<<

PoS(LATTICE 2007)019 ferent lattice dif using http://pos.sissa.it/ pseudoscalar arious v singlet from ++ , our 0 ρ v m fla Licence. light e and the of π f of . 0 as r of spectrum such alue v the y Theory ution-NonCommercial-ShareAlik the quantities ysical Attrib ield ph F compute basic the Commons that e v oscop computing for Lattice in Creati on discuss the I of results onomy terms progress the calculations Astr spectr QCD. the the Symposium and under QCD on lattice compare ∗ 2007 of author(s) describe Physics the lattice 8QQ I also Glasgow by Germany of . I w , Building ugust of hadr er g A International G12 wned vie o [email protected] ur McNeile re d sity elvin Speak formalisms I mesons. QCD. 30-4 yright ∗ XXV K ensb g Cop .K. uly c

Craig Har Department The Univer Glasgow U E-mail: J The Re PoS(LATTICE 2007)019 , 2 a y of of er on η el- for are the the are ail- v that v ving v for from QCD man a xpen- of so , small. calcu- lattice lattice lattice de the ] partic- we half ha e 2 ground and mass than McNeile y [2 η focus alidating of be of the ariational Ho with Of v for an v The with been the mass w wing QCD and . the them of e See ith interpolating disconnected will Craig will v second vie . mesons, vie I of mass the W es ) of ha re structure re required viour collaboration MeV part where eloped ++ the a unquenched for discuss the lattice a v . part 0 =2+1 mak by t mass are 4260 f strange constant In In 800 beha ( de there candidates for n for correlators. calculations and for Y ] acuum the first this don’ pseudoscalar and start v inside [3 are I mesons I and and for correlators. decay important the and highly QCD around computation =2 mixing. light and results constant a an In f calculations 0 QCD non-singlet although Also singlet y be n a pion is η QCD. quenched the - understood. mesons an the to e our configurations η quantities lattice disconnected collaboration one the estimate v using QCD X(3872), with is by This olv connected , between fla well as , =2 v ) quantities, lattice mesons. ant pseudoscalar these f are more v between only in of mesons. n qcd ETM include between vy spectrum. y not singlet runs. calculations, than xpected lattice is t such e 2317 rele of ++ caused from who ( hea e, the s mixing 0 our is ] v man y still singlet consistent v be don’ D preliminary 2 the because [1 older ference there be on mesons 2 I lattice calculations model η is formalisms. fla products to are . that from ferences our non-singlet of dif the v The w pseudoscalar on intensi include will the simulation om dif quantities as fla and focus the from our vie QCD lying fr generation ge. quarks of v decay lattice a ork meson re mesons, compute the that means w results spectroscop results thought the lar 2 there w fla that such 2). basic sea lo singlet last are η to longer is this of with mass the lattice are that = collaboration for compute results pseudoscalar of ferent =2 for who the ) scalar freedom 1 in the our w ered of 2 f mesons recent v mesons dif v quarks + η the n The much and of ( vie case out ++ of fla 2 meson mesons . of errors mass suggests found 0 m correlators 0 re possible LHPC with 0 sea 0 for singlet y of results of and η a r disco = light for η the with el is ( plot of the map the v grees noisy the C calculation This of it a ask the P our for le the be summary between omissions de of sub-groups and v J of ]. been w that of ours GeV QCD an η fla fully masses [8 e v statistical not wer more who the the QCD v oscopy is ork sho xperience notation point status 88 ws MeV pseudoscalar fla to . po e arious I w meson the 2 ha the the spectroscop The xperiments are ]. act v mass for will compare η f e ≈ 1 . sho the complication try small [7 of of 600 noisiness spectr 2+1 the 1 ge is the The There In people are lattice that w that to the in the ector this ], is will on starting ]. lar ]. in v or singlet the I vie oduction 5 [4 the figure unquenched of with [4 er results calculations. , use although re at v mostly anomaly hadr computing w states The There In Another I Figure In note [4 talk light intrinsic d ays The Intr meson we e w standard vie w natural v will 2 ular results. 2. the opments lattice the ne re technique the glueball ETMC I a able mass, al lattice a meson η Har 1. axial si mass calculations calculations diagrams, lations operators. were Ho PoS(LATTICE 2007)019 2 is in x- an by η 12 e . The 250 fect me- 0 final (2.2) (2.1) . as 0 ef a the of ∼ η state wed fm. McNeile 2.2 with compute a as of 1 . vie freedom to to arded 0 and re order g Craig < with of η xcited re is e mass matrix a indirectly the meson the the also attempt and by first grees will (compare is ut 1, de mixing b the study 0 + smearing calculation is that recent η This 2 to GeV 0 glue , a ], = ours, η η v pseudoscalar light f [5 , 2 , n ) and to lattice ours. fla s been ! The v 5 a γ ) ) with 0.87(5) ariational ¯ s and fla 0 0 v ( ( ( = 2+1 technique singlet also 2 a S S 2 0 s s = from = quarks η η η = = 24 32 s ) ) f m our ]. has t . ]. f approach η f of 2 ( ( v n = = ) form n n P P n s η , π [10 ]. fla L L [11 49 η η 2 and . to calculations 32 04 m [7 a 4 . . , ) ) ariational √ 0 the with There 6 22 22 5 5 1 0 0 v r . . . terms / with = ( ( ( 3 ) staggered 6 5 5 2006 modern to a S S = = n n 0 d used from in GeV with r 5 η η = = = 0 0 QCD between ed A 2 γ GeV ) ) r r ¯ 0 0 0 v t t η d MeV) r r r ( ( UKQCD CS used formalism fer P P n s were + lattice of A couple η η u dif 548 and QCD QCD at 0.958 5 0.55(2) mesons impro lattice

2.1 γ ], ¯ = calculations u = will mass ETMC ETMC ETMC UK UK CP-P 0 ( = [6 will interaction channels. ++ η η s ) om 5 0 = t m 0 m (mass the using γ staggered ( CS fr n s y 3 2 1 0 A G η η lattice for presented equation collaboration the and

