Interjet Energy Flow/Event Shape Correlations

TL;DR

This paper develops a perturbative framework to quantify interjet energy flow in $e^+e^-$ dijet events by correlating it with event shapes. The approach uses factorization and resummation, combining hard, jet, and soft functions and applying Laplace transforms to resum logarithms of the energy flow variables while controlling non-global effects via shape weights. The authors derive a resummed expression for the $\varepsilon$ and $\nu$-dependent cross section and present numerical results showing how the observable depends on the event-shape parameter $a$ and the region $\Omega$, including a comparison between quark- and gluon-initiated jets. These results provide analytic insight into the link between color flow and energy radiation and suggest extensions to multijet or hadronic collisions.

Abstract

We identify a class of perturbatively computable measures of interjet energy flow, which can be associated with well-defined color flow at short distances. As an illustration, we calculate correlations between event shapes and the flow of energy, Q_Omega, into an interjet angular region, Omega, in high-energy two-jet e^+e^- -annihilation events. Laplace transforms with respect to the event shapes suppress states with radiation at intermediate energy scales, so that we may compute systematically logarithms of interjet energy flow. This method provides a set of predictions on energy radiated between jets, as a function of event shape and of the choice of the region Omega in which the energy is measured. Non-global logarithms appear as corrections. We apply our method to a continuous class of event shapes.

Figures (5)

• Figure 1: Sources of global and non-global logarithms in dijet events. Configuration 1, a primary emission, is the source of global logarithms, configuration 2 results in non-global logarithms.
• Figure 2: Illustration of the effect of the parameter $a$ in the weight (\ref{['fbarexp']}) on the shape of the event: a) shape for $a = 1$, b) shape for $a = 0$, c) shape for $a = -1$. The jet axes are in the vertical direction. The radial normalization ($\bar{\varepsilon} Q$) is arbitrary, but the same for all three plots.
• Figure 3: Factorized cross section (\ref{['factor']}). The vertical line denotes the final state, separating the amplitude (to the left) and the complex conjugate amplitude (to the right).
• Figure 4: Differential cross section $\frac{\varepsilon d \sigma/(d\varepsilon d\hat{n}_1)}{d \sigma_0/d \hat{n}_1}$, normalized by the lowest order cross section, at $Q = 100$ GeV, as a function of $\varepsilon$ and $a$ at fixed $\nu$: a) $\nu = 10$, b) $\nu = 50$. $\Omega$ is a slice (ring) centered around the jets, with a width of $\Delta \eta = 2$.
• Figure 5: Ratios of differential cross sections for quark to gluon jets $\frac{C_A}{C_F} \left(\frac{\varepsilon d \sigma^q/(d\varepsilon d\hat{n}_1)}{d \sigma_0^q/d \hat{n}_1}\right) \left(\frac{\varepsilon d \sigma^g/(d\varepsilon d\hat{n}_1)}{d \sigma_0^g/d \hat{n}_1}\right)^{-1}$ at $Q = 100$ GeV as a function of $\varepsilon$ and $a$ at fixed $\nu$: a) $\nu = 10$, b) $\nu = 50$. $\Omega$, as in Fig. \ref{['num1']}, is a slice (ring) centered around the jets, with a width of $\Delta \eta = 2$.