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


Outline

• Remarks on heavy quark masses

• Mass schemes

• Charm and Bottom Mass Determinations

• Relativistic Sum Rules

• Conclusions

André H. Hoang


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!


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.


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:


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


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


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


The Impact of Schemes

André H. Hoang

Inclusive B decays:


Impact of Precision

André H. Hoang


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


Semileptonic B Decays

André H. Hoang

Experimental Data:



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)



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)

?

?



André H. Hoang

Fit Results:

?

(2007)

(2007, only BELLE)→ expansion scheme?

→ mass scheme ?

→ uncertainties

→ higher orders needed

underestimated

?



André H. Hoang

→ take one mass as an input

Gambino


Sum Rules

André H. Hoang

nonperturbative power corrections very small


Sum Rules

André H. Hoang

Non-Relativistic:

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

partial result: Pineda, Signer


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


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



André H. Hoang

Buchmüller etal.

(based on Gambino,Uraltsev )

What is going on?


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


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)



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: )



André H. Hoang

Impact of more conservative treatment of continuum data :



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


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


Charm mass: new results

with bottom mass


André H. Hoang


Bottom mass: preliminary results

with bottom mass


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)




Bottom mass: preliminary results

with bottom mass


André H. Hoang


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)

Documents

Heavy Quark Masses Review