Flavor-Changing Non-Global Logarithms

TL;DR

Flavor-Changing Non-Global Logarithms tackles flavor-dependent non-global logarithms arising from soft ${q}\bar{q}$ emissions that cross jet boundaries. By expanding the leading NGLs as a series in the jet radius $R$ and deriving exact results through ${R^2}$, the authors show this truncation remains accurate to about ${\sim}5\%$ for ${R\le1}$, enabling practical analytic control. They introduce subtractive jet flavor (SJF), an infrared-safe modification of naive jet flavor achieved by subtracting the flavor-dependent NGLs, and validate the approach using fixed-order event generation (e.g., MadGraph) with explicit NNLO constructions and LO/NLO tests. The work outlines an all-orders perspective via large-${n_f}$ and small-${R}$ limits, suggesting a factorization-resummation program and establishing a robust benchmark for flavor-dependent NGLs in parton showers and phenomenology.

Abstract

Non-global logarithms are low energy correlations between the substructure of a jet and the event in which it is immersed. We study the leading non-global logarithms that arise from soft quark--anti-quark emission and calculate their coefficient as a series in the jet radius, $R$, in arbitrary processes. We calculate the exact coefficient through quadratic order in $R$, and show that this truncation is within $5\%$ of the complete result for radii up to $R = 1$. These quark flavor-dependent non-global logarithms are also responsible for the infrared unsafety of a naïve definition of jet flavor that is simply the net sum of quark flavors in the jet of interest. We propose a small modification of this naïve jet flavor that we call subtractive jet flavor in which the problematic soft logarithms are explicitly subtracted. We further demonstrate how our analytic results can be interfaced with automated numerical fixed-order codes to extract subtractive jet flavor cross sections.

Figures (5)

• Figure 1: Illustration of the configuration we study in this paper in which non-global logarithms from soft quark emission appear. All particles in the jet of interest are red, and the jet's region in the experiment is the dashed cone. A soft gluon is emitted, which subsequently splits to a quark $q$ and anti-quark $\bar{q}$ pair. The quark lands in the jet, while the anti-quark does not.
• Figure 2: Illustration of the non-analytic structure within the contour (solid black) about the unit circle in the complex $z=e^{i\phi_2}$ plane. There is a pole located at $z_*=\min[e^{-\eta_2},e^{\eta_2}]$ (cross) and logarithmic branch cuts (dashed) along the line segments $z_\text{$A$,cut}\in\left[0,e^{i\phi_A}\min[e^{\eta_2-\eta_A},e^{-\eta_2+\eta_A}]\right]$ and $z_\text{$B$,cut}\in\left[0,e^{i\phi_B}\min[e^{\eta_2-\eta_B},e^{-\eta_2+\eta_B}]\right]$.
• Figure 3: Comparisons of the order-$R^2$ truncation of the flavor-dependent non-global logarithms in $pp\to V+j$ events versus the complete contribution as calculated through numerical integration, as a function of the jet radius $R$. Left: The term proportional to ${\bf T}_J^2$, the Casimir of the jet. Right: The term proportional to ${\bf T}_A^2+{\bf T}_B^2$, the sum of Casimirs of the colliding beams.
• Figure 4: Plot of the leading order cross section for $(bu)$ jet flavor from $pp\to W^+bu$ events with $p_{\perp,W} > 1000$ GeV, as generated in MadGraph v3.6.4. The jet contributes to the cross section for this flavor if the $b$ and $u$ are clustered within the jet radius $R$.
• Figure 5: Plots comparing the cross sections for non-global quark configurations in the process $pp\to W^+bu\bar{u}$, as a function of the transverse momentum cut $p_{\perp,\text{cut}}$ on the light quarks. Three values of the jet radius about the direction of the $b$ quark are considered: $R=0.8$ (upper left), $R=0.5$ (upper right), and $R=0.2$ (bottom). Cross sections calculated from MadGraph sampling $10^4$ phase space points are plotted in blue with numerical uncertainty included, while the solid red line is two times the non-global logarithm prediction of Eq. \ref{['eq:nglpred']}, plus a constant offset cross section. All quantities are expressed as a fraction of the leading-order cross section of the process $pp\to W^+b$, Eq. \ref{['eq:lowb']}.