Recent results Recent results from lattice from lattice calculationscalculationsShoji Hashimoto (KEK)Shoji Hashimoto (KEK)

Aug. 20 @ ICHEP 2004, Aug. 20 @ ICHEP 2004, BeijingBeijing

30 years of lattice QCD30 years of lattice QCDK. Wilson (1974) QCD potential

QCD coupling const

Flavor physicsHadron spectrum

Phase transition

Dynamical fermions

Lattice 2004Lattice 2004• Jun 21-26 @ Fermilab; 22nd in the series• 20 plenary talks; 216 parallel/posters

Lattice talks at ICHEP 04

• Kaneko, unquenched mini-review• Hatsuda, review of hot and dense QCD• Di Giacomo, chiral phase transition in Nf=2• Mescia, Kl3 form factor for Vus; BK in Nf=2• Tomboulis, RG in SU(N) LGT• Hari Dass, teraflop cluster in India

Topics to be coveredTopics to be covered• Flavor physics

related quantities, responsible for

More fundamental questions:

• Requirements for unquenched lattice simulations

• Fundamental parameters of QCD

Lattice QCD at the frontier of elementary particles

Plan of this talkPlan of this talk1. Issues in recent QCD simulations

• Chiral extrapolation, fermion formulations…

2. Fundamental parameters• QCD coupling constant, quark masses

3. Kaon physics• Form factors, kaon B parameter

4. Heavy quarks• Decay constants, form factors…

1. Issues in recent lattice

QCD simulations― ― dynamical fermions, dynamical fermions, chiral extrapolation, chiral extrapolation, fermion formulationfermion formulation

Lattice QCDLattice QCD• Non-perturbative

definition of QCD• Monte Carlo simulation

is possible.

• “First principles” calculation, but with approximations:

– finite a– finite L– large mq

need extrapolations; source of systematic errors.

lattice spacing a

lattice size L

quark field

gauge field

~ 0.1-0.2 fm

~2-3 fm

Dynamical fermionsDynamical fermions• Calculating the fermion determinant

= numerically very hard.

Quenched: neglect it Unquenched: include it

• How hard it is depends on the fermion formulation on the lattice.

Lattice fermionsLattice fermionschiral symmetry

flavor symmetry

numerical simulation

Wilson /O(a)-improved Wilson

violated; will recover in the continuum

okayexpensive; harder at small quark masses

twisted mass violated2 flavors; a flavor mixing mass term

less expensive at small quark

masses

staggered (Kogut-Susskind)

exact U(1) out of U(4)

4 tastes; non-trivial mixing fast

Ginsparg-Wilson (domain-wall, overlap)

exact at finite a

okaymost expensive; still exploratory

Chiral extrapolationChiral extrapolation• Lattice simulation is

limited in a heavier quark mass region mq~(0.5-1)ms.

pion decay constant

ChPT predicts the chiral log near the chiral limit.

with a fixed coefficient.

chiral log

Staggered simulation can push the quark mass much lower.

MILC (2004) Nf=2+1

JLQCD (2002) Nf=2

2 2lnm m

““Lattice QCD confronts Lattice QCD confronts experiment”experiment”

HPQCD, MILC, UKQCD, Fermilab (2003)

“Gold-plated lattice observables agree with experiments within a few %.”

“Only with 2+1 flavors.”

Is everything okay?

PRL92, 022001 (2004)

Locality/UniversalityLocality/Universality

4 tastes (unwanted)

Fourth-root trick:

no doubling

Can it be written as a local field theory?

Otherwise, there is no guarantee that the theory is renormalizable as a quantum field theory, i.e. continuum limit is the QCD.

is non-local: Bunk et al, hep-lat/0403022;Hart, Muller, hep-lat/0406030.

=?

Issue still controversialIssue still controversial“We believe that existing staggered quark results

make it unlikely that there are fundamental problems with the formalism we are using.”

