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Christine Davies University of Glasgow

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Christine Davies University of Glasgow Lattice field theory - a European perspective Christine Davies University of Glasgow European strategy meeting Krakow September 2012 Tuesday, 11 September 2012 Applications of Lattice QCD/Lattice field theory Annual proceedings of Particle physics lattice conference: http://pos.sissa.it/ QCD parameters Hadron spectrum Hadron structure Nuclear physics Glueballs and exotica CKM elements QCD at high temperatures Theories beyond the and densities Standard Model Nuclear masses and properties Quantum gravity condensed matter physics computational physics Astrophysics computer science ... Tuesday, 11 September 2012 Lattice QCD = fully nonperturbative QCD calculation RECIPE • Generate sets of gluon fields for Monte Carlo integrn of Path Integral (inc effect of u, d, s, (c) sea quarks) • Calculate valence quark propagators to give “hadron correlators” • Fit for masses and matrix elements • Determine a and fix m q to get results in physical units. • extrapolate to a =0 ,m u,d = phys for real world • cost increases as a 0 ,m l phys a and with statistics, volume.→ → Tuesday, 11 September 2012 REPORTS mud, corresponding to Mp ≅ 135 MeV, are difficult. vector meson (r, K*) octets that do not require (25, 26)and forour setup(27)], simulating di- They need computationally intensive calculations, the calculation of disconnected propagators. rectly at physical mud in large enough volumes, with Mp reaching down to 200 MeV or less. Typical effective masses are shown in Fig. 1. which would be an obvious choice, is still ex- 5) Controlled extrapolations to the contin- 3) Shifts in hadron masses due to the finite tremely challenging numerically. Thus, the stan- uum limit, requiring that the calculations be size of the lattice are systematic effects. There dard strategy consists of performing calculations performed at no less than three values of the are two different effects, and we took both of at a number of larger mud and extrapolating the lattice spacing, in order to guarantee that the them into account. The first type of volume de- results to the physical point. To that end, we use scaling region is reached. pendence is related to virtual pion exchange be- chiral perturbation theory and/or a Taylor expan- Our analysis includes all five ingredients tween the different copies of our periodic system, sion around any of our mass points (19). listed above, thus providing a calculation of the and it decreases exponentially with Mp L.Using 5) Our three-flavor scaling study (27) showed light hadron spectrum with fully controlled sys- MpL > 4 results in masses which coincide, for that hadron masses deviate from their continuum tematics as follows. all practical purposes, with the infinite volume values by less than approximately 1% for lattice 1) Owing to the key statement from renor- results [see results, for example, for pions (22) spacings up to a ≈ 0.125 fm. Because the sta- malization group theory that higher-dimension, and fore baryons (23, 24)]. Nevertheless, for one tistical errors of the hadron masses calculated in local operators in the action are irrelevant in the of our simulation points, we used several vol- the present paper are similar in size, we do not continuum limit, there is, in principle, an un- umes and determined the volume dependence, expect significant scaling violations here. This is limited freedom in choosing a lattice action. which was included as a (negligible) correction at confirmed by Fig. 2. Nevertheless, we quantified There is no consensus regarding which action all points (19). The second type of volume de- and removed possible discretization errors by a would offer the most cost-effective approach to pendence exists only for resonances. The cou- combined analysis using results obtained at three the continuum limit and to physical mud.Weuse pling between the resonance state and its decay lattice spacings (19). an action that improves both the gauge and products leads to a nontrivial-level structure in We performed two separate analyses, setting fermionic sectors and heavily suppresses non- finite volume. Basedon(20, 21), we calculated thescalewith MX and MW. The results of these physical, ultraviolet modes (19). We perform a 9.the Quantumcorrections necessary chromodynamicsto reconstruct the reso- two sets29are summarized in Table 1. The X set is series of 2 + 1 flavor calculations; that is, we nance masses from the finite volume ground- showninFig.3.Withbothscale-settingproce- 2 include degenerate u and d sea quarks and an state energy and included2 them in the analysis dures, we find that the masses agree with the overall χ toadditional the centrals sea quark. valueWe fix isms determined.to its approxi- ( If19). this initial χ is larger than thehadr numberon spectrum observed in nature (28). of degrees ofmate freedom,physical value. i.e.To largerinterpolate thanto the thephys- number4) Though of individimportantualalgorithmic inputs minusdevelop- one,Thus, thenour study strongly suggests that QCD all individualical value, errorsfour areof our enlargedsimulations bywere arepeated commonments factorhave taken suchplace thatrecentlyχ2/d.o.f.