Flow between extremal one-point energy correlators in QCD

Abstract

The energy density generated by a vector current is characterized by a single parameter $a_{\mathcal{E}}$ bounded by unitarity to $-1/2 \leq a_{\mathcal{E}} \leq 1$, with extremal values saturated by free theories of different matter content. Through confinement, QCD transmutes fermionic matter into scalars, revealing a nontrivial flow between extremal correlators. We reconstruct this flow using perturbative QCD and chiral perturbation theory. The observable is accessible with currently available experimental data.

Figures (3)

• Figure 1: QCD flow for $a_{\mathcal{E}}$ between the fermionic (UV, $a_{\mathcal{E}}\to -1/2$) and bosonic (IR, $a_{\mathcal{E}}\to 1$) extremal correlators. The gray region is forbidden by unitarity. The black solid line shows the predictions from $\chi$PT and data-driven methods. Spread of black lines shows the uncertainty associated with missing hadronic channels. The colored lines represent the N${}^k$LO predictions in perturbative QCD (pQCD), with line spread given by the uncertainty associated with $m_c$, $m_b$, $\alpha_s(m_Z^2)$ and the renormalization scale $\mu$. We indicate the charmonium and bottomonium regions. Experimental measurements of Table \ref{['tab:aE_measurements']} are shown.
• Figure 2: Left: Total cross section for $e^+e^-\rightarrow \text{hadrons}$ and decomposition into subprocesses. The solid black line is total sum of six sub-processes by the Monte Carlo simulation with PHOKHARA 10.0. The red dots were extracted from $R$ ratio in PDG data. Difference between both curves is due to other channels becoming important. Right: evolution of $a_{\mathcal{E}}$ of the one-point correlator for individual processes. The pair-production of pseudoscalars, $e^+e^-\rightarrow \pi^+\pi^-$, $K^+K^-$, $K^0 \bar{K^0}$, all saturate the upper limit of $a_{\mathcal{E}} = 1$, while $e^+e^-\to 3\pi$ saturates the lower limit $a_{\mathcal{E}}=-1/2$.
• Figure 3: Relative weight of the hadronic channels between $1.12\,\text{GeV}$ and $1.936\,\text{GeV}$. The colors group channels into 4 groups, depending on the value of $a_{\mathcal{E}}$ for those.