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Definition and Extraction of Bottom and Charm Quark Masses

Definition and Extraction of Bottom and Charm Quark Masses. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A. Outline. Remarks on Quark Masses bottom charm Incl. B decay moments vs. Sum Rules. Remarks on Quark Masses. possible.

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Definition and Extraction of Bottom and Charm Quark Masses

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

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

  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! Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007

  4. Classes of Short Distance Masses Different classes are “optimal” schemes for different types of processes. MS schemes: • subtraction of UV-div’s in dim reg ( ), running • for processes where quark is energetic or off-shell Jet schemes: • moments of jet functions describing collinear gluon radiation • for jet observables (e.g. thrust in the dijet limit) Threshold schemes: • 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) Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007

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

  6. Threshold Masses Threshold schemes: • for processes where quarks are close to mass-shell PS mass: • from oth moment of static potential in mom space • cut-off dependent Beneke Renormalon subtracted masses: Pineda 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. (3-loop) hep-ph/0008102 1S mass Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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