Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Mueller-Navelet Jets at Hadron Colliders

J. R. Andersen, V. Del Duca, S. Frixione, C. R. Schmidt, W. J. Stirling

TL;DR

This paper reexamines Mueller-Navelet jets at hadron colliders in light of realistic experimental cuts and x-definitions. It shows that a D0-like upper bound on the momentum transfer $Q^2$ and the choice of x-reconstruction substantially modify the standard Mueller-Navelet BFKL predictions, especially at Tevatron energies, and that energy-momentum conservation effects are essential. Through analytic refinements and a BFKL Monte Carlo, the authors quantify how these factors alter cross sections and the extracted BFKL intercept, and they demonstrate that equal transverse-momentum cuts induce large non-BFKL logarithms. They advocate asymmetric cuts and kinematics-aware MC approaches to reliably isolate BFKL dynamics, with implications for interpreting Tevatron data and for planning LHC analyses.

Abstract

We critically examine the definition of dijet cross sections at large rapidity intervals in hadron-hadron collisions, taking proper account of the various cuts applied in a realistic experimental setup. We argue that the dependence of the cross section on the precise definition of the parton momentum fractions and the presence of an upper bound on the momentum transfer cannot be neglected, and we provide the relevant modifications to the analytical formulae by Mueller and Navelet. We also point out that the choice of equal transverse momentum cuts on the tagging jets can spoil the possibility of a clean extraction of signals of BFKL physics.

Mueller-Navelet Jets at Hadron Colliders

TL;DR

This paper reexamines Mueller-Navelet jets at hadron colliders in light of realistic experimental cuts and x-definitions. It shows that a D0-like upper bound on the momentum transfer and the choice of x-reconstruction substantially modify the standard Mueller-Navelet BFKL predictions, especially at Tevatron energies, and that energy-momentum conservation effects are essential. Through analytic refinements and a BFKL Monte Carlo, the authors quantify how these factors alter cross sections and the extracted BFKL intercept, and they demonstrate that equal transverse-momentum cuts induce large non-BFKL logarithms. They advocate asymmetric cuts and kinematics-aware MC approaches to reliably isolate BFKL dynamics, with implications for interpreting Tevatron data and for planning LHC analyses.

Abstract

We critically examine the definition of dijet cross sections at large rapidity intervals in hadron-hadron collisions, taking proper account of the various cuts applied in a realistic experimental setup. We argue that the dependence of the cross section on the precise definition of the parton momentum fractions and the presence of an upper bound on the momentum transfer cannot be neglected, and we provide the relevant modifications to the analytical formulae by Mueller and Navelet. We also point out that the choice of equal transverse momentum cuts on the tagging jets can spoil the possibility of a clean extraction of signals of BFKL physics.

Paper Structure

This paper contains 10 sections, 48 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Dijet production at fixed $x$'s in the naive BFKL approach
  3. The standard Mueller-Navelet analysis
  4. Dijet production with an upper bound on $Q^2$
  5. Dijet production at $x$'s fixed as in the D0 set-up
  6. Dijet production and energy-momentum conservation
  7. Equal transverse momentum cuts: a dangerous choice
  8. Dijet cross sections at fixed perturbative order
  9. Dijet production in the BFKL theory with an asymmetric cut
  10. Conclusions

Figures (4)

  • Figure 1: The dependence of the LL BFKL gluon-gluon subprocess cross section on the dijet rapidity separation $\Delta y$, without (Eq. (\ref{['kintsol']}), upper dashed line) and with (Eq. (\ref{['qmaxnaive']}), lower solid line) the $Q^2_{\rm max}$ cut. The 'data points' are the same quantities calculated using the BFKL Monte Carlo discussed in Section \ref{['sec:MCBFKL']}, with $\alpha_s$ fixed and no additional kinematic cuts. Also shown are the asymptotic $\Delta y\gg 1$ approximations, Eqs. (\ref{['asympsol']}) and (\ref{['asympmax']}). The parameter values are $\alpha_s = 0.164$, $\hbox{$E_\perp$} = 20$ GeV, $Q^2_{\rm max} = 1000$ GeV$^2$.
  • Figure 2: The dependence of the LL BFKL gluon-gluon cross section on $\Delta y$ in the standard Mueller-Navelet calculation (Eq. (\ref{['kintsol']})) (upper solid line) and on $Y$ for the D0 setup (Eq. (\ref{['qmaxcomb']})). Four curves are shown for the definition of $x$'s applied in the D0 analysis: Dashed line for the requirement $\Delta y>0$, dotted line for $\Delta y>2$, dash-dotted for $Q^2_{\rm max}$ of Eq. (\ref{['qmax2']}) and finally the lower, fat dash-dotted line for the asymptotic behaviour (Eq. (\ref{['asympcombmax']})) using $Q^2_{\rm max}$ of Eq. (\ref{['qmax2']}). The histograms are filled using the MC.
  • Figure 3: Dijet rates, as defined in Eq. (\ref{['ratedef']}), for various cuts ${\cal C}$. The cases of $\sqrt{S}=630$ GeV (left) and of $\sqrt{S}=1800$ GeV (right) are both considered. Dotted curves and circles have been rescaled by factor of 10 (left) and 50 (right). See the text for details.
  • Figure 4: The dependence of the gluon-gluon subprocess cross section on the offset ${\cal D}$, for fixed separation $\Delta y = 3$. The resummed prediction Eq. (\ref{['qmaxdelta']}) is shown as a solid line, with the results of the corresponding BFKL Monte Carlo calculation superimposed. The dash-dotted line is the LO contribution, and the dashed line is the ${\cal O}(\alpha_s)$ contribution of Eq. (\ref{['expdeltasol']}). The parameter values are $\alpha_s = 0.164$, $\hbox{$E_\perp$} = 20$ GeV, $Q^2_{\rm max} = \infty$.