― HPQCD, MILC, UKQCD

Open question = project out a single taste from the staggered operator (possible?) and see if it is local.

Positive indication from eigenvalue distribution: Follana et al, hep-lat/0406010; Durr et al, hep-lat/0406027

There are many other sensible people who cannot simply believe without a theoretical proof.

Major unquenched simulationsMajor unquenched simulationsHere, let us assume that the fourth-rooted

staggered fermion is a correct (or at least effective) description of QCD.

Current major unquenched simulations include• Wilson, O(a)-improved Wilson

– Nf=2: CP-PACS, JLQCD, QCDSF, UKQCD, qq+q, SPQcdR– Nf=2+1: CP-PACS/JLQCD

• Staggered– Nf=2 and 2+1: MILC

• Domain-wall– Nf=2: RBC

Some recent results …

2. Fundamental 2. Fundamental parametersparameters

― ― QCD coupling constant, QCD coupling constant, quark massesquark masses

QCD coupling constantQCD coupling constant

perturbation theoryknown to 2-loop

From lattice simulation: •scale q* from Upsilon

spectrum (less sensitive to chiral extrap, volume effect, etc.)

•coupling constant αV from short distance observables; perturbative expansion.

PDG 2004

HPQCD (2003)Nf=2+1

Updates at Lattice 2004Updates at Lattice 2004•QCDSF-UKQCD (Horsley et al.)

– O(a)-improved Wilson fermion

– finer lattice added, aid the continuum limit. Result unchanged.

•HPQCD (Mason et al.)– improved staggered

(MILC)– 3-loop calculation! error

reduced by a factor of 2.The disagreement with the Wilson-type fermion is not well understood.

( ) 0.1175 0.0015MSs ZM

preliminary

Light quark massesLight quark masses

One-loop perturbation,or partly non-perturvative

Lattice simulationInput from mπ and mK.

is sensitive tochiral extrap. ms is less.

PDG 2004

Some of these are from lattice.

Strange quark massStrange quark mass• ms becomes lower by the

sea quark effects (CP-PACS, JLQCD, Nf=2)

• Systematic error due to perturbative matching could be larger: QCDSF-UKQCD (2004), VWI with non-perturbative renorm, error stat only

• Update in 2004: Nf = 2+1 data– HPQCD-MILC-UKQCD– CP-PACS/JLQCD

Lower end of the PDG band(2GeV) 78 10 MeVMS

sm My average:

Quark mass ratioQuark mass ratio2

22

1 ( ) 1,ˆs K

M

m mO m

m m

M

with EM corrections subtracted.

: NLO ChPT

Update 2004:HPQCD-MILC-UKQCD•staggered Nf=2+1•consistent analysis including NLO ChPT

•higher order terms are also included.

The result suggests significant NNLO contributions.

Charm quark massCharm quark massNot too heavy =

brute force continuum limit is possible.

• 2002~2003: Continuum limit with non-perturbative matching (quenched)

• Update 2004: UKQCD, Nf=2 at a fixed lattice spacing, preliminary result

( ) GeVc cm m

( ) 1.32 0.08 GeVc cm m My recommendation:

c.f. BaBar inclusive Vcb analysis: ( ) 1.33 0.10 GeVc cm m

Bottom quark massBottom quark massToo heavy to proceed

with the brute force.• Use HQET, matching

to continuum with non-perturbative or higher order PT

• Update 2004Di Renzo-Scorzato NNNLO matching

• 1/m correction is missing ~ 30 MeV.

( ) GeVb bm m

( ) 4.2 0.1 GeVb bm m My recommendation:

( ) 4.22 0.06 GeVb bm m c.f. BaBar inclusive Vcb analysis:

3. Kaon physics3. Kaon physics― ― Kaon decay constant, Kaon decay constant,

form factors, B form factors, B parameterparameter

|V|Vusus| the Cabibbo angle| the Cabibbo angle• Precisely determined

through • Theoretical input is

the form factorwhich is 1 in the SU(3) limit.