strong

,

η and were man 0 m r in the for of CP-P threshold d the mesons of ], 5 of 0 γ mesons GeV results [4 0.78 test results d η pseudoscalar via states , of MeV) + to decay η oscopy u mass 5 CS/JLQCD 0.548 γ ETMC scalar the 800 A the basis u = decay 0.61 the singlet ]. spectr η of [9 PS theoretical the be m Summary from The on interpretation CP-P that preliminary our m light v / ]. 1: around are V because fla e will hadr . The Both The The m [10 masses d The the results Feldmann periment, MeV 3. state light state, important Figur (mass Har son fm, PoS(LATTICE 2007)019 - is ut of sq en on b and v one The with light e ution oper 1 ution, scalar ) calcu- lattice sum or with McNeile the included in meson based challeng- 980 the ( is table of (1430), κ 0 QCD contrib ? qq 0 contrib are mesons. a erlap Craig in quenched K 2001. π v π the decay π o η ution η mass in see non-singlet equals of the (yet) ] interpolating lattice no and from the ]. the we the of mesons all? our [19 mesons strong ρ q sq v molecule, to classification qs q mass [15 at contrib do PDG resonance. for with from meson al. a fla the for its in comment mass xistence where QCD. due at used meson scalar or e of ferent are: 12 2 2 This ], from . . . light 7 not state, 0 0 1 than meson mesons . dif Roper ++ results data GeV meson 1 The [19 fect when 0 light   − κ lattice 0 the or tetraquark, ef data. 6 1 QCD K the ∼ ]. qs , . . 41 Bardeen tetraquark, of . 1 1 the widths m ∆ the noisy + 13 1 , the ution from for recent multiplets 0 , of by ρ xperimental decays calculations e see and lattice f lattice tetraquark see non-singlet quenched [12 as 0 0 2 2 π π more π π decay n a SU3 we to η η K K some meson the non-singlet contrib state our results paper ws with glueball, f are ] v + lightest properties from do lattice such 0 of main masses into vie fla the the our ] e, [17 4 include re v easier the + ] v mostly the and calculations 0 a so the lattice ] it a fla [16 together of is contain the [18 mesons answer states 100 is es only All mesons. [14 and it the P-w use al. before - consistent I MeV 560 265 290 al. to I + see if . lattice et Michael quark) the Γ ++ 0 subtracted mass xperimental mak 50 3 via et strange-light decays, 0 e are there collect data scalar ant lightest e Group be I 2 that and w the v vsek and light no a state, through This to for ]. . table the potentially Light decay SCALAR is QCD we κ for classify ++ MeV κ Mathur in 660 985 Lightest table [19 S-w 1: of 0 1474 1414 Prelo loop pertinent to discussion), M that the information 2: freedom. in reasons needs a generic via there to McNeile able of a of mesons ersial QCD results T mass products. v I 1 1 theory for that able some is correlators 1/2 1/2 quenched T states questions ] ++ q results missed decay going the hence 0 y detailed In grees e ) [14 for e important oscopy lattice decay k non-singlet contro v collect de number QCD am collect I The a I ha I the κ (see 1430 operators. more lattice . than 2 the (980) also (where our The correlator QCD. 1 ( (1450) spectr from 0 mesons discuss v 0 0 of Meson are a is or perturbation a K on lattice may corrected, F fla w The clear it miss ersial table table no so v scalar hadr The Although In In I There not The been chiral masses d one, operators the ++ via 0 mesons. to 3.1 ing. the contro qq light interpolating Har lations. quark-antiquark has ators, still mostly calculations, by unquenched . PoS(LATTICE 2007)019 P ++ ac- lat- 0 mass The using result er higher results v McNeile The the as clo w The on meson. ed − Craig ]. v + 1 ++ non-singlet calculation 0 [22 mesons. xperimental e the our impro . focused 0 ++ v of a 0 the QCD fla ely v to and the program 1 mass non-singlet b er lattice v and the ) ) ) lightest ) calculation ) − 9 clo light 2 45 13 34 19 ( + . ( ( ( ( lightest the GeV compared 1 that 1 of 0 ed 0 34 . 42 58 51 . a v 1 . . . ∼ the for 1 QCD non-perturbati ws 1 1 1 m the s of MeV, unquenched sho masses f ) impro 0 0 2 0 2 n 2P 2P an lattice 40 mass masses ( ] ] between ] the ] 5 UKQCD’ ] from 221 ] between Figure [16 [16 tadpole [19 for [18 . = s [20 2 [21 0 al. al. reported al. a from al. mass al. et et CS’ m cancel), al. QCD at al. meson, et in unquenched A et − et ) et Group figure 1 b an vsek vsek in m 980 lattice CP-P ( in Hart 0 Burch ference Mathur Lang as Bardeen ]. a ], Prelo Prelo w Dif from systematics from [23 [17 the configurations plotted 2: e of that are result results auge g of conference Figur mass Michael final fermions hope oscopy quenched. this used the ference ed the and v The configurations At dif . spectr . (in collection with ++ on partially and A 0 impro mass MeV ], for 3: hadr the [8 McNeile calculation d the ference 245 able stands T Har tion for consistent chirally of dif than tice PoS(LATTICE 2007)019 . ) 1 a a 3 ]. η is ω of b ge for the π U im- test and ut The also sec- S with [25 lar mass b I mass. in 1450 to the lattice useful and results from people singlet in ( in study mass 0 Fu, McNeile channel. with the structure of G in ρ be a closeness dominant , deal staggered the same to our pion were state mass. simple well. ar vidence the v by calculations of most to e the decay ed interpolating the the plot Craig meson v the fla the ould mass with 0 is I decay with DeT of a w pion meson quite 3 of some has of discussed discussed ++ mass about the QCD the It some determinant, masses xample lightest 0 correlator for e impro the to open As starting because are "what class the part for ws between forbidden it need the ++ are. of figure an 0 bad square meson light is as: lattice quark consistent just Bernard, sho with 1 In we specific A with threshold that both b 3 is w . the inconsistent the vidence decays the staggered ]. e xample, ne pseudoscalar being square applied of ference only masses e are of ++ decay are The wed particular it 0 [29 y the lattice decay dif π the a theory had ]. the Figure are calculations. π also Other sho of collaboration for of the where y west non-singlet threshold, good e fermions. mass the ]. the of [29 the consistent singlet something lo → if ours. MeV reformulated W is η the [4 and function v 0 , our on π the ) QCD a a least v our say be the and ETM gime discuss fla mass track v 142 MeV I that at re fla as rooting introduce for to the the vsek, to fla at fermions. the collaboration a 1430 can w meson because function or ( perturbation w Urbach what mass 600 the lattice 0 the ) decays small. a quark in ge just No required. K independence 6 collaborations to of ]. Prelo of twisted of seem see be from as lar belo and ] ETM results is sea wed. claimed 1235 required by lightest open [24 chiral to to threshold and ( 1 were 250 [26 1 test too the mass with staggered is does allo b + viour threshold of threshold, the molecule?" 2 results ed with not 2 the xperimentally a v caution decay actually check e Michael = η unquenched forbidden. from The beha ], meson (1450) calculations is 2 f threshold, analysis thought 0 + originally independent a as decay η in n width as by a preliminary masses, staggered π UKQCD channel [18 state ] the π w then w getically + are π of impro e 1 ω some between theoretical ely calculations mesons v calculation ρ b the collaboration π QCD al. e π and width results v [24 and the ], because this ha η and 2 ener and et ] the of original using quark preliminary methods. with its the the the is [17 = with "is → channels QCD of relati QCD [25 f in channel qqq the xplained computed π 0 MILC lattice sea ference n e q and and is a η xperimental plot structur some as e deal dif ++ successful such tracking lattice or Mathur the masses w 0 state puzzling, → a decay to lattice an lattice with preliminary the MILC Most 2 more fermions vsek 0 state state oscopy will by qq big ++ plot the as McNeile a η is decay collaboration estimate meson w xtended 0 I I a w collaboration calculations from e disconnected qq as the the ++ 4 ho ] open with with is ut the 0 Prelo ++ the the vious is and spectr the lightest ) b , by 0 This noted are questions ], 2+1 decay [28 it This , of of alidate such on of MILC pre ETM π v with the , that learn results As non-singlet staggered xperimental ork [27 figure there with hadron?". 1260 ω the e meson. study light o to ( , calculations w that unquenched of their hadr vsek 0 1 In The The In T The Although Some 2 mass mass ed Determining mass a a our d Michael v meson. this the the ger v =2 f 0 f fermions. the decay of meson n The enough correlators from Har lar the Prelo pro the Later meson. mass fla The include mesons QCD of 3.2 by where octet. cases tion of operator think PoS(LATTICE 2007)019 w + x and that ho ( grees space ψ de all McNeile gued candidate ock quark ar F dependence form (a after Craig measurement, the the is state tetraquark of olume actor recently v f This ++ e particular 1 v between threshold. ]. mass ha 0.4 form include one ] strong [31 a meson. links pion xcited to of (980) A decay 0.55 c 0 (1235) [30 that (1450) e 1 a 0 mesons. c b a via 2 of η 0.35 0.5 of π auge first formed g is square 0.45 with the functions restricted entional of 0.3 v e of ETMC a=0.09 fm, L=2.2fm xperiment 2 0.4 is v amplitudes. η e calculations, a structure ETMC a=0.09 fm, L=2.2fm ETMC a=0.07 fm, L=2.2fm collaboration con ++ ++ ETMC, a=0.09 fm, L=2.2 fm w inserting 0 0 pi + +pi, ETMC, a=0.09 fm, L=2.2 fm +- to a the channel MILC a=0.12 fm, L=2.4 fm 1 ω 2 2 0.35 the resonance or 0.25 function as QCD of 7 GeV GeV ++ 2 2 a at w 0.3 π π 0 no operator m m e-function as CLQCD in ) v measure x auge, a 0.25 ( and lattice state look g 0.2 accessible to w ψ state The state in ) to 1 0.2 attempted. the r the b state dependence + or of used x tool. lattice 0.15 0.15 tried then ( directly lightest attempts ψ fixing the 0.1 done of Mass olume not also is v by in the 4: scattering been 0.1 0.05 e are a e Mass the v commonly 1 1 2 2 theoretical

