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I. Scimemi, with Ambar Jain and Iain Stewart, MIT, Cambridge. The top quark jet mass at 2 loops. 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
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I. Scimemi, with Ambar Jain and Iain Stewart, MIT, Cambridge The top quark jet mass at 2 loops
Extract mt from jet reconstruction with precision “in principle” less than ΛQCD ►Define an observable sensitive to mt ►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 Target
The relevant scales are Q,m,G,LQCD The physical picture Fleming, Hoang, Mantry, Stewart ArXiv:0703.207
Observables The main observable is Where And
Q-scale out Calculable perturbatevely m-scale out We want this at 2 loops
Most of results for tree-l and 1-L shown by A. Hoang. B at 2-loops The calculation of this part now completed=Finite part of 2-loop diagrams.
The Lagrangian for (b)HQET In light cone coord. and Wilson lines
Tree level …and 2 loop Broadhurst, Grozin Wilson lines attach here!
The one loop integral have the form Integrals The 2 loop integrals have the form(solved with IBP)
Renormalization The Z(s,m) has the usual expansion in a
renormalization The 2-loop contribution due to one loop renormalization is obtained with convolutions
Anomalous dimension The consistency relations now involve convolutions..
Anomalous dimension 1-loop result 2-loop results
Properties of B 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 G
B at 2-loops: pole mass Plot for B(s, G, m=2 GeV) and pole mass B
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
Plot for B( , G, m=2 GeV) and jet mass B at 2-loops: jet mass B
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, arXiv0709.3519 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 and work in progress). modeling the soft function
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. Conclusions