• Previous estimate (Leutwyler-Roos 1984, 20

years ago!) includes model dependence at

K l

(0)f

2(( ) )sO m m

First lattice calculation:Becirevic et al., hep-lat/0403217

•quenched •measures the SU(3) breaking using clever double ratios as in |Vcb| by Fermilab

•Result

consistent with Leutwyler-Roos 0.961(8)

(0) 0.960 0.005 0.007f

Leptonic decay for |VLeptonic decay for |Vusus||

• can be used to determine |Vus|, once fK is known from lattice (Marciano, hep-ph/0402299)

• use the MILC result Nf=2+1 hep-lat/0407028

/ 1.210(4)(13)Kf f

2 2( ) | |K usB K f V

The accuracy is now competing with the semi-leptonic determination.

Kaon B parameterKaon B parameter

(1 ) constK KB 8 2 23

( ) ( )V A V A

KK K

K sd sd KB

f m

•Need chiral symmetry to avoid mixing of wrong chirality operators.

•Previous world average:

(2 GeV) 0.63(4)(9)KB

•Unchanged since 1997 (central value from JLQCD staggered)

•2nd error from quenching ~ 15% (Sharpe 1996)

Quenched BQuenched BKK: recent results: recent results• Improved staggered:

Lee-Sharpe (2003), Gamiz et al. at Lattice 2004.

• Domain wall: CP-PACS (2001), RBC (2002), RBC at Lattice 2004.

• Overlap: DeGrand (2003), Garron et al. (2003).

• Wilson, w/o subtraction: SPQcdR (2004).

• Chirally twisted mass: ALPHA at Lattice 2004.

Much better scaling; non-perturbative renorm. 0 (2 GeV) 0.58(4)fN

KB

My average (quenched):

Quenching effect on BQuenching effect on BKK??• Dynamical quark

effect was not clearly seen before (Ishizuka et al. (1993), Kilcup (1993), Lee-Klomfass (1996), Kilcup et al. (1996))

– Reduce by a few % (Soni, 1995)

– Increase by 5±15% (Sharpe, 1998)

• Maybe, because the unimproved staggered quark has too large scaling violation.

New results in 2004• Flynn et al. (UKQCD), O(a)-improved Wilson fermion, Nf=2, hep-lat/0406013

• RBC, dynamical domain-wall fermion, Nf=2, at Lattice 2004

• Gamiz et al. (UKQCD), improved staggered, on MILC config, at Lattice 2004 (too early to quote numbers; expect results in near future)

Unquenched BUnquenched BKK

RBC (2004), preliminary• Sea quark mass

dependence is seen.

• BK is lower in the chiral limit.

• SU(3) breaking (md≠ms) effect -3%.

My average: 09(2 GeV) 0.58(4)( )KB

•Central value is from quenched, as the RBC work is still preliminary; second error represents quenching effect

•cf. the previous number 0.63(4)(9)

4. Heavy quarks4. Heavy quarks― ― Decay constants, B Decay constants, B

parameters, form factorsparameters, form factors

DD(s)(s) meson decays meson decays

• CLEO-c and BESIII promise to measure the D(s) decays at a few % accuracy.

• Provides a stringent check/calibration of lattice method for B physics

Leptonic decays

Semi-leptonic decays

• Decay constants; form factors

• Determination of |Vcs|, |Vcd|

• Provides input for the corresponding B meson form factor analysis.

( )sD l

,D Kl l

D meson decay constantsD meson decay constantsRecent developments•Better control of systematic error in quenched QCD (ALPHA (2003), de Divitiis et al. (2003))

•Nf=2+1 calculation– Wingate et al. (2003)– MILC at Lattice 2004.– Fermilab-MILC-HPQCD at

Lattice 2004.59

1014

263 33 MeV

224 28 MeV

sD

D

f

f

(MeV)sDf

preliminary

c.f. new CLEO-c result: 201(41)(17) MeVDf

Semi-leptonic D decaysSemi-leptonic D decays

Form factors New Nf=2+1 calculation by Fermilab-MILC at Lattice 2004.

