1. Y. Sumino (Tohoku Univ.) Development in theory of heavy quarkonia and precision determination of heavy quark masses

2. ☆ Plan of Talk 1. Before 1998: Theoretical problem IR renomalon 2. Around 1998: Drastic improvement Discovery of cancellation of renormalons Interpretation 3. After 1998: Theoretical development and applications EFT, higher-order calc. Spectroscopy Determinations of m b, m c (m t ) Determination of  s Physical picture (gluon config.)

5. Folklore: pert., non-pert. Inconsistency with OPE for: non-pert. Brambilla, Pineda, Soto, Vairo tree 2-loop 1-loop

6. Asymptotically = Most dominant part is indep. of !  n-th term of -V LL ill defined Renormalon in the QCD potential Aglietti, Ligeti

7. Pineda Hoang,Smith,Stelzer,Willenbrock Beneke Accuracy of perturbative predictions for the QCD potential improved drastically around year 1998. If we re-express the quark pole mass ( ) by the MS mass ( ), IR renormalons cancel in. cancel Expanding for small, the leading renormalons cancel. much more convergent series Residual renormalon:

8. Leading log approximation Exact pert. potential up to 3 loops Anzai,Kiyo,Y.S. N=0 N=3

9. Y.S. pert., non-pert. Folklore ruled out

12. Rapid growth of masses of excited states originates from rapid growth of self-energies of Q & Q due to IR gluons. Brambilla, Y.S., Vairo

13. 3. After 1998: Theoretical development and Applications EFT, higher-order calc. Spectroscopy Determinations of m b, m c (m t ) Determination of  s Physical picture (gluon config.)

14. Application to quarkonium spectroscopy and determination of. Global level structure of bottomonium is reproduced. Brambilla, Y.S., Vairo Fine and hyperfine splittings of charmonium/bottomonium reproduced. Determination of bottom and charm quark MS masses: Brambilla, Y.S., Vairo In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: Relation between lattice and MS is accurately measured (quenched approx.) Y.S. Recksiegel, Y.S (prediction) (exp.09)

16. Application to quarkonium spectroscopy and determination of. Global level structure of bottomonium is reproduced. Brambilla, Y.S., Vairo Fine and hyperfine splittings of charmonium/bottomonium reproduced. Determination of bottom and charm quark MS masses: Brambilla, Y.S., Vairo In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: Relation between lattice and MS is accurately measured (quenched approx.) Y.S. Recksiegel, Y.S (prediction) (exp.09)

17. Application to quarkonium spectroscopy and determination of. Global level structure of bottomonium is reproduced. Brambilla, Y.S., Vairo Fine and hyperfine splittings of charmonium/bottomonium reproduced. Determination of bottom and charm quark MS masses (also prospects for m t ): In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: Relation between lattice and MS is accurately measured (quenched approx.) Y.S. Recksiegel, Y.S (prediction) (exp.09) Brambilla, Y.S., Vairo

18. Motivation for precision determinations of heavy quark masses Bottom quark Top quark Constraints on b  mass ratio of SU(5) GUT models Input param. for b  physics (e.g. ) LHC b, Super-B factory The only quark mass without MS mass in current PDG data Test of MSSM prediction for Higgs mass at LHC More generally, tests of Yukawa couplings at LHC and beyond. cf. LHC ILC What mass?

19. Application to quarkonium spectroscopy and determination of. Global level structure of bottomonium is reproduced. Brambilla, Y.S., Vairo Fine and hyperfine splittings of charmonium/bottomonium reproduced. Determination of bottom and charm quark MS masses (also prospects for m t ): In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: Relation between lattice and MS is accurately measured (quenched approx.) Y.S. Recksiegel, Y.S (prediction) (exp.09) Brambilla, Y.S., Vairo

20. Particle Data Group 2010

21. Prospects for precision determination of m t from M tt (1S) Hoang, et al. Hagiwara,Y.S.,Yokoya Kiyo, et al. in the threshold region @ future Linear Collider (threshold region) @LHC significantly smaller than 1GeV?

22. Application to quarkonium spectroscopy and determination of. Global level structure of bottomonium is reproduced. Brambilla, Y.S., Vairo Fine and hyperfine splittings of charmonium/bottomonium reproduced. Determination of bottom and charm quark MS masses: Brambilla, Y.S., Vairo In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: Relation between lattice and MS is accurately measured (quenched approx.) Y.S. Brambilla,Tomo,Soto,Vairo Recksiegel, Y.S (prediction) (exp.09)

23. ☆ Summary 1. Before 1998: Theoretical problem IR renomalon 2. Around 1998: Drastic improvement Discovery of cancellation of renormalons Interpretation 3. After 1998: Theoretical development and applications EFT, higher-order calc. Spectroscopy Determinations of m b, m c (m t ) Determination of  s Physical picture (gluon config.)

24.  dependence and convergence of M tt (1S)

26. Interquark force

28. Wilson coeff. non-pert. contr. cancel Y.S. Including 3-loop QCD pot. Brambilla,Tomo,Soto,Vairo