Max-Planck-Institute for Physics Munich André H. Hoang SFB Workshop, Rwth Aachen, February 21-22 2007 Bottom and Charm Mass from Inclusive B Decays TexPoint.

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Max-Planck-Institute for Physics Munich André H. Hoang SFB Workshop, Rwth Aachen, February Bottom and Charm Mass from Inclusive B Decays TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAA

SFB Workshop, Rwth Aachen, February André H. Hoang - 2 Outline Quark masses in QCD Heavy Quark Effective Theory from inclusive B decays Conclusions based on: Bauer et al. PRD (2002) Bauer et al. PRD (2004) Gambino etal. EPJC (2004) Hoang et al. PLB (2005) Buchmüller et al. PRD (2006)

SFB Workshop, Rwth Aachen, February André H. Hoang - 3 Remarks on Quark Masses

SFB Workshop, Rwth Aachen, February André H. Hoang - 4 Remarks on Quark Masses

SFB Workshop, Rwth Aachen, February André H. Hoang - 5 Remarks on Quark Masses

SFB Workshop, Rwth Aachen, February André H. Hoang - 6 Remarks on Quark Masses

SFB Workshop, Rwth Aachen, February André H. Hoang - 7 Remarks on Quark Masses Heavy Quark Effective Theory: also: Inclusive moments (“wide” cuts)

SFB Workshop, Rwth Aachen, February André H. Hoang - 8 Bottom mass from B decays Experimental Data: (BABAR, BELLE, CLEO, DELPHI) 87 measurements Lepton energy moments Hadron invariant mass moments (BABAR, BELLE, CLEO) 5 measurements Bauer,Ligeti,Luke,Manohar,Trott n=1,2 different “half-integer” moments: worse OPE, only 1-loop not included in the analysis

SFB Workshop, Rwth Aachen, February André H. Hoang - 9 Bottom mass from B decays Theoretical Input: Bauer,Ligeti,Luke,Manohar,Trott 1) Pole scheme HQET expression: 2) Eliminate : 3) Implement threshold : 4) Expand in (upsilon expansion) and 3 HQET parameters eliminated renormalon cancellation use same and number of active flavors

SFB Workshop, Rwth Aachen, February André H. Hoang - 10 Bottom mass from B decays Fit Procedure: Bauer,Ligeti,Luke,Manohar,Trott 92 measurements 7 fit parameters: 10 different expansion schemes: - 1S, PS, kinetic, pole, - eliminate OR keep Correlation error matrix: Experimental corr. matrix

SFB Workshop, Rwth Aachen, February André H. Hoang - 11 Bottom mass from B decays Results: Bauer,Ligeti,Luke,Manohar,Trott Order behavior tree Description of data PDG

SFB Workshop, Rwth Aachen, February André H. Hoang - 12 Bottom mass from B decays Results: Bauer,Ligeti,Luke,Manohar,Trott PDG Room for improvement: a)full 2-loop partonic analysis b)even better and more data (no voids!) + nonpert. HQET matrix elements ! + correlation matrix for all parameters ! Identical to: Hoang, hep-ph/ Consistent with Buchmüller etal. same central value as Kuhn, Steinhauser, Sturm (2007)

SFB Workshop, Rwth Aachen, February André H. Hoang - 13 Charm mass from B decays AH,Manohar spin-averaged B,B* and D,D* masses and correlation matrix renormalon cancellation: Perturbative Input: Chetyrkin etal. Melnikov etal. a)same and active running flavors b)finite charm mass corrections: c)expand out in everywhere Hoang

SFB Workshop, Rwth Aachen, February André H. Hoang - 14 Charm mass from B decays AH,Manohar 8 Expansion methods: a) OR directly b)solve for analytically OR fit numerically c)take as input OR General feature: spread of different methods larger than perturbative error estimate for each method exp.error B data theo. error B moments

SFB Workshop, Rwth Aachen, February André H. Hoang - 15 Charm mass from B decays AH,Manohar 8 Expansion methods: a) OR directly b)solve for analytically OR fit numerically c)take as input OR exp.error B data theo. error B moments half of range obtained for all 8 methods add linearly Buchmüller etal.

SFB Workshop, Rwth Aachen, February André H. Hoang - 16 Comment on sum rules AH,Jamin, 2004 usual fixed order: fixed RGI-A : RGI-B : pert. Behavior of moments: