The top quark jet mass at 2 loops Radcor2007, Firenze I. Scimemi, with Ambar Jain and Iain Stewart, MIT, Cambridge The top quark jet mass at 2 loops

Radcor2007, Firenze Target 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

The physical picture The relevant scales are Q,m,G,LQCD Radcor2007, Firenze The physical picture The relevant scales are Q,m,G,LQCD Fleming, Hoang, Mantry, Stewart ArXiv:0703.207

Observables The main observable is Where And Radcor2007, Firenze

Radcor2007, Firenze Factorization scheme

Q-scale out m-scale out We want this at 2 loops Radcor2007, Firenze Q-scale out Calculable perturbatevely m-scale out We want this at 2 loops

B at 2-loops Most of results for tree-l and 1-L shown by A. Hoang. Radcor2007, Firenze B at 2-loops 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.

The Lagrangian for (b)HQET In light cone coord. and Wilson lines Radcor2007, Firenze

Wilson lines attach here! Radcor2007, Firenze Tree level …and 2 loop Broadhurst, Grozin Wilson lines attach here!

Integrals The one loop integral have the form Radcor2007, Firenze Integrals The one loop integral have the form The 2 loop integrals have the form (solved with IBP)

Renormalization The Z(s,m) has the usual expansion in a Radcor2007, Firenze Renormalization The Z(s,m) has the usual expansion in a

Radcor2007, Firenze renormalization The 2-loop contribution due to one loop renormalization is obtained with convolutions

Radcor2007, Firenze Anomalous dimension The consistency relations now involve convolutions..

Radcor2007, Firenze Anomalous dimension 1-loop result 2-loop results

Properties of B One can calculate B for a stable top quark Radcor2007, Firenze 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 B Plot for B(s, G, m=2 GeV) and pole mass Radcor2007, Firenze B at 2-loops: pole mass Plot for B(s, G, m=2 GeV) and pole mass B

Definition of the jet mass Radcor2007, Firenze Definition of the jet mass RADCOR2007

Jet Mass Both the MSb mass and the jet mass are renormalon free. Radcor2007, Firenze 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

B at 2-loops: jet mass B Plot for B( , G, m=2 GeV) and jet mass Radcor2007, Firenze B at 2-loops: jet mass Plot for B( , G, m=2 GeV) and jet mass B

Radcor2007, Firenze Jet mass and MS mass

Convolution with the soft function Radcor2007, Firenze Convolution with the soft function

modeling the soft function Radcor2007, Firenze modeling the 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, 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).

Radcor2007, Firenze Conclusions 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. RADCOR2007

Radcor2007, Firenze Thanks