–Staggered light, clover heavy–Dominant syst error from heavy quark

discretization (~7%)

2 2 2 22 0 2

2 2( ) ( ) ( ) ( )D K D K

K D D K

m m m mK p V D p f q p p f q q

q q

2 0 2,( ) ( )f fq q

(0) 0.73 0.03 0.06D Kf

preliminary

(0) / (0) 0.88(4)(7)D D Kf f

SU(3) ratio

c.f. new BES result: 0.93(19)(7) CLEO-c: 0.86(7)(+6-4)(1)

c.f. new BES result: 0.78(4)(3)

Competing with CLEO-c in Competing with CLEO-c in precision?precision?

Error estimates for fD: Simone (Fermilab) at Lattice 2004

Perturbative matching of heavy quark action

Need 2-loop calc.

Statistics + smaller sea quark mass

Machine power

Discretization error; finer lattice

5% accuracy is within reach in a few years; 1-2% is more challenging.

B meson mixingB meson mixing

• Lattice QCD is the prime tool to calculate them.

• Long history since ~ 1990• Heavy quark is involved;

HQET is useful.• Unquenching!

2 2| |Bd tdBf BM V 2

22

| |,

| |s ssBs ts

d B td

B B

B B

fm BM V

M m f BV

•Decay constant fB•B parameter BB

•SU(3) breaking parameter ξ

Without chiral extrap: Without chiral extrap: ffBsBs• Improved precision in

quenched QCD by continuum extrapolation (de Divitiis et al. (2003), ALPHA (2003))

• JLQCD (2003), Nf=2, O(a)-improved, high statistics

• Wingate et al. (2003), Nf=2+1, staggered sea

• MILC at Lattice 2004, Nf=2+1, not shown

1.5σ disagreement: not yet understood; effect of +1 flavor is not likely (sea quark mass dependence is small). 230 30 MeV

sBf

My estimate:

Chiral extrapolation: Chiral extrapolation: ffBBNeed to include the

effect of pion loops (chiral log)

2 22

2 2

3(1 3 )log

4 (4 )B

m mgf

f

s sB B

B B

f m

f m

JLQCD (2003), Nf=2

1200

301.13(3) (2)(( ) )sB

B

f

f

HPQCD, Nf=2+1, staggered sea, at Lattice 2004•Chiral log is seen; consistent

with the estimate of JLQCD

My estimate:0.050.061.22sB

B

f

f

Grinstein ratioGrinstein ratioMore controlled chiral extrapolation for ratios

( / ) /( / )sB B Kf f f f

Becirevic et al. (2003)

• Chiral log partially cancels. • Unquenched analysis to be

done..

JLQCD (2003), Nf=2, uses the Grinstein ratio.

( ) /( )

( ) /( )s s

s s

B B B B

D D D D

f m f m

f m f m

( / ) /( / )s sB B D Df f f f

• Chiral log cancels at LO• Take advantage of expected

CLEO-c data( / ) /( / ) 1.010(3)(8)(5)

s sB B D Df f f f JLQCD preliminary (2003):

B parameterB parameterBB is less problematic.

2 22

2 2

3(1 3 )log

4 (4 )B

m mgB

f

•Coefficient of the chiral log term is small: (1-3g2) ~ -0.05.

•Lattice data are consistent with a constant.

