Event Shape/Energy Flow Correlations

TL;DR

This work develops a general framework to study correlations between interjet energy flow and event shapes in $e^+e^-$ dijet events. By introducing a tunable event-shape class $ar f(a)$ and correlating it with energy flow into an interjet region via a Laplace transform, the authors construct a factorized cross section that can be resummed in both the energy-flow variable and the event-shape variable. They derive the all-orders factorization into hard, jet, and soft functions, establish RG equations for resummation, and present explicit NLL results for the shape/flow correlations, including a clean recovery of the thrust resummation at $a=0$. Numerical results illustrate the behavior of the correlations with respect to the jet geometry, the transform parameter $ u$, and the jet flavor, demonstrating controlled global logarithms and suppression of nonglobal effects. The approach provides a versatile tool for probing color flow in jet events and lays groundwork for applications to more complex processes and hadronic collisions.

Abstract

We introduce a set of correlations between energy flow and event shapes that are sensitive to the flow of color at short distances in jet events. These correlations are formulated for a general set of event shapes, which includes jet broadening and thrust as special cases. We illustrate the method for electron-positron annihilation dijet events, and calculate the correlation at leading logarithm in the energy flow and at next-to-leading-logarithm in the event shape.

Figures (8)

• 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 can give non-global logarithms.
• Figure 2: A kinematic configuration that gives rise to the non-global logarithms. A soft gluon with momentum $k$ is radiated into the region $\Omega$, and an energetic gluon with momentum $l$ is radiated into $\bar{\Omega}$. Four-vectors $\beta_1$ and $\beta_2$, define the directions of jet 1 and jet 2, respectively.
• Figure 3: The relevant two-loop cut diagrams corresponding to the emission of two real gluons in the final state contributing to the eikonal cross section. The dashed line represents the final state, with contributions to the amplitude to the left, and to the complex conjugate amplitude to the right.
• Figure 4: Factorized cross section (\ref{['factor']}) after the application of Ward identities. The vertical line denotes the final state cut.
• Figure 5: Differential cross section $\frac{\varepsilon d \sigma/(d\varepsilon d\hat{n}_1)}{d \sigma_0/d \hat{n}_1}$, normalized by the Born 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 ring (slice) centered around the jets, with a width of $\Delta \eta = 2$.