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Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007
Max-Planck-Institute for PhysicsMunich
André H. Hoang
Definition and Extraction of Bottom and Charm Quark Masses
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
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!
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)
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
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
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:
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
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
Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007
André H. Hoang - 10
Global Fits Experimental Data:
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)
Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007
André H. Hoang - 12
Global FitsFit Results:
?
→ expansion scheme?
→ mass scheme ?
→ uncertainties underestimated ?
Number for kinetic mass without seem to be incompatible with sum rules.
(2007)
Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007
André H. Hoang - 13
Global FitsFit Results:
?
(2007)
(2007, only BELLE)
Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007
André H. Hoang - 14
Sum Rules
nonperturbative power corrections very small
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)
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
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
Joint WS on Vxb at B-factories, Heidelberg , Dec 14-16 2007
André H. Hoang - 18
Charm mass from B decays
Buchmüller etal.
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)
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.)
(3-loops fixed o.)
(2-loops, accounting for countour analysis)
Contour analysis
should be done (w.i.p.)