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Christine Davies University of Glasgow

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Christine Davies University of Glasgow Lattice field theory - a UK perspective Christine Davies University of Glasgow PPAP town meeting September 2012 Sunday, 16 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 ... Sunday, 16 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.→ → Sunday, 16 September 2012 9. Quantum chromodynamics 29 overall χ2 to the central value is determined. If this initial χ2 is larger than the number of degrees of freedom, i.e. larger than the number of individual inputs minus one, then all individual errors are enlarged by a common factor such that χ2/d.o.f. equals unity. If the initial value of χ2 is smaller than the number of degrees of freedom, an overall, a-priori unknown correlation coefficient is introduced and determined by requiring that the total χ2/d.o.f. of the combination equals unity. In both cases, the resulting final overall uncertainty of the central value of αs is larger than the initial estimate of a Gaussian error. This procedure is only meaningful if the individual measurements are known not to be correlated to large degrees, i.e. if they are not - for instance - based on the same input data, and if the input values are largely compatible with each other and with the resulting central value, within their assigned uncertainties. The list of selected individual measurements discussed above, however, violates both these requirements: there are several measurements based on (partly or fully) identical data sets, and there are results which apparently do not agree with others and/or with the resulting central value, within their assigned individual uncertainty. Examples for the firstcaseareresultsfromthe hadronic width of the τ lepton, from DIS processes and from jets and event shapes in e+e− final states. An example of the second case is the apparent disagreement between results from the τ width and those from DIS [264] or from Thrust distributions in e+e− annihilation [278]. Lattice QCD hadron physics 12 expt h (2P) rb2 fix params b rb1(2P) postdcns ['' rb0 $-decays 10 d' ' r predcns b [ rb2(1P) d [ b1 [(1D) Lattice b hb(1P) rb0 ) DIS 2 8 e+e- annihilation ' B*' Bc c * * Bc0 Z pole fits Bc Bc 6 * Bs B *s 0.11 0.12 0.13 B B ' 4 ' rc2 ! (" ) MESON MASS (GeV/c s r lattice QCD most s # dc h c1 c rc0 dc J/s accurate method D 2 2 Ds Figure 9.3: Summary of values of αs(MZ)obtainedforvarioussub-classes of measurements (see Fig. 9.2 (a) to (d)). The new world averadge value of K 2 / αs(M )=0.1184 0.0007 is indicated by the dashed line and 0 the shaded band. Z ± Due to these obstacles, we have chosen to determine pre-averages for each class of measurements, and then to combine those to the final world average value of αs(MZ ), using the methods of error treatment as just described. The fivepre-averagesare summarized in Fig. 9.3; we recall that these are exclusively obtained from extractions which are based on (at least) full NNLO QCD predictions,glueball and are published in m peer-reviewed journals at the time of completing this Review.Fromthese,wedeterminemasses s the new world average value of 93.4 1.1MeV ± Sunday, 16 September2 2012 αs(MZ )=0.1184 0.0007 , (9.23) Figure 7. Summary of the glueball masses compared± to experimental meson masses. The experimental results are from the PDG [29] and from Anisovich et al. [57–59]. June 29, 2012 14:54 by other experiments. We plot the results for I = 0 mesons in [57, 58], but plot the 2++ states from [59]. These additional meson states from Anisovich et al. [57–59]havebeen used to find some experimental glueball candidates [61] from the quenched calculations of Morningstar and Peardon. Bali [62] has plotted the quenched glueball spectrum with the experimental masses of the charmonium system. 