is

1.8 1.8 0.8 0.8 1.6 1.6 0.6 0.6 1.4 1.2 1.4 1.2 node done 3: m GeV m m GeV m ha is e a Figur charmonium, be Because study oscopy objects state that in there calculations aluable Figur to can v the found test is spectr a these y phenomenology past fields. QCD on that This one the still the X(3872)) . ) hadr x The In ( are d the freedom, lattice ψ ut ) component of r b indicates Har because for if antiquark continuum PoS(LATTICE 2007)019 0 a a = τ K a to in f we ) ely the K and that γ v do (3.1) out via weak γ on → also masses widths, lightest mesons McNeile ) vy-light constant → 3.1 just rule hence computed xperiment Hence mesons formalism 0 sensiti I are calculation the non-singlet state e hea 980 χ electro a vidence with ( a ( not e Craig 0 e decay ++ Γ decay a v that 0 our that here the calculations quite v from origin, ha scalar equation does similar the er Michael fla σ v w 0 a in the constant. is a strong with pseudoscalar the found f no decays glueballs we the at ] do model hadron and additional compute depend of of identifying light ho ] of to we 13 the [17 of ] the non-singlet decay can the from [33 constant for 390 ) ay xception constant. 0 of [33 viding γ constant e of the a MeV w scale, ]. − constants, width f γ 298 433 found pion connection constant 0 McNeile ards a pro of constants ] f e-function" [17 → of ards decay 320 only v decay the interesting the a decay σ CS, 0 [42 calculation decay Edw decay a ( coupling thus f aluable the A decay be of 0 Edw structure "w Γ alue constant v The a decay QCD for and v f 1, of a rule rule 0 ]. of for and the constant a ≈ the that and CP-P lattice ould the M of alue ery model hadron [29 small w of Method to decay A Peardon v v to sum sum leptonic alue lattice o renormalisation = . It 0 for v e and K a 8 i ge models decay ery v constant f tw Dudek 0 ] K ely measured v and Dudek also a the v lar | a that to is the [39 to e similar A from ] constant qq on The ] ]. measurement results v xample, | sensiti decay other e ]. calculation is 0 ang ha [38 xperimental lattice. UKQCD leptonic [34 notes h [35 0 e 37 respecti or a unquenched are W calculation. , f hadron this F results decay The some Thanks the the xtracted a coupling QCD the . 0.5 e meson. of [36 Group of depends from ]. a and Morningstar . that of Hiller should 0 on ) 0 using , QCD pion use a a Some Narison that f [32 and Maltman MeV xperimental had collect e to 980 lattice and 4: the σ ]. ( the I Pennington ables 0.9 width 0 A Shakin . mesons recently 130 theory to 4 a widths xperiment. of mesons [41 The the able e definition eV ]). to discussion widths. T o suppressed ++ Diehl k reported in 2.5 has quenched the computed of were 0 e to constant observ 4 ] decay is tw a auge table v [40 as by of correlator K as g The proposed configurations meson. oscopy ∼ w of K w photon In ] [32 the decay been ) that it . also ++ further also o γ structure relati from decay ) 0 → γ ], [34 singlet content actor , a SU3 auge reported ) f spectr tw has state g are comparison. small. the a eV MeV → (see the [17 as accessible on k for e The 1300 our scalars. discussed photon v w σ ( ] pure v 0 in be In 1450 molecule ( . quark o ( is π "small" 480 1 multi-quark Γ 0 hadr meson rules Narison In A Using There Computing Pennington [17 Fla tw a lightest within d ∼ light  the compute the be 0 4 ++ qqq . a f on of to mean are for to 3.3 should q decay and Har See the principle hadron current. 0 2 determine sum qualitati and mesons lattice. PoS(LATTICE 2007)019 . . , et 5 ++ for has 0 Mc- Hart non- (3.2) were PDG arten MeV MeV quark scalar lattice matrix hidden nature, mixing mixing ]. studied ork lightest table McNeile glueball reported. the the w is eing in sea Caprini in is [48 the Using the 1800 in W of of singlet coarse being from Craig of strong techniques mixing most act a and qq qq ]. w decay a candidates. ork entered fect our hence light. the calculations. calculations at QCD. glueball the no mesons lattices v w ef [29 mass artif ] ] glueballs 1710(50)(80) utions is 1300 fla ery and = ++ ++ the v only with [46 [47 the the for 0 0 s MeV ++ where ADS/CFT ut as 0 molecule, molecule, interaction for b w the contrib is glueball glueball glueball introduced M from quenched mixing , , , QCD strange Lee’ xperimental study test 0 quenched between comment e unquenched 1200 in singlet glueball, qq qq qq unquenched η vidence this to to MeV then strong e , hed consistent 1955, and to and the as is η meson ++ sizable found y on our comes mixing from 0 in v a ) by an tetraquark, tetraquark, Quenc 400 mesons ++ light fla qq more that possible weak, arten be is 0 ++ interest state, 600 0 estimated is w lattice ++ is unquenched dominant ( states the are 0 M 0 of π K π π π eing f recently ) range no ++ fected o π π π π spectrum K 3 , ] 0 there could the 74(10)% W ++ The ef for ( proposed decay 1730(50)(80) were 2 with 2 singlet tw the between glueball- the only = as there 85 [45 on the as mesons. . w 9 in be 0 on w ) there ++ our and PDG. for are operators 0 on ] v that 100 weak. = It al. results glueball M - section whether mesons. MeV 980 the fla ++ 544 109 137 where qq only mixing ( [46 case elements probably mass ) as et 0 that hed 0 Γ in to spectrum meson 40 200-500 f a w phenomenology the question focus ) found the and and from as this the Lee ] or ++ quenc 1710 were ( 0 Chen ) N In this should matrix will 0 lightest parameters obtained for f U [43 1710 states then xperiment I and quotes ] ( included. e ++ 0 600 QCD, interesting. studied MeV f 0 ( the mesons constructs discussed The light qq 980 441 fm. The be 0 1505 1724 [42 there and glueball f QCD. eper M results question continuum states. M of ) signal T arten ++ ]. answer As the 1200-1500 the 0.1 0 and a the qq that also lattice the the ]. the masses. [18 of states. their and eing ) can summary 1500 pertinent that to mass ( q [19 σ and W 0 Peardon that ( q calculations, f singlet theoretical found particularly we ) quenched studied raises , the 2002 Hart by Also collaboration ) PDG glueball oscopy is some predicts and (980) and our between ay glueball (1370) (1500) (1710) principle in spacing 0 600 just ) v ]. 0 0 0 Meson f w only QCD ( f f f ork the claims σ ++ This 0 in from ] fla glueball predicted ( 1370 f operators the unquenched w 0 . found [47 ( glue spectr correlator ] ) 0 are in model f Michael [43 One on ++ tables can lattice in on SESAM mixing old the the 0 operators, [46 ++ lattice while GeV Light and 600 0 ( ed the 1 4 glueballs ], summarise and 0 5: eper the done hadr f glueball There I The The Morningstar quark Lee + T fix d [44 if are 2 a able ++ xample. operators at singlet T Har in spacing between and between glueball The been under between Neile e dynamics so critiqued and or inside summary interpolating al. The 0 PoS(LATTICE 2007)019 to to ed qq ++ un- the and and The 0 were fit better of due The with is McNeile glueball glueball check ursts be ariational it done. b ]. attempted. v Configura- be ++ ++ fm, action singlet unquenched Morningstar so as 0 0 ]. fermions [50 be to Craig the er may w to [8 The 0.2 0.2 v combined our reduction the v and, can ∼ A clo ant from with ilson ] of scalar fla needs v a mass W mesons, ed ]. (600) [45 (980) (1710) (1370) (1500) v sources 0 the 0 0 0 spacing 0 rele the f data f f ++ f f mass [50 ++ 0 al. of result is operators. mesons 0 of with additional ]. spacing et The al. the impro . an ++ this lattice xtrapolation [50 5 et This 0 of e smearing singlet 0.15 QCD, ws singlet spacing Chen lattice least to Hart single our sho tadpole =780 MeV figure by v π singlet a 5 ery action. calculations interpolating m spatial by in v lattice fla at lattice and =520 MeV single UKQCD-II π our is of continuum v a couple dependence m the the a action basis figure fla QCD done and with At At of 2 action ], as action in will . ) types as 0 plaquette results ρ auge er o 0.1 10 w [47 where g m v (a/r spacing slope lattice tw mass lightest the unquenched auge ∼ ed clo states them) g ilson v mesons. of qq for the W ed qq with operators m Quenched SESAM Wilson, Wilson gauge, UKQCD-I Tad clover, Wilson gauge, UKQCD-II NP clover, Wilson gauge, UKQCD-II Tad clover, Iwasaki gauge, v used lattice mesons ++ of near smaller spacings plot asaki 0 of the ], UKQCD-I impro and the ++ ], Iw results 0 the [49 impro =775 MeV obtain unquenched π [48 used e =600 MeV types glue that y the lattice m π v written operators slightly 0.05 m of the a study summary that , both singlet both with suppression Symanzik A to found xisting ] y a SESAM e only masses unquenched range the as an [22 with of w of the QCD, collaboration of from xtrapolation. the fit it produced , e action, pion CS oscopy e use interpolating fects. non-perturbati ], v A analysis. are calculations ef the qq ha 0 because operators

