New perspectives for heavy flavour physics from the lattice A Rainer Sommer LPHA Collaboration DESY, A Research Centre of the Helmholtz Association Les rencontres de Moriond, March 2009 Rainer Sommer New perspectives for heavy flavour physics from the lattice
The principle First principle “solution” of QCD experiments, hadrons fundamental parame- ters & hadronic matrix m p = 938 . 272 MeV elements = 139 . 570 MeV M π m K = 493 . 7 MeV α ( µ ) m D = 1896 MeV m u ( µ ) , m s ( µ ) = 5279 MeV m B m c ( µ ) , m b ( µ ) F B , F B s , ξ . . . Rainer Sommer New perspectives for heavy flavour physics from the lattice
The principle First principle “solution” of QCD • The Lagrangian experiments, hadrons fundamental parame- • Non-perturbative regulator: lattice with spacing a ters & hadronic matrix m p = 938 . 272 MeV elements = 139 . 570 MeV M π m K = 493 . 7 MeV α ( µ ) m D = 1896 MeV m u ( µ ) , m s ( µ ) = 5279 MeV m B m c ( µ ) , m b ( µ ) F B , F B s , ξ . . . Rainer Sommer New perspectives for heavy flavour physics from the lattice
The principle First principle “solution” of QCD • The Lagrangian experiments, hadrons fundamental parame- • Non-perturbative regulator: lattice with spacing a ters & hadronic matrix m p = 938 . 272 MeV • Technology elements = 139 . 570 MeV M π m K = 493 . 7 MeV α ( µ ) m D = 1896 MeV m u ( µ ) , m s ( µ ) = 5279 MeV m B m c ( µ ) , m b ( µ ) F B , F B s , ξ . . . Rainer Sommer New perspectives for heavy flavour physics from the lattice
The principle First principle “solution” of QCD • The Lagrangian experiments, hadrons fundamental parame- • Non-perturbative regulator: lattice with spacing a ters & hadronic matrix m p = 938 . 272 MeV • Technology elements = 139 . 570 MeV M π m K = 493 . 7 MeV α ( µ ) m D = 1896 MeV m u ( µ ) , m s ( µ ) = 5279 MeV m B m c ( µ ) , m b ( µ ) F B , F B s , ξ . . . Rainer Sommer New perspectives for heavy flavour physics from the lattice
The principle First principle “solution” of QCD • The Lagrangian experiments, hadrons fundamental parame- • Non-perturbative regulator: lattice with spacing a ters & hadronic matrix m p = 938 . 272 MeV • Technology elements = 139 . 570 MeV M π m K = 493 . 7 MeV α ( µ ) m D = 1896 MeV m u ( µ ) , m s ( µ ) = 5279 MeV m B m c ( µ ) , m b ( µ ) F B , F B s , ξ . . . continuum limit a → 0 Rainer Sommer New perspectives for heavy flavour physics from the lattice
Some sample results from the literature Review of E. Gamiz lattice 2008 examples of results m MS (3 GeV ) = 0 . 986(10) GeV HPQCD c m MS b ( m b ) = 4 . 20(4) GeV HPQCD √ m Bs F Bs ξ = = 1 . 211(38)(24) FNAL/MILC F B √ m B = 243(11) MeV FNAL/MILC F B s = 241(3) MeV HPQCD F D s Rainer Sommer New perspectives for heavy flavour physics from the lattice
Some sample results from the literature Review of E. Gamiz lattice 2008 examples of results m MS (3 GeV ) = 0 . 986(10) GeV HPQCD c m MS b ( m b ) = 4 . 20(4) GeV HPQCD √ m Bs F Bs ξ = = 1 . 211(38)(24) FNAL/MILC F B √ m B = 243(11) MeV FNAL/MILC F B s = 241(3) MeV HPQCD F D s Precision up to 1 % is claimed Rainer Sommer New perspectives for heavy flavour physics from the lattice
The machinery The present numbers quoted for phenomenology with small errors are dominated by “rooted staggered” sea quark computations [ MILC-collaboration ] rooting : (sea quarks) ◮ − → non-local ◮ locality (= renormalizability = correctness) argued to be recovered as a → 0 [ Bernard,Golterman,Sharpe ] series of ingredients: Symanzik effective theory – chiral PT, replica trick NRQCD (or Fermilab action) for b-quarks ◮ power law divergences g 2 k 1 a → 0 0 ∼ − →∞ a [log( a )] k m b a m b delicate analysis of continuum limit Rainer Sommer New perspectives for heavy flavour physics from the lattice
The machinery staggered chiral perturbation theory m → ( m u + m d ) / 2 & a → 0 in one (necessary due to rooting) many parameter fits Rainer Sommer New perspectives for heavy flavour physics from the lattice
The machinery Baysian fits a → 0 from high order polynomial in a with few points Rainer Sommer New perspectives for heavy flavour physics from the lattice
The machinery It appears good to perform independent computations with an independent technology ◮ manifestly local ◮ non-perturbative subtraction of power law divergences Such computations are in progress ... but first let us understand that LQCD is a challenge Rainer Sommer New perspectives for heavy flavour physics from the lattice