[for example equalsis unity.the theory of the strong interaction, at low with a slightly diff2erent ms.Wevary mud in a If the initialrange valuethat extends of χdownisto smallerMp ≈ 190 thanMeV. the numberTable 1. Spectrum of degreesresults in ofgiga freedom,–electron volts. anThe overall,statistical (SEM) and systematic uncertainties a-priori unknown2) QCD correlationdoes not predict coehadronfficientmasses isin introducedon the last digits andare determinedgiven in the first byand requiringsecond set thatof parentheses, respectively. Experimental the total χphysical2/d.o.f.units: ofOnly thedimensionless combinationcombinations equalsmasses unity.are Inisospin-averaged both cases,(19). theFor each resultingof the isospin finalmultiplets considered, this average is (such as mass ratios) can be calculated. To set the within at most 3.5 MeV of the masses of all of its members. As expected, the octet masses are more overall uncertaintyoverall physical ofscale, theany centraldimensionful valueobserv- of αsaccurateis largerthan the thandecuplet themasses, initialand estimatethe larger the ofstrange a content, the more precise is the Gaussian error.able can be used. However, practical issues in- result. As a consequence, the D mass determination is the least precise. fluence this choice. First of all, it should be a This procedurequantity that iscan onlybe meaningfulcalculated precisely if theand individualX measureExperimentalments(28 are) known notMX to(X set) MX (W set) be correlatedwhos toe experimental large degrees,value is w i.e.ell known. if theySec- arer not - for instance0.775 - based on the0.775 same(29) (13) 0.778 (30) (33) input data,ond, andit should if thehave inputa weak valuesdependence areon largelymud, K* compatible with0.894 each other and with0.906 the(14) (4) 0.907 (15) (8) so that its chiral behavior does not interfere with N 0.939 0.936 (25) (22) 0.953 (29) (19) resulting centralthat of oth value,er observables. withinBe theircause we assignedare con- uncertaintL ies. The1.116 list of selected individual1.114 (15) (5) 1.103 (23) (10) measurementssidering discussedspectral quantities above,here, however,these two con- violatesS both these1.191 requirements: there1.169 are(18) (15) 1.157 (25) (15) several measurementsditions should guide basedour c onhoice (partlyof the particle or fully)X identical data1.318 sets, and there are1.318 results 1.317 (16) (13) whose mass will set the scale. Furthermore, the D 1.232 1.248 (97) (61) 1.234 (82) (81) which apparentlyparticle should do notnot d agreeecay under withthe othersstrong in- and/orS* with the resulting1.385 central value,1.427 within(46) (35) 1.404 (38) (27) their assignedteraction. individualOn the one hand, uncertainty.the larger the strange ExamplesX* for the firstcaseareresultsfromthe1.533 1.565 (26) (15) 1.561 (15) (15) hadronic widthcontent ofof the theparticle,τ lepton,the more p fromrecise the DISmass processesW and from1.672 jets and event shapes1.676 in(20) (15) 1.672 + − determination and the weaker the dependence on e e finalm states.. These facts Ans exampleupport the use ofof t thehe W secondbaryon, case is the apparent disagreement between ud + − results fromthe theparticleτ widthwith the h andighest thosestrange fromcontent. DISOn Fig. [264]3. The orlig fromht hadr Thruston distributions in e e annihilationthe o [278].ther hand, the determination of baryon dec- spectrum of QCD. Hori- uplet masses is usually lessLatticeprecise than those oQCDf zontal lines andhadronbands are physics the octet. This observation would suggest that the experimental values the X baryon is appropriate. Because both the with their decay widths. W and X baryon are reasonable choices, we Our results are shown by -decays carry out two analyses, one$with MW (the W set) solid circles. Vertical error and one with MX (the X set).LatticeWe find that for all bars represent our com- three gauge couplings, 6/g2DIS= 3.3, 3.57, and 3.7, bined statistical (SEM) and both quantities give consistent results, namely systematic error estimates. + - annihilation a ≈ 0.125, 0.085, and 0.065e fm,e respectively. To p, K,and X have no error fix the bare quark masses, Zwe poleuse tfitshe mass ratio bars, because they are pairs M /M ,M /M or M /M ,M /M .We used to set the light quark p W K W p X K X mass, the strange quark determine the masses of the baryon octet (N, S, 0.11mas 0.12s and the 0.13overall L, X) and decuplet (D, S*, X*, W) and those scale, respectively. members of the light latticepseudoscalar QCD(p, K most)and ! s (" # ) EMBARaccurateGOED UN methodTIL 2PM U.S. EASTERN TIME ON THE THURSDAY BEFORE THIS DATE: Figure1226 9.3: 21 NOVEMBER22008 VOL 322 SCIENCE www.sciencemag.org Summary of1500 values of αs(MZ)obtainedforvarioussub-classes of measurements (see Fig. 9.2 (a) to (d)). The new world average value of 2 αs(M )=0.1184 0.0007 is indicated by the dashed line and the shaded band.
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