[42 QCD

auge The

t

1 the 3 5 spectr 2 4

0

0 used g

for r

m CP-P ++ analysis Summary in and on SCALAR results ariational (with don’ v unquenched 5: continuum spacing than ilson a from e hadr a glue In Unfortunately The used strong. Peardon W d quenched do as ++ also calculation the tions squares to quenched Figur interpolating Har mesons with technique In lattice mass, w and calculations, 0 PoS(LATTICE 2007)019 0 ) y y y et r of of 0 ]). ed ed by the the the not use still The data the the pion used = of ay The e some QCD agree study [55 ork lattice v ut for ]. p w use ψ w be gion used ( McNeile to the 5 to of ]. resolv (b ha that The γ er π re alue scattering Mathur [61 ) as v of v ψ ]. 0 [51 plots than π w lattice calculations. 12. ]? interpolating ψ al. need . cle gely π Craig determine really xample used group 5 = 0 small ution [43 q e gh a γ mass et y calculations q [44 p lar groups quenched  ur ψ ( the is square be scale only QCD rather for qq π as QCD ( were 41 eper common method . w comparison T the ge scale 1 contrib MeV from a quark This algorithm fit entuck Other Edinb from (see ) with data, of lar K ge be the lattice should σ and This actions consistently use 544 the ( operator Colangelo e fitting to lar state the ) ]. Method e to to of in QCD. ]. fitting quenched v states ] y limit Hart recent mak ferent [58 e 600 moment ferent from [22 function 57 ( quenched MeV three algorithm. resonance can ++ 0 , by recent dif published a f ] the 0 dif a width disconnected curv the adapti found will the because limit as acts [25 Entrop the 290 a is the e of [51 at the v as used necessary from and quenched of interpolating light from that for w artif has This All ork is continuum as xample, units in for Bayes recently partly q e w . it ]. ] some the corrections q study fitting 5 adapti ersy MeV the or results 60 width e ut study v use w), qq F The [52 of signal v b , results this for lattice continuum a to Maximum ysical . QCD result size to 440 vie 11 operator of a [59 ph by Using the ws re the collaborations some area The Bayes the of operators, . form contro section orse, with a in adapti e result. mostly , in a get vie w finite part v QCD ) I in the limit re the and for as y to MeV fected resonance mass e correlator ] acti the MILC w their k af of a corrections Bayes 1430 agree compare spacing. ( glueball an [53 more 180 constant ? I using distinguish and slightly groups conference. unquenched groups. the The interpolating the less is K there not ) plenary single Roper with about as to quenched claimed π al., this a of pure of applied 2 so L be this continuum lattice the w did − conditions et the decay e past other to This fects at v lo section ferent use the of fects ed resonance used small. = the ef fit vidual HPQCD meson ha the ] ef dif as er p fix pion than I xperiment to a course). the this be status should v ( discuss concerns recently study In e o of indi at [54 actions π MeV. size mass ] is In of of to ) constant the of of from to π Lasscock boundary L ]. al. 2 will olume [18 pions the presented oscopy ainst 550 units. v fm state localized limit. action masses formulations, I been 56 plot et finite = mass , . results ag al. I results ∼ xponential (see view e found s decay group p ) v ++ 6 of concern No m number at ( er [55 spectr 0 y the staggered the pion finite 2 Hybrid ha asaki v lighter π 0.469 a 600 ysical results quantified this and xtrapolations ( lattice o 0 e , on ]. e = f < pion Iw the ) amuma ph v results multi-e be the computed and ation 0 q figure ed spacing. m r s ] a with [31 compare ha continuum v in of m entuck to hadr the much latest 600 In I Mathur There Another I Sug The ( K d Brief < better estig [31 0 calculate compare the ilson f v s used ery 4.1 in mass need impro computed by , obtain states Har mass W correlators. operators. in to with m 4. al. QCD studied v group’ with the to I calculations doing lattice confirmed PoS(LATTICE 2007)019 - a to to by for for due The or from from refer chiral ]. 1, groups closely meson. a need e McNeile xample, look function v noted e data ρ of [68 method a to to ery is or ference results v ] other may as the F Craig . dif w 71 sensiti ratio comparison actor of , we f a ne viously with There mass poor the the constant [70 cluster be pre ] (the as of ving, decay use ] similar w collaboration As [68 I mass. of a constant. 0.6 , meson decay could matching [62 disagree 7 impro data do fect ETM the ] pion is to ef ector This decay the problems of v [67 collaboration the MILC figure the constant. slightly the 0.5 the to the In of automatic this. of when method. ratio from from collaborations up e just a an , v QCDSF decay mass for 6 groups ALPHA interesting as calculations that square ] errors. mix and eloped ETM and 0.4 with 2 be ] the v problem [67 the π ETMC, a=0.09fm, L=2.2 fm RBC/UKQCD a=0.12 fm, L=1.9 fm expt CERN, a=0.08 fm, L=1.8 fm NPLQCD, a=0.125fm, L=2.5fm HPQCD,a =0.09 fm, L=2.5 fm MILC, a=0.06fm, L=2.9 fm QCDSF, a=0.07, 0.08 fm figure 66 with de f and by QCD , reasons of ] results 12 GeV mass, ] comparing in ould 2 mass of π ficult [65 66 w m the , were [64 nonperturbati eral used systematic dif It QCDSF 0.3 v their than a of lattice pion [65 as se of meson that function the results, CERN w and via the a be lot plot, ] ], ratio a the definitions in HPQCD as 66 group with treated. ector [64 , the v ], 0.2 presented ratio is ]. that could use method ] of to [65 hides A acts, [63 obtained unquenched techniques mass Z the [69 66 CERN is , constant of HPQCD in artif ay plots either mass There ], the [65 w CERN 0.1 that 6 analysis method [63 el. decay nucleon analysis the better the v pion NPLQCD quality APE) constants encouraging from oscopy of le actor This group or the ratio f figure the pion quenched (or the ery from of run), 0 much data v in the spectr of or decay gh MeV NPLQCD is 0.1 it 0.2 The ],

