Max-Planck-Institute for Physics Werner-Heisenberg-Institut Munich André H. Hoang Vxb Workshop, SLAC, Oct , 2009 Heavy Quark Masses Review

Vxb Workshop, SLAC, Oct , 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 , 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 , 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 , 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 , 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 , 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 , 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 , 2009 The Impact of Schemes André H. Hoang Inclusive B decays:

Vxb Workshop, SLAC, Oct , 2009 Impact of Precision André H. Hoang

Vxb Workshop, SLAC, Oct , 2009 Bottom Quark Mass Determinations André H. Hoang Spectral Moments of Inclusive B Decays Sum Rules → relativistic → non-relativistic Kuhn etal. rel. sum rule nonrel. sum rule B decays nonrel. sum rule

Vxb Workshop, SLAC, Oct , 2009 Semileptonic B Decays André H. Hoang Experimental Data:

Vxb Workshop, SLAC, Oct , 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 , 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 , 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 , 2009 Semileptonic B Decays André H. Hoang → take one mass as an input Gambino

Vxb Workshop, SLAC, Oct , 2009 Sum Rules André H. Hoang nonperturbative power corrections very small

Vxb Workshop, SLAC, Oct , 2009 Sum Rules André H. Hoang Non-Relativistic: NNLL RG-improved analyis (w.i.p.) partial result: Pineda, Signer

Vxb Workshop, SLAC, Oct , 2009 Charm Quark Mass Determinations André H. Hoang Spectral Moments of Inclusive B Decays Sum Rules → relativistic Kuhn etal. rel. sum rule B decays rel. sum rule lattice

Vxb Workshop, SLAC, Oct , 2009 Charm Quark Mass Determinations André H. Hoang rel. sum rule B decays rel. sum rule lattice

Vxb Workshop, SLAC, Oct , 2009 Semileptonic B Decays André H. Hoang Buchmüller etal. (based on Gambino,Uraltsev ) What is going on?

Vxb Workshop, SLAC, Oct , 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 LL NLL NNLL NNNLL

Vxb Workshop, SLAC, Oct , 2009 Relativistic Sum Rules:. André H. Hoang → Method with the most advanced theoretical computations: Chetyrkin, Kuhn, Steinhauser ( ) 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 , 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 , 2009 Relativistic Sum Rules:. André H. Hoang Impact of more conservative treatment of continuum data :

Vxb Workshop, SLAC, Oct , 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 contour improved Karlsruhe method

Vxb Workshop, SLAC, Oct , 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 MeV total*: ± 34 MeV *: if continuum errors of Karlsruhe group are adopted

Vxb Workshop, SLAC, Oct , 2009 Charm mass: new results with bottom mass with QED corrections André H. Hoang

Vxb Workshop, SLAC, Oct , 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*: ± 72 MeV

Vxb Workshop, SLAC, Oct , 2009 Bottom mass: preliminary results with bottom mass with QED corrections André H. Hoang

Vxb Workshop, SLAC, Oct , 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)