1. 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

2. 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

3. 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:

4. Observables
The main observable is
Where
And
Radcor2007, Firenze

5. Radcor2007, Firenze
Factorization scheme

6. 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

7. 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.

8. The Lagrangian for (b)HQET
In light cone coord.
and
Wilson lines
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9. Wilson lines attach here!
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Tree level
…and 2 loop
Broadhurst, Grozin
Wilson lines attach here!

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

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

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

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

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

15. 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

16. 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

17. Definition of the jet mass
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Definition of the jet mass
RADCOR2007

18. Jet Mass Both the MSb mass and the jet mass are renormalon free.
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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. 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

20. Radcor2007, Firenze
Jet mass and MS mass

21. Convolution with the soft function
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Convolution with the soft function

22. modeling the soft function
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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, 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 and work in progress).

23. 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

24. Radcor2007, Firenze
Thanks