The Fermilab Lattice Gauge Theory Project

URA Annual ReviewFermilab

March 12!13, 2004

Paul MackenzieFermilab Theoretical Physics

mackenzie@fnal.gov

Additional material at:http://lqcd.fnal.gov.

Paul Mackenzie

Recent big progress with unquenched improved staggered fermions.

Several groups compared their simplest

calculations. 10" disagreement quenched

→ few per cent agreement unquenched.

C.T.H. Davies et al., Phys.Rev.Lett.92:022001,2004, hep-lat/0304004.

What about slightly more complicated quantities?Do other light quark methods agree?

Paul Mackenzie

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High-Precision Lattice QCD Confronts Experiment

C. T. H. Davies,1 E. Follana,1 A. Gray,1 G. P. Lepage,2 Q. Mason,2

M. Nobes,3 J. Shigemitsu,4 H. D. Trottier,3 and M. Wingate4

(HPQCD and UKQCD Collaborations)

C. Aubin,5 C. Bernard,5 T. Burch,6 C. DeTar,7 Steven Gottlieb,8 E. B. Gregory,6

U. M. Heller,9 J. E. Hetrick,10 J. Osborn,7 R. Sugar,11 and D. Toussaint6

(MILC Collaboration)

M. Di Pierro,12 A. El-Khadra,13 A. S. Kronfeld,14 P. B. Mackenzie,14 D. Menscher,13 and J. Simone14

(HPQCD and Fermilab Lattice Collaborations)1Department of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom2Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, New York 14853

3Physics Department, Simon Fraser University, Vancouver, British Columbia, Canada4Physics Department, The Ohio State University, Columbus, Ohio 43210

5Department of Physics, Washington University, St. Louis, Missouri 631306Department of Physics, University of Arizona, Tucson, Arizona 857217Physics Department, University of Utah, Salt Lake City, Utah 84112

8Department of Physics, Indiana University, Bloomington, Indiana 474059American Physical Society, One Research Road, Box 9000, Ridge, New York 11961-9000

10University of the Pacific, Stockton, California 9521111Department of Physics, University of California, Santa Barbara, California 93106

12School of Computer Science, Telecommunications and Information Systems, DePaul University, Chicago, Illinois 6060413Physics Department, University of Illinois, Urbana, Illinois 61801-3080

14Fermi National Accelerator Laboratory, Batavia, Illinois 60510(Dated: 31 March 2003)

We argue that high-precision lattice QCD is now possible, for the first time, because of a newimproved staggered quark discretization. We compare a wide variety of nonperturbative calculationsin QCD with experiment, and find agreement to within statistical and systematic errors of 3% or less.We also present a new determination of α(5)

MS(MZ); we obtain 0.121(3). We discuss the implications

of this breakthrough for phenomenology and, in particular, for heavy-quark physics.

PACS numbers: 11.15.Ha,12.38.Aw,12.38.Gc

For almost thirty years precise numerical studies ofnonperturbative QCD, formulated on a space-time lat-tice, have been stymied by our inability to include theeffects of realistic quark vacuum polarization. In thispaper we present detailed evidence of a breakthroughthat may now permit a wide variety of nonperturbativeQCD calculations including, for example, high-precisionB and D meson decay constants, mixing amplitudes, andsemi-leptonic form factors— all quantities of great im-portance in current experimental work on heavy-quarkphysics. The breakthrough comes from a new dis-cretization for light quarks: Symanzik-improved stag-gered quarks [1, 2, 3, 4, 5, 6, 7, 8].

Quark vacuum polarization is by far the most expen-sive ingredient in a QCD simulation. It is particularly dif-ficult to simulate with small quark masses, such as u andd masses. Consequently, most lattice QCD (LQCD) sim-ulations in the past have either omitted quark vacuumpolarization (“quenched QCD”), or they have includedeffects for only u and d quarks, with masses 10–20 timeslarger than the correct values. This results in uncon-

trolled systematic errors that can be as large as 30%. TheSymanzik-improved staggered-quark formalism is amongthe most accurate discretizations, and it is 50–1000 timesmore efficient in simulations than current alternatives ofcomparable accuracy. Consequently realistic simulationsare possible now, with all three flavors of light quark. Anexact chiral symmetry of the formalism permits efficientsimulations with small quark masses. The smallest u andd masses we use are still three times too large, but theyare now small enough that chiral perturbation theory isa reliable tool for extrapolating to the correct masses.

In this paper we demonstrate that LQCD simulations,with this new light-quark discretization, can deliver non-perturbative results that are accurate to within a few per-cent. We do this by comparing LQCD results with exper-imental measurements. In making this comparison, werestrict ourselves to quantities that are accurately mea-sured (< 1% errors), and that can be simulated reliablywith existing techniques. The latter restriction excludesunstable hadrons and multihadron states (e.g., in non-leptonic decays); both of these are strongly affected by

The fundamental particles called quarksexist in atom-like bound states, such as protons and neutrons, that are held

together by the strong force.The heavier vari-eties of quark, such as the bottom quark, candisintegrate to produce other, lighter parti-cles, and the pattern of the decay rates is con-strained,but not determined, in the theory offundamental particles, the standard model.That pattern, especially the part involving the bottom quark, is sensitive to new physicalphenomena.But although accurate measure-ments of the rates have been made, the window on new physics has been obscured.This is because the binding effect of thestrong force between quarks modifies thedecay rates: unless correction factors can beaccurately worked out, the data cannot befully interpreted for signs of any physics thatis as yet unknown. This has been the case foralmost 40 years.But at last,Davies et al.reportan advance in lattice quantum chromo-dynamics, a method of calculating the effectof the strong force, that promises the calcula-tional precision required (C.T.H.Davies et al.Phys.Rev.Lett. 92, 022001; 2004).

The standard model describes allobserved particles and their interactions.Particles interact by exchanging other parti-cles that convey force. For example, in anatom, electrons bind to protons by swappingphotons with one another.This is the electro-magnetic force, described by the theory ofquantum electrodynamics (QED). In a proton, two types of quark, called ‘up’ and‘down’, are bound together so tightly, byexchanging particles called gluons,that this isknown as the strong force.Its associated theoryis quantum chromodynamics,or QCD.In thestandard model there is a third force,the weakforce, which is the mediator of radioactive !-decay. Another example of the weak forcein action is the decay of a heavy bottom quarkinto an up quark, through the emission of a W particle (which then itself decays to anelectron and an anti-neutrino; Fig.1a).

Despite its success, the standard modelleaves many questions unanswered. Forexample, although the observable Universeis made of matter and there is no evidence forsignificant quantities of antimatter, equalamounts of both should have been created inthe Big Bang. When matter and antimattermeet, they annihilate each other: if a smallasymmetry between matter and antimatterdid not exist at the time of the Big Bang, there

would be no matter in the Universe today. Sohow did that asymmetry arise?

If heavy particles that existed in the earlyUniverse decayed preferentially into matterover antimatter, that could have created thematter excess. In the standard model, twotypes of quark,bottom and strange,do decayasymmetrically.But this effect alone is far toosmall to account for the asymmetry. How-ever, there are many theories that predict the existence of other, massive particles thatcould readily produce the asymmetry. And

news and views

NATURE | VOL 427 | 12 FEBRUARY 2004 | www.nature.com/nature 591

Lattice window on strong forceIan Shipsey

A long-awaited breakthrough has been made in lattice quantumchromodynamics — a means of calculating the effect of the strong forcebetween sub-atomic particles that could, ultimately, unveil new physics.

because of the connection between asym-metry and mass, these theories also addressother puzzles, such as why electrons arealmost 10,000 times lighter than bottomquarks.

Searching for evidence of these particlescan be done directly or indirectly: powerfulaccelerators, reaching ever higher energies,could create these mysterious particles; orthere is the precision approach of looking forsubtle deviations in the properties of knownparticles, influenced by the unknown. If

Figure 1 Bottom’s up. a, An idealized representation of the decay of a free bottom quark into an upquark. In the standard model of particle physics, the process occurs through the weak force, mediatedby a W particle, and also produces an electron and an anti-neutrino. b, In the real world, however,there is no such thing as a free quark. Instead, a bottom quark exists in a bound state with otherquarks — such as in a B meson, bound by the exchange of gluons to an anti-quark. Gluons and quarkpairs are constantly emitted then reabsorbed; only a fraction of this ‘sea’ of particles is shown here.c, So the realistic picture of the decay of a bottom quark is complex. The B meson — a bottom quarkand anti-quark pair — becomes a pion (an up quark and an anti-quark), but the route is obscured bythe mass of gluons and quarks (of which, again, only a fraction are shown). Calculating the details ofthe process is fiendishly complicated. But new advances in lattice quantum chromodynamics meanthat precise theoretical correction factors can be worked out, and the problem effectively reduced tothe simple process shown in a.

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© 2004 Nature Publishing Group

The progress has been reported in nice articles in Physics Today and Nature.

Paul Mackenzie

Many of the mostimportant deliverablesof lattice QCD are inthis class and a special focus of our group’s work:

B B bar, Bs Bs bar mixing,B, D leptonic and semileptonic decay.

M. Ciuchini hep-ph/0307195.

These are examples of “golden quantities of lattice QCD”: single stable!hadron processes.

Paul Mackenzie

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Example of current work : D→πlν.Cleo!c will measure fD /D→πlν and fDs/D→Klν to 2". Interesting and rare CKM independent test of lattice heavy!light methods.

M. Okamoto et al., at Lattice 2003, hep-lat/0309107.

One!loop perturbative calcutions $in progress% will leave 8!10" perturbative uncertainties.Goal: make all other uncertainty significantly smaller than this.

f+DK=0.75

f+Dpi=0.63

$Preliminary!%

Paul Mackenzie

The clusters are currently housed in the New Muon Lab.

The 176 node Pentium 4 cluster.~100 GFlops.

Fermilab lattice cluster effort is led by Don Holmgren.

Paul Mackenzie

2000: 80 node Pentium III 700 MHz duals, Myrinet.

2002: 128 node Pentium 4 2.4 GHz duals, Myrinet.

2004 plan: 256 node 3.2 GHz, Infiniband? 350 GF.

2005: 512 node 4 GHz, Infiniband? '1M. 1 TF.

2006: 1024 node 5 GHz, Infiniband? '1.5M. 3 TF.

2002: 48 node Pentium 4 2 GHz duals, Myrinet.

Paul Mackenzie

256 node, P4 singles?Infiniband switch.

128 P4 singles, reuse Myrinet switch.Incremental cost: '1/MF.

Paul Mackenzie

US “Lattice QCD Executive Committee” $Sugar, chair, Brower, Christ, Creutz, Mackenzie, Negele, Rebbi, Sharpe, Watson% reports to DoE on plans and needs of US lattice QCD.

At February, 2004 HEPAP meeting, Bob Sugar, in a well!received talk, reported the “absolute minimum support required for health of field”.

Our answer: '3M/year. In FY04/05, 5 TF QCDOC + 1 TF cluster.

DoE!HEP response: '2M/yr.

Discussions are ensuing.