Seeing through the confinement screen: DGLAP/BFKL mixing and light-ray matching in QCD

Abstract

We argue that collider observables such as hadron number flux can be matched onto a linear combination of detectors/light-ray operators in perturbative QCD. The spectrum of detectors in QCD is subtle, due to recombination between the DGLAP and BFKL trajectories. We explain how to define and renormalize these trajectories at one-loop, systematically incorporating their recombination. The leading and subleading soft gluon theorems play an important role, and our analysis suggests the presence of an infinite series of further subleading soft theorems for squared-amplitudes/form factors. Combined with our light-ray matching hypothesis, the anomalous dimensions of recombined DGLAP/BFKL detectors yield a prediction for the energy dependence of the number of particles in a jet, as well as other predictions for more general energy-weighted hadron measurements. We compare these predictions to Monte-Carlo simulations, finding good agreement.

Figures (31)

• Figure 1: Detectors appearing in the EFT expansion (\ref{['eq:particlenumbermatching']}) of the particle number operator $\mathbb{N}(\vec{n})$ are obtained by drawing a vertical line (red) through the Chew-Frautschi plot at $J_L=2-d$, and tabulating its intersections (red circles) with Regge trajectories. Each detector gives a contribution like $(\Lambda_\mathrm{QCD}/Q)^{\Delta_L}$ to matrix elements of the particle number operator at high energies. Thus, the highest intersection gives the leading contribution at large $Q$. For the purposes of illustration, we show part of the Chew-Frautschi plot of pure YM theory in $d=4$ at one-loop --- the full Chew-Fratuschi plot of QCD will have an infinite number of additional trajectories. Recombination of the DGLAP and BFKL trajectories (dashed gray lines) creates an enhanced correction (\ref{['eq:crazysquareroot']}) to $\Delta_L$ for the leading detector.
• Figure 2: A plot of $1-\Delta_L$ as a function of $\nu=-1-J_L$, determined via (\ref{['eq:mapoutcfplot']}) for simulated $\gamma^*$ and $h^*$ decay in Pythia. The 1-loop analytical results for the recombined trajectories (taking into account uncertainties in the choice of matching scale) are shown in light blue.
• Figure 3: The Penrose diagram of the construction of the gluon DGLAP detector from two field strength tensors $F$ at future null infinity $\mathscr{I}^+$.
• Figure 4: The Feynman diagrams of the DGLAP detector for (a) gluon case, (b) quark case, and (c) anti-quark case.
• Figure 5: Feynman diagrams and corresponding Feynman rules for the composite operators $\mathcal{O}$ and $J_\mu$, with the convention of all-outgoing momenta. Diagrams (\ref{['fig:diagrama']}) and (\ref{['fig:diagramb']}) represent the $g^0$ and $g^1$ contributions to $\mathcal{O}$, respectively, while the $g^2$ contribution is not shown. In diagram (\ref{['fig:diagramb']}), permutations refer to cyclic permutations of the triplets $\{a,\mu,k_1\}$, $\{b,\nu,k_2\}$, and $\{c,\rho,k_3\}$. Diagram (\ref{['fig:diagramc']}) shows the Feynman rule for the current operator $J_\mu$.