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Y. Sumino (Tohoku Univ.)

Development in theory of heavy quarkonia and precision determination of heavy quark masses. Y. Sumino (Tohoku Univ.). ☆ Plan of Talk. Before 1998: Theoretical problem IR renomalon Around 1998: Drastic improvement Discovery of cancellation of renormalons Interpretation

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Y. Sumino (Tohoku Univ.)

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

  2. ☆Plan of Talk Before 1998: Theoretical problem IR renomalon Around 1998: Drastic improvement Discovery of cancellation of renormalons Interpretation 3. After 1998: Theoretical development and applications EFT, higher-order calc. Spectroscopy Determinations ofmb, mc (mt) Determination of as Physical picture (gluon config.)

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

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

  5. 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:

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

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

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

  9. 3. After 1998: Theoretical development and Applications EFT, higher-order calc. Spectroscopy Determinations ofmb, mc (mt) Determination of as Physical picture (gluon config.)

  10. 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 In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: (prediction) (exp.09) • Relation between lattice and MS is accurately measured (quenched approx.) • Y.S.

  11. 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 In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: (prediction) (exp.09) • Relation between lattice and MS is accurately measured (quenched approx.) • Y.S.

  12. 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 mt): Recksiegel, Y.S In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: (prediction) (exp.09) Brambilla, Y.S., Vairo • Relation between lattice and MS is accurately measured (quenched approx.) • Y.S.

  13. 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 b-physics (e.g. ) LHCb, Super-B factory • The only quark mass without MS mass in current PDG data • Test of MSSM prediction for Higgs mass at LHC What mass? cf. LHC ILC More generally, tests of Yukawa couplings at LHC and beyond.

  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 (also prospects for mt): Recksiegel, Y.S In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: (prediction) (exp.09) Brambilla, Y.S., Vairo • Relation between lattice and MS is accurately measured (quenched approx.) • Y.S.

  15. Particle Data Group 2010

  16. 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?

  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: • Brambilla, Y.S., Vairo Recksiegel, Y.S In particular, mass of is predicted correctly. Recksiegel, Y.S. However, mass of disagrees: (prediction) (exp.09) • Relation between lattice and MS is accurately measured (quenched approx.) • Y.S. • Brambilla,Tomo,Soto,Vairo

  18. ☆Summary Before 1998: Theoretical problem IR renomalon Around 1998: Drastic improvement Discovery of cancellation of renormalons Interpretation 3. After 1998: Theoretical development and applications EFT, higher-order calc. Spectroscopy Determinations ofmb, mc (mt) Determination of as Physical picture (gluon config.)

  19. m dependence and convergence of Mtt(1S)

  20. Interquark force

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

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