The challenge multiple scale problem always difficult for a numerical treatment Rainer Sommer New perspectives for heavy flavour physics from the lattice
The challenge multiple scale problem always difficult for a numerical treatment lattice cutoffs: a − 1 Λ UV = L − 1 Λ IR = Rainer Sommer New perspectives for heavy flavour physics from the lattice
The challenge multiple scale problem always difficult for a numerical treatment lattice cutoffs: a − 1 Λ UV = L − 1 Λ IR = L − 1 a − 1 ≪ m π , . . . , m D , m B ≪ O ( e − LM π ) m D a � 1 / 2 ↓ ↓ L � 4 / M π ∼ 6 fm a ≈ 0 . 05 fm L / a � 120 Rainer Sommer New perspectives for heavy flavour physics from the lattice
The challenge multiple scale problem always difficult for a numerical treatment lattice cutoffs: a − 1 Λ UV = L − 1 Λ IR = L − 1 a − 1 ≪ m π , . . . , m D , m B ≪ O ( e − LM π ) m D a � 1 / 2 ↓ ↓ L � 4 / M π ∼ 6 fm a ≈ 0 . 05 fm L / a � 120 beauty not yet accomodated: effective theory, Λ QCD / m b expansion Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives ◮ new algorithms ◮ new machines ◮ development / demonstration of effective field theory strategies Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: algorithms ◮ mass preconditioning [ M. Hasenbusch ] ◮ multiple time scale integrators [ C. Urbach et al. ] ◮ odd number of flavours, m s � = m c : RHMC [ M. Clark, A. Kennedy ] ◮ Domain decomposition + deflation [ M. L¨ uscher ] performance improved enormously: from time ∝ m − n quark , n � 3 to Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: algorithms ◮ mass preconditioning [ M. Hasenbusch ] ◮ multiple time scale integrators [ C. Urbach et al. ] ◮ odd number of flavours, m s � = m c : RHMC [ M. Clark, A. Kennedy ] ◮ Domain decomposition + deflation [ M. L¨ uscher ] performance improved enormously: from time ∝ m − n 618 485 377 M π ∼ 282 MeV quark , n � 3 to t [min] 200 150 DD-HMC 100 50 [ M. L¨ uscher, 2008 ] Accelerated DD-HMC 0 0 50 100 150 200 250 ( am sea ) −1 Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: machines For illustration: the German situation (roughly) year machine speed/Tflops share for a typical collaboration 1984 Cyber205 0.0001 /100 1994 APE100 0.0500 /4 Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: machines For illustration: the German situation (roughly) year machine speed/Tflops share for a typical collaboration 1984 Cyber205 0.0001 /100 1994 APE100 0.0500 /4 2001 APE1000 0.5000 /4 2005 apeNEXT 2.0000 /2 Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: machines For illustration: the German situation (roughly) year machine speed/Tflops share for a typical collaboration 1984 Cyber205 0.0001 /100 1994 APE100 0.0500 /4 2001 APE1000 0.5000 /4 2005 apeNEXT 2.0000 /2 2009.5 BG/P 1000.0000 /20(?) Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: machines For illustration: the German situation (roughly) year machine speed/Tflops share for a typical collaboration 1984 Cyber205 0.0001 /100 1994 APE100 0.0500 /4 2001 APE1000 0.5000 /4 2005 apeNEXT 2.0000 /2 2009.5 BG/P 1000.0000 /20(?) Growth (recently) stronger than Moore’s law Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: machines For illustration: the German situation (roughly) year machine speed/Tflops share for a typical collaboration 1984 Cyber205 0.0001 /100 1994 APE100 0.0500 /4 2001 APE1000 0.5000 /4 2005 apeNEXT 2.0000 /2 2009.5 BG/P 1000.0000 /20(?) Growth (recently) stronger than Moore’s law unrelated to “Konjunkturpaket I/II” Rainer Sommer New perspectives for heavy flavour physics from the lattice
Perspectives: algorithms & machines Example: 128 × 64 3 , a = 0 . 04 fm , L = 2 . 6 fm at m q = m s / 2: (2 trajectories)/hour=(1 MD unit)/hour on 1024 node BG/P (1/64 Pflops) 618 485 377 M π ∼ 282 MeV normalized autocorrelation of Plaq t [min] 1 200 0.5 ρ 150 0 DD-HMC −0.5 0 20 40 60 80 100 120 140 100 τ int with statistical errors of Plaq 30 50 20 Accelerated DD-HMC τ int 10 0 0 50 100 150 200 250 ( am sea ) −1 0 0 20 40 60 80 100 120 140 W execution time of 2 τ int = # MD unit per effective independent measurement accelerated DD-HMC 256 × 128 3 at the physical point ( M π = M physical ) seems in reach π Rainer Sommer New perspectives for heavy flavour physics from the lattice
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