1. The top quark, effective operators, FCNC and the LHC Rui Santos (U. Southampton) WHEPP XI, Ahmedabad 2010

2. the past: - Indirect limits – cross sections converted to branching ratios - Direct limits – from top decays (Tevatron only) Do indirect limits have any meaning? Can we do slightly better?

3. the (1/fb) future:

4. the (100/fb) future:

5. Any hint of FCNC welcome FCNC (top) in the SM and beyond Very old table from J. Aguilar-Saavedra– anyone has a new column to add?

6. X strong electroweak Effective operator approach Λ is the scale of new physics. The X particle is from a new untested model (the same SM particles in the external lines). It can have the same or a different Lorentz structure. All terms are invariant under the SM gauge group.

7. Operators and observables In a simple world, in the top FCNC case suppose we had only three observables and three operators! However… …this is not the case. Therefore we have to find as many physical observables as possible. The number of operators we already know is huge. Even in this simple case we need ● Great precision from the theoretical side ● Great precision from the experimental side to look for the small deviations from the SM.

8. Different from the usual approach used by experimentalists (which will be different in top physics at the LHC): a) write a piece of a lagrangian that contains your favorite interaction b) search for some final state with a diagram that contains the anomalous vertex c) further reduce the number of free parameters by setting for instance f=h d) using the experimental result, set a bound on the remaining constant

9. Why is it different? a) take the operators (there are much more) c) contribution to single top production b) contribution to FCNC top decays

10. Why is it different? e) contribution to top + gauge boson f) and to non-FCNC top decays d) and to t tbar production

11. 1. Write all possible dimension 6 operators that have at least one top quark DIY - a minimal set of effective operators for top physics Complete list of dimension 6 effective operators: Buchmüller e Wyler, Nucl. Phys. B268 (1986) 621. 2. Use equations of motion to further reduce the number of operators

12. 3. or don't use them and instead use the freedom to check your results

13. 4. if you include 4-fermion operators you loose the beautiful proportionality

14. Results 1. single top FCNC production (in pb) is not only direct production DIRECT GLUON-GLUON GLUON-QUARK Surprisingly the cross is proportional to the branching ratio (these results are for "strong" operators only)

15. Results 2. 4-fermion operators spoils the beautiful proportionality to the BR

16. Results 3. Including the "electroweak" opeartors - It can be strong or electroweak electroweakstrong The electroweak sector can be probed even if the strong sector is negligible. Excess in the cross section could be wrongly interpreted as coming from FCNC in the strong sector. The numbers have to be added to the SM cross section.

17. Results 3a. Tevatron LHC10 and LHC14

18. Results 4. Electroweak or strong? Look for observables that distinguish electroweak from strong effective couplings. Sector where new physics comes from can (sometimes) be tested

19. Results 5. relating observables 1. Use the Tevatron results for single top production. 2. B physics constraints from "Deciphering top flavor violation at the LHC with B factories" Fox et al,Phys. Rev. D78 054008, 2008. Tevatron bound

20. Discussion This looks good but… How to distinguish between the different operators? How model independent is the approach? What is the scale of new physics we are probing? Where do we find theories that predict large FCNC related to top? Anomalous non-FCNC effective couplings can be used for the Tevatron asymmetry – what can we say with the effective theory approach?

21. Thank you