heavy quark masses review
DESCRIPTION
Heavy Quark Masses Review. Outline. Remarks on heavy quark masses Mass schemes Charm and Bottom Mass Determinations Relativistic Sum Rules Conclusions. Remarks on Quark Masses. possible. - PowerPoint PPT PresentationTRANSCRIPT
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)