mass. that

0.18 0.16 0.12 0.14 subject

ur

terms, on π CERN ], the 4

data GeV f . data ) w 6: [59 ratio 2 ∼ logs, [62 find the a e hadr pion I The The No ( the Edinb superfine d vy-light ge the O the xtrapolation All MILC Figur Har renormalisation the together of the chiral at Jansen hea to pur compare ence e agreement PoS(LATTICE 2007)019 ρ ρ to be rho One type pion pion to mass mass decay Bruns CERN a theory ETMC the masses meson. McNeile the ρ for lightest the of ourable data. need between and the These of v field cancellation unquenched a issue. twisted the f e the Craig and xcited e v e rest quadratic v ] no mass of of from this lattice errors and ha at is or 8 [68 square fecti at the element threshold masses. ef all, mass found mass the pion w ] there visit The linear the a figure groups the 4 analyse of the 66 pion re . ut , y mixing statistical to kinematically in b to in for to for ] xtrapolate [65 the the e man collaboration light domain errors. simple decay 76 shift used more , time to e decay function meson errors, v ery the that is CERN ETMC a v a to [75 group ETM ρ 5% the 3 It w formulae ge used a as . is outside P-w for although 2 widely the lar estimated No ) w from a staggered, π ], L of 2 amplify CERN no . not ( ed [4 gulators 2 model via viour ) airly to v data. meson f re + PS ref The momentum results produced 2 π e mass 2 v decay were 13 gime, beha m / M xtrapolation of consistent, PS e the tends impro π re ha ector pions, dependence the q (M lattice ferent v box. o 2 o wed unit use dif mixing no tw plot tw that meson the MeV chiral xtrapolation mass sho collaboration light e with ρ gh masses the one of w that This 1 into ur were 400 ]. ne the Comparing by the remarkably studied a ETM to 74 side with chiral of e , suggests models for v are there Edinb the the nucleon 8 300 the decays ha additional [73 fit fected consistent is function. the mass This ρ for meson the L calculations and constants. the fect 0 ]. so where unaf 1 published models ρ

the in

the

figure ef were

0.8 1.2 group

PS ref PS

PS e / F / F point [73 v en, that in the ector QCD gely decay produced where in ha that plot will oscopy Urbach v orld results. tak as gimes ] momentum of 2 I lar w of ) w three re data is masses 8 π the of is L a and [77 This 2 Adelaide in spectr lattice ( some decay real meson . this The xtrapolation Ratio decay method pion ratio channel + on unit e ρ ρ ]. both on from The π 2 figure the ρ for 7: from the the m the [66 π e decay hadr one with Michael In In The The π Meißner q d the ρ chiral 2 collaboration is of for group Usually with and using Figur Har reduced study when meson. fermions. and mass, 4.2 data of reason dependence PoS(LATTICE 2007)019 ] ] ed [77 [24 (4.1) Bruns prelim- McNeile check be Meißner Craig limit). include fits I and collaboration the olume mass. v Bruns ]. MILC from by [77 pion the 0.5 ρ ) the 0.5 infinite 2 2 and π ρ scheme. the paper of ] M M obtained of ( the the [72 ln 0.4 4 π (in square mass 0.4 M counting from 3 gy ficients the c 9 the ] + of 0.3 2 of wer 3 π ener coef 2 po i M ETMC, a=0.09 fm, L=2.2 fm UKQCD/RBC, a=0.12 fm, L=1.9 fm MILC, a=0.12fm, L=2.4 fm Expt ETMC, a=0.09 fm, L=2.9 fm ETMC, a=0.07 fm, L=2.2 fm c 2 a Figure RBC-UKQCD [GeV c 2 self GeV π 14 0.3 2 0.2 π M the + function and m 2 π a from the of M dependence as 1 to c data 0.1 size coupling). + gulator mass 0 due ρ π 0.2 re meson the ρ M is S ω 0 = M

1

Quark that

ector published

ρ 0.9 0.8 0.7 0.6 ρ [GeV] v M 9: M from ficient e and g. light ], 0.1 (e coef modified [68 Figur the 3 a c of recommend oscopy ] the used ETMC mass 0 [77 estimates 1 spectr

1.1

0.8 0.7 0.9 0.6

V with GeV m from The ation on v other 8: e hadr data term deri Meißner d ainst The inary The Figur Har and ag PoS(LATTICE 2007)019 = to of for the the via the not 0 r alue then final ] (5.1) push mass spac- ], v is vious , CKM chiral to ysical ysical of lattice careful change kind [78 ob McNeile the ph ph problem obtained [56 a splittings the decay the staggered discussed important The MeV quantity ely scale in determined the mass be 2S-1S lattice calculations using v See yle to as of ed The some into ], crucial Craig assigned that v of w e to the other single nai Bo the xtract v the can the 10%. y is it good [82 e a I he requires as 241(3) 0 of 0 data. set a meson by of collaboration units r set to using if r ]. = as impro mesons man spacing. to ρ that number s units to 0 from ? sensiti CS of also hadrons D such of r are a [72 a f wed A K π used xample e f fm with fm e called ery are lattice xtrapolation. or vie mass alue v be for prerequisite lattice e ours ]. HPQCD also principle olv xample, of ? used v lattice re ρ CP-P v e for v requires is is K 0.49 groups in uncertainty dependence in in the [64 can fla the are As from or = 0 or is π K F quantities, result This f 0 f chiral r this spacing introduced being quantity older r 0.469(7) time, As problems that QCD most 2+1 ] a mass . of ]. = this the γ on ratio. σ There mass nucleon are use still 0 other π properties [82 ratio reduced f [80 r long of + use that 3 recent ρ estimated ], lattice with is alue ? determine 4.1 a s the w to lattice v be determination quark of the the it principle K program. an mass the 65 [72 the to from the calculations is . There to of for No In 1 meson. the K → of out The / , mesons. control shift from ρ = Sommer ? B with about wn a 2 0 , using 15 K HPQCD’ mass equation of r γ needs lattice is studying ) determined tension although kno spacing 0 0 charmonium calculations in + mass masses. staggered spacing. e r r scalar the ], that pointed the determine ( up v When ρ with determined ρ ] in mass e F This or ed on to potential. ha [81 v been is v calculation string determined. and theoretical → ]. RBC-UKQCD lattice [79 QCD potentials, gi the discussion fm, clear quark the lattice model is B Unfortunately the the has is [64 of error full xample the on the quark as e the impro mass e it unquenched in of 0.49 choices v , quark splittings via spacing lattice ρ ysical en or should vy = xample spacing alue resonance scale ha v the MeV F e use 0 v 4.2 spacing ph vy t calculations. conference such Marciano r decay current from