1. Max-Planck-Institute for Physics Munich André H. Hoang Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 Definition and Extraction of Bottom and Charm Quark Masses TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAA

2. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 2 Outline Remarks on Quark Masses bottom charm Incl. B decay moments vs. Sum Rules

3. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 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!

4. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 4 Classes of Short Distance Masses MS schemes: o subtraction of UV-div’s in dim reg ( ), running o for processes where quark is energetic or off-shell Jet schemes: Different classes are “optimal” schemes for different types of processes. o moments of jet functions describing collinear gluon radiation o for jet observables (e.g. thrust in the dijet limit) Threshold schemes: o for processes where quarks are close to mass-shell Also note: The issue of defining a short-distance mass is independent of defining renormalon-free matrix elements for power corrections ! (“1S” scheme, “kinetic” scheme, “shape fct” scheme)

5. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 5 Threshold Masses Threshold schemes: o for processes where quarks are close to mass-shell Kinetic mass: 1S mass: Shape fct mass: Bigi, Uraltsev Ligeti, Manohar, AHH Neubert o from B meson form factor sum rules o cut-off dependent o from mass o scale independent o from moments of B-decay shape function o cut-off + renormalization scale dependent

6. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 6 Threshold Masses PS mass: Beneke Pineda Threshold schemes: o for processes where quarks are close to mass-shell o from oth moment of static potential in mom space o cut-off dependent Renormalon subtracted masses: There is no “optimal” threshold mass. All can do a good job when used and defined correctly. Relating masses from different classes can introduce correlations to other parameters. 1S mass (3-loop) hep-ph/0008102

7. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 7 … mass issue has big impact Heavy Quark Effective Theory:

8. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 8 Quark Mass Tables CKM-WS Yellow Report hep-ph/030432 → numerical program → include shape fct mass

9. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 9 Bottom Quark Mass Spectral Moments of Inclusive B Decays Sum Rules → relativistic → non-relativistic

10. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 10 Global Fits Experimental Data:

11. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 11 Global Fits Theoretical Moments: theory input: perturbative QCD power corrections expansion scheme: A)short-distance mass (MSbar) B)eliminated mass scheme: threshold mass ( (A) kinetic, (B) 1S ) A) expansion B) expansion input: meson mass difference A) Gambino, Uraltsev (2004) B) Bauer, Ligeti, Manohar, Trott (2004) technology for full exists: (Anastasiou, Melnikov, Petriello) are done ! (Becher, Boos, Lunghi)

12. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 12 Global Fits Fit Results: ? → expansion scheme? → mass scheme ? → uncertainties underestimated ? Number for kinetic mass without seem to be incompatible with sum rules. (2007)

13. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 13 Global Fits Fit Results: ? (2007) (2007, only BELLE)

14. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 14 Sum Rules nonperturbative power corrections very small

15. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 15 Sum Rules Relativistic: Kühn, Steinhauser, Sturm (2006)3-loop for n=1 (update) Boughezal, Czakon, Schutzmeier (2006)3-loop for n=1 (update)

16. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 16 Sum Rules Non-Relativistic: NNLL RG-improved analyis (w.i.p.) partial result: Pineda, Signer

17. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 17 Charm Quark Mass Spectral Moments of Inclusive B Decays Sum Rules → relativistic

18. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 18 Charm mass from B decays Buchmüller etal.

19. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 19 Charm Mass from Sum Rules AH,Jamin, 2004 usual fixed order: fixed RGI-A : RGI-B : pert. Behavior of moments: (2-loops)

20. Joint WS on Vxb at B-factories, Heidelberg, Dec 14-16 2007 André H. Hoang - 20 Charm Mass from Sum Rules AH,Jamin, 2004 Kühn, Steinhauser, (Sturm) (2001/2006) Boughezal, Czakon, Schutzmeier (2006) (2-loops fixed o.) (3-loops fixed o.) (2-loops, accounting for countour analysis) Contour analysis should be done (w.i.p.)