Energy Flow in Interjet Radiation

TL;DR

This work develops a perturbative framework to predict the distribution of transverse energy flowing into a region between high-$p_T$ jets in hadronic collisions. By factorizing the cross section into PDFs, a hard-scattering matrix, and a soft function described by Wilson-line operators, the authors perform leading-log resummation in $Q_\Omega/p_T$ via renormalization-group evolution in color space, providing explicit LO hard/soft matrices for key partonic channels. The approach yields predictions for the energy-flow ratio $\rho$ in a valence-quark approximation and shows how interjet radiation encodes color-flow information and can probe underlying event dynamics. The study highlights the role of non-global logarithms and outlines future work to extend beyond the valence approximation and to include more complex radiation patterns between jets.

Abstract

We study the distribution of transverse energy, Q_Omega, radiated into an arbitrary interjet angular region, Omega, in high-p_T two-jet events. Using an approximation that emphasizes radiation directly from the partons that undergo the hard scattering, we find a distribution that can be extrapolated smoothly to Q_Omega=Lambda_QCD, where it vanishes. This method, which we apply numerically in a valence quark approximation, provides a class of predictions on transverse energy radiated between jets, as a function of jet energy and rapidity, and of the choice of the region Omega in which the energy is measured. We discuss the relation of our approximation to the radiation from unobserved partons of intermediate energy, whose importance was identified by Dasgupta and Salam.

Figures (6)

• Figure 1: Diagrams for the calculation of the anomalous dimension matrix, as in Eq. ( \ref{['omegaVint']}). The double lines represent eikonal propagators, linked by vertices $c_I^{\rm (f)}$ and $c_L^{\rm (f)}{}^*$, in the amplitude and its complex conjugate. The vertical line represents the final state.
• Figure 2: Color identity corresponding to Eq. ( \ref{['identity']}).
• Figure 3: Real and imaginary parts of $E_{\alpha\beta}$ for $q \bar{q} \rightarrow q \bar{q}$ with $\Omega$ chosen as in Eq. ( \ref{['patchdef']}), with $\phi_{min} = \pi/4$, $\phi_{max}=3\pi/4$, and $\eta_{max} = -\eta_{min} = 1$. For the real parts we plot only the diagonal elements, ${ \hbox{Re}} E_{\alpha \alpha}$, since the interference terms, ${ \hbox{Re}} E_{\alpha \beta}$ with $\alpha\ne\beta$, are just the averages of the former. Note ${ \hbox{Im}} E_{\alpha \alpha}=0$, and that for an $n\times n$ anomalous dimension matrix, only $n-1$ imaginary parts of the $E_{\alpha\beta}$ with $\alpha\ne \beta$ are independent.
• Figure 4: Real and imaginary parts of $E_{\alpha\beta}$ for $q \bar{q} \rightarrow g g$.
• Figure 5: The distributions $\rho(x=Q_\Omega/p_T)$ for the region $\Omega$ defined in Sec. 4.1, with the observed jet at $\eta=0$ with $\mu_F = p_T = 50$, 300 and 500 GeV. This calculation was carried out in valence quark approximation for ${\rm p\bar{p}}$ scattering, at ${ \sqrt{s}=1.8}$ TeV.