I. Scimemi, with Ambar Jain and Iain Stewart, MIT, Cambridge 1 EF07,Paris

Extract m t from jet reconstruction with precision “in principle” less than Λ QCD ►Define an observable sensitive to m t ►Identify the physical scales of the problem ►parameterize soft gluons ►calculate perturbative pieces ►Including top’s width effects, Γt~1.4 GeV For the moment we look at Main formalism in the talk of A. Hoang 2 EF07,Paris

The relevant scales are Q,m,  QCD Fleming, Hoang, Mantry, Stewart ArXiv: EF07,Paris

The main observable is Where And 4 EF07,Paris

5

We want this at 2 loops Calculable perturbatevely 6 EF07,Paris

Most of results for tree-l and 1-L shown by A. Hoang. The calculation of this part now completed=Finite part of 2-loop diagrams. 7 EF07,Paris

and In light cone coord. Wilson lines 8 EF07,Paris Note that m j cannot be Msbar otherwise power counting is violated Inclusive in decay productsMass scheme choice

Tree level …and 2 loop Wilson lines attach here! Broadhurst, Grozin 9 EF07,Paris

The one loop integral have the form The 2 loop integrals have the form (solved with IBP) 10 EF07,Paris

The Z(s,  ) has the usual expansion in  11 EF07,Paris

The 2-loop contribution due to one loop renormalization is obtained with convolutions 12 EF07,Paris

The consistency relations now involve convolutions.. 13 EF07,Paris

1-loop result 2-loop results 14 EF07,Paris

It is possible to express B with a dispersion relation  One can calculate B for a stable top quark  The RGE are the same for stable and unstable tops  The smearing introduces explicitly a new scale  15 EF07,Paris

Plot for  (s,  GeV) and pole mass  16 EF07,Paris Preliminary

17 EF07,Paris The position of the peak does not change linearly under evolution

EF07,Paris 18 The mass so defined in this way has the correct linear properties when evolving

EF07,Paris 19 Plot for  (,  L=1  GeV) and jet mass 

Both the MSb mass and the jet mass are renormalon free. The MSb mass is known at 3 loops. Now the jet mass at 2 loops. Numerically the loop corrections to mj are much smaller than the loop corrections to MSb- mass 20 EF07,Paris

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22 EF07,Paris In order to get the final result one has still to do the convolution with soft function

In order to have contact with data we must perform a convolution with a soft function. An interesting model presented recently by A. Hoang and I. Stewart, arXiv The main features are,  This model wants to be valid both in the peak region and in the tail.  The convolution of J’s and S scale like a local object.  For consistency, the renormalon ambiguity in the partonic part and in the jet function should be removed (see A. Hoang talk). 23 EF07,Paris

We have analyzed the jet function at 2 loops using EFT. The matching of the jet mass with pole and MSb mass is now ready at 2 loops order, as well as anomalous dimension. For a complete 2 loops result also the partonic part of the soft function should be calculated at the same order. Next Step: The extension of this formalism for LHC top production. 24 EF07,Paris

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Plot for  (,  GeV) and jet mass  26 EF07,Paris