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The top quark jet mass at 2 loops

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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The top quark jet mass at 2 loops

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

  2. 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

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

  4. Observables The main observable is Where And

  5. Factorization scheme

  6. Q-scale out Calculable perturbatevely m-scale out We want this at 2 loops

  7. 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.

  8. The Lagrangian for (b)HQET In light cone coord. and Wilson lines

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

  10. The one loop integral have the form Integrals The 2 loop integrals have the form(solved with IBP)

  11. Renormalization The Z(s,m) has the usual expansion in a

  12. renormalization The 2-loop contribution due to one loop renormalization is obtained with convolutions

  13. Anomalous dimension The consistency relations now involve convolutions..

  14. Anomalous dimension 1-loop result 2-loop results

  15. 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

  16. B at 2-loops: pole mass Plot for B(s, G, m=2 GeV) and pole mass B

  17. Definition of the jet mass

  18. 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

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

  20. Jet mass and MS mass

  21. Convolution with the soft function

  22. 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

  23. 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

  24. Thanks

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