Threshold Hadronic Event Shapes with Effective Field Theory

Abstract

Hadronic event shapes, that is, event shapes at hadron colliders, could provide a great way to test both standard and nonstandard theoretical models. However, they are significantly more complicated than event shapes at e\(^+\)e\(^-\) colliders, involving multiple hard directions, multiple channels, and multiple color structures. In this paper, hadronic event shapes are examined with soft-collinear effective theory (SCET) by expanding around the dijet limit. A simple event shape, threshold thrust, is defined. This observable is global and has no free parameters, making it ideal for clarifying how resummation of hadronic event shapes can be done in SCET. Threshold thrust is calculated at next-to-leading fixed order (NLO) in SCET and resummed to next-to-next-to-leading logarithmic (NNLL) accuracy. The scale-dependent parts of the soft function are shown to agree with what is expected from general observations, and the factorization formula is explicitly shown to be renormalization group invariant to 1-loop. Although threshold thrust is not itself expected to be phenomenologically interesting, it can be modified into a related observable which allows the jet p\(_T\) distribution to be calculated and resummed to NNLL+NLO accuracy. As in other processes, one expects resummation to be important even for moderate jet momenta due to dynamical threshold enhancement. A general discussion of threshold enhancement and nonglobal logs in hadronic event shapes is also included.