Abstract
Many collider observables suffer from non-global logarithms not captured by standard resummation techniques. Classic examples are the light-jet mass event shape in the limit of small mass and the related hemisphere soft function. We derive factorization formulas for both of these and explicitly demonstrate that they capture all logarithms present at NNLO. These formulas achieve full scale separation and provide the basis for all-order resummations. A characteristic feature of non-global observables is that the soft radiation is driven by multi-Wilson-line operators, and the ones arising here map onto those relevant for the case of narrow-cone jet cross sections. Numerically, the contributions of non-global logarithms to resummed hemisphere-mass event shapes are sizeable.
Highlights
Energy flow is an example of a non-global observable
Using an efficient new method to perform the angular integrations [15], this result has been extended to 12 (!) loops [16].1. In addition to these fixed-order considerations, a method to approximately resum the non-global logarithms was proposed [17, 18]. At leadinglogarithmic accuracy it reduces to an iterative solution of the BMS equation [19]
In our effective-field-theory framework, the non-global logarithms are obtained from an RG-evolution equation which generalizes the BMS equation to arbitrary logarithmic accuracy
Summary
The derivation of the factorization formula follows the same steps in both cases and is similar to the one relevant for wide-angle cone-jet cross sections presented in [20]. We will first sketch the derivations of the theorems and specify the ingredients. We relate the soft functions to the ones which arise in the case of the narrow-cone jet cross sections. Due to this relation, we can use the results [20] for these and only the hard functions need to be computed
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