Gi hea spacing. we good by the to with for ρ mass as to the hea 90 collaborations lattice ]. xtrapolation determine y don’ use. the the e determine Roper not set lattice lattice 231(3) fm the to [80 lattice potential, think section to and of to we mass lattice Also t to decays, accurate results is , the are of the ay unquenched in lattice the π the . f oscopy w the an the renormalisation of us as produced replaced the from 0.469 don’ quark V that e force the consistent mass I of that continuum weak precision v = consistenc from , at ert A ρ because fect vy 0 spectr meson number gely er v the r such ϒ quantities analysis sacrificed on collaborations, ef interaction v ]. on MILC/HPQCD popular lar is system, hea from the in w" of be con we higher xtrapolation. idea, element [57 the F ϒ Obtaining determine ector e requires o using the has hadr accurately "ne v fm, er T Quantities Ho One Other The based to strong 0 v d ws Determining DeGrand another hadrons the using r e good ery xtrapolations by choices number matrix light use e 5. Har sho units, the chiral their non-perturbati an from phenomenology QCD. of from to state. a of ing, semi-leptonic where v 0.49 of splitting in quarks PoS(LATTICE 2007)019 , t 0 a to to r be β by no the see fm. im- at that e (5.2) of mass ed about v RBC- ferent is set we xtrapo- may used doesn’ the ha fix McNeile e 0.48 y 6 dif the massless estimates ] that 10 . to data we for changed of the part 0 5 Ω this than [68 2 limits" Craig is + − performed table all / suggested fm about s some to should (-9)(13) note 0.44 w β 49 0 the in 0.55 . m dependence figure r when I some 0 0.45(1) 0.47(3) 0.48(2) 0.454(7) 0.469(7) as comparison. rather number > . chiral in a 0 q fm, 0.497 and formalism r 0.5702(75)(50) collect air mass relation m results I domain such for and between fermions data 6 on unf changed, calculations 0 0.49 discussions . collaboration the r spacing 0 xtrapolation is with fm, r ilson The an ysical, e er linear The of for ]. of v mass table of ALPHA ph ] than mass plot units. masses ETM the g-W 0 clo [41 In mass r be lattice 0.467 data. [87 the chiral action of alues the continuum ed a ratio making at of small. v interactions, ed summary ρ ρ v model al. A π π all In er quark ysical f f twisted g ut may v m m & of w summary ed be fix b et part 2 0 be cancel K/K* nucleon quark ph 0 Ginspar g or Method r the clo at ) fix alues needs in the q impro act report v quark strong 0 the of the all may determinations r on action. for I ork mass, to am w might calculations. the g to quenched the artif should domain Upsilon As w wer b mass ed so From that . of v lo 16 summary limit. to + lattice the intercept is 10 quark 1 "decoupling gy ( lattice Bhattacharya of pion under starting lattice because domain f for the - actions 2 2 2 2 0 2 0 = impro n chiral dependence 2+1 scale solutions actions, with as 2 0 the and are chosen dependence ˆ strate g systematics from figure 0 ] e phrase r with obtaining WF of here, stable the ] the ficient. v ] , in 0 mass leading the calculations. [58 w such to other 57 Summary ha r onshell set are the , [83 ] some no ]. coef 6: the the to the an reduced of also square erlap/D dependence 90 [80 plot 0 Aoki [24 fm QCD that mass of are v , r results I ] ] ] ] ] ] o ], as for ] able calculations approximate xtrapolate determined [8 the actions, 49 AL T e and ypocritical w ement . [8 10 only [82 [85 [78 h v [84 [84 part Peardon 0 mass [86 action, [68 be for ed their are is quark using lattice than v 0 ∼ er al. ainst r hadrons This v 0 acts, and in can r Group figure et ag that impro 0 Some of with linearly oscopy r clo from g . ETMC In slightly ] artif UKQCD impro JLQCD JLQCD action QCDSF QCDSF 0 collaboration Sommer reduced b 0 understanding collaboration r of using r unquenched ) spacing included 72 the using er a w e collaboration , ( act. of spectr v the of v of constant. O by alue Sommer being not sho to on [88 lattice clo problem MILC nai v operators a artif e recent lattice Morningstar ) alue / to HPQCD/MILC/FN v quadratically spacing formalisms, q 0 am v that See dependence r hadr 0 m ha I The One The My Fully The ement the r UKQCD d v I the related gue lattice eep dependence ar that lattice a limit. of lattice pro k so Har RBC-UKQCD the is UKQCD O(a appear late mass coarser PoS(LATTICE 2007)019 I ], w in of CS see lat- no year year [72 cou- open A issue Until scalar to ferent lattice calcu- an McNeile ]. are dif the studied. in required. This ++ This , CP-P studies spacing continuum 0 channels. [92 be cross-check has a are the Craig to claimed the ] unquenched quarks by lattice lattice of decay entually between RBC-UKQCD spacing. in unquenched collaborations crucial meson [91 e sea Ev needs v a for 1 the important. calculations a technique b time, Although the operators from s the set ]. other 1 lattice still S-w the issue of first to spectrum QCD data of [50 consensus doing operators, are channel. certainly that the the open be is Lüscher’ mass used importance collaboration using GeV range been for It lattice channel machines 1 0.8 be by e interpolating decay the with lattice will a about v in mass, w ha ays MILC the units. with ] decay w meson open bigger biggest there interpolating al pion belo 25 ρ on the to increasing an mesons , 0.6 reducing collaborations, or open dealt the 2 tetraquark ++ ysical of of questions the operators [24 0 due of for y ph q be to light GeV the be olumes, 17 2 should q UKQCD/RBC a=0.12 fm, L=1.9 fm UKQCD/RBC a=0.12 fm, L=1.9 ETMC, a=0.09 fm, L=2.2 fm. fm (QCDSF-UKQCD) Clover, a =0.08 decays π entually v with in 0 xample, m v MILC r e 0 man e around r and will partly program. 0.4 will because singlet square study or and the F that for applied ysical that strong to and the our whether states ph up QCD as algorithms v issue of results collaboration to w to alue ] ETM meson, fla v hope on of force. calculations 0.2 staggered gest + as [68 ocating clear − starting ements, the the do lattice studying lar ork o 1 ed v MILC I final type v T w function adv w definite QCD , in a to strong a coupling that no er the from ETMC v for not as on xotic resonances impro 0 pions, This the e 0 are impro are r 0.4 we

