solid curves refer to contributions with correlations $\sigma_{corr}^D$, with geometrical factors obtained setting $r=r_0$ and $r=r_{eff}$ respectively. Right-panel: ratio between $\sigma_{corr}^D$ and $\sigma_{fact}^D$ as a function of center of mass energy.
• Figure 4: $b\bar{b}b\bar{b}$ production cross-section at $\sqrt s=14\,TeV$ and $\sqrt s=5.5\,TeV$ as a function of $p_t^{min}$, the minimum value of transverse momenta of the outgoing $b$ quarks; the dashed curves refer to the double-parton scattering factorized term $\sigma_{fact}^D$, while upper and lower solid curves refer to $\sigma_{corr}^D$ with geometrical factors obtained setting $r=r_0$ and $r=r_{eff}$ respectively.
• Figure 5: ratio between $\sigma_{corr}^D$ and $\sigma_{fact}^D$ at $\sqrt s=14\,TeV$ (left-panel) and $\sqrt s=5.5\,TeV$ (right-panel) as a function of $p_t^{min}$.