JLQCD (2003), Nf=2

56 5662 17( ) 0.836(27)( ), 1.017(16)( )sB

B bB

BB m

B

B mixing summaryB mixing summaryLellouch, ICHEP 2002

My average,ICHEP 2004

203(27)(+0-20) 189(27)

238(31) 230(30)

235(33)(+0-24) 214(38)

276(38) 262(35)

1.18(4)(+12-0) 1.22(+5-6)

1.18(4)(+12-0) 1.23(6)

(MeV)Bf

(MeV)sBf

ˆ (MeV)B Bf B

ˆ (MeV)s sB Bf B

/sB Bf f

Semi-leptonic B decaysSemi-leptonic B decays B l for the |Vub| determination; form factors

•lattice calculation is feasible at the large q2 region

•First Nf=2+1 calc this year both on the MILC conf, different heavy quark formulations

2 0 2( ), ( )f q f q

Fermilab (2004)HPQCD (2004)

2( )f q

0 2( )f q

No significant effect of quenching; chiral log not yet studied.

|V|Vubub| determination| determinationCLEO analysis (2003): use the exp data above q2 > 16 GeV2 and input lattice form factor averaged over four quenched lattice calc.

0.450.35

3| | 10

2.88 0.55 0.30 0.18

ubV

New Belle measurement (140 fb-1):

0.620.483.90 0.71 0.23

CLEO (2003)

with unquenched lattice calculation

expect O(x10) statistics in near future

Heavy-to-heavy for |VHeavy-to-heavy for |Vcbcb||Zero recoil form factors of

•Precise calculation is possible using clever ratios

Fermilab (1999,2001), Nf=0

(*)B D l

Update by the Fermilab group at Lattice 2004, Nf=2+1

No significant effect of quenching

preliminary

Implication for the CKM fitImplication for the CKM fitChange in the input

parameters:

• BK: 0.86(6)(14) → 0.81(6)(+0-13)

• fBs√BBs (MeV): 276(38) → 262(35)

• ξ: 1.24(4)(6) → 1.22(+5-6)

Plots provided by the UTfit collaboration (Pierini).

εK band becomes slightly narrower. Sea quark effect is being included.

Assuming the Unitarity…Assuming the Unitarity…Put a constraint on these hadronic parameters from

the UTfit with other inputs.

Topics not coveredTopics not covered• Spectrum, both light

and heavy• Exotics including

pentaquarks• decays:

ΔI=1/2 rule, ε’/ε• Hadronic decays

including DsJ• Nucleon decay matrix

elements

• Details of the lattice methods; heavy quark formulation, etc.

• epsilon-regime of QCD; determination of low energy constants appearing in the ChPT.

• Other theoretical developments

K

SummarySummary

• Many interesting physics results from the staggered Nf=2+1 simulation have appeared; chiral regime is reachable and the extrapolation is under good control.

• There is a risk of being irrelevant to QCD. (the fourth-root trick = locality?)

• Results with other (more robust) fermion formulations will follow especially using new generation machines.

Previous quenching errors are now being eliminated by real simulations.

We are very close to the first-principles simulation of QCD. Through the flavor physics, lattice QCD can put constraints on the SM, and thus contribute to the search for new physics.

Thanks toThanks to• I. Allison, Y. Aoki, C. Bernard, N. Christ, C.

Dawson, J. Flynn, E. Gamiz, A. Gray, R. Horsley, T. Iijima, T. Izubuchi, T. Kaneko, Y. Kayaba, A. Kronfeld, J. Laiho, C.-J. D. Lin, Q. Mason, C. Maynard, F. Mescia, J. Noaki, M. Okamoto, T. Onogi, C. Pena, M. Pierini, G. Schierholz, J. Shigemitsu, J. Simone, A. Soni, A. Stocchi, S. Tamhankar, Y. Taniguchi, N. Tsutsui, M. Wingate, H. Wittig, N. Yamada.

• members of the CP-PACS/JLQCD collaborations

• the organizers and the audience!

Backup slidesBackup slidesMachines, …Machines, …

Machines for lattice QCDMachines for lattice QCD• QCDOC

– 10 TFlops (RBRC) + 10 TFlops (UKQCD) in Sep. 2004

– another 10 TFlops in Mar. 2005

• apeNEXT– 10 TFlops (INFN) in late 2004.

• PC clusters at many institutes