consensus

and

0.38 0.36 0.46 0.44 0.42 lattice

0 am meson. fm r for of years via ], I the ) we Ho no light vidence oscopy successful w vidence e ]. [89 resonances e required lightest approaches alue fe 980 the v ( from algorithm still the channel. [74 is decay 0 calculations spectr the a section to is with past The all technique some calculations, with on that “some” s unquenched the this the due with decay 10: results QCD is calculation. calculations, to e hadr pragmatic In In There After QCD d Conclusions the dealing ery xtrapolation v mostly lations collaboration Figur Har on lattice QCDSF-UKQCD e pling 6. tice mesons, e There QCD strong presented problems particles Lüscher’ of then PoS(LATTICE 2007)019 of . send- two- ferent ]. J part in 2+1 McNeile in QCD. collabo- dif Michael, for = as Int. , , ams quark limit n(f) and gr Craig collaboration. from ETM ]. 159–207, . Chris lattice in dia dynamical action light of the oximation ved 243–305, MILC arXiv:0709.0008 thank inter (2000) era results o with oy-steiner formalisms, , . masses r I continuum appr thank the pseudoscalar discussions ong impr A15 I om ]. the hep-lat/0107021 (2006) [hep-lat] fr states str [ hed . for QCD . for disconnected in meson from compare the 429 precision masses. Phys. . and simulations 0 quenc eta’ paper of to [hep-ph] hep-ph/0607133 mass a [ baryon lattice ]. in 054502, those high ]. Rept. esonance Methods qcd Mod. the and Debbio, r ays . and of J 553, w sector mesons 1 meson eta this xcited Del ferent e b Phys. gs ]. (2002) al . Int. mesons to , wilson non-perturbatively scalar , the of [hep-lat] dif hig older reading the (2006) McNeile, of of quality D65 hep-lat/0211040 ved singlet Luigi Neutr [ hep-ph/0610139 . eport o C. the , v r for The for scalar arXiv:0709.4224 from the C48 , mesons 18 fects Re . of patterns J and k0*(800) Impr Ef to y , , Flavor states of estimate nonet status [hep-lat] , appropriate arXiv:0706.1262 Urbach, 074503, world: hep-lat/0403007 al. al. results The , [ Bernard, A Phys. hep-lat/0610021 results al. An [ Michael Phys. , Man be C. fermions on , et. et. . et. eshold the al. ed el. hep-ph/0509265 Richards, and [ Eur (2003) 204, v er hadr thr mesons pseudoscalar , et. low-lying g Chris on le Claude 014501, M. mesons: spacing g comparable longer Lesk Allton Allton to , of arXiv:0708.1295 the of y D67 I. e h , C. sta determination R. R. . . no and preliminary in Moussallam, v are Aoki (2006) scalar V s Michael oac C. C. heavy fails Re 747–756, (2004) lattice S. B. qcd study with percent scattering use C. . w vies may that Horsle ]. ]. . k Irving, light structur appr ne to and T2006 D70 Da Scalar the fixed pi of arXiv:0709.4564 Phys. C. . cross-checks ooting v , , (2006) r Lattice LA Lattice at at of me The mesons A. , , Roger Re results oscopy Quark do , . qcd qcd oS Lattice al. al. qcd A21 attern P Why Collaboration, to , P Collaboration, Collaboration, wing gory in et. et. Collaboration, errors anson, Phys. calculations Christine spectr mass QCD CS , -singlet qcd lattice Pennington, Collaboration, Phys. Liu, Gre allo A Sw ada for on . esentations R. Creutz, W McNeile, wledgements B. S. data. Basak Descotes-Genon Feldmann, QCD Schierholz, for ences . thank epr hep-ph/9907491 hep-ph/0601110 hadr lattice r hep-lat/0702023 Mod. flavour masses flavor [ twisted lattice [hep-lat] fermions [ UKQCD CP-P E. UKQCD C. ETM S. E. T S. H. M. K.-F JLQCD M. I important me quest d e v is [7] [6] [5] [8] [3] [4] [1] [2] [9] [15] [14] [13] [12] It the Har ha lattice [10] [11] ing ration Gerrit Refer Ackno PoS(LATTICE 2007)019 97 is the , 0++ . . v in 1p 027, (2004) meson ed Lett. Re McNeile limit of what lattice . er and G33 v 094503, g and of g states D70 om Re 054506, and (2006) . s ]. fr Phys. Craig v e states sta , , non-singlet Phys. ]. Re . (2004) ghost J Phys. flavor continuum , , (2001) and T2005 glueball dynamical elator xcited ]. lattice 094505, mesons masses e and structur D70 the Phys. in two qcd LA . , v on D64 hep-ph/0607110 its corr 114024, . , with oS physics v Re singlet Scalar is hing P with loops scalar (2006) , hadr Re qcd of meson lattice al Radially oac scalar fermions for (2006) what arXiv:0705.3314 Phys. D73 light oscopy om [ , , . particle Chir fr hep-lat/0105015 oscopy Phys. the v quarks σ of Appr [ lattice , , Scalar of D73 Masses s Re er Zhang, hep-lat/0106008 on ed . esults [ the verlap Sroczynski, spectr loops w v r om o er J. ]. spectr fr is g st al Z. Re vie Soni, g hep-lat/0209063 e flavor ir [ Phys. quarks: Thack on operties 054505, and hir F Re , harmonia with ]. A. sta c 1439–1458, , actions and meson c Pr Michael, ed H. , 014509, wher Phys. al. hadr of er Ma, , and quark C. ved and g o . and g J. et. (2002) lattice ee , mixed Mesons . (2007) sigma(600) quarks: Scalar 19 Miller 266–268, and sta Light ao (2002) thr impr the , Michael, ]. Liu, S. decays ginos, Y esults mesons D65 and ved r . and Isgur adiation: A22 . ved al. o Or r Y on v C. vsek, o M. D65 with with lattice: N. . (2003) . et. Re K. v ]. hep-lat/0604009 . W Lett. impr and scalar Liu, [ photon McNeile, impr the Prelo qcd Re Lattice 119 McNeile, [hep-lat] fermions C. C. elation, S. wo a0(1450) on uchi, ally Khan Phys. hep-lat/0402030 T [ , C. with Phys. ed Eichten, ]. spectrum qcd: hir Phys. corr and Ali er c ons lattice Izub C. , E. Suppl. Hart, 014508, puzzling McNeile g Chen, . ons hep-lat/0701021 g ards, qcd . T A. of , Mod. lattice Fu, mesons C. A. Y hed oc. hadr the , [hep-lat] sta ]. ]. ]. ]. 094505, gator hadr Z. Collaboration, Pr Edw The ]. hep-lat/0510080 of the , of Irving, [ (2006) , study wson, two-flavor ar opa Duncan, Location, G. on C. al. Scalar A oup x(3872) Dynamical pr hep-ph/0607140 Light , , Da tests Excited unquenc , [ A. Phys. R. fects (2004) D74 , hed DeT A. et. , ? Gr . al. al. oscopy , C. Ef v in al. and al. al. to 014506, C. ]. Qcd and quarks et. et. Collaboration, Re D70 et. scalar Nucl. arXiv:0707.2402 Collaboration, Collaboration, et. Collaboration, . hep-ph/0406196 gory et. quenc Data , [ , v spectr vsek, vsek, 172001, 1–1232. CS Bardeen, Pennington, Bernard Re oscopy hed Gre A . (2006) on Phys. Dudek , R. A. Mathur Mathur coupling Frigori Aubin W Bernard, B. Narison, Prelo Prelo Burch J. . article . harmonium hep-lat/0407037 hep-lat/0601026 hep-ph/0512256 hep-lat/0104002 hep-lat/0510066 hadr qcd (2006) particles [ its [ partially [ [hep-ph] quenc Phys. dynamical [ arXiv:0709.4582 spectr [ D73 (2006) fermions 074508, c UKQCD W UKQCD N. S. CP-P T S. J. R. E. C. C. S. C. CLQCD N. M. P d [17] [19] [21] [18] [34] [22] [20] Har [16] [33] [23] [26] [25] [24] [27] [28] [30] [31] [32] [29] PoS(LATTICE 2007)019 , . , v om Re qcd with fr the (2006) Phys. McNeile C70 scalar glueball , of D63 -singlet pion . Phys. . v lattice , v (2004) mesons: D73 . Re 067, v fitting Re study p-wave Craig study qcd ved ]. (2005) vector scalar o xcited D70 simulations Re flavour of e in . iso scalar v Phys. st Phys. , qcd and (2001) lattice Re B605 , lattice fir the Phys. lightest A , 06 om the o(a)-impr fr opic arXiv:0705.0861 Lett. and volving ained-curve constants esonance the Phys. ]. , of r in in , mesons 014017, 014510, ance, xcitations JHEP glueballs v ]. qcd lattices e , ]. qcd with Phys. constr anisotr masses , Decay lowest scalar decays an opic (2006) Picka (2006) constants constant adial qcd ]. b hep-lat/0608026 scalar lattice r spectrum of [ J. decays the lattice mixing om of in b D73 fr of D74 in adaptive . glueball onic . and decay anisotr in Michael, v v decay and lattice meson An Re Re on C. ]. ]. and glueball hadr 114504, width The om Mixing constants nucleon fr mesons scalar hep-lat/0003012 and the [ spectrum masses and Phys. Michael, Phys. ]. the , . , hep-lat/0010019 On [ method: (2006) hep-lat/0607032 decay 20 C. of [ , elements ]. factorization Scalar qcd potentials Michael, Michael, Mass , e hep-ph/9906267 Charmless the , [ Pseudoscalar D74 054503, eper glueball C. C. McNeile, al. mesons . k*0(1430) bayes T of v s(11)(1535) ]. matrix 114503, ang, C. xplor Static et. lattice Re The quark M. and and e Y , and McNeile, 244–247, xcitations and 14–22, e (2000) and to al. scalar C. hed Roberts, and hep-lat/0108022 hep-lat/9910008 Leutwyler ]. [ [ ]. Phys. (2001) et. empirical K.