Definition and Extraction of Bottom and Charm Quark

Definition and Extraction of Bottom and Charm Quark Masses André H. Hoang Max-Planck-Institute for Physics Munich Joint WS on Vxb at B-factories, Heidelberg , Dec 14 -16 2007

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

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

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

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

Threshold Masses Threshold schemes: PS mass: 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: Beneke 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) 1 S mass 6 hep-ph/0008102 Joint WS on Vxb at B-factories, Heidelberg , Dec 14 -16 2007

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

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

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

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

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

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

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

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

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

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

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

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

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

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