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Heavy Quark Masses Review

Heavy Quark Masses Review. Outline. Remarks on heavy quark masses Mass schemes Charm and Bottom Mass Determinations Relativistic Sum Rules Conclusions. Remarks on Quark Masses. possible.

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Heavy Quark Masses Review

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  1. Heavy Quark Masses Review Vxb Workshop, SLAC, Oct 29 - 31, 2009

  2. Outline • Remarks on heavy quark masses • Mass schemes • Charm and Bottom Mass Determinations • Relativistic Sum Rules • Conclusions Vxb Workshop, SLAC, Oct 29 - 31, 2009

  3. Remarks on Quark Masses possible We only want to use short-distance mass scheme that do not suffer from the renormalon inherent to the pole scheme! Vxb Workshop, SLAC, Oct 29 - 31, 2009

  4. Short-Distance Masses short-distance mass without ambiguity perturbation series that contains the pole mass ambiguity of What’s the best way to define ? • infinitely many possible schemes exist • but only certain classes might be used for certain types of problems. How relevant it is to find a good scheme depends on the size of the uncertainties one has anyway or is willing to accept. Vxb Workshop, SLAC, Oct 29 - 31, 2009

  5. Short-Distance Masses short-distance mass without ambiguity perturbation series that contains the pole mass ambiguity of Note: Short-distance masses do in general still have an ambiguity that is parametrically of Vxb Workshop, SLAC, Oct 29 - 31, 2009

  6. Top Quark Mass Schemes Different types of short-distance masses for different types of processes Top Resonance Jet/resonance mass schemes Top Threshold 1S, PS mass schemes High Energy/Off-shell MS/MSbar schemes Vxb Workshop, SLAC, Oct 29 - 31, 2009

  7. Bottom and Charm Masses and are not very large. Only two distinct classes need to be defined in practice. Threshold Schemes: • B/D physics (inclusive decays) • Quarkonia: • non-relativistic sum rules Kinetic mass: • from B meson form factor sum rules • cut-off dependent Bigi, Uraltsev 1S mass: Ligeti, Manohar, AHH • from pert. mass • scale independent Shape fct mass: • from moments of B-decay shape function • cut-off + renormalization scale dependent Neubert Vxb Workshop, SLAC, Oct 29 - 31, 2009

  8. Bottom and Charm Masses and are not very large. Only two distinct classes need to be defined in practice. MSbar Mass Scheme: • high-energy, inclusive processes • off-shell, highly virtual b and c quarks Vxb Workshop, SLAC, Oct 29 - 31, 2009

  9. The Impact of Schemes Inclusive B decays: Vxb Workshop, SLAC, Oct 29 - 31, 2009

  10. Impact of Precision Vxb Workshop, SLAC, Oct 29 - 31, 2009

  11. Bottom Quark Mass Determinations • Spectral Moments of Inclusive B Decays • Sum Rules • relativistic • non-relativistic rel. sum rule rel. sum rule nonrel. sum rule B decays nonrel. sum rule nonrel. sum rule Kuhn etal. Vxb Workshop, SLAC, Oct 29 - 31, 2009

  12. Semileptonic B Decays Experimental Data: Vxb Workshop, SLAC, Oct 29 - 31, 2009

  13. Semileptonic B Decays Theoretical Moments: perturbative QCD power corrections • theory input: • Gambino, Uraltsev (2004) • Bauer, Ligeti, Luke, Manohar, Trott (2004) • expansion • expansion • input: meson mass difference • expansion scheme: • mass scheme: threshold mass ( (A) kinetic, (B) 1S ) • short-distance mass (MSbar) • eliminated Vxb Workshop, SLAC, Oct 29 - 31, 2009

  14. Semileptonic B Decays Fit Results: (2007) ? ? • expansion scheme? • mass scheme ? • uncertainties • higher orders needed underestimated Number for kinetic mass without seem to be incompatible with sum rules. Vxb Workshop, SLAC, Oct 29 - 31, 2009

  15. Semileptonic B Decays Fit Results: (2007) ? ? • expansion scheme? • mass scheme ? • uncertainties • higher orders needed (2007, only BELLE) underestimated Vxb Workshop, SLAC, Oct 29 - 31, 2009

  16. Semileptonic B Decays Gambino • take one mass as an input Vxb Workshop, SLAC, Oct 29 - 31, 2009

  17. Sum Rules nonperturbative power corrections very small Vxb Workshop, SLAC, Oct 29 - 31, 2009

  18. Sum Rules Non-Relativistic: NNLL RG-improved analyis (w.i.p.) partial result: Pineda, Signer Vxb Workshop, SLAC, Oct 29 - 31, 2009

  19. Charm Quark Mass Determinations • Spectral Moments of Inclusive B Decays • Sum Rules • relativistic rel. sum rule rel. sum rule B decays B decays rel. sum rule lattice lattice lattice rel. sum rule Kuhn etal. Vxb Workshop, SLAC, Oct 29 - 31, 2009

  20. Charm Quark Mass Determinations rel. sum rule rel. sum rule rel. sum rule B decays B decays rel. sum rule lattice lattice lattice Vxb Workshop, SLAC, Oct 29 - 31, 2009

  21. Semileptonic B Decays What is going on? Buchmüller etal. (based on Gambino,Uraltsev ) Vxb Workshop, SLAC, Oct 29 - 31, 2009

  22. Mass and Coupling Running NLL LL NNNLL NNLL • Excellent convergence of the running of quark masses and QCD coupling • No obvious failure of perturbation theory even down to 1 GeV Vxb Workshop, SLAC, Oct 29 - 31, 2009

  23. Relativistic Sum Rules: . • Method with the most advanced theoretical computations: Chetyrkin, Kuhn, Steinhauser (1994-1998) Boughezal, Czakon, Schutzmeier (2006) Kuhn, Steinhauser, Sturm (2006) Mateu, Zebarjad, Hoang (2008) Kiyo, Meier, Meierhofer, Marquard (2009) • Experimental data for not available in most of the continuum region: • take continuum theory for missing data • Lattice results for moments of scalar and pseudoscalar current correlators: Allison, Lepage, etal, (2008) Vxb Workshop, SLAC, Oct 29 - 31, 2009

  24. Relativistic Sum Rules: . Analyses with smallest errors I: Chetyrkin, Kuhn, Meier, Meierhofer, Marquard Steinhauser (2009) • theory predictions and errors taken for missing data • and taken as theory parameters, , fixed order Analyses with smallest errors II: HPQCD, Chetyrkin, Kuhn, Steinhauser, Sturm (2008) • Lattice data for moments instead of experimental data (lattice error: ) Vxb Workshop, SLAC, Oct 29 - 31, 2009

  25. Relativistic Sum Rules: . Impact of more conservative treatment of continuum data : Vxb Workshop, SLAC, Oct 29 - 31, 2009

  26. Relativistic Sum Rules: . Accounting for theory error beyond -variation: Dehnadi, Mateu, Zebarjad, AHH (in preparation) • different scale choices in and • Integration path dependent renormalization scales (contour improved) Different reasonable choices: fixed order use and , use and , use and with , use and with , use and , use and , use and , contour improved Karlsruhe method fixed order Vxb Workshop, SLAC, Oct 29 - 31, 2009

  27. Charm mass: new results Dehnadi, Mateu, Zebarjad, AHH (preliminary) ± 22 MeV ± 20 MeV with bottom mass total*: ± 27 MeV total*: ± 24 MeV with QED corrections ± 50 MeV ± 30 MeV total*: ± 34 MeV total*: ± 51 MeV *: if continuum errors of Karlsruhe group are adopted Vxb Workshop, SLAC, Oct 29 - 31, 2009

  28. Charm mass: new results with bottom mass with QED corrections Vxb Workshop, SLAC, Oct 29 - 31, 2009

  29. Bottom mass: preliminary results ± 16 MeV ± 22 MeV with bottom mass total*: ± 23 MeV total*: ± 27 MeV with QED corrections ±15 MeV ±70 MeV total*: ± 23 MeV total*: ± 72 MeV *: if continuum errors of Karlsruhe group are adopted (will have larger impact on mb than on mc) Vxb Workshop, SLAC, Oct 29 - 31, 2009

  30. Bottom mass: preliminary results with bottom mass with QED corrections Vxb Workshop, SLAC, Oct 29 - 31, 2009

  31. Conclusions & Outlook General remarks: • Parametric ambiguity in short-distance mass definitions is • Very good consistency of all reliable methods • Many methods have issues that make me believe that errors are underestimated. • Bottom mass determination consistent with parametric estimate • Charm mass determination (all of them!) have much smaller errors Specific remarks: (based on our preliminary analysis) • Charm mass error of Karlsruhe group should be enlarged by at least a factor of two. • Bottom mass error of Karlsruhe group might have to be enlarged by a factor of two if larger errors are adopted for the continuum region where not data exists. Vxb Workshop, SLAC, Oct 29 - 31, 2009

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