Flavor-changing nonglobal logarithms

Nonglobal logarithms are low energy correlations between the substructure of a jet and the event in which it is immersed. We study the leading nonglobal logarithms that arise from soft quark-antiquark emission and calculate their coefficient as a series in the jet radius, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>R</a:mi> </a:math> , in arbitrary processes. We calculate the exact coefficient through quadratic order in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>R</c:mi> </c:math> , and show that this truncation is within 5% of the complete result for radii up to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>R</e:mi> <e:mo>=</e:mo> <e:mn>1</e:mn> </e:math> . These quark flavor-dependent nonglobal 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 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.