5 Conclusions and future prospects The most conservative interpretation of our results is that the masses in terms of lattice representations are broadly consistent with results from quenched QCD. We do not see any evidence for large unquenching effects, however a definitive calculation requires a continuum extrapolation, and the inclusion of fermionic operators. In Tab. 7 we tentatively assign J PC quantum numbers to 10 glueballs. Of particular note in Tab. 4 is that Meyer and Teper [25] do not see the two spin exotic states identified by Morningstar and Peardon [2]. In their summary of the glueball + spectrum Morningstar and Peardon note that their spin exotic glueball 2 − could actually + + + be part of 5 −,7−, or 11 − glueball. Mathieu [42] have also compared the results for glueball masses from Morningstar and Peardon with those from Teper and Meyer. + Our result for the mass of the 0 − are consistent with the result from Morningstar and Peardon [2], although our errors are large for this heavy state. Meyer and Teper[4, 25]used – 13 – 6 0 + Finally, NB µ µ− is the number of observed signal The expected and observed CLs values are shown in (s)→ 0 + 0 + + + 0 Fig. 2 for the B µ µ− and B µ µ− channels, events. The observed numbers of B J/ψK , Bs s → → 0 + → → each as a function of the assumed branching fraction. J/ψφ and B K π− candidates are 340 100 4500, → ± 0 + 19 040 160 and 10 120 920, respectively. The three The expected and measured limits for Bs µ µ− and 0 + → ± ± B µ µ− at 90 % and 95 % CL are shown in Table II. normalization factors are in agreement within the uncer- → tainties and their weighted average, taking correlations The expected limits are computed allowing the presence 0 + 21st Century Lattice QCD norm 14 10 of B µ µ− events according to the SM branching into account, gives α 0 + =(3.19 0.28) 10− (s) Bs µ µ− → norm → 11 ± × fractions, including cross-feed between the two modes. and α 0 + =(8.38 0.39) 10− . B µ µ− Lattice QCD hadron physics© 2012 Andreas Kronfeld/Fermi Natl Accelerator Lab. → ± × For each bin in the two-dimensional space formed by The comparison of the distributions of observed "x# (2 GeV) 0.8 0.3 u $ d the invariant mass and the BDT we count the number events and expected background events results in a p- 0 + Lattice QCD predictions of candidates observed in the data, and compute the ex- value (1 CLb) of 18 % (60 %) for the Bs µ µ− 0 +− → Lattice QCD postdictions (B µ µ−)decay,wheretheCL values are those cor- pected number of signal and background events. → b 0.7 [ experiment The systematic uncertainties in the background and responding to CLs+b =0.5. db signal predictions in each bin are computed by fluctu- A simultaneous unbinned likelihood fit to the mass pro- 0.2 ating the mass and BDT shapes and the normalization jections in the eight BDT bins has been performed to 0 + 0.6 factors along the Gaussian distributions defined by their determine the B µ µ− branching fraction. The sig- s → associated uncertainties. The inclusion of the systematic nal fractional yields in BDT bins are constrained to the 0 + 0 + 0 + uncertainties increases the B µ µ− and B µ µ− BDT fractions calibrated with the B h h− sam- → s → (s) → 0.5 ’ proton structure 0 + +1.8 9 upper limits by less than 5%. ple. The fit gives (B µ µ−)=(0.8 ) 10− , [ 0 ∼+ 0 + s 1.3 0.1 The results for B µ µ− and B µ µ− decays, B → − × fits to experiments s where the central value is extracted from the maximum ’’ integrated over all mass→ bins in the corresponding→ signal 0.4 J/s [ B LHP arXiv:1001.3620 x of the logarithm of the profile likelihood and the uncer- dc c RBC arXiv:1003.3387 region,( areu summarizedd) in Table I. The distribution of tainty reflects the interval corresponding to a change of ETM arXiv:1101.5540 the invariant mass for2 BDT2>0.5 is shown in Fig. 1 for 0.5. Taking the result of the fit as a posterior, with a 0 + − m0 (GeV+ ) B µ µ− and B ! µ µ− candidates. ’ s → → positive branching fraction as a flat prior, the probabil- 0.3 s UTd : the complete0.0 fit 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 ity for a measured value to fall between zero and the SM Ds B expectation is 82 %, according to the simulation. The s 2 one-sided 90 %, 95 % CL limits, and the compatibility DECAY CONSTANT (GEV) 0.2 D Figure 4: Nonsinglet average momentum fraction x − vs. m from LHP (114), B ! "u d π with the SM predictions obtained from the likelihood, are K RBC and UKQCD (115), and ETM (116). The last has 2+1+1 flavors ofsea / in agreement with the CLs results.
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