Heavy Quark Masses Review

Max-Planck-Institute for PhysicsWerner-Heisenberg-Institut

Munich

André H. Hoang

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Heavy Quark Masses Review

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Outline

• Remarks on heavy quark masses

• Mass schemes

• Charm and Bottom Mass Determinations

• Relativistic Sum Rules

• Conclusions

André H. Hoang

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Remarks on Quark Masses

André H. Hoang

possible

We only want to use short-distance mass scheme that do not suffer from the renormalon inherent to the pole scheme!

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Short-Distance Masses

André H. Hoang

short-distance mass without ambiguity

perturbation series that contains the pole mass ambiguity of

What’s the best way to define ?

• infinitely many possible schemes exist

• but only certain classes might be used for certain types of problems.

How relevant it is to find a good scheme depends on the size of the uncertainties one has anyway or is willing to accept.

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Short-Distance Masses

André H. Hoang

short-distance mass without ambiguity

perturbation series that contains the pole mass ambiguity of

Short-distance masses do in general still have an ambiguity that is parametrically of

Note:

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Top Quark Mass Schemes

André H. Hoang

Different types of short-distance masses for different types of processes

Top Resonance Jet/resonance mass schemes

Top Threshold 1S, PS mass schemes

High Energy/Off-shell MS/MSbar schemes

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Bottom and Charm Masses

André H. Hoang

and are not very large.

Only two distinct classes need to be defined in practice.

Threshold Schemes:

Kinetic mass:

1S mass:

Shape fct mass:

Bigi, Uraltsev

Neubert

o from B meson form factor sum rules

o cut-off dependent

o from pert. mass

o scale independent

o from moments of B-decay shape function

o cut-off + renormalization scale dependent

• B/D physics (inclusive decays)

• Quarkonia:

• non-relativistic sum rules

Ligeti, Manohar, AHH

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Bottom and Charm Masses

André H. Hoang

and are not very large.

Only two distinct classes need to be defined in practice.

MSbar Mass Scheme: • high-energy, inclusive processes

• off-shell, highly virtual b and c quarks

Vxb Workshop, SLAC, Oct 29 - 31, 2009

The Impact of Schemes

André H. Hoang

Inclusive B decays:

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Impact of Precision

André H. Hoang

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Bottom Quark Mass Determinations

André H. Hoang

• Spectral Moments of Inclusive B Decays

• Sum Rules → relativistic

→ non-relativistic

Kuhn etal.

rel. sum rule

rel. sum rule

nonrel. sum rule

B decays

nonrel. sum rule

nonrel. sum rule

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Semileptonic B Decays

André H. Hoang

Experimental Data:

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Semileptonic B Decays

André H. Hoang

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, Luke, Manohar, Trott (2004)

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Semileptonic B Decays

André H. Hoang

Fit Results:

→ expansion scheme?

→ mass scheme ?

→ uncertainties

→ higher orders needed

underestimated

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

(2007)

?

?

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Semileptonic B Decays

André H. Hoang

Fit Results:

?

(2007)

(2007, only BELLE)→ expansion scheme?

→ mass scheme ?

→ uncertainties

→ higher orders needed

underestimated

?

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Semileptonic B Decays

André H. Hoang

→ take one mass as an input

Gambino

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Sum Rules

André H. Hoang

nonperturbative power corrections very small

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Sum Rules

André H. Hoang

Non-Relativistic:

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

partial result: Pineda, Signer

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Charm Quark Mass Determinations

André H. Hoang

• Spectral Moments of Inclusive B Decays

• Sum Rules → relativistic

Kuhn etal.

rel. sum rule

rel. sum rule

B decays

B decays

rel. sum rule

rel. sum rule

lattice

lattice

lattice

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Charm Quark Mass Determinations

André H. Hoang

rel. sum rule

rel. sum rule

B decays

B decays

rel. sum rule

rel. sum rule

lattice

lattice

lattice

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Semileptonic B Decays

André H. Hoang

Buchmüller etal.

(based on Gambino,Uraltsev )

What is going on?

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Mass and Coupling Running

André H. Hoang

• Excellent convergence of the running of quark masses and QCD coupling

• No obvious failure of perturbation theory even down to 1 GeV

LLNLL

NNLLNNNLL

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Relativistic Sum Rules: .

André H. Hoang

→ Method with the most advanced theoretical computations:

Chetyrkin, Kuhn, Steinhauser (1994-1998)

Kuhn, Steinhauser, Sturm (2006)

Boughezal, Czakon, Schutzmeier (2006)

Mateu, Zebarjad, Hoang (2008)

Kiyo, Meier, Meierhofer, Marquard (2009)

→ Experimental data for not available in most of the continuum region:

• take continuum theory for missing data

→ Lattice results for moments of scalar and pseudoscalar current correlators:

Allison, Lepage, etal, (2008)

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Relativistic Sum Rules: .

André H. Hoang

Analyses with smallest errors I: Chetyrkin, Kuhn, Meier, Meierhofer, Marquard Steinhauser (2009)

• theory predictions and errors taken for missing data

• and taken as theory parameters, , fixed order

HPQCD, Chetyrkin, Kuhn, Steinhauser, Sturm (2008) Analyses with smallest errors II:

• Lattice data for moments instead of experimental data (lattice error: )

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Relativistic Sum Rules: .

André H. Hoang

Impact of more conservative treatment of continuum data :

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Relativistic Sum Rules: .

André H. Hoang

Accounting for theory error beyond -variation:

• different scale choices in and

• Integration path dependent renormalization scales (contour improved)

Dehnadi, Mateu, Zebarjad, AHH (in preparation)

Different reasonable choices:

1) use and ,

2) use and ,

3) use and with ,

4) use and with ,

5) use and ,

6) use and ,

7) use and ,

fixed order

fixed order

contour improved

Karlsruhe method

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Charm mass: new results

with bottom mass

with QED corrections

André H. Hoang

Dehnadi, Mateu, Zebarjad, AHH (preliminary)

± 20 MeV ± 22 MeV

± 30 MeV± 50 MeV

total*: ± 24 MeV total*: ± 27 MeV

total*: ± 51 MeVtotal*: ± 34 MeV

*: if continuum errors of Karlsruhe group are adopted

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Charm mass: new results

with bottom mass

with QED corrections

André H. Hoang

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Bottom mass: preliminary results

with bottom mass

with QED corrections

André H. Hoang

±70 MeV

±15 MeV

± 22 MeV± 16 MeV

*: if continuum errors of Karlsruhe group are adopted (will have larger impact on mb than on mc)

total*: ± 27 MeV total*: ± 23 MeV

total*: ± 23 MeV total*: ± 72 MeV

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Bottom mass: preliminary results

with bottom mass

with QED corrections

André H. Hoang

Vxb Workshop, SLAC, Oct 29 - 31, 2009

Conclusions & Outlook

• Parametric ambiguity in short-distance mass definitions is

• Very good consistency of all reliable methods

• Many methods have issues that make me believe that errors are underestimated.

Specific remarks:

André H. Hoang

• Bottom mass determination consistent with parametric estimate

• Charm mass determination (all of them!) have much smaller errors

General remarks:

• Charm mass error of Karlsruhe group should be enlarged by at least a factor of two.

• Bottom mass error of Karlsruhe group might have to be enlarged by a factor of two if larger errors are adopted for the continuum region where not data exists.

(based on our preliminary analysis)