Calculating jet mass beyond leading logarithmic order is an unsolved problem in QCD. There are many subtleties, such as non-global logs. This is work in progress, with some preliminary work (arXiv:1102.0561) by Randall Kelley, Matthew D. Schwartz and Hua-Xing Zhu.

Calculations of jet masses at hadron colliders are complicated by multiple scales: the jet mass m, the jet size R, the jet energy E and the outside of jet energy omega. The precition from SCET can be compared to theexact 2-loop distribution. They should agree in the singular region. Taking the difference we find

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

that the curves don't go to zero on the left side implies there are large logarithms of tau_omega which are not being correctly reproduced in the singular limit. In general, it seems impossible to calculate jet masses to high presision.

However, in (arXiv:1102.0561) it was argued that it was argued that in the small R limit, the factorization simplifies. In particular, the soft function refactorizes

 

In addition, we propsed the anomalous dimension splits in a particular way. We call this the Gamma_cusp ansatz. With this ansatz, the approach to zero is even better:

Additional plots can be seen here for jet mass constructed with the Cambridge/Aachen algorithm and here for jet mass constructed with a simple cone algorithm centered on the thrust axis.