-C. ]. D. unihiro , Scalar D62 H. (2006) light ways . K parity Calculation Peardon, Herdoiza, Hart, Hart v McNeile McNeile (1999) C. . a0(1450) w hep-lat/9901004 and Bali of D63 T J. hep-lat/0405001 [ esonance and Re hep-ph/0512364 . unquenc G. C. A. C. A. spectrum e r , [ v Ne arten, S. ang, ]. and 034502, 014015, B642 mesons Even , M. ]. ]. B462 Re , om W qcd G. Chua, sequential fr eing natur Phys. al. H. and , Roper Lett. a0(980), 0++ W 034509, Hiller nucl-th/0406030 , Lett. [ et. (2002) (2000) the 132001, Glueball The Phys. D. , , , al. lattice oscopy and G. Colangelo, C.-K. . The to mesons Krassnigg, Phys. al. al. quarks et. Collaboration, D65 D61 hep-ph/0306199 G. for , Phys. singlet and [ Collaboration, Collaboration, Collaboration, Collaboration, Collaboration, (1999) and . . hep-lat/0510074 hep-ph/0310312 , [ [ A. v v et. et. (2006) spectr of 042203, 074017. sea qcd mesons Shakin Re Re Cheng, Lasscock Lee Collaboration, 96 Morningstar on D60 . . Diehl Holl, Maltman, Mathur J. M. G. Chen Chen v .-J. Caprini, . . hep-lat/0604001 hep-ph/0508104 hep-ph/0105194 hadr [ heavy-light [ Re Implications Phys. (2004) (2001) lattice spectrum wilson [ Lett. 014516, scalar Phys. 034504, masses algorithm [hep-lat] 137–143, UKQCD C. UKQCD UKQCD H.-Y A. I. C. K. TXL Y SCALAR W M. UKQCD UKQCD Y N. B. d [41] [42] [37] [43] [40] [36] [44] [39] [38] [48] [45] [49] [46] Har [35] [50] [47] [51] [52] [53] PoS(LATTICE 2007)019 ]. , ]. on on al Nucl. lattice , the Suppl. hir ecision McNeile c Is 95 Phys. , 094507, pr wall , and oc. limit quarks quarks , constants T2007)022 and Pr Lett. ittig, Craig qcd . (2-fm)**3 High ations v W quarks (2005) a (2007). domain wilson wilson oS(LA Re decay angians Phys. H. P on 3–18, , gr continuum lattice light D72 ]. constants la and with hep-lat/0701009 and . light light collabor [ in v , Phys. qcd Nucl. al hep-lat/0610059 y , hed mass , [ e Re with qcd (2001) Shigemitsu, hir with with 014504, 082, decay T2007)090 c qcd wall go? ]. J. masses ukqcd 94 full 056, quenc arXiv:0706.1726 to Shark Phys. Qcd Qcd , twisted in , and J. and esonances oS(LA r The (2007) lattice fermions (2007) fective P qcd ]. meson eady ]. domain K. qcd Suppl. , r ]. (2007) Ef rbc 02 antalo, antalo, D76 for oc. 02 T T mass we . ]. the f(k)/f(pi) oject Lepage, Pseudoscalar v e Pr ittig, lattice flavor . a-quark maximally lattice hep-lat/0107023 N. N. pr P oussaint, by [ ee-flavor Re JHEP Ar W fects T Michael, etr , age, om ef JHEP T G. thr full v and 2+1 and and fr H. ]. , twisted D. Phys. C. , in Sa masses: meson Phys. hep-lat/0606023 om al. [ , J. and vies, fr and 21 , esults , analysis 243–251, 16 et. Nucl. volume r quarks Da M. , simulations Okiharu, = quark . m(b) simulations: constants H. hep-lat/0409039 Petronzio, Petronzio, ]. McNeile, hep-lat/0006026 F data [ . [ inite and hep-lat/0610066 Dynamical constants 094501, ]. [ l(s) T F , R. R. esults Allton (2001) C. Sommer wilson and r . , , physics and and hep-lat/0503014 al. C. decay C. [ pseudoscalar R. fermion ealistic with 179, r , fermion decay ginos, et. Niedermayer and ds light B518 (2007) . at Ishii, Or Irving, 261–263, F 377–399, Haefeli, wall light hep-lat/0701012 Luscher Luscher ollana, [ and two N. C. spectrum K. F C. D75 Lett. (2006) oscopy meson Heitger d simulation . M. M. 136–174, milc v A. E. J. simulations k, [hep-lat] Boucaud (2005) with ]. ]. ]. and (2000) dynamical . Re qcd domain Lepage, , the xperiences P Phys. pi, spectr . Collaboration, e Simulating upsilon , T2006 P for qcd (2007). 140 of , hep-lat/0311039 304–311, Giusti, Giusti, (2005) st [ Tsumura, hed Bedaque, the Durr B588 hep-lat/0506030 Charmed G. . LA ir Phys. al. [ Dd-hmc L. L. The F , , F K. of S. flavour , . oscopy meson . oS et. P al. i: ii: Status Suppl. B721 P al. 3–16, Lattice vies, (2007) Actions Phys. , UKQCD Collaboration, et. massless? Collaboration, 2+1 Collaboration, Unquenc eler et. Da oc. quarks spectr Light T2007)005 122002, Debbio, Debbio, anuma, Collaboration, Pr Phys. and Beane, H. yle, B650 on Nucl. (2004) lattices. . lattices. , Gock Colangelo, Gray Jansen, Sug Urbach, Bernard, Aubin T Del Del R. Aoki, Bo garithms oS(LA . hep-lat/0701013 hep-lat/0011074 hep-lat/0507013 hadr valence determination [ [ [ arXiv:0707.3309 P Nucl. [hep-lat] Phys. 129 lattice: (2007). up-quark fine lo qcd fine Lett. (2005) G. HPQCD C. S. A. L. C. K. S. C. L. P H. RBC M. C. UKQCD ALPHA ETM d [61] [64] [60] [63] [57] [65] [55] [59] [58] [62] [66] [56] Har [54] [72] [67] [69] [71] [70] [68] PoS(LATTICE 2007)019 . . v v , Re Re Phys. ved hed qcd , o (1991) the D73 the meson Nucl. McNeile . , , v to 20 (2005) Phys. Phys. quenc fermions om decay , T2006 rho , Re continuum lattice T2007)133 fr Craig 237–254. width om LA ]. C40 qcd in the o(a)-impr xperiment fr . Suppl. s and ]. e J fermions oS of Phys. of oS(LA lattices P al , meson s P oc. , decay , (1991) onts lattice applications Pr qcd Phys. opic Chir gut-susskind in bilinear 839–854, . wilson pseudoscalar o its flavor 125–130, k vector confr ]. sector B364 of meson Eur a ved behaviour Phys. , and o lattice two oung, ρ ved anisotr of al qcd Y o (1994) ]. simulations lambda(ms-bar) (2005) ]. Phys. full on the meson Impr fields Nucl. D. with of dynamical Chir ]. , impr of observables u, hep-lat/0103023 ]. decay om R. B411 [ lattice of theories The fr B628 W hep-lat/0511014 Nucl. e [ fermion calculations , i: with and -1 and S. onic oscopy ospects fects Phys. Wright, Lett. for gaug wall ef . pr M. ecision simulations ]. ameter f V lattice Hadr J. 229–237, volume calculation spectr ]. 034504, actions mesons S. hep-lat/0212039 and Nucl. par [ fermions Phys. Determination om Thomas, , on cutof , and lattice , . qcd fr ]. e domain ess and High-pr finite ver hep-lat/0104013 22 W g hep-ph/0402299 in al. glueball , [ (2001) [ uning gr hadr (2006) in hybrid o T Michael, ]. clo esults A. theory al. et. gularization Lar , lambda r hep-lat/0212020 , e pr 054502, [ , |v(us)| r hep-lat/0309171 C. Sharpe, Lattice scale [ al. et. 1-+ D73 B519 , ficient the al. Light with of . ed R. , gy of ]. v et. Ef . 094502, al. and 231803, of dynamical Booth Tsushima, ar et. lattice vies S. ]. particles al. Re (2003) Lett. et. S. limit oscopy: ener K. for Da Infr hep-lat/0301024 yang-mills et. 177–184, hed Leinweber [ , al Irving 405–407, Lee, ]. H. (2001) D68 the hep-lat/0304004 (2004) . Phys. [ B. . . Phys. Aoki hir Peardon, C. , spectr McNeile v T , c W Sommer su(2) Aoki 93 set unstable calculation S. D. J. hep-lat/9704011 Re D64 A. C. (2003) [ , C. determination R. Thomas, in S. [hep-lat] to . of qcd potential the qcd (2004) ]. ]. 074505, v . Meissner M. determination hep-lat/9807015 Lett. es quarks [ W Re 022001, . A Gupta, v way Collaboration, Phys. 129 , ecise B556 Lattice and , A. ate obing quark , R. w hep-ph/0502212 Armour Re partially-quenc , Pr al. U.-G. alpha-s Lattice [ (2003) . Pr ne al. Phys. of oscopy Lett. W et. hep-lat/0610106 , (2004) ener dynamical Signatur A [ 114504, 4043–4061, Suppl. and g and et. , static , quarks Collaboration, 2 D68 Phys. Collaboration, Collaboration, 92 Collaboration, . hep-ph/0411223 qcd , Collaboration, Collaboration, ce eler [ v = oc. spectr Phys. 183, 014513, CS The , Re Pr for Leinweber Allton, DeGrand, Marciano, A Bruns Morningstar non-de (1998) (1997) on Lett. n(f) apolation . Luscher Li, Gock J. B. Schierholz, Bernard J. Sommer R. v Bhattacharya, A. lattice C. . . . . xtr hep-lat/9310022 hep-lat/0504022 hadr Phys. D58 and (2006) with Phys. (2006) [ lattice D56 353–361. dynamical static arXiv:0708.3705 Re [ constants e in (2007). 97–119, M. C. UKQCD QCDSF-UKQCD M. T M. ALPHA UKQCD C. R. JLQCD T CP-P HPQCD D. C. P W G. d [92] [91] [90] [89] [88] [87] [85] [86] Har [73] [83] [82] [84] [81] [74] [80] [75] [76] [77] [79] [78]