Y. Sumino (Tohoku Univ.)

1. Understanding Heavy Quark-AntiQuark System by Perturbative QCD Y. Sumino (Tohoku Univ.)

2. Current Status of Static Potential 3-loop pert. QCD (fixed-order) vs. lattice comp. Anzai, Kiyo, YS

3. ☆Plan of Talk Before 1998: Theoretical problem IR renomalon Around 1998: Drastic improvement Discovery of cancellation of renormalons Interpretation 3. After 1998: Applications Spectroscopy Decays Determinations ofmb, mc (mt) Determination of as Gluon config. inside quarkonium Casimir scaling violation for static potential

4. Pineda, Soto

5. Titard, Yndurain; Pineda Yndurain

6. [GeV] tree 1-loop 2-loop Folklore: pert. , non-pert. Cf. Inconsist with OPE for: Brambilla, Pineda, Soto, Vairo

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 [GeV-1] Anzai,Kiyo,Y.S. N=3 N=0 N=0 N=3 [GeV-1] Exact pert. potential up to 3 loops

9. Y.S. Validity range of pert. prediction extends to larger at higher orders. Folklore ruled out pert. , non-pert.

10. m dependence and convergence of Mtt(1S) General feature of QCD beyond large b0or leading-log approx. . Couples to total charge as

11. m dependence and convergence of Mtt(1S) General feature of QCD beyond large b0or leading-log approx. . Couples to total charge as

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

15. Brambilla,YS,Vairo Recksiegel,YS

16. A ‘Coulomb+Linear potential’ is obtained by resummation of logs: YS Free of IR renormalons Pert. prediction valid at

17. A ‘Coulomb+Linear potential’ is obtained by resummation of logs: YS Coulombic pot. with log corr. at short-dist. Coefficient of linear pot.

18. 3. After 1998: Many Applications Spectroscopy Decays Determinations ofmb, mc (mt) Determination of as Gluon config. inside quarkonium Casimir scaling violation for static potential

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: • Brambilla, Y.S., Vairo Recksiegel, Y.S • Two exceptions in ~2003: • charmoniumhyperfine splitting • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Two exceptions in ~2003: Recksiegel, Y.S.; Kniehl, Penin, • charmoniumhyperfine splitting Pineda, Smirnov, Steinhauser • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) Y.S. • Brambilla, Petreczky, Tormo, Soto, Vairo

21. 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 Recksiegel, Y.S • Two exceptions in ~2003: Recksiegel, Y.S.; Kniehl, Penin, • charmoniumhyperfine splitting Pineda, Smirnov, Steinhauser • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) Y.S. • Brambilla, Petreczky, Tormo, Soto, Vairo

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 Recksiegel, Y.S • Two exceptions in ~2003: • charmoniumhyperfine splitting • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Two exceptions in ~2003: Recksiegel, Y.S.; Kniehl, Penin, • charmoniumhyperfine splitting Pineda, Smirnov, Steinhauser • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) Y.S. • Brambilla, Petreczky, Tormo, Soto, Vairo

24. 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 Recksiegel, Y.S • Two exceptions in ~2003: • charmoniumhyperfine splitting • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Two exceptions in ~2003: Recksiegel, Y.S.; Kniehl, Penin, • charmoniumhyperfine splitting Pineda, Smirnov, Steinhauser • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) Y.S. • Brambilla, Petreczky, Tormo, Soto, Vairo

25. Motivation for precision determinations of heavy quark masses • Bottom quark • Top quark • Constraints on b-tmass ratio of SU(5) GUT models • Input param. for bphysics: e.g. ) LHCb, Super-B factory • The only quark mass without MS mass in current PDG data. • Tests of Yukawa coupling at LHC and beyond. What mass? cf. LHC ILC

26. Particle Data Group 2012

27. Prospects for precision determination of mtfrom Mtt(1S) Hagiwara,Y.S.,Yokoya Kiyo, et al. Hoang, et al. in the threshold region @ future Linear Collider (threshold region) @LHC significantly smaller than 1GeV?

28. 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 Recksiegel, Y.S • Two exceptions in ~2003: • charmoniumhyperfine splitting • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Two exceptions in ~2003: Recksiegel, Y.S.; Kniehl, Penin, • charmoniumhyperfine splitting Pineda, Smirnov, Steinhauser • bottomonium hyperfine splitting • Solved in favor of pert. QCD predictions. • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) • Relation between lattice and MS being accurately measured • (realistic precision determination in near future) Y.S. • Brambilla, Petreczky, Tormo, Soto, Vairo

30. ☆Energy density surrounding heavy quarks

31. Markum,Faber Campbell,Jorysz,Michael Deldar Bali ….. supported by lattice measurements Casimir scaling hypothesis cf. 2nd Casimir op. for rep. R 2-loop by cancel protected by C-inv. 3-loop Anzai, Kiyo, YS Casimir scaling violation Tiny violation predicted, compatible with current lattice data.

32. ☆Summary • Before 1998: Theoretical problem • IR renomalon • Around 1998: Drastic improvement • Discovery of cancellation of renormalons • Interpretation, a linear rise at • 3. After 1998: Applications • Spectroscopy • Decays • Determinations ofmb, mc (mt) • Determination of as • Gluon config. inside quarkonium • Casimir scaling violation for static potential

33. Renormalon in the QCD potential Aglietti, Ligeti n-th term of -VLL ~L ill defined Asymptotically = Most dominant part is indep. of !

36. Interquark force

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

39. Brambilla,YS,Vairo Recksiegel,YS

40. for