Definition and Extraction of Bottom and Charm Quark Masses

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


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Outline

• Remarks on Quark Masses

• bottom

• charm

• Incl. B decay moments vs. Sum Rules


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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!


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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)


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Threshold Masses


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


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Threshold Masses

PS mass:Beneke

Pineda


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


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… mass issue has big impact

Heavy Quark Effective Theory:


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Quark Mass Tables

CKM-WS Yellow Report

hep-ph/030432

→ numerical program

→ include shape fct mass


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Bottom Quark Mass

• Spectral Moments of Inclusive B Decays

• Sum Rules → relativistic

→ non-relativistic


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Global Fits Experimental Data:



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)



Global FitsFit Results:

?

→ expansion scheme?

→ mass scheme ?

→ uncertainties underestimated ?

Number for kinetic mass without seem to be incompatible with sum rules.

(2007)



Global FitsFit Results:

?

(2007)

(2007, only BELLE)



Sum Rules

nonperturbative power corrections very small



Sum Rules Relativistic:

Kühn, Steinhauser, Sturm (2006) 3-loop for n=1 (update)

Boughezal, Czakon, Schutzmeier (2006) 3-loop for n=1 (update)



Sum Rules Non-Relativistic:

NNLL RG-improved analyis (w.i.p.)

partial result: Pineda, Signer



Charm Quark Mass

• Spectral Moments of Inclusive B Decays

• Sum Rules → relativistic



Charm mass from B decays

Buchmüller etal.



Charm Mass from Sum Rules

AH,Jamin, 2004

usual fixed order: fixed

RGI-A :

RGI-B :

pert. Behavior of moments: (2-loops)



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.)

Documents

Definition and Extraction of Bottom and Charm Quark Masses