Dijet production as a centrality trigger for p-p collisions at CERN LHC

TL;DR

The paper introduces a centrality trigger based on hard dijet production near zero rapidity to distinguish central from peripheral pp collisions at Tevatron and LHC. It develops a quantitative framework linking the transverse distribution of hard gluons, via the two-gluon form factor and dipole models, to the impact-parameter dependence of dijet production and to the approach toward the black-body limit in central events. The authors predict tangible changes in final-state observables, including boosted transverse momenta at small rapidities, suppressed forward fragmentation, and enhanced mid-rapidity activity, which can be exploited to study strong gluon fields and to search for new particles. These insights have practical implications for event selection, detector studies, and the modeling of high-density QCD effects in proton collisions at the LHC.

Abstract

We demonstrate that a trigger on hard dijet production at small rapidities allows to establish a quantitative distinction between central and peripheral collisions in pbar-p and p-p collisions at Tevatron and LHC energies. Such a trigger strongly reduces the effective impact parameters as compared to minimum bias events. This happens because the transverse spatial distribution of hard partons (x >~ 10^{-2}) in the proton is considerably narrower than that of soft partons, whose collisions dominate the total cross section. In the central collisions selected by the trigger, most of the partons with x >~ 10^{-2} interact with a gluon field whose strength rapidly increases with energy. At LHC (and to some extent already at Tevatron) energies the strength of this interaction approaches the unitarity ('black-body') limit. This leads to specific modifications of the final state, such as a higher probability of multijet events at small rapidities, a strong increase of the transverse momenta and depletion of the longitudinal momenta at large rapidities, and the appearance of long-range correlations in rapidity between the forward/backward fragmentation regions. The same pattern is expected for events with production of new heavy particles (Higgs, SUSY). Studies of these phenomena would be feasible with the CMS-TOTEM detector setup, and would have considerable impact on the exploration of the physics of strong gluon fields in QCD, as well as the search for new particles at LHC.

Figures (14)

• Figure 1: Schematic illustration of the two classes of $pp$ collisions at high energies. The transverse spatial distributions of the hard partons ($x \geq 10^{-2}$) is indicated by the dark shaded disks, those of the soft partons ($x \ll 10^{-2}$) by the light shaded disks; $b$ denotes the impact parameter of the $pp$ collision. (a) At large $b$ no overlap between hard partons occurs. (b) At small $b$ the distributions of hard partons overlap, leading to production of hard dijets (and, possibly, heavy particles).
• Figure 2: Schematic illustration of the effect of the black-body (unitarity) limit on hardon production in the forward/backward rapidity region in central $pp$ collisions. A small--$x$ spectator parton (i.e., a parton not involved in the centrality trigger) from the left proton propagates through the strong gluon field (indicated by the shaded area), acquiring a large transverse momentum, $p_{\perp, \text{BBL}} \gg \Lambda_{\text{QCD}}$. The small--$x$ parton is then resolved in a collision with a large--$x_R$ parton from the right proton, resulting in hadron production in the backward rapidity region.
• Figure 3: The normalized impact parameter distribution for generic inelastic collisions, $P_{\text{in}} (s, b)$, Eq. (\ref{['P_in_def']}), obtained with the parameterization of the elastic $pp$ amplitude of Islam et al.Islam:2002au ("diffractive" part only). The plot shows the "radial" distribution in the impact parameter plane, $2 \pi b \, P_{\text{in}} (s, b)$. The energies are $\sqrt{s} = 500\, \text{GeV}$ (RHIC) and $14000\, \text{GeV}$ (LHC).
• Figure 4: Our model for the $x$--dependence of the average transverse gluonic size squared of the nucleon, $\langle \rho^2 \rangle$ at the scale $Q_0^2 = 2 \div 4 \, \text{GeV}^2$ relevant to $J/\psi$ production. Short--dashed line:$\langle \rho^2 \rangle = 0.28 \, \text{fm}^2$, as extracted from the $t$-slope of the $J/\psi$ production cross section measured in various experiments Frankfurt:2002ka. Long--dashed line: Sum of the constant value $\langle \rho^2 \rangle = 0.28 \, \text{fm}^2$ and the pion cloud contribution calculated in Ref. Strikman:2003gz. Solid line: The parameterization Eq. (\ref{['rho2_x_simple']}), based on the experimental value of $\alpha^{\prime}_{\text{hard}}$, Eq. (\ref{['alphap_hard']}) Chekanov:2002xi.
• Figure 5: The change of the normalized $\rho$--profile of the gluon distribution, $F_g (x, \rho; Q^2)$, Eq. (\ref{['rhoprof_def']}), with $Q^2$, as due to DGLAP evolution, for $x = 10^{-3}$. The input gluon distribution is the Glück--Reya--Vogt parametrization at $Q_0^2 = 3 \, \text{GeV}^2$, with a dipole--type $\rho$--profile, Eq. (\ref{['dipole_b']}), of size determined by the parametrization Eq. (\ref{